METHOD AND APPARATUS FOR INEXPENSIVE RADIO FREQUENCY (RF) SOURCE BASED ON 2-STAGE 1NJEC

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I. Cross-Reference to Related Application

[0001] This application claims the benefit of U.S. Provisional Patent Application No,

6.1/569,773, filed December 12, 201.1 , which is hereby incorporated by reference in its entirety, as if set out below.

I Field of the Disclosure

[ΘΘΘ2] The present disclosure is generally related to an inexpensive radio frequency (RF) source based on magnetrons and, in particular, to an inexpensiv RF source based on 2-stage injection-locked magnetrons with a 3-dB hybrid combiner for precise and rapid control of output power and phase capable of driving superconducting RF cavities.

III. Summary

[ΘΘΘ3] Intensity frontier high-energy superconducting linear accelerators (linacs) have evoked a lot of interest the world over. The high-intensity, high-energy accelerators increase the scientific potential of the country and serve as a basis for projects such as Accelerator- Driven Systems (ADS), which could lead to homeland energy independence and energy security because of their capability to incinerate the minor acdnides and long-lived fission products in radiotoxic waste and/or "spent" nuclear fuel. The accelerators also can be used for utilization of Thorium as a nuclear fuel and can drive safe sub-critical nuclear reactors. [0004] One of the general sub-systems of the ADS projects and the high-energy physics intensity frontier facilities is a high-energy, high-current, Continuous Wave (CW), superconducting proton linac. For operation of these accelerators, high-power CW RF sources that are controlled in phase and in power, providing a precise stability of phase and amplitude of the accelerating field in each individual superconducting cavity (SC) of the linac, are desirable. Powering of each superconducting cavity separately and independently is desirable to suppress parasitic phase oscillations of the accelerating field in superconducting cavities, as described, for example, in H. Padamsee, j.

Knobloeh, T. Hays in "RF Superconductivity for Accelerators", Wiley & Sons, Inc, 1998, J. R. Delayen, MPPH155, PAC 01 Proceed., Chicago, XL, USA, 2001, and T.L. Grimm, W. Hartung, I ^' . Kandil, H. halil, J. Popielarski, C. Radcliffe, J. Vincent, R.C. York, ΊΉΡ66, Linac 04 Proceed., Lubeck,Gerrnany, 2004.

[00 )5] However, relatively inexpensive high-power RF sources meeting the requirements of the intensity frontier accelerators and ADS projects have not yet been developed and tested. Traditional RF sources such as high-power CW klystrons, inductive Output Tubes (IOTs), and solid-state amplifiers for the required power up to several hundreds of kilowatts (kW) are a significant fraction of the capital costs of these projects.

[ΘΘΘ6] CW magnetrons based on commercial prototypes are potentially less expensive than any of the traditional RF sources such as high -power CW klystrons, IOTs, and solid-state amplifiers. This is all the more likely to be the case since CW magnetrons with power of tens to hundreds of kW are well within current manufacturing capabilities.

[0007] We have invented a high-power CW RF source providing a rapid control of output power and phase to feed the superconducting cavities of the intensity frontier linacs for high-energy physics facilities and ADS projects. The RF source is based on inexpensive commercial CW magnetrons operating in an injection-locked mode with a 3-dB hybrid combiner.

[ΘΘΘ8] injection-locking in magnetrons realizing operation of the forced oscillators is well known, but only recently have researchers demonstrated that the real capabilities of injection-locked magnetrons are acceptable to provide RF power to superconducting linacs. [0009] The capabili ties of injection-locked magnetrons to provide RF power to superconducting linacs have been studied by considering transient processes describing the operation of a magnetron locked by a signal with varying frequency, which varies slowly in the magnetron frequency domain, as described, for example, in G.

azakevitch, Y.U Jeong, V.M. Pavlov, B.C. Lee, NIM A 528, (2004), 115 - 119, G.M. Kazakevieh, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, PRST-AB, 12, 040701 (2009), and G.M. Kazakevieh, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, NIM A 647 (2011) 10- 16. A mathematical model describing the transient processes has been developed and well verified in experiments, as described, for example, also in G. Kazakevitch, Y.U Jeong, V.M. Pavlov. B.C. Lee, NIM A 528, (2004), 1 1 - 119, G.M. Kazakevieh, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, PRST-AB, 12, 040701 (2009), and G.M,

Kazakevieh, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, NIM A 647 (2011) 10- 16. The model and its experimental verification has demonstrated the capability of phase control with a quite linear response of the injection-locked magnetron, which is one basis of our invented RF source, as described, for example, in G, Kazakevieh and V. Yakoviev, "'Magnetron option for a pulse linac of the Project X," Project X document 896,

Mlp://project -docdb.fnal.gov, and Grigory Kazakevieh, Rolland Johnson, Gene Flanagan, Frank Marhauser, Mike Neubauer, Vyachesiav Yakoviev, Brian Chase, Sergey Nagaitsev, Ralph Pasquinelli, Nikolay Solyak, Vitali Tupikov, Daniel Wolff, WEPPC059, IPAC12 Conference Proceed., New Orleans, LA, 2012.

[0010] Our inventive RF source has been experimentally modeled in certain aspects by CW injection-locked magnetrons, as described, for example, in Grigory Kazakevieh, Rolland Johnson, Gene Flanagan, Frank Marhauser, Mike Neubauer, Vyachesiav Yakoviev, Brian Chase, Sergey Nagaitsev, Ralph Pasquinelli, Nikolay Solyak, Vitali Tupikov, Daniel Wolff, WEPPC059, I AC12 Conference Proceed., New Orleans, LA, 2012, Grigory Kazakevieh, Gene Flanagan, Rolland Johnson, Frank Marhauser. Michael Neubauer, Todd Treado, Vyachesiav P. Yakoviev, Brian Chase, Sergei Nagaitsev, Ralph I Pasquinelli, WEPPC060, TP AC 12 Proceed., New Orleans, LA, 2012, and G. Kazakevieh, V. Yakoviev, R. Pasquinelly, B. Chase, G. Flanagan, F. Marhauser and D. Wolff "Experimental modellin of a Magnetron Transmitter for Superconducting Intensity Frontier Linacs," Project X document 1130, htlp://project -docdb.fnal.gov. The experimental modeling demonstrated a proof of principle of our inventive RF source, which may be controlled in phase and power quite rapidly which can he done by a suitable Low Level RF (LLRF) system. Analysis of the RF source modeling shows that our inventive RF source may provide regulation of better than 0.2 degree root mean square (RMS) and 0.2 percent RMS for phase and amplitude of the accelerating field, respectively, in a superconducting cavity.

[0011] Powering of a superconducting cavity by an injection-locked CW magnetron with an LLRF control has been successfully demonstrated in experiments, as described, for example, in H. Wang, K. Davis and R. Rimmer, I. Tahir, A.C. Dexter, G. Burt and R.G. Carter, THPEBG67, IPAC10 Proceed., Kyoto, Japan, 2010, and A.C. Dexter, G. Burt, R.G. Carter, I. Tahir, IT Wang, K. Davis and R. Rimmer, PRSR-AB 14, 032001 (2011).

[0012] We have invented a novel, innovative, and useful high-power CW RF source based on two injection-locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner. Our novel, innovative, and useful high-power CW RF source, based on two injection-locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner, may be used for intensity frontier accelerators and ADS projects. Our inventive RF source is controlled rapidly and precisely in power and phase.

[0013] The 3-dB hybrid combiner provides vectorial summing of power of both 2-stage

magnetrons feeding the superconducting cavities of a linac. Rapid control of power feeding the superconducting cavity and, respectively, control of the accelerating voltage may be provided by an LLRF system managing a phase difference on the inputs of the 2-stage magnetrons. The phase control of the accelerating voltage may be provided by a phase control on both 2-stage magnetrons inputs simultaneously. Thus, the control of power and phase in the RF source is transformed into a control of phase and phase difference, which are quite linear and wideband, as described, for example, in G.

Kazakevich and V. Yakovlev, "'Magnetron option for a pulse linac of the Project X," Project X document 896, lutp://pfoiec†.x-docdbina1.gov.

[0Θ1.4] Utilization of 2-stage magnetrons combined from two magnetrons differing in power by - 15 dB allows reduction of the locking power for the RF source. The ratio of the output power to the locking power of 30-40 dB has been reached in experiments with the 2-stage injection-locked magnetron, as described, for example, in G.M. Kazakevich, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, PRST-AB, 12, 040701 (2009), and G.M. Kazakevieh, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, MM A 647 (2011) 10-16. This allows utilization of relatively inexpensive solid- state drivers which further decreases the capital costs of the linac. Overall, the estimated cost of our inventive high-power RF source may be guesstimated to be anywhere from several times to an order of magnitude less than the cost of traditional RF sources at the same power range.

[0015] In a particular embodiment, a device is disclosed that includes means for providing a high-power continuous wave (CW) radio frequency (RF) source based on two injection-locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner. The device also includes means for operating the high-power CW RF source based on the two injection-locked 2-stage CW magnetrons with outputs combined by the 3-dB hybrid combiner to drive superconducting cavities of a linac.

[0016] In another particular embodiment, a method is disclosed that includes steps for

providing a high-power continuous wave (CW) radio frequency (RF) source based on two injectio -locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner. The method also includes steps for operating the high-power CW RF source based on the two injection-locked 2-stage CW magnetrons with outputs combined by the 3-clB hybrid combiner to drive superconducting cavities of a linac.

IV. Brief Description of the Drawings

[§§17] The following figures fonn part of the present specification and are included to further demonstrate certain aspects of the present invention. The present invention may be better understood by reference to one or more of these drawings in combination with the description of embodiments presented herein.

[0018] Consequently, a more complete understanding of the present disclosure and advantages thereof may be acquired by referring to the following description taken in conjunction with the accompanying drawings, in which the leftmost significant digit(s) in the reference numerals denote(s) the first figure in 'which the respective reference numerals appear, wherein:

[0019] Figure 1 is a diagram illustrating a simplified conceptual scheme of a magnetron radio frequency (RF) source comprising two 2-stage (2 -cascade) continuous wave (CW) magnetrons operating in injection-locked mode and loaded by a. 3-dB hybrid combiner. This RF source provides fast and rapid control of both power and phase;

[ΘΘ2Θ] Figure 2 is a diagram illustrating an embodiment of an apparatus including means for providing a high-power continuous wave (C W) radio frequency (RF) source based on two injection-locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner and means for operating the high -power CW RF source based on the two injection-locked 2-stage CW magnetrons with outputs combined by the 3-dB hybrid combiner to dri ve superconducting cavities of a linac; and

[0021] Figure 3 is a flow diagram of an illustrative embodiment of a method including steps for providing a high-power continuous wave (CW) radio frequency (RF) source based on two injection-locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner and steps for operati g the high-power CW RF source based on the two injection-locked 2-stage CW magnetrons with outputs combined by the 3-dB hybrid combiner to dri ve superconducting cavities of a linac.

V. Detailed Description

[0022] Illustrative embodiments of the present invention are described in detail below, in the interest of clarity, not all features of an actual implementation are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers ^' specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of the present disclosure.

[0023] Particular embodiments of the present disclosure are described with reference to the drawings. In the description, common features are designated by common reference numbers.

[0024] Referring to Figure 1, a diagram illustrating a simplified conceptual scheme of a

magnetron radio frequency (RF) source comprising two 2-stage (2 -cascade) continuous wave (CW) magnetrons operating in injection-locked mode and loaded by a 3-dB hybrid combiner is depicted and indicated generally, for example, at 100. This RF source provides fast and rapid control of both power and phase.

[0025] Referring to Figure 2, a diagram illustrating an embodiment of an apparatus is depicted and indicated generally, for example, at 200. The apparatus 200 includes means for providing a high-power continuous wave (CW) radio frequency (RF) source based on two injection-locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner 210 and means for operating the high-power CW RF source based on the two injection-locked 2-stage CW magnetrons with outputs combined by the 3-dB hybr d combiner to drive superconducting cavities of a linac 220.

[0026] Referring to Figure 3, a flow diagram of an illustrative embodiment of a method is depicted and indicated generally, for example, at 300. The method 300 includes steps for providing a high-power continuous wave (CW) radio frequency (RF) source based on two injection-locked 2-stage CW magnetrons with outputs combined by a 3-dB hybrid combiner 310 and steps for operating the high-power CW RF source based on the two injection-locked 2-stage CW magnetrons with outputs combined by the 3-dB hybrid combiner to drive superconducting cavities of a linac 320.

[0027] Attached herewith as an Appendix to this specification are various documents

describing more details about various illustrative embodiments, which Appendix to this specification is incorporated by reference as if set forth below. More details about various illustrative embodiments may be found by referring to the Appendix.

[0028] The present invention is well adapted to carry out the objects and attain the ends and advantages mentioned, as well as those that are inherent therein. While the present invention has been depicted, described and is defined by reference to exemplary embodiments of the present invention, such a reference does not imply a limitation of the present invention, and no such limitation is to be inferred. The present invention is capable of considerable modification, alteration, and equivalency in form and function as will occur to those of ordinary skill in the pertinent arts having the benefit of this disclosure. The depicted and described embodiments of the present invention are exemplary only and are not exhaustive of the scope of the present invention.

Consequently, the present invention is intended to be limited only by the spirit and scope of the appended claims, giving full cognizance to equivalents in all respects. [0029] The particular embodiments disclosed above are ili.ustrat.ive only, as the present invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of composition or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered wkhin the scope and intent of the present invention. In particular, every range of values (of the form, "'from about a to about h," or, equivalent!}', ''from approximately a to b," or, equivalently, "from approximately a-b") disclosed herein is to be understood as re.ferri.ng to the power set (the set of all subsets) of the respective range of values, in the sense of Georg Cantor. Accordingly, the protection sought herein is as set forth in. the claims below.

[0030] ^r I¾e particular embodiments of the present invention described herein are merely

exemplary and are not intended to limit the scope of this present invention. Many variations and modifications may be made without, departing from the intent and scope of the present invention. Applicants intend that ail such modifications and variations are to be included within the scope of the present invention as defined in the appended claims and their equivalents.

[ΘΘ31.3 While the present, invention has been illustrated by a description of various

embodiments and while these embodiments have been described in considerable detail, it is not the intention of the Applicants to restrict, or any way limit, the scope of the appended claims to such detail. The present invention in its broader aspects is therefore not limited to the specific details, representative apparatus, methods, and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the scope of Applicants' general inventive concept. Appendix to the Specification

Inexpensive RF source based on 2-stage injection-locked magnetrons with a 3-dB hybrid combiner for precise and rapid control of output power and phase

G. Kazakevich, V. Yakovlev

Intensity frontier high-energy superconducting linacs have evoked lot of interest the world over. The high-intensity, high-energy accelerators increase scientific potential of country and serve as a basis for projects of the Accelerator Driven System (ADS) which lead to homeland energy independence because of their capability to incinerate the minor actinides and long-lived fission products of radiotoxic waste. The accelerators also can be used for utilization of Thorium as a nuclear fuel and can drive safe sub-critical nuclear reactors.

One of general sub-system of the ADS projects and High-energy physics intensity frontiers facilities is a high energy, high current, Continuous Wave (CW),

superconducting proton linac. For operation of the accelerator are necessary high-power CW RF sources controlled in phase and in power providing a precise stability of phase and amplitude of the accelerating field in each individual superconducting cavity (SC) of the linac. Powering of each superconducting cavity separately and independently is necessary to suppress parasitic phase oscillations of the accelerating field in

superconducting cavities. [1-3].

However not yet been developed and tested relatively inexpensive high-power RF sources meeting the requirements of the intensity frontier accelerators and ADS projects. Traditional RF sources such as high-power CW klystrons, IOTs, and solid-state amplifiers for the required power up to several hundreds kW are a significant fraction of capital cost of the projects.

The CW magnetrons based on commercial prototypes are potentially less expensive than the above-listed traditional RF sources the more so since the CW magnetrons with power of tens to hundreds kW are well within current manufacturing capabilities.

We have invented a high-power CW RF source providing a rapid control of output power and phase to feed the superconducting cavities of the intensity frontier linacs for the High-energy physics facilities and ADS projects. The RF source is based on inexpensive commercial CW magnetrons operating in injection-locked mode with a 3-dB hybrid combiner

Injection-locking in magnetrons realizing operation of the forced oscillators is well known, but only recent papers demonstrated real capabilities of the injection-locked magnetrons acceptable to power the superconducting linacs.

The capabilities have been studied considering transient process describing operation of a magnetron locked by a signal with varying (slowly in the magnetron frequency domain) frequency, [4-6]. A mathematical model describing the transient process has been developed and well verified in experiments, [ibid.]. The model and it experimental verification demonstrated capability of a phase control with a quite linear response of the injection-locked magnetron, what is a basis of the invented RF source, [7, 8].

The invented RF source has been experimentally modeled by CW injection-locked magnetrons, [8-10]. The experimental modeling demonstrated proof of principle of the invented RF ^' source, controlled in phase and power quite rapidly that can be done by a suitable Low Level RF (LLRF) system, Analysis of the RF source modeling shows that the invented RF source will provide regulation of belter than 0.2 degree RMS and 0.2 percent RMS for phase and amplitude of the accelerating field, respectively, in the superconducting ca vi ty

Powering of a superconducting cavity by injection-locked CW magnetron with a LLRF control has been successfully demonstrated in experiments described in [11, 12].

References

[I] H. Padamsee, J. Knobloch, T. Hays in "RF Superconductivity for Accelerators", Wiley & Sons, Inc, 1998

[2] J. R. Delayen, MPPH155, PAC 01 Proceed., Chicago, IL, USA, 2001.

[3] T.L. Grimm, W. Hartung, T. Kandil, H. Khalil, J. Popielarski, C. Radcliffe,

J. Vincent, R.C. York, THP66, Linac 04 Proceed., Lubeck,Germany, 2004.

[4] G. Kazakevitch, Y.U Jeong, V.M. Pavlov, B.C. Lee, NIM A 528, (2004), 115-119.

[5] G.M. Kazakevich, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, PRST-AB, 12, 040701

(2009)

[6] G.M. Kazakevich, V.M. Pavlov, Y.U. Jeong, and B.C. Lee, NIM A 647 (2011) 10- 16.

[7] G. Kazakevich and V. Yakovlev," Magnetron option for a pulse linac of the Project

X", Project X document 896, http ://pro j ectx-docdb . trial . go v

[8] Grigory Kazakevich, Roliand Johnson, Gene Flanagan, Frank Marhauser,

Mike Neubauer, Vyacheslav Yakovlev, Brian Chase, Sergey Nagaitsev,

Ralph Pasquinelli, Nikolay Solyak, Vitali Tupikov, Daniel Wolff, WEPPC059,

IPAC12 Conference Proceed., New Orleans, LA, 2012.

[9] Grigory Kazakevich, Gene Flanagan, Roliand Johnson, Frank Marhauser,

Michael Neubauer, Todd Treado, Vyacheslav P. Yakovlev, Brian Chase,

Sergei Nagaitsev, Ralph J. Pasquinelli, WEPPC060, IPAC12 Proceed.,

New Orleans, LA, 2012.

[10] G. Kazakevich, V. Yakovlev, R. Pasquinelly, B. Chase, G. Flanagan, F. Marhauser and D. Wolff "Experimental modelling of a Magnetron Transmitter for

Superconducting Intensity Frontier Linacs", Project X document 1130,

http://pi jectx-docdb.fnal.gov

[I I] H. Wang, K. Davis and R. Rimmer, I. Tahir, A.C. Dexter, G. Burt and R.G. Carter, THPEB067, IPAC10 Proceed., Kioto, Japan, 2010.

[12] A.C. Dexter, G. Burt, R.G. Carter, I. Tahir, H. Wang, K. Davis and R. Rimmer, PRSR-AB 14, 032001 (2011) Claim

A novel high-power CW RF source based on two injection-locked 2-stage CW

magnetrons with outputs combined by a 3-dB hybrid is invented for intensity frontiers accelerators and ADS projects. The RF source is controlled rapidly and precisely in power and phase.

The invented magnetron RF source, Fig. 1, consist of two 2-stage (2-cascade) CW magnetrons operating in injection-locked mode and loaded by a 3-dB hybrid combiner.

Matched loaAs

Figure 1: Simplified scheme of the magnetron RF source based on CW 2-stage injection- locked magnetrons. The RF source provides fast control of power and phase.

The combiner provides vectorial summing of power of both 2-stage magnetrons feeding superconducting cavities of the linac. Rapid control of power feeding the cavity and, respectively, control of the accelerating voltage will be provided by a LLRF system managing phase difference on the inputs of the 2-stage magnetrons. The phase control of the accelerating voltage is provided by a phase control on both 2-stage magnetrons inputs simultaneously. Thus the control of power and phase in the RF source is transformed into a control of phase and phase difference, which are quite linear and a wideband, [7].

Utilization of 2-stage magnetrons combined from two magnetrons differing in power by ~ 15 dB allows reducing the locking power for the RF source. The ratio of the output power to the locking power of 30-40 dB has been reached in experiments with the 2-stage injection-locked magnetron, [5, 6]. This allows utilizing relatively inexpensive solid-state drivers which decrease additionally capital cost of the linac.

Estimated cost of the invented high-power RF source is in few times less than the cost of traditional RF sources at the same power range. Conceptual scheme of the two-stage phase-locked CW magnetron generator

The concept is motivated with successful results obtained in stabilization of the S-band 2.5 MW pulsed magnetron and necessity in inexpensive well stabilized in frequency and phase high- power quasi-CW RF source with a fast control of output power and phase to feed the

Superconducting Cavities (SC) of pulse linacs.

The scheme allows 100% control of amplitude and phase in each SC cavity

Varying phase of the input signal for one of two-stage generator one can vary RF power on the output port of the hybrid. Varying phase of signals on both inputs properly one can vary both, the amplitude and the phase of the output signal.

The scheme is relatively inexpensive since the high-power commercial CW magnetrons are inexpensive and require relatively inexpensive and simple power supplies.

The scheme includes 2 modules, each contains of 3 active units: a solid state driver and two magnetrons. Other elements are passive; hence the scheme can be quite reliable.

MAGNETRON RF SOURCE FOR THE PROJECT X PULSED LINAC

Grigory Kazakevich , Rolland Johnson, Mike Neubauer, Muons, Inc., Batavia, 60510 IL, USA Brian Chase, Sergey Nagaitsev, Ralph Pasquinelli, Nikolay Solyak, Vyacheslav Yakovlev,

Fermilab, Batavia, 60510 IL, USA

Abstract individual feeding of the cavity from a separate IOT or

Each Superconducting Cavity (SC) in the Project X klystron transmitter. This option looks technically pulsed linac, requires a 1.3 GHz RF source with ~ 40 kW plausible, but the number of transmitters increases project pulsed power at 8% duty cycle. The utilization of costs. Thus, development of a relatively inexpensive RF klystrons assumes driving 2 cryomodules (each with 8 source with adequate amplitude/phase dynamic range to cavities) from a single klystron with 640 kW pulsed excite each cavity independently is an important option power, 7.5 ms pulse duration, and 10 Hz repetition rate. for the Project X. A concept of such RF generator is Such a klystron can be developed by industry, but the proposed and is considered in this work.

proposed concept assumes that only the vector sum of the

accelerating voltage in the SC needs to be controlled. As PARAMETERS OF THE RF SOURCE an alternative solution, we propose and consider a The stripping foil converting the H ^" into protons at the potentially less costly pulsed RF source using two output of the pulse linac demands the following individually phased 2-stage phase-locked magnetron parameters of the injected H ^" beam because of heating generators based on industrial CW magnetrons combined problem:

with a 3 dB hybrid for fast independent control of the Beam current: 1 mA;

accelerating voltage and phase in each SC. Features and Beam energy: 8 GeV;

performance capabilities of such RF sources for Beam pulse width: 4.2 ms;

application in the Project X pulsed linac are discussed. Repetition rate: 10 Hz.

The SC filling time is limited by Lorentz forces.

INTRODUCTION However, recent FNAL experiments [3] showed that it is

Project X is an accelerator facility that is under possible to stabilize the cavity if total RF pulse duration development at Fermilab, [1], to support multiple physics (including filling and acceleration) does not exceed 10 ms programs at the intensity frontier. Project X is based on a even when the external quality factor of the cavity is 3 GeV CW SC H ^" linac providing 3 MW of total beam 1 T0 ⁷ . In order to be on safe side, the filling time is chosen power to the 3 GeV program for experiments in rare to be 3 ms, and the total RF pulse duration is 7.2 ms. processes and for nuclear physics related to ADS The ILC SC bandwidth is about 100 Hz at the external program. Simultaneously Project X will provide a 2 MW Q-factor value of ¾ _ί =1.3Τ0 ⁷ . The cavity frequency proton beam at 60-120 GeV for long baseline neutrino deviations caused by a microphonic effect (so called the oscillation experiments. For this option 4.2% of the CW microphonics amplitude) is expected to be not greater H ^" beam will be redirected by a pulsed dipole magnet than 30 Hz. The maximal power required for acceleration from 3 GeV CW linac to the 1.3 GHz 8 GeV pulsed linac

with a stripping foil at the output to convert H ^" into

protons. Further acceleration of the proton beam for the

neutrino experiments will be accomplished by the FNAL (1) existing Recycler/Main Injector at the injection energy of Here V is the energy gain per cavity (25 MeV for 1 m 8 GeV. long ILC cavity) for zero synchronous phase, (r/Q) is the

The pulsed linac will utilize the standard ILC-type 1.3 cavity impedance, Q _E is the cavity external Q-factor, / is GHz SC, [2], at the acceleration gradient of 25 MeV/m the cavity frequency, φ ~ -10 degrees is the synchronous that is a realistic value for pulse operation. The cavity phase, 6f is the microphonic amplitude. The cavity is filling time and the full RF pulse duration are chosen to be detuned in order to compensate reactance of the beam. 3 ms and 7.2 ms, respectively. The total number of SC For considered case the power P _g is 31.5 kW per SC. required for acceleration of the H ^" at the given gradient is Taking into account power overhead for cavity control 200. Power to feed each cavity is approximately 40 kW. system operation, one gets the required RF power of 40 Several options for driving the SC were considered. The kW per each cavity. The generator has to provide dynamic first one is based on a high power klystron feeding a range in power at least 40% to vary the SC accelerating number of SC (16 cavities in 2 cryomodules). The scheme field in the range of ~ 20% in order to compensate the does not allow independent tuning of the phase and microphonics. The bandwidth of the field variation has to voltage in the cavity that is necessary for weakly be at least 10 kHz which is the bandwidth of the feed relativistic particles. The second option is based on forward and the feedback loops for the microphonic suppression control system.

Work is supported by the US DOE

"grigory @muonsinc.com A FORCED OSCILLATOR MODEL FOR A k Noise ^ 1 i ^{s tne n} °i ^se coefficient,

FREQUENCY-LOCKED MAGNETRON U _A it) is the magnetron time -dependent anode voltage,

Recent articles describing good results in stabilization

of magnetrons, [4, 5], initiated our concept to utilize magnetron nominal anode voltage, generators based on relatively inexpensive commercial is modulus of the magnetron cavity CW magnetrons. Since a magnetron is an auto-oscillator,

self exciting by noise with random frequency inside the voltage.

magnetron cavity bandwidth and in the device the output The model was used to simulate frequency instability of a power does not depend on amplitude of the forcing signal, frequency/phase locked S-band 2.5 MW pulse magnetron. it is correct to present the frequency-locked magnetron as The forcing signal was the wave with initial power of =30 a forced oscillator. A simple model presenting the kW reflected from an accelerating cavity concurrently magnetron as a forced oscillator, [4], demonstrated that serving as an external stabilizing resonator. Equation (2) the frequency-locked magnetron provides high stability in was solved jointly with a similar one (without the noise frequency and phase if the forcing signal exceeds the first term) describing oscillations in the accelerating cavity harmonic noise signal in the magnetron cavity at the loaded by beam and fed by the magnetron through a magnetron excitation. The magnetron model was reciprocal ferrite isolator with 0.4 dB and 18 dB of described by equation of the forced oscillation in the forward and inverse losses, respectively. Results of magnetron cavity coupled with a waveguide and loaded simulations and measurements were in an excellent by the magnetron current. The second order equation was agreement, [4, 8], that proved correctness of the model. transformed into a first order abridged equation utilizing Measured intrapulse frequency instability of the the Slowly Varying Envelope Approximation (SVEA) frequency-locked magnetron relatively the forcing signal method, [6]. Start-up of the magnetron generation is frequency at the initial detuning magnetron-forcing signal described by first harmonic noise caused by a jump of the value Af= 0.43 MHz is shown in Fig. 1, [4]. The magnetron voltage, [7]. The obtained first order equation measurements were done at operation of the accelerating (2), [4], describes transient state of the magnetron and cavity at nominal beam loading with coupling coefficient allows computing in time domain variation of the of 5.4. The accelerating cavity was situated in a 12-orbits, magnetron frequency vs. the forcing signal variations and high-current classical S-band microtron with internal time dependent magnetron current. injection and the cavity beam loading was calculated e

parameter of the magnetron cavity, operating at the Time, με

frequency of ύ , V _M and V _FM are complex amplitudes

Figure 1 : B- measured intrapulse frequency instability of of the oscillation in the magnetron cavity and forcing the frequency-locked magnetron relatively the forcing oscillation, respectively, Y _0M [1/Ohm] is the external signal frequency, left axis. E- measured variations of the magnetron current in relative units, right axis.

waveguide conductance of the magnetron cavity, I _M is

the complex amplitude of the first harmonic of the The frequency instability at given amplitude of the forcing signal depends on the initial detuning, Af, between magnetron current, and <p _M is the phase of V _M {t). the forcing signal and the magnetron, Table 1, [4].

The noise source V _Noise is added in the equation (2) to Table 1. The magnetron r.m.s. frequency (5f) and phase excite oscillations in the magnetron. It is equal, [7, 8], to: (dcp) variations vs. the Af value.

V

V _Noise {t) --

Here: V _M0 is the nominal magnetron (cavity) voltage, Excellent results in application of the frequency-locked can expect higher frequency and phase stability in the CW magnetron feeding a SC at a kW level of power, [5], proposed magnetron RF source than it was described in are in agreement with results received with the 2.5 MW [4]. More effective frequency locking of a pulsed mode pulsed magnetron, [4], and also stimulated our concept of magnetron one can expect if the forcing signal is initiated a magnetron generator with fast variation of power and ahead of the pulsed voltage feeding the magnetron.

phase. Time of establishment of the output power is determined by the magnetrons filling times which does

CONCEPT OF A TWO-STAGE not exceed microseconds. So, the proposed concept FREQUENCY-LOCKED MAGNETRON should be able to control the output power with the GENERATOR WITH A FAST CONTROL bandwidth at least of hundreds kHz.

As it was shown in Fig. 1, the frequency of the OF POWER AND PHASE frequency-locked magnetron in fact is insensitive to

The concept [9] is based on a two-stage magnetron increment of the magnetron current, i.e. to variation of the generator concept in which the output power of the magnetron voltage, [4]. It allows utilization of simple and second magnetron is ~15 dB higher than the output power relatively inexpensive magnetron power supplies instead of the first one. Both magnetrons are coupled through of Advanced Modulators allowing fast variation of the phase ferrite circulators. The forcing signal exciting the output voltage (and current) as it was proposed in [5]. first (low power) magnetron is provided by a solid state For higher efficiency one needs to optimize the high- driver protected from the first magnetron output signal power CW magnetrons parameters considering range of with a phase ferrite circulator as well. To provide fast the power control.

control of the output power we propose to use the second

one through a 3-dB hybrid. In this case the power should

Figure 2: Simplified scheme of the two-stage magnetron [6] Joint US-CERN-JAPAN international school on generators with fast control in amplitude and phase based frontiers in accelerator technology, 9-18 Sept. 1996, on CW commercial magnetrons. World Scientific, ISBN 981-02-3838-X.

[7] V.N. Zavorotilo, O.S. Milovanov. Collect. Articles

Note that in described in [4] stabilizing scheme the

"Accelerators", No. 16, 1977, Moscow, Atomizdat., locking frequency itself has a drift caused by incremental

pp. 34-37, (In Russian).

beam loading in the high-current microtron with the

[8] G.M. Kazakevich, V.M. Pavlov, Y.U. Jeong, and internal injection. However, the frequency instability

B.C. Lee, PRST-AB, 12, 040701 (2009) r.m.s. values of the locked magnetron relatively the

[9] G. Kazakevich and V. Yakovlev," Magnetron option locking frequency are in the range of (3.6· 10 ^"6 -4.6· 10 ^"6 ) at

for a pulse linac of the Project X," Project X 0.43 MHz < Af < 0.85 MHz, [4], as it is shown in Table 1.

document 896, http://projectx-docdb.fnal.gov:8080

The proposed schematic, Fig. 2, is based on stable

/cgi-bin/ShowDocument?docid=896

locking frequency provided by solid state drivers, so one

Experimental modeling of a Magnetron Transmitter for Superconducting

Intensity Frontier Linacs

Technical notes

G. Kazakevich, V. Yakovlev, R. Pasquinelli, B. Chase, G. Flanagan, F. Marhauser and D. Wolff

11/25/2012 m /« ; ^■ :> gj¾ Fermiiab

The RF average power required for the CW proton and ion GeV-scale intensity frontier superconducting linacs for High Energy, HE, physics investigations and for Accelerator Driven System, ADS, projects is within the range of several MW to tens of MW. Traditional CW RF sources as klystrons, lOTs, solid state amplifiers for such power are a significant fraction of the cost of these projects.

► The concept most applicable for the proton and ion accelerators is the powering of each Superconducting Cavity, SC, by an individual Low Level RF (LLRF) vector controlled RF source. The vector control includes a management of the SC feeding power and phase to keep optimized the phase and the amplitude of the accelerating field, [1-3] in each individual cavity to prevent the beam emittance growth, [4]. The CW power per cavity is within the range of tens kW to hundreds kW depending on the beam current.

► The CW magnetrons based on commercial prototypes are potentially less expensive than the above-listed RF sources the more so since the CW magnetrons with power of tens to hundreds kW are well within current manufacturing capabilities.

► A 2.45 GHz model of high-power RF transmitter based on injection-locked CW 1 kW magnetrons demonstrated features necessary for the vector control by a LLRF system.

Fermiiab

Y hy magnetrons ?

'Magnetrons exceed 80% efficiency, goal 50% minimum

in p raphas mode.

•In quantities of 50 stations 30 kW magnetrons $8K

$2-3 per Watt for system of two paraphased

less than half th cost of other solutions

•Injection locking is proven technology

•Gain on order of 15 dB requring 500 watts drive power

•Proven highly sophisticated LLRF controls for paraphasing •Need to measure phase noise performance

November, 2£S2 R. Γ Pasi!ii!fjaK

Courtesy of R.J. Pasquinelli; 2012 Fall Project X Collaboration Meeting, 11.27-28.2012, FNAL, Batavia, IL

Fermilab

► The principle of the vector control in magnetrons assuming a control in power and phase is realized by control in phase based on a concept of operation of a magnetron, injection-locked by a signal with varying (slowly in the magnetron frequency domain) frequency/phase in assumption that the injection-locked magnetron phase response is quite linear and fast.

^ The concept of operation of a magnetron locked by a wave with slowly-varying frequency has been considered and well verified, [5-7], in numerical modelling and in experiments.

^ lo the presented work we have verified experimentally thai the phase

response of the magnetrons injection-locked by a signal with slowly varying frequency/phase is quite linear and fast to suppress parasitic phase modulation superconducting cavities through a LLRF vector control.

& We performed experimental modelling demonstrating proof of principle of the proposed magnetron transmitter based on two 2-cascade injection-locked

magnetrons applicable to utilize the vector control necessary for powering of the superconducting cavities with electronic damping of parasitic phase

modulations.

A CONCEPT OF THE MAGNETRON TRANSMITTER

CONTROLLED IN PHASE AND POWER

Fig. 1. Block diagram of the CW magnetron transmitter based on 2-cascade injection-locked magnetrons with a control in power and phase.

► This transmitter configuration allows for the wideband phase and magnitude control following from accelerator RF vector regulation requirements.

► The transmitter consists of two 2-cascade injection-locked magnetrons with outputs combined by a 3-dB hybrid. The phase management is provided by a control of phase in both channels simultaneously, while the power management is provided by a control of phase difference on the inputs of the 2-cascade magnetrons, [8].

► The 2-cascade injection-locked magnetrons are proposed to decrease the locking power by -40 to -30 dB relativel the combined output power, [9].

Fermiiab

TECHNIQUES MODELLING THE MAGNETRON

TRANSMITTER

► All features of the transmitter were modelled using two CW 2.45 GHz magnetrons with output power up to 1 kW. The magnetrons were chosen to be locked at the same frequency. Both magnetrons were powered by a single pulse modulator with partial discharge of storage capacitor of 200 μΡ commutated by HTS 101-80-FI IGBT switch,

gnetrons and the modulator components from arcs the modulator has that rapidly interrupts the HV if the modulator load current exceeds

The modulator operating parameters:

Output voltage: U _0ut = 1 -5 kV

Repetition rate: 0.25 Hz

Pulse duration: 2.5-15 ms

Output current: "out = 0.3-1.0 A

T im e, s

Fig. 4. Pulse shapes of voltages of magnetrons

operating simultaneously

Fermilab

I*- Features of the transmitter based on

injection-locked CW magnetrons have been

modelled using two magnetron modules, Figs.

Fig. 5. The magnetron experimental module in which a CW magnetron operates as an injection-locked oscillator.

► The CW magnetrons were mounted on the WR430 waveguide sections coupled with a waveguide-coax adapters. The adapter and the section designs were optimized using CST Studio model to minimize reflection and maximize transmittance in the

magnetron-adapter system. Accordingly the CST Studio modelling for the

Fig. 6. Photo of a single CW magnetron module optimized designs the parameters S^ intended to work in injection-locked mode and S ₂₁ values are: -26.3 dB and

-0.102 dB respectively.

Fermiiab

Verification of operation of the each CW magnetron in injection-locked mode was performed in pulsed regime while each magnetron was pre-excited by CW TWT amplifier driven by N5181A Agilent synthesizer as it is shown in Fig. 7, [9]. The setup was used to measure intrapulse phase variations of the injection-locked magnetron, Fig. 8a-b, utilizing an interferometer including a trombone φ (a phase shifter), and a double balanced m

Fig. 7. Setup with the interferometer to measure phase

variations of the injection-locked magnetron.

Fermiiab

variation with the injection- FIG. 8a. Typical measured phase variations of the locked magnetron was injection-locked CW magnetron operating in pulsed mode at pulse duration of 8 ms at P _0ut /P _Lock =19-20 dB.

measured in [10, 1 1], when the Inset b shows zoomed in time phase variation during first phase control was OFF. 1.0 ms of the pulse.

^ The transient process of phase modulation in the injection-locked magnetron takes of ~ 200 ns. This implies that a Low Level RF controller may have a closed loop bandwidth of < 100 kHz and will be able to suppress all expected system disturbances suppressing the parasitic frequency/phase modulation with the frequency as low as tens of Hz, as it was demonstrated in [10, 1 1] for magnetron operating in CW mode with a superconducting cavit in the feedback loop.

Fermilab

EXPERIMENTAL VERIFICATION OF THE MAGNETRON

TRANSMITTER MODEL

^ The setup modelling the power control of the injection-locked CW 2.45 GHz low- ower magnetrons with 3-dB 180 degrees hybrid combiner is shown in Fig. 9.

Fig. 9. Experimental modelling of the power control

concept and power combining with the CW, 2.45 GHz,

1 kW injection-locked magnetrons.

Fermilab

► ResMRSef ®η ^eswe^ sc jft i^ of the phase shift <p _M by the trombone φ II are plotted in Fig. 10 showing measured power on the combiner outputs "∑", curve B, and "Δ", curve C, considering the hybrid insertion losses of 0.4 dB and 0.7 dB, respectively. Curve E shows fit of the curve B by a sin((p _M ) function.

► Good agreement of the measured combined power curve B, with the fit trace, curve E, demonstrates quite good linearity of the phase response of the injection-locked magnetrons with power combining since the sin(<p^ function is linear at iow value of argument and the phase control in magnetrons assumes just such a control using an appropriate LLRF vector system generating the slowly-varying controlling signal.

Phase shift a>„ in trombone φ II, radians

Fig. 10. Plot of control of combined power by phase difference in the combined injection-locked magnetrons.

Fermiiab

► Bandwidth of the combined in power injection-locked magnetrons was measured with setup shown in Fig. 9, using phase modulation with amplitude of 20 degrees in the synthesizer. The trombone φ II length at the measurement was chosen to provide maximum power in the "∑" combiner output. Signal from the combiner output "∑" has been compared in phase with the synthesizer signal by the interferometer. The phase response of the injection-locked magnetrons with power combining measured with the interferometer at the frequency of phase modulation of 30 kHz is shown in Fig. 11 .

Time, ms

Fig. 11. Trace of phase modulation measured for the magnetrons with power combining, injection- locked at phase modulation of the locking signal. The modulation amplitude is 20 degrees and the modulating frequency is 30 kHz.

Fermi!ab

► Var$fi¾t#fe£ %to ^ of the injection-locked magnetrons with power combining by the 3-dB hybrid vs. frequency of the phase modulation of the locking signal, Fig. 12. The Bode plot demonstrates linearity and bandwidth of the Injection-locked magnetron phase response on the phase control by the forcing signal. Maximum frequency of the phase modulation responded by the magnetron as it follows from Fig. 12 is at ieast of 1 MHz. This value shows a bandwidth for phase control in the injection-locked magnetrons with power combining at ratio of the output power to the locking power of -16 dB. The bandwidth of the phase response is acceptable to suppress the phase modulation of the

acceieraiinc field in the SC caused by mechanical noises or/and the magnetron power suoplies ripples. ► The measured linearity of the phase

response, Fig. 10, and the transfer characteristic of the phase control, Fig. 12, prove principle of phase control of injection- locked magnetron by a slowly varying signal,

► Since the power control in the proposed transmitter is transformed into phase

Frequency of phase modulation, kHz control, the vector control in the transmitter

Fig. 12. Measured with interferometer transfer with power combining was proven in the characteristic of the phase control for injection- experiments.

locked magnetrons with power combining.

Fermilab

► Phase variation ^' of the injection-locked magnetrons ^" With the power combining has been measured using setup shown in Fig. 9. At the measurements the trombone φ II length has been chosen to provide maximum signal on the hybrid port "∑". Main part of the trace measured with calibrated interferometer, Fig. 13, has a smooth shape with instantaneous phase noise of few degrees.

The measured frequency variation at t > 50-100 ms corresponds to parasitic frequency modulation in the injection-locked magnetron with effective amplitude of f _eff « 22 Hz.

Time, s

Fig. 13. Interferometer trace on the output "∑" of the hybrid

The increase of the modulation index in comparison with the value obtained with single injection-locked magnetron results most likely from more noticeable discharge of the modulator charging capacitor loaded by two magnetrons that causes larger deviation of the magnetron current. Noticeable phase variations measured on the leading edge of the modulator pulse look like the phase variations measured with single injection-locked magnetrons operating in pulsed mode. They may result from

multipactoring in magnetrons, when pulsed voltage is applied, or/and variation of the magnetron cathode emitting properties because of back-streaming electrons cleaning the emitting surface.

Fermiiab

► Operation of the ^' 2-cascade injection-locked magnetron has been modelled combining two the magnetron modules in series through an attenuator to provide injection-locking in the second magnetron by lowered (in the attenuator) signal from the first injection-locked magnetron, [12], as it is shown in Fig. 14. Both of the injection- locked magnetrons were fed simultaneously by the pulse modulator at pulse duration

0.000 0.001 0.002 0.003 0.004 0.005

Time, s

Fig. 16. Phase deviations of the 2-cascade injection-locked magnetron measured for pulse duration of~ 5 ms at various values of the attenuator. Curves B and D show measured traces at 20 dB and 13 dB attenuator values, respectively.

► The traces of phase variation of the 2-cascade injection-locked magnetron look as the measured trace of the injection-locked magnetrons with power combining, The phase deviations measured at ratio of the output power to locking power of 26.5 dB correspond to parasitic modulation with modulating effective frequency of f _eff ~ 34 Hz. At the ratio of the output power to locking power of 33.5 dB the phase deviations of the 2-cascade magnetron correspond to parasitic modulation with modulating frequency of f _eff * 40 Hz.

Fermiiab

I*- The phase response of the 2-cascade injection-locked magnetron model on the fasi 180 degrees phase flip has been measured using setup shown in Fig. 14, [ibid.]. The 180 degree phase flip in the TWT drive signal is accomplished, Fig. 17, with a pulse generator and double balanced mixer on the TWT amplifier input.

► The transient process in the phase flip response, Fig , 16, takes of -200 ns. This value is in good agreement with results obtained in [1 1] and corresponds to measurements with phase modulation. The 39 trace in Fig. 14 shows that the 2-cascade

T im e , m s injection-locked magnetron is applicable foi

Fig. 17. Response of the frequency-locked 2- a phase control at the bandwidth in MHz cascade magnetron on a fast 180 degrees

phase flip measured at ratio of the output range.

power to locking power of 33.5 dB,

[7] G. Kazakevich et al., NIM A 647, 10-16, 201 1.

References [8] G. Kazakevich, V. Yakovlev," Magnetron option

[1] H. Padamsee, J. Knobloch, T. Hays in RF for a pulse linac of the Project X", Project X

Superconductivity for Accelerators, 1998 document 896, http://projectK-docdb.fnai.QOV

[2] J. R. Delayen, PAC01 Proceed. , 2001. [9] G. Kazakevich et al., WEPPC059, IPAC12 [3] T.L. Grimm, et al., Linac04 Proceed., 2004. Proceed., 2012.

[4] N. Solyak et al., LINAC10 Proceed., 2010. [10] H. Wang et al., IPAC10 Proceed., 2010.

[5] G.Kazakevitch at al., NIM A 528, (2004), 1 15. [1 1 ] A.C. Dexter et al., PRST-AB, 14, 032001 , 201 1.

[6] G. Kazakevich et al., PRST-AB, 12, 040701 , 2009 [12] G. Kazakevich et al., WEPPC060, IPAC12

Proceed., 2012.

m ^r -m Fermilah

Summary

► In the presented wor we have verified experimentally thai the phase response of the magnetrons (with a power combining) injection-locked by a si n l with slowly varying frequency/phase Is quite l near and fast to suppress parasitic phase modulation in superconducting cavities through a LLRF vector control.

► We performed experimental modelling demonstrating proof of principle of the proposed magnetron transmitter based on two 2-cascade injection-locked CW magnetrons with power combining applicable to provide the vector control necessary to power the superconducting cavities with electronic damping of parasitic phase modulations caused by mechanical noises and ripples from magnetrons power supplies,

► We have verified applicability of the proposed CW injection-locked magnetron transmitter to power superconducting cavities in pulsed Intensity frontier llnacs accelerating long trains of bunches utilizing a vector control to suppress

instabilities of the accelerating field.

WEPPC'059 Proceedings of IPAC2012, New Orleans, Louisiana, USA

A TWO-STAGE INJECTION-LOCKED MAGNETRON FOR ACCELERATORS WITH SUPERCONDUCTING CAVITIES*

Grigory Kazakevich", Rolland Johnson, Gene Flanagan, Frank Marhauser, Mike Neubauer,

Muons, Inc., Batavia, 60510 IL, USA

Vyacheslav Yakovlev, Brian Chase, Sergey Nagaitsev, Ralph Pasquinelli, Nikolay Solyak,

Vitali Tupikov, Daniel Wolff, Fermilab, Batavia, 60510 IL, USA

Abstract Project X and other SC accelerators. The concept of such

A concept for a two-stage injection-locked CW an RF source and its modelling are discussed in the paper. magnetron intended to drive Superconducting Cavities

(SC) for intensity- frontier accelerators has been proposed. AN INJECTION-LOCKED MAGNETRON ^' .J The concept considers two magnetrons in which the AS AN RF SOURCE FOR SC

"■■ output power differs by 15-20 dB and the lower power ACCELERATORS

r: magnetron being frequency-locked from an external

A general requirement for the state of the art intensity source locks the higher power magnetron. The injection- frontier SC accelerators of weakly-relativistic particles is locked two-stage CW magnetron can be used as an RF

high phase stability of the RF source feeding the SC. The 7 power source for Fermilab's Project-X to feed separately

; allowable phase instability of ~1 degree, [3], results from each of the 1.3 GHz SC of the 8 GeV pulsed linac. We

the beam transverse and longitudinal emittance 7; expect output/locking power ratio of about 30-40 dB

simulations to avoid beam loss. Also, it is necessary that assuming operation in a pulsed mode with pulse duration

the accelerating voltage be stable to within 1 %, [ibid] . To -■. of ~ 8 ms and repetition rate of 10 Hz. The experimental

provide phase stabilization of the RF sources it is » setup of a two -stage magnetron utilising CW, S-band, 1 necessary to use feedback of a Low Level RF (LLRF) 7 kW tubes operating at pulse duration of 1-10 ms, and the system. Power control, necessary for operation with SC, 7 obtained results are presented and discussed in this paper.

can be done as proposed in [4].

INTRODUCTION In the context of magnetron RF sources, intended to drive the SC, this task is formally similar to consideration

Intensity frontier high-energy accelerators of proton and of a frequency-locked magnetron controlled by a slowly 7 ion beams are crucial for Accelerator Driven Systems, varying phase/frequency. Such a task has been 7 ADS, (intended to drive sub-critical reactors, ADSR) and successfully solved theoretically using a numerical .:, research projects including the Project X, which is an simulation of transient processes in the frequency- locked 7 _: accelerator facility under development at Fermilab [1], magnetron considering it as a forced oscillator [5-7]. designed to support multiple physics programs at the Experimental validation of the simulation was performed ! ^"' intensity frontier. Additionally, Project X could be used to with a 2.5 MW S-Band pulsed magnetron [ibid]. Figure 1 7: advance the concepts for an ADSR. Subsequent stages of shows excellent agreement between simulation and

Project X could include an 8 GeV pulsed linac for future measurements [6, 7] for the locking power of -18 dB. 7; muon and/or neutrino facilities.

The pulsed linac will utilize the standard 1.3 GHz ILC- 7 type SC [2], with an accelerating field of 25 MV m. The

7; cavity filling time and the full RF pulse duration are

7 chosen to be about 3 ms and 8 ms respectively. The total

7 number of cavities is 200. With a beam current of ~1 mA

7 the power required to feed each cavity is ~ 40 kW.

Several options for driving the SC are being considered.

7 One option is based on a single high power klystron

Time, με

¾ feeding a number of SC (16 cavities in 2 cryomodules).

7 However the scheme does not allow independent tuning Figure 1: Variation of the simulated (G), and measured 7 of the phase and accelerating voltage in the cavities which magnetron frequency (D), vs. the locking frequency (B). ;,: is highly important for weakly-relativistic particles.

V Another option is based on individual feeding of each Analysis of results obtained in [5-7] was subsequently 7 ^: : cavity from a separate IOT or klystron transmitter. This used to compute the phase deviations of the 2.5 MW >K option looks technically plausible, but the number of magnetron locked by the slowly varying frequency at transmitters significantly increases project cost. Thus, a power of -18 dB. Figure 2 shows simulated phase ; potentially less expensive RF source to excite each cavity deviations of the frequency-locked magnetron relatively independently is an important option to be considered for to the locking frequency, curve E, and the measured deviations, curve G, which are in agreement as well. The

77 'Work is supported by the US DOE grant DE-SC0006261 intrapulse phase deviations are ~1 degree; such stability is ¾. ^# grigory@muonsinc.com; gkazakevitch@yahoo.com adequate for the Project X pulsed linac requirements. g:ISBN 978-3-95450- Π5-:Ι. 07 Accelerator Technology and Mass Systems

7- 2348 T 7 Superconducting RF .^oceedia^i of IFAC2012, New Orieass, Louisiana, USA WEPPC059

Figu

deviations of the 2.5 MW frequency-locked magnetron. Figure 4: Scheme with an interferometer to measure

These results, and the experimental results obtained phase deviations of the frequency-locked magnetron. with a commercial in ection-locked CW ma netron 8, 9 ,

m

fo

G

in

co

co

Fi

op erating as a pre-excited frequency-locked oscillator.

The magnetron module was fed by a pulsed modulator

using partial discharge of a storage capacitor. The

modulator voltage slope was less than 0.9% when the

modulator was loaded concurrently by 2 magnetrons and

the pulse duration was 10 ms. The magnetron was pre- excited by a precise CW oscillator with a TWT amplifier.

First measurements were done using down-conversion

with an intermediate frequency (IF) = 10 kHz and a

magnetron pulse duration of 2.5 ms. A vector network

analyzer (HP 8753ES) synchronized with the type

N5181A CW oscillator was used as the heterodyne. Phase Figure 5, a-d: Phase deviations of the frequency-locked deviations were measured and found to be δφ (rms) =1.2 CW magnetron operating with pulse duration of 8 ms. deg. during the main part of the magnetron pulse, The first plot shows phase deviations during the full 8 demonstrating good phase stability of the frequency- ms pulse. Figure 5b shows phase deviations in beginning locked magnetron in the pulsed regime. of the pulse, it can be seen that the time-to-lock is <50 μβ.

Further measurements were performed with an The subsequent plots show phase deviations in middle interferometer, Figure 4, for pulse duration of =8 ms. The and last parts of the 8 ms pulse. All the plots show scheme reduced the phase noise caused by the vector instantaneous phase deviations of less than a few degrees network analyzer in the down- conversion measurements. in main part of the pulse (t >120 μβ) for the pre-excited The measurements were performed at a locking power frequency-locked magnetron operating in pulse mode. and a magnetron outpu of: PL _OC k~7.3 W and Pout ~ Slow drift of the phase during the long pulse is explained 580 W respectively (or dB). by two competing processes: an increase of the

Measured phase deviations are plotted in Figure 5, a-d.

07 Accelerator Technology ami aie Systems ISBN 978-3-95450- 1 t5-t 07 Siioerconriectuig RF 2349 WEPPC059 .^ ceedin^i of IFAC2012, New Orleans, Louisiana, USA

magnetron current because of overheating of the cathode ratio of the magnetron output power to locking power was caused by bombardment of returning electrons, and a =33.5 dB and =20 dB for the two-stage and single stage decrease of the magnetron current associated with a drop magnetrons respectively. These results were obtained in in the magnetron voltage because of a discharge of the ordinary regimes at long pulse duration. The measured storage capacitor. The later process dominates in the time-to-lock for single stage and two-stage frequency- second half of the pulse. The obtained phase deviations locked magnetrons <50 μβ is adequate for SC accelerators are acceptable for a phase control with a LL F system. including the Project X pulsed linac. The obtained results show that the proposed concept of a two-stage (cascade)

EXPERIMENTS WITH A TWO-STAGE magnetron based on CW commercial tubes is a promising FREQUENCY-LOCKED MAGNETRON one for feeding SC intensity frontier accelerators.

A model of the two-stage (cascade) magnetron,

proposed to drive the SC of the Project X pulsed linac and

other intensity frontier accelerators, was built with two

similar CW 2.45 GHz magnetrons with output power up

to 1 kW operating in pulsed regime. The magnetrons were

chosen to be locked at the same frequency. Both

magnetron modules were fed by a single modulator,

previously used for the single magnetron measurements.

The magnetron with the lower nominal anode voltage was

fed through a divider. The modulator pulse duration was

chosen to be 5 ms to avoid the aforementioned noticeable

drop of the magnetron current. The first magnetron was

frequency-locked by a CW signal; the second one was

excited by the output signal of the first one through an

attenuator lowering the locking power for the second

^: Figure 6: Scheme for measurements of the phase stability

: of the 2-stage CW magnetron in pulsed regime. Figure 7, a-d: Measured phase deviations of the two-stage

The measurements were performed at attenuation of -20 frequency-locked magnetron in pulsed regime. Traces B ^' dB and -13 dB corresponding to the ratio of Pout-ii/Pi,ock-i ~ and D correspond to ratio Pout-ii/PL _oc k-i ~ 33.5 dB and 26.5 ! 33.5 dB and 26.5 dB, respectively. The phase variation dB, respectively.

\ for the 5 ms pulse duration are shown in Figure 7, a-d.

: The plots show slow phase variations caused mainly by REFERENCES

: an intrapulse drop of the magnetron voltage. The phase [1] Project X and the Science of the Intensity Frontier, noise value of the 2-stage magnetron is a few degrees. http://projectx.fnal.gov

: Time-to-lock of the 2-stage magnetron is <50 μβ. [2] S. Nagaitsev, "3-8 GeV Pulsed Linac Design and

Options,"Project X database, http://projectx

CONCLUSION docdb.fnal.gov

We demonstrated the operation of the frequency locked [3] N. Solyak et al., WE 101 , LINAC 10, Tsukuba, japan : CW single-stage and two-stage S-Band magnetrons in a [4] G. Kazakevich et al., WEPPC060, IPAC12, i pulsed regime. Both models provide smooth phase NewOrleans, USA

'■ deviations caused in general by modulator parameters and [5] G.M. Kazakevitch et al, M A 528 (2004) 115-119 ; the magnetron cathode properties. Instantaneous phase [6] G.M. Kazakevich et al, PRST-AB, 12, 040701, 2009 : noise of the single stage and the two-stage magnetron are [7] G.M. Kazakevich et al., NIM A 647 (2011) 10-16 ■in range of few degrees. Measured ratios of the peak [8] H. Wang et al., ΊΉΡΕΒ067, 1PAC30, Kyoto, Japan i power to noise in the magnetron spectra are >45 dB. The [9] A.C. Dexter et al., PRST~AB,14, 032001, 201 1

;:ISBN 978-3-95450-115-1 07 Accelerator Technology and Main Systems

T 7 Superconducting RF Proceedings of IPAC2012, New Orieass, Louisiana, USA

A HIGH-POWER 650 MHZ CW MAGNETRON TRANSMITTER FOR

INTENSITY FRONTIER SUPERCONDUCTING ACCELERATORS

Grigory Kazakevich*, Gene Flanagan, Rolland Johnson, Frank Marhauser, Michael Neubauer,

Muons, Inc., Batavia, 60510 IL, USA

Todd Treado, CPI, Beverly, 01915 MA, USA

Vyacheslav P. Yakovlev, Brian Chase, Sergei Nagaitsev, Ralph J. Pasquinelli,

Fermilab, Batavia, 60510 IL, USA

Abstract Consequently, the costs of traditional high-power CW

A concept of a 650 MHz high-power magnetron RF sources, such as TV klystrons or Inductive Output , transmitter with a fast control in phase and power, based Tubes (IOTs), for separate feeding of the superconducting on two-stage injection-locked CW magnetrons, has been cavities of the GeV scale accelerators become prohibitive. ■;; proposed to drive Superconducting Cavities (SC) for The state of the art solid-state RF sources for 650 MHz at , ^' intensity- frontier accelerators. The transmitter consists of the required power are yet rather expensive as well. J, two 2 -stage magnetrons with outputs combined with a 3- Hence the proposed concept of the magnetron transmitter dB hybrid to fulfil a fast control of output power required with driving power of about 1 kW or less, being based on . for SC accelerators. The output power is controlled by prototypes of commercial tubes looks as a solution varying phase in the input of one of the 2 -stage potentially lowering costs of projects of the intensity ; magnetrons. For output power up to 250 kW we expect frontier high-energy accelerators.

the output/locking power ratio to be about 30 to 40 dB in One of the primary concerns of using the magnetron ^■ : CW or quasi-CW mode with long pulse duration. The transmitter to power superconducting cavities is the ; phase control bandwidth in MHz range has been management of phase with a Low Level RF (LLRF) ; evaluated measuring transient time of the phase jump system generating a controlling signal which slowly ■ with a 2-stage CW magnetron model operating in pulsed varies phase on input of a 2-stage frequency-locked ί regime. Description of the magnetron transmitter concept magnetron. The task is formally similar to one ί and it's modelling using frequency- locked commercial, considering operation of a magnetron locked by slowly ^': CW, 1 kW, S-Band magnetrons operating in pulsed varying frequency/phase, [3-5]. This task was regime with long pulse duration is presented and successfully solved theoretically considering the ; discussed in this paper. frequency-locked magnetron as a forced oscillator and proven experimentally [ibid]. Unlike Adler's approach _: . _:

INTRODUCTION [6], the developed technique analysing transient process

The state of the art superconducting linacs for proton in the locked magnetron allows numerical simulations of the frequency/phase deviations in time domain. Analysis and ion beams capable of accelerating protons and ions to

several GeV with an average beam current of 1 to 10 mA of the simulations, successful experiments with the /■ or more are prospective for intensity frontier accelerator frequency-locked magnetrons, [3-8], and particularly our ^;

experimental results obtained with a frequency-locked 2- _: physics and are the basis for Accelerator Driven Systems

stage (cascade) magnetron model, [9] motivated our ;; (ADS), which have evoked significant interest the world

concept of the high power 650 MHz frequency-locked over because of their capability to provide operation of

magnetron transmitter with a phase and power control. sub-critical reactors in nuclear power stations, to

First experimental modelling of the magnetron - incinerate the minor actinides and long-lived fission

transmitter has been performed using CW 2.45 GHz ; products of radiotoxic waste, and for potential utilization

of Thorium as a nuclear fuel, [1, 2]. magnetrons with power up to 1 kW, operating in a pulsed ;

mode. The paper describes the experimental setup and the \

The high-intensity SC accelerators intended for non- obtained results.

relativistic or weakly relativistic particles require separate

and independent feeding of each superconducting cavity

with its own RF source controlled in phase and power in EXPERIMENTAL FACILITY

order to avoid growth of transverse and longitudinal The experimental facility was developed and built to ^: . emittances that may even result in beam loss. The RF study the operation of the CW single and two-stage source power, P _a , required for each SC accelerating a frequency-locked magnetrons in pulsed regime with long , weakly relativistic proton beam with energy gain of V _a pulse duration. The setup for the first experiments _: i can be estimated by: includes a pulsed modulator to feed the magnetrons, two ^:;

P = V I■ single-stage magnetron modules with RF components, wide-band CW Travelling- Wave Tube (TWT) amplifier ?

Here is the accelerated current. Assuming that V _a =20

driven by a synthesizer, and measuring equipment, [9] . MeV, I _a =10 mA one gets P _a ~ 200 kW per the cavity.

The modulator, [9], provides concurrent operation of -

*grigory@muonsinc.com; gkazakevitch@yahoo.com two magnetrons with a controlled in the range of -39 deg ;!

07 Accelerator Technology ami aie Systems IS BN 978-3-95450- H5-1 ^■' 07 Superconducting RF WEFPC060 .^ ceedin^i of IFAC2012, New Orleans, Louisiana, USA

to 30 deg shift of the high voltage pulse relatively to the

zero-crossing of the magnetron filament current allowing

one to check the influence of the filament magnetic field

on the magnetron phase stability.

CONCEPT OF A MAGNETRON TRANSMITTER FOR SC

Figure 2: Computed power on the 3-dB 900 hybrid output ACCELERATORS

ports vs. ratio of power P4/P2 on it input ports.

A concept of the magnetron transmitter (with phase and

power to be controlled by a LL F) is presented in Figure STUDY OF TWO-STAGE AND SINGLE-

magnetron.

: Figure 1 : Conceptual scheme of the two-stage CW The first magnetron was frequency-locked by the TWT i

:

:

;

'

;

;

:

;

:

;

■

i

MSBN 978-3-95450-115-1 07 Accelerator Technology and Main Systems

T 7 Superconducting RF .^oceedia^i of IFAC2012, New Orieass, Louisiana, USA wfi'.ppc<¾<

Measured phase deviations of the 2-stage frequency- The slow phase drift (trace L, where the phase detector locked magnetron vs. the attenuator value are plotted in is not saturated) is caused by two competing processes: an Figure 5. More detailed traces are presented in [9]. increase of the magnetron current due to pulsed

Figure 7: Single frequency-locked magnetron phase

deviations vs. the filament phase.

07 Accelerator Technology awl aie Systems ISBN 978-3-95450- 1 t5-t 07 Suoercondectiiig RF

Magnetron option for lse linac of the Proje

G. Kazakevich ¹ , V. Yakovlev ²

1Muons, Inc., ² Fermilab

June.1.2011

Concept of the Project X multi-experiment accelerator facility

The Project X provides high-intensity 3 GeV the proton CW beam for rare processes experiments and for nuclear physics experiments related to ADS program.

The Project X should also provide a neutrino beam for long baseline neutrino oscillation experiments. The neutrino beam requires 2 MW proton beam at the energy of 60-120 GeV, that will be produced by the FNAL Main Injector.

Injection to the Recycler/Main Injector takes place at 8 GeV. The stripping foil heating problem demands the following parameters of the RF feeding system of the pulse linac:

3-8 GeV pulse linac parameters

As it determined with a stripping foil

Energy increment: 25 MeV/cavity

Accelerated current: 1 mA

Cavity filling time: ~3 ms

Beam pulse duration: 4.3 ms

Repetition rate: 10 Hz

External Q-factor: 10 ⁷

Resonance frequency: 1 .3 GHz

Cavity bandwidth: 130 Hz

P ^r c ^■ - 30 kW

P _c Overhead: 16%

PC TOTAL" 35 kW

P ^r C AVER. " 2.6 kW

High-power Klystron option of RF source

Concept: L-band klystron feeds 2 cryo-modules with

16 Superconducting Cavities (SC)

Klystron pulse power (including losses)

Klystron average power:

Pulse duration:

Repetition rate:

Number of klystrons for the pulse linac:

Klystrons developed to drive SC

Type VKP-7952A VKP-7957A

Frequency, MHz 700 499.76

Voltage, kV 92 76 63

Beam current, A 16.8 17.7 17

Output power, kW 1020 822 608

Efficiency, % 66 61 57

Gain, dB 43 40.7 42.3 VKP-7952A klystron lay-out

Issues of the high-power klystron RF option

Feeding of a number of cavities from one RF source allows control of the vector sum of the cavity voltage only. This is very serious issue for weakly relativistic beam because of:

► Errors in the power distribution system;

► Microphonics,, which is a problem for a narrow-band cavity.

Cost estimate for the klystron option of RF source i l l

9 £ ,£L K ^Q JS. " 8 _& B 8 B 8 y2 %-Jf II i r%. i 2¾ ft. s %-Jf i i ¾L _< # iLjS oL I I 8 i s iok j&Jf lH» ¾ 1 ¾_Jf fcJS 8HB and included in cost

Klystron (Including development): $ 0.5 M

Modulator (Including development): $ 0.5 M

Modulator Pulse transformer (in oil): $ 0.15 M

Ferrite circulator (including matched loads): $ 0.04 M

Klystron filament stabilizer; Interlock system: $ 0.1 M

Solid State RF driver: $ 0.02 M

Klystron solenoid +PS (Includ. development): $ 0.2 M

Cost estimate for 13 transmitters: $ 18.5 M

RF distribution system: $ 0.5 M

/ΟΓ option of RF source*

Efficiency of ~ 60% and would take advantage of TV

transmitters for lower frequency systems

For 1.3 GHz only 'recently' developed, little reliability data (short cathode-grid spacing), low gain, 2x higher voltage modulator than klystron and needs more system

development (drive power 500W)

1300 MHz IOT manufacturers: CPI (30 kW), E2V (16 kW -no longer in catalog), Thales (16 kW) and recently Mitsubishi (built 30 kW prototype for KEK ERL program)

11 cost ranqe from 400 -800 k$ is based

* S. Chu, http://projectx-docdb.fnal.gov/cgi- bin/RetrieveFile?docid=663&version=1&filename=1300MH Z.pdf

CW high-perveance low-voltage klystron and

SSA options of RF source*

Klystron efficiency is -60% and gain is -40 dB

Klystron manufacturers: CPI sells a 'reliable' 1 1 kW tube and has a design for a 30 kW, 19 kV tube (would build one for 440 k$) and Toshiba is developing a 25 kW tube (probably for KEK) For JLab 12 GeV accelerator upgrade: 1 .5 GHz, 13 kW CW klystrons were developed

SSA advantages: Low-voltage PS

Disadvantages:

"Ibid

Magnetron option of RF source

Magnetron pulse power (including losses) : ^« 40 kW

Magnetron average power: 2.6 kW

Pulse duration: 7.3 ms

Repetition rate: 10 Hz

Number of magnetron generators for the linac: 200

Industrial CW Magnetrons (915 MHz and 896 MHz)

Model Number U , kV

CWM-SOt 1 s¾ 0

€Wti ^» 7§t ^ C 75

L10016-1 4>CI 50

L10016-1 R 15 4.0 SO f ne magnetrons emciencv is

Magnetron works as a forced oscillator, but NOT as an amplifier!

► Thus, magnetron output power does not depend on the amplitude of the frequency/phase locking signal.

► Variation of the frequency/phase locked magnetron

voltage and current In some range does not affect

the magnetron frequency/phase stability-

► Driving signal with amplitude much more than first

harmonic noise amplitude is enough for frequency/phase locking. Usually it's from -8 to ^« 20 dB in power scale,

Tlie forced oscillator roods! was checked in simulations and measurements; both are in an excellent agreement

► Multi-stage magnetron scheme is available.

Linac with SC solution:

Two independentif phase-controlled multi-stage frequency/ phase-locked C¥¥ magnetron generators + 3 dB hybrid.

That allows a rapid and deep independent control of power and phase of the magnetron generator.

Frequency/phase locked two-stage magnetron generator for a deep and rapid control of power and phase

atched leads

Cost estimate for magnetron option of RF source

High power magnetron: $ 9.5 k

Low power magnetron: $ 1.5 k Four ferrite circulators (with matched loads): $ 50 k

Two Solid State RF drivers: $ 40 k

3 dB hybrid: $ 5 k

Power supply for a generator: $ 50 k

Cost estimate for one transmitter: $ 167 k

Cost estimate for 200 transmitters: $ 33.4 M

Conclusion

Proposed concept of a frequency/phase locked magnetron RF source with following features:

► Provides inclepeiideiit feeding of a separate SC with a rapid, Independent and deep control of amplitude and phase In each

[1] G.M. Kazakevich, et al., Nucl. Instr. and Meth. A (2011 ), doi:10.1016/j.nima.2011.04.030

[2] A.C. Dexter et al., PRST-AB 14, 032001 (2011) N de.ir Instrum ts and Mefh ds in Physics Resear h A 647 (2011 ^" ) ^" 10-16

lotrapu!se frequency stability of a magnetron frequency-locked

through a wave reflected from an accelerating cavity

Grigory M. azakevich ³ ·* Viatcheslav M. Pavlov ³ , Young Uk jeong ^s , Byung Cheoi Lee ^b

B;:dl:er Infini e of Mideo Physics, PA , Novosibirs , Ac den-.icio.r, /. vrcnt ev t t, 630090, Russio

' ^■ ' Korea Atomic Energy Research Institute, RO. ή ^' χ 05, Yiisov.g, D eion 305 -600, South Korea

A T I C L E ί N i ^: O A S T 8 A C T

Ariirie history: A laboratory-size Free Electron Laser (FEL) driven by a classical S-band inicrotron fed by a 2.5 MW magnetron d c ived 24 January 201 1 generates terahertz radiation lunabie in a wide range. The FEL provides output pulse power of ~ SO W in the Received :n revised form wavelength range of 100- 300 ttm with a pulse duration oi ^' 2-4 fis. The FEL parameters are available due to 19 April 201 1 stabilization of the accelerated beam current and the magnetron frequency. The latter is stabilized by the Accented 19 April 2011

Available online 5 May 2! frequency locking in the magnetron through a wave reflected from the microtron accelerating cavity, which also setves as an externa! stabili ing resonator, providing the RF reference signal for the magnetron. The

Keywords: simple RF stabilizing scheme provides the r.m.s. magnetron frequency instability, δί » 0-13 kHz relative to Magn ron the reference frequency at the frequency pulling bandwidth of 0.43 - 0,85 MHz and at the initial power of the frequency locking

reflected wave as 30 kW. The developed stabilization provided stable and reliable operation of the FEL for Acce!oratii cavity

Microvrori more than 10 years. Measured and simulated results are described in this paper.

Heterodyne technique © 7.01 1 Elsevier B.V. All riehts reserved. frequency pulling

1. introduction To stabilize the bunch repetition rate the magnetron frequency lias been locked through the wave reflected from the accelerating

The developed variable-energy, high-current, 12 -orbit microtron cavity. This simple RF scheme including the magnetro coupled with [1 ], driving a terahertz FEL [21, utilize;-; a simple RF system with a the accelerating cavity through a non-reciprocal resonance ferrite magnetron auto-generator and the 1-type internal injection system isolator with inverse losses of 18 dB allowed us to stabilize the [3], with a thermionic cathode. This makes the miaotrori a simple, magnetron with the frequency of the accelerating field, which serves compact and low-cost one, Optimization of the cathode design with as a reference frequency, intrapuise frequency instability of the multi-layer thermal shielding and suppression of boron diffusion frequency-locked magnetron has been studied by comparing the with a graphite holder makes die cathode stable and reliable during computed time-dependent reference (accelerating) frequency drift, a long life time [4]: however an incremental beam loading of the caused by the incremental beam bailing that results from the accelerating cavity is inherent to the internal injection. The beam electron back-stream, with the time-dependent magnetron freloading is caused by back-streaming non-resonance electrons hitting uency. The last one was simulated, solving a system of the abridged die cathode, which results in incremental heating of the emitting equations [5,6], lor the transient state of the magnetron and the surface and also in incremental emission current [4j. The rising accelerating cavity. The accelerating cavity loading current contained emission current in the high-current microtron results in an increin the system of equations was computed by 2-0 tracking for ail mental beam loading causing a drop of the accelerating field in the orbits of the microtron. The magnetron frequency also has been microtron cavity; this results in a drop of the accelerated current measured with a heterodyne technique [6-S]. Results of the compuduring the macro-pulse that is inadmissible lor FEL operation. To tatio and simulatio in the time domain are in excellent agreement stabilize the accelerated current we compensated the incremental with measured variations of the magnetron frequency and demonbeam loading by increasing the magnetron power through increstrate good stabilizing properties of the developed frequency locking mental magnetron voltage. However such a method of stabilization scheme. The results obtained from the computations, simulation and increases intrapuise instability of the magnetron frequency because measurements are presented and discussed in this article of the frequency pushing in the magnetron, resulting in an additional

bunch jitter, which is unacceptable for operation of the terahertz FEL. 2. Computation of the accelerating frequency drift caused by the back-streaming electrons in a high-current microtron with the internal injection

* Corresponding anther. Contact address: ^5 Oakridge Dr., Apt. 9, Aurora,

II. 60502, USA. Tel.: + 630 779 6477; fax: -t 1 630 340 6039.

-mail ddres s: gka akeviteh@yaheo com. To compute the reference frequency variations, we computed grigcrii@iri smc.com (C . Kazakevicn . the incremental overheating of the cathode caused by the

0!68-900¾$ - see front matter © 2011 Elsevier B.V. All tights reserved,

do; · 10.t 016/j ma.201 1 04.030 ί Λΐ. Kazakevich ci ai / Nudear Instruments and Methods in Physics Research A 64/ ( ji ^' i) IG--i6

Hg. i. } 2-D tracking of the f;r. ^r -t microtron orbit. Numbers ii d 2 show the Mere .4=73 A/K ^J err; ² and e<j) _C =2.6S eV re the Richardson constant "■arrow slits ma e yiori the -yxis for as g of the electrons (b; ^ckin^ and the work function for haB ₆ . respectively, k is the Boitzmann of the back-streaniing electrons emitted from the cathode edge int a d hitting constant and i ^' is the emitter temperature in Kelvin. The correthe emitter.

sponding value of the maximum current density at the emitter operating temperature of 1900 is }c a =k 900Κ,0,0) ¾ back-streaming non-resonance electrons and the incremental 49 A/cm ² .

emission current resulting from the cathode overheating. ConThe average energy of the electrons hitting the emitter surface sidering constant accelerated current stabilized with incremental and increasing the emitter temperature per RF period was magnetron power, we computed the accelerating frequency drift calculated as [4]

1

Here £.-, is amplitude of the electric field strength on the cavity Ι4χί

(4)

^• Joe the circular eigen frequency of the

accelerating cavity. _f —% _m \xn, ' ^s the Besse! function of the first

Here s thermal conductivity and χ is thermal diffusivity kind, φ is an initial phase, ¾ ₀ i ---2.405 is the first zero of the Besse! k _c i

coefficient measured at high temperatures [ 10]. Solution of this function and i¾— _\ /k _r -k^. The calculated amiplitu.de of the field equation. AJ!t), Fig. 3. shows the rise of the temperature of the strength on the cavity axis is ¾~.35.527 MV/m, which correemitting surface during the macro -pulse.

sponds to operating parameters of the microtron. The correspond Note that the back-streaming electrons start heating the ing amplitude of the electric field strength at the center of the emitting surface when the magnetron generation starts up, while emitter surface is ¾/ ₀ ί fc>/¾/cosh{ li _z d _c )≤= 10.35 MV/m. the resonance electrons appear with a delay At ~ 3rc ~

The current density of the LaB _s single crystal emitter can be Qa ·¾/( ΐ -;- :) KC. Here Q _iJC -9800 is the measured value of the expressed as a function of r, φ considering the Schottky effect as accelerating cavity wall Q-factor. β —5,4 (measured value) is the cavity coupling coefficient and _; ; - 0.174 μ5 is the accelerating

-e<p _c -;- 3.79 x 10 y^csfr^liG'' cavity fi lling time.

Combining the Eqs. (4) and (2 ) one computes the time- dependent emission current resulting from the emitter CM. Kaz evi . / Nu icf r Insm:;nents and Mem ds Physics K seard? A 647 (2011) W~ ^' i6

acting on the taii was estimated via integration aiong the hunch axis of tii electric field of charged disks with radius of and taking into account relativists: motion of the head part. At the total energy on the first turn of as 1 MeV this gives a longitudinal held of 0.(31 V m from the moving head charge interacting with the moving taii charge. Note that injection in the microtron occurs at i he accelerating field > 10 V/m: further acceleration happen;; at the field > 35 M ^' v'/m. The energy spread caused by the longitudinal field for the first orbit is < 2 keV at the tota! energy of ¾ ί IvleV. The longitudinal field e!ongates the bunch at most by 1.4% on the first orbit; elongation of the bunch on next orbits is iess because of higher energy, Therefore the space charge effects were ignored during acce!eration in the microtron.

3 4 As noted above, the incremental emission current at the Tinie _: incremental magnetron power feeding tiie accelerating cavity and at the constant accelerated current results in incremental i . 3. Compu ed time- ep r: eiit growth of the e ^m i r temperature caused by

back- streaming eiectrc-ns for the i-type injection with a single crystal ^' 2.5 mm in beam !oading. The beam loading coefficient. η _ε [ 1 1,4], characterdiameter ; _f; oafhorfr; at ^' iV--- 1900 . ero of the time scale otrr;sporids to izing the cavity loading with resonant and non-resonant electrons s artup of the rriagr- tror. generatio is expressed as the ratio of the total beam power, P _e . to the cavity

" ^J _(: :

overheating due to the electron back-stream The accelerating frequency drift resulting from the incremental beam loading and caused by the back-streaming electrons

{T, _: , ÷AT(f),r,Q)rdr (Si overheating the cathode was estimated using the following equation [4] :

Here To = 1900 K is the initial emitter temperature.

Note that the 1 -D model, Eq. (4), does not consider spatial F(i) «

2n 2Qoc ^■ MO) 1 )

distribution of temperature along the emitting surface, while the

small part of the emitter area located close to the microtron where η _ε0 is the initial beam load ing coefficient: and i _L G) is the median plane has higher temperature. Therefore integration of initial value of the emission current. Note that the process of the the expression Eq. (5) over total cathode surface leads to over- frequency variation resulting from the beam loading and caused estimation of tiie emitted current, A 2-D computation shows that by the elect ron back- stream overheating the cathode is very slow tiie overheated cathode area is approximately equal to one half of in time domain of the accelerating field, Therefore one can the total emitter area. T he considered correction gives an agreeassume that the values of the cavity voltage amplitude. Vr. the ment within a; 10% of the measured increment of the emitted fit st harmonic current amplitude, W, and the harmonic phase, <pw, current, Fig. 4, trace B. Tiie plotted traces were measured at the are const ant for many periods of the accelerating field. The operating microtron frequency /-2.S01 GHz and at the permacomputed drift of the accelerating frequency for measured trace nent microtron magnetic field B— 0.1065 T, following from trace iAt) with i j) :¾ 0.92 A, Fig. 4. curve 8, is shown in Fig, 5. B. Fig. 4. the average value of the emission current measured in

optimized regime is - 1.1 A, which corresponds to injected charge

of at most 0,2 nC. Assuming for simplicity a uniformly distributed 3. Calculation of magnetron frequency variations awsed isy cylindrical shape injected bunch with the length of 8 mm and beam loading in the coupled system of the magnetron and transverse radius of r _c one estimates the energy spread and accelerating cavity

elongation of the bunch caused by axial interaction of the head

and the tail parts, assuming that each cylindrical part is equal in The technique allowing simulation of the magnetron frecharge and 4 mm long, Longitudinal electric field of the head quency variations considers the transient state in the system CM. Kazakevich et al / N ci ar instruments and ethod in Physics Research A 64/ (zOl ^' i ) 1C/-1G

Time, μ-= v' _c , MV

Fig. 5, Comp red arift of the frequency of the accelerating fieia resulting from the

beam increments; leadi g that is caused by the e!ectror: back-itreani. 3 ^; ig. 6. Calculated load characteristic of the micTorron acccleratirig canity. including the accelerating cavity and the magnetron coupled / _^ 2.801 GHz and at the permanent microtron magnetic field through a ferrite isolator, Using the SVF.A method, [5], the o. u¾; _; ·

transient state of the system including the acce!erating cavity in the analogous equation for the magnetron, Q. _M is the loaded and the magnetron is described by the following system of magnetron cavity quality factor, (¾ _¾ ., s 1500 is the wall quality abridged equations [6j: factor, ί;¾ _Μ is the circular eige ti ^' requency of the magnetron cavity.

; _c {f} is the normalized dimension!ess time-dependent slowly varymoduius of the magnetron cavity voltage V _M as

ing emission current, TIF = (sin(feo£/2)/(feoi./2)) is the transit-time

0 2) factor, i. ~ J 7,8 mm is the cavity height, iivyj = ^' ^c- _i -ϊ-\νϊ. ant;

is equal to

ψ„— arctan(w¾, with w&, and w¾, defined as

Vzr. {ton £j/o('ic¾ (.hr.■ QjCOSi COt );?'.'

Here UA_ _T ~0.8UA_H is the threshold of the anode voltage. .(ton.tl o< _. feoXn(f(le.t))Sm(<»t)df.

The typical values of .¾i{V ^' _w ) and b _M (V _M ). the conductance and the susceptance of the magnetron cavity, respectively, were taken

The time-dependent normalized emission current. i,_{t), in accordance with ef. [ 12j. Fig, 7 shows dependences of these ' _f cir) ; and ! were obtained from measurements, Fig. 4, The values on the relative magnetron cavity voltage VM

calculated normalized function |/ _c (Vc) | is plotted in fig. 6 as the The voltage of the reflected wave in the waveguide {i he solid line. For comparison the dots show the computed accelermagnetron output signal) is

ated current with normalized amplitude at the 1 2th orbit, Iij ),

The calculations were done for the operating microtron frequency ^' - " ^¾, W ^"' ϊ' CM. Kaz evi

ant; accelerating cavities we used additional equations consideris turned OFF. the operating magnetron is considered as a forced ing the power relationships between the magnetron and the oscillator due to the presence in Eq. (8) of the non-zero term with mictotron cavities through the voltages in the reflected and Vm expressing the wave reflected from the accelerating cavity.

The simulated magnetron frequency variations at a magnetron-accelerating cavity detuning value of A ≥ ¾¾c/2Qr —

'C = Vc-V ,r (Vi) 0.43 MHz are plotted in Fig. S, curve B. Here _0£: is the accelerating

The voltages in the forward waves for the magnetron and the cavity eigenfrequency.

microtion cavities are expressed as The accelerating frequency drift, curve D. computed above.

Fig, 5. fits the curve B, Fig. 8, well demonstrating good coincidence in the main part of the time scale with the plotted result of the

( 14) simulation, curve B, although the two curves were obtained with

1 the different described techniques. The coincidence demonstrates that the simulated magnetron frequency follows the computed

Here « _M c— 0,4 dit is the transfer coefficient from the magnetron reference frequency drift with very high accuracy. This points to to the microtron cavity and o: _M — 1 S.0 dB is the transfer coeffithe very good stabilizing properties of the described simple cient from the microtfon cavity to the magnetron. Both coeffifrequency- locking scheme and confirms that the variation of the cients characterize the ferrite isolator. accelerating (the reference) frequency at the internal injection is

The values of V _K and y _iM can be expressed as function;; of caused by the incremental beam loading in the accelerating cavity by considering Eqs. (13) and ( 14); and is a result of the cathode overheating from the back-streaming electrons. Comparison of the reference frequency variation presented in time domain, curve D, with the magnetron frequency

(15) variations, curve B. Fig, 8. shows the time required to stabilize the magnetron. The time is ¾ 1 .5 ps at the existing parameters of the

frequency-Socking scheme. The r.m.s. value of the difference

The time-dependent amplitude of the wave reflected from the frequency for the plots B and D in the time interval 2,5-6,5 p.s, accelerating cavity has been measured using a 20 dB waveguide when the magnetron is well stabilized, is s; 19 ItHz. It corredirectional couplet at various values oi ^' the magnetron-acceleratsponds to a computed magnetron frequency instability relative to ing cavity detuning parameter. the stabilizing frequency better than 7 >·: 10 ^{" b} at the magnetron

Presenting Vg^ as Vg^— Vjaj exp <p _m ) one calculates the frequency of as 2,8 GHz during this time interval. Note that the time-dependent variations of the magnetron frequency: limited number of particles considered in the 2-D tracking gives

systematic error, whit

the frequency variations of the magnetron frequency instability.

coupled through the ferrite isolator with the microtron accelerating cavity was done using Eqs. (8), (9) and ( 15), for various

detuning parameters of the microtion cavity. For the calculations, 4. easure ents of intrapiiise frequency variations of the we determined the proper phase relationship for the waves frequency-locked magnetron and comparison with entering and radiated from the magnetron RF port by comparing compiited data

the computed time-dependent amplitude of the reflected wave at

various phases with the measured one. The phase providing an We have measured the intrapu!se magnetron frequency variaappropriate coincidence was chosen for further simulations. Mote tions by a heterodyne technique [6-8] utilizing a signal branched that the length of the microtron waveguide line has been out with a 20 dB directional coupler from the wave feeding the optimized at the first criticality of the accelerator to get minimum accelerating cavity. The signal was mixed through a double frequency pushing in the magnetron loaded with the accelerating balanced mixer with a signal from a precise synthesizer to get cavity through the ferrite isolator. The optimized length between the intermediate frequency, which is approximately equal to the ί Λΐ. Kazakevich ci ai / Nudezr Instruments and Methods in Physics Research A 64/ ( ji ^' i) IG--i6

Fig. 9. Simulated (solid iinei;} and measur d (bold 5oiid line? with ei or Pa Fig. 10. . eas red variations of the magnetron frequency, curve with error bars variations cf The magnetron frequency in the magnetron- accelerating cav and the computed reference frequency drift, curve B. bold soiid iine.

sy t m, at various values of the magnetrotvaccelerating cavity detuning Af:

4f=0.43 MHz. (2) 4f=0.68 Hi and (3) 4 =085 MHz. reciprocal value of the fiilitsg time for the accelerating cavity. In

■ his case, variations of the frequency in the coupled magnetron - accelerating cavity system are to good accuracy equal to the

instantaneous variations of the intermediate frequency. The latter

were determined by measuring periods of die intermediate

frequency using a digital oscilloscope [6,8], Measured time- dependent variations of the magnetron frequency at various Af 9- - values are shown by bold lines with error bats in Fig. 9. For

comparison in this figure, the solid lines show the results of the

magnetron frequency simulation.

For these measurements the nticrotron was optimized for the -

FEL operation and provided at the 12th orbit an accelerated

current of 42-45 mA with a pulse duration of ¾ 6 us. Fig. 4. trace Time, its

D. The measurements were done at various values of the magneFig. 5 L Measured intrapulse frequency instabiiity of the frequency-locked magtron-accelerating cavity detuning. The magnetron power was net on relative to the reference frequency, curve y. left" axis. Curve E; s ows optimized in the range of 1.7--2 W to get minimum increment measured variations of the magnetron current m relative units, right axis. of the emission current.

The measurements show very good agreement with the

deve!oped simulation technique based on the abridged equations

i'ai* ί

describing the transient state for die system of accelerating cavity Magnetron intrapulse r.m.s. frequenc ( hase; anations vs. t ^; magnetron- and magnetron coupled with a ferrite isolator together with the accelerating cavity detuning.

2-D tracking of the electrons in the microixon. The measurements

also confirm the applicability of the developed technique for Af ; 6/ &ψ (deg.) afij (r.u.) computation of the accelerating frequency drift caused by non-

043 0.010 0.42 3.57 x U ^e resonance back-scattering electrons in the nticrotron with inter0.68 0.012 0.53 4.2S x 10 - ^e na) injection. Fig. 10 shows excellent coincidence of the measured 0.85 0.01:5 0.58 4.64 x U ^a magnetron frequency variations with the computed reference

frequency drift in the considered time interval at Δ/~.0.43 MHz.

Variations of the magnetron frequency measured at Af— corresponding to the frequency variations, computed in accor0.43 MHz relative to the computed reference (accelerating) fredance with Ref. (8): the fourth column shows the magnetron quency are plotted in Fig. Π , curve B, with error bars. The plot r.m.s. frequency instability in relative units vs. the Af value. demonstrates very high intrapulse frequency stability of the Analysis of die measured plot B in Fig. 1 1 and analysis of data magnetron with the frequency locking scheme utilizing the from Table 1 show high stabilizing properties of the simple frequency pulling. Curve £ shows the magnetron current variafre uency-locking scheme while the magnetron without the tions in relative units during the pulse. The magnetron current frequency locking has the measured frequency pushing of has been measured using a calibrated wide-hand current trans* O.t MHz/A in the considered time interval [ 13j. Hence the former. The ripples in the magnetron current with amplitude less considered frequency-locking scheme improves the frequency than 1.5% result from the non-uniformity of the multi-ceil charstability of the magnetron ~ 30-50 times, depending on the ging line of the magnetron modulator. frequency pulling bandwidth.

The r.m.s. values of the intrapu!se variations of the magnetron The plot B in Fig. 1 1 does not demonstrate any increment i frequency, 6f, measured relative to the reference frequency in the the magnetron frequency vs. the incremental magnetron current, time interval 2.5-6.5 ps vs. the magnetron-accelerating cavity in spite of the noticeable increment of the last one and corredetuning, Δ/, which is the bandwidth of the magnetron frequency sponding increments in the magnetron voltage and magnetron pulling, are shown in Table I . The third column in the table shows power. Moreover the plot shows that the measured amplitudes of the r.m.s. values of the magnetron phase variations, δφ, the frequency ripples in fact coincide with the error values at the 16 CM. Kaz kevl h s al i dear Instruments and iWemeds in Physics Research A 647 (201 !; 10-16

measurements. This ai!ows one to assume that rhe ripples system. The measurements demonstrated that the stabilized measured in the magnetron frequency, Fig. 11 , plot B, which are magnetron operates as a forced oscillator, being insensitive in practically in phase with the measured ripples oi the magnetron some range to variation in the magnetron voltage and hi the current are most likely a signal induced in the RF measuring magnetron power,

circuitry, which was not insulated wet! enough from the modulator grounding bus-bar. Thus the ripples measured in the

magnetron frequency are a result of the magnetron current Acknowledgment

ripples in the magnetron modulator grounding bus-bar and can

therefore be considered as noise in the measurements.

The work was supported by KAER! with Korea Government

Note that the phase oscillations of the bunch relative to the

Fund and by B1NP in frames of scientific collaboration. We are equilibrium phase i the high-current ^' niicrotron contribute o the

thankful to Dr. R.fvL Thunnan- eup for fruitful discussions. accelerating (reference) frequency variations; however the oscillations are damped due to so called "phase mixing." in which the

superposition of osciitations Iron; all orbits at various frequencies References

and phases contributes to oscillations with frequencies of

~/o(i+/!+¾)/Qoc [14]. [ 1 ] CM. Kazakevitch, Y.U. jeong, B.C. Lee, S.G. Cho, |. Leo, V.P. Beiov, N.C

Gavriiov, in: Proceedings of the PAC 2001 Conference, i ag , 200 : , pp. 2739--2741.

S. Sismmar ; Y.U. jeor.g. CM. azukevitch, B.C. Lee. S. . Kim, S.O. Cho. B.H. Cha, J. Lee,

P.D. Vobiv, N.G. Gavrilov, V.V. ubarev. G.N. K panov, Nucl. instr. and Meth.

Detailed analysis of the simple frequency locking scheme A 475 (2001 ) 47-50.

[3J S.P. Kapite, V.N. Melelrf'.in, in: E. . R e (Bd.), Ihe Microtron, vol. 1 , utilized to stabilize the frequency of the magnetron feeding the i-:arwood Acad mic Publishers. London. 1 78, ρρ. υ-1 2.

accelerating cavity of the S-band niicrotron has been pet formed. [4 : CM. Ksjakevich. V.M. Pavlov, CL Kuznetsw, Y.U Jeorig, S.H, Park. B.C. Lee. Two different techniques for calculation of the variation of the j. AooL Phys. 102 (2007) 034507.

(5 : Joint US -CERN - :APAN International School cri Frontiers in Accelerator frequency of the accelerating field and the magnetron frequency Tecbaetogy, 9-18 September 1996. World Scientific, ;SB 9S 1- 02 -383S- X. variation were proposed and used to analyze the frequency [6 : CM. Kazakevich. V..M. Pavlov. Y.U. jeong. B.C. Lee, Phys. Rev. 12 (20091 locking in the magnetron with the irequency pulling through 04070 .

[7 ] CM Kazakevich, Y.U. Jeong, B.C. Lee. j. Lee, Nucl. Jnstr. and etlv A 483 the wave reflected from the accelerating cavity. The performed ^" (2002) 31 -335.

measurements with excellent agreement confirmed results of the [8 : C . Kazaieviob, O.K. Baker. ].:. Mirshfield, Y. Jiang. M.A. LaPomte. A. Mart; ^; '., computations and demonstrated that stabilization of the 2.S MW S.V. Sbchelkunov, Ρ,.ι. SUxum, V.P. Yakoviev. Nucl. nistr. and Meth, ft 621 S-band magnetron with the frequency pulling realized in the (2010) 238-24·) .

J91 L.11. Landau, ELM, Lifshifz, Course of Theoretical Physics, vol. 6. Nauka, simplest scheme provides a frequency inst ability r.m.s. of at most Moscow, 1986 (in Russian). Fluid Mechanics, pp. 2SS-239.

of 10-13 kHz, which corresponds to the relative frequency ■10 j Takaho Tanaka, J. Phys. C 7 (1974) L177-L180.

instabi!ity of 3.6 x 10 ^β -4.6 x 10 ^"" " at the bandwidth of the [11 ] ILL. osarev. Ph.D. Thesis, Insntute of Physical Problems. Moscow. 1971 (m

Russian).

frequency pulling of 0. 3--0.S5 MHz and at the initial power in [1 ] V.N. Zavorotilo. O S. Mhovanov. Accelerators, in: Collected Articles No. 16, the reflected wave of ¾ 30 kW. Performed simulation using 2-D 1977, Atomizda .. Moscow, pp. 34-37 (in Russian)

tracking in the microtron and the abridged equations for a [ 1 i] CM. azakevitch, Y.C jeong, v'.fvi, Pavlov, B.C. Lee. Nucl. insfi'. and fviefh. A

528 (2004) 115-1 19.

transient process in the magnetron-accelerating cavity coupled [ 14] E.L. Kosarev. High power electronics, in: P.L. Kapitza. L.A. Vainstein (Eds.). system well describes stabilization of the magnetron in the Collected Articles. Nauka, Moscow, 1965, pp. 2S3-305 (in Russian).

PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 12, 040701 (2009)

Magnetron-driven microtron injector of a terahertz free electron laser

Grigory M. Kazakevich* and Viatcheslav M. Pavlov

B dker Institute of Nuclear Physics RAS, Academician Lavr ntycv II, Novosibirsk, 630090, Russia

Young Uk Jeong and Byung Cheol Lee

Korea Atomic Energy Research Institute, P.O. Box 105, Yusong. Taejon. 305-600, South Korea

(Received 29 November 2008; published 15 April 2009)

A magnetron-driven microtron injector has been developed for a terahertz free electron laser (FEL). An internal injection system was chosen for the microtron to achieve a compact and inexpensive design. The system provides acceleration of electrons with low emittance and energy spread that is highly important for the FEL. However, the intrapuise instabilities of the accelerated current and the bunch repetition rate inherent to the injection system make problems for the FEL operation. Simulations of the beam dynamics and the transient process allow one to compute the load characteristic of the accelerating cavity and the time- dependent accelerated current. The simulation techniques also allow one to calculate time- dependent deviations of the magnetron frequency in the coupled system of the accelerating and magnetron cavities, as well as deviations in the bunch repetition rate. The computations validate proposed concepts for increasing the intrapuise current stability with appropriate time-dependent variation of the magnetron power and decreasing the bunch repetition rate instability through a simple microwave scheme utilizing the microtron accelerating cavity concurrently as an external stabilizing resonator for the magnetron. The realized concepts and optimization of the microtron regimes using the simulated phase motion of the accelerated bunch provide stable operation of the terahertz FEL, tunable in the range of 1-3 THz with extracted macropulse power up to 50 Watts at the raacropulse energy of 0.2 mj.

DOI: 10.1103 PhysRevSTAB. ί 2.040701 PACS numbers: 41.60.Cr, 07.57.Hm

I. INTRODUCTION Based on 2D beam tracking in the microtron median plane, we studied this phenomenon using a numerical

A compact driven by MI-456A magnetron high-current

simulation of the transient state of the accelerating cavity microtron injector [ I] has been developed for a laboratory- loaded by the electron beam [5], The simulation shows a size terahertz free electron laser (FEL), tunable in the range

significant drop in the accelerated current during the macof 1-3 THz [2]. The 12-orbit microtron employing the I- ropulse for measured increments of the emission current. type internal injection [3] provides stable operation of the

To keep the accelerated current constant during the macroFEL. Parameters of the magnetron and parameters of the

pulse, we tuned the modulator charging line to provide microtron optimal for the FEL operation are shown in

linear enhancement of the magnetron current, in this case, Tables ί and II, respectively.

as follows from simulation and measurements, the accel¬

Precise motion of the accelerating cavity inside the

microtron magnet allows one to extract the accelerated erated current has a fiat top providing intrapuise stability of electrons from various orbits; this varies kinetic energy the beam current suitable for FEL operation. However, the of the beam approximately from 4.4 to 6.5 MeV and incremental magnetron current deteriorates the intrapuise provides generation of the terahertz FEL in wide range. frequency stability of the magnetron autogenerator be¬

The regime of the microtron requires the macropulse cause of the frequency pushing. Correspondingly the emission current of ~1 A. Such a value of the emission bunch repetition rate stability becomes worse, leading to current causes noticeable pulsed overheating of the catha drop of the lasing energy. Note that at lower energy the ode surface because of the back- sire anting electrons. The microtron at optimal regime accelerates higher current; phenomenon in the microtron with internal injection

causes increments of the emission current during the macTABLE I. The magnetron main parameters.

ropulse and, as a result, incremental beam loading in the

accelerating cavity [4], This causes a drop of the accelerMagnetron operating frequency, MHz 2800 ± 5

Magnetron cavity coupling coefficient » i0 ating field resulting in a decrease of the accelerated current

Magnetron cavity wail Q-factor —1500 at a constant power feeding the accelerating cavity.

External waveguide conductance, Ohm ^{" 1} 2.363 X 10 ^" '

Magnetron pulse power 2.5 MW

* Current address: Fermi National Accelerator Laboratory, P.O. Magnetron macropulse current width 7.3 / Box 500, Batavia, IL 60510, USA. Magnetron duty factor ≤ 0.002 gkazakevitc h (?) yahoo. com

1098-4402/09/12(4)/040701(10) 040701 -1 2009 The American Physical Society KAZAKH VICH, PAVLOV, JEONG, AND LEE Ph s. Rev. ST Accel. Beams 12, 040701 (2009)

TABLE II. Main parameters of the microtron. tion in the median plane x°k and using the Lorentz force equation:

Microtron cavity eigenfrequency, MHz 2800

Microtron cavity coupling coefficient 5.4

Microtron cavity wall Q-factor 9800 e ^■ {E( r, t) + [v X B]}. 0 )

External waveguide conductance, Ohm ^{- 1}

1 X 1(Γ ⁵

Shunt impedance 1 .08 MOhm

Here E( r, t) is the electric field acting on the electron at the

Electron beam energy increment per turn 0.544 MeV

Microtron permanent magnetic field 0.1065 T point with coordinate r arid the time t, i> is the velocity of

12th orbit accelerated macropuise current 45-50 mA the electron at this point at time /, and B is the magnetic

Accelerated macropuise current width 6 _j tis

field acting on the electron (B includes the rf component in the accelerating cavity and the permanent microtron field).

Unlike the ordinary tracking simulations described in a e.g., the 8th orbit accelerated macropuise current is ~ number of articles [6,7], we compute concurrently the load 70 mA. characteristic of the accelerating cavity, J _c (Vc), where I _c

A simple microwave scheme based on the frequency is the cavity loading current. This allows one to compute pulling in the magnetron and utilizing the reflected wave the accelerated current in the time domain considering the from the accelerating cavity was developed to stabilize the loading current effect. Moreover, this allows one to commagnetron frequency and the bunch repetition rate. The pute frequency and phase deviation of the accelerated scheme was numerically simulated using the transient state bunches that are important for the FEL injector.

of the system including the magnetron resonance system Thus simulating the tracking, we determine the current and the accelerating cavity coupled through a ferrite insudensity of the nth particle at time t at the point (x, y, z) lator. The simulation and the measurements are in good which is equal to

agreement and showed that the developed microwave

scheme effectively decreases the frequency instability of j _n (x, y, z. t) = q · v„(t _0n , t) ^■ S(y)S[x - x„(t _0n , f)] the magnetron autogenerator. This reduces the bunch repetition rate instability during the macropuise to a level that is

acceptable for terahertz FEL operation. Simulation of the Here t _0n — n · ^ , n— 0, 1 , . . , N 1 , N is number of the beam dynamics and consideration of the transient state in particles, T is period of oscillations in the cavity, and the accelerating cavity demonstrates the equilibrium phase

variation during the transient process that deteriorates FEL for existent particles, operation. The performed calculation shows how to opti for nonexistent particles, mize the microtron regimes minimizing the variation. A

FEL macropuise energy ~ 0.2 mJ was obtained employwhere I _o is the maximum of the cathode emission current. ing the optimization. The current density j _n is nonzero only inside the cavity.

The concepts of the intrapulse stabilizations realized in The first harmonic of the current density is equal to the magnetron-based microtron driving the terahertz FEL N-l

at optimized regimes, 2D tracking, simulation of the stabidt{e ^→ ° ^> ' - ]„(x, y. z, t _Gn . n} lizations, and measured results including data obtained at n=0

the FEL operation Eire presented and discussed in this (3) article,

Then the loading current I _c correspondingly to [8] is

II, SIMULATION OF THE PLANE TRACKING IN

THE M ICRO TRON WITH INTERNAL INJECTION ·'· , kit) / ¾ (r) * e(r)dV, (4)

Ad

Simulation of the tracking in the microtron was done for

where i _c (t) is the normalized dimensionless time- the TMoio mode of the accelerating field in a cylindrical

dependent slowly varying emission current, M is used for cavity having radius R and length L with I-type internal

normalization:

injection.

Considering the plane motion of the electrons, one L/2

M e ₇ \f _ = 0, z) · expf - Ίω ^■ _Q ^■ —)dz, assumes that the nth particle having a macroparticle charge

of q enters into the cavity at the time of /¾„. At the time of ?,

the particle is located at the point with coordinates of y _n — e ( r) is a distribution of normalized electric field in 0, XM _Q ,,, t), and ζ,, (%„. f) having velocity of £>„(¾„, t). the cavity, and v is the average velocity of the electron

The coordinates :Ϊ„(Ι¾„, t) and velocities v _zr \t( _jn , t) have Oo - c)- been calculated for a given amplitude of the cavity comFor the TM _{0) 0} -mode in a cylindrical cavity, the distriplex voltage V _c — \ V _C \, in 2D code considering the mobution of the normalized electric field is expressed as

040701 -2 MAGNETRON-DRIVEN MICROTRON INJECTOR OF A , Phys. Rev. ST Accel. Beams 12, 040701 (2009)

[mm]

FIG. 1. 2D tracking in median plane of the microtron. In the c left corner is shown the tracking of the first orbit and the layout of the accelerating cavity having narrow radiai slits for passage arctan- of the electrons.

The following dimensionless variables have been used for

τ η " Numerical simulation of the tracking in the median plane and disposition of the accelerating cavity relative to the axes (z, x) are shown in Fig. i.

In terms of these variables, the motion of the nth elecNote that the described method allows one to consider tron and the current terms w _n and w _S!: are described by the all accelerated particles, synchronous and nonsynehronous following equation set (6) with the initial conditions for the as well, in the loading current.

nth particle (7). Equations (5) and (6) in (6) for the current Computed ampl itudes of the loading current, / _c , and the terms w _Cn and w _Sn are integrated inside the cavity only for accelerated current extracted from the 12th orbit, I _I2 (the 0 < Ζ„(φ„) < L ₀ . microtron output current) as functions of the amplitude of

The equations were integrated up to the last (12th) orbit the accelerating voltage, V _C , are plotted in Fig, 2.

for several cavity voltages V and for optimum value of the Figure 3 shows computed phases of the loading current, microtron magnetic field B = 0.1065 T. The field corre<Pi _r , and of the extracted current from the 12th orbit, φ^ , sponds to the eiectrosi beam energy increment per turn at as functions of the accelerating cavity voltage. In the inset, the magnetron frequency of 2.8 GHz. The electrons hitting (2), are shown detailed plots of the loading current and the cavity wails (inside or outside of the cavity) were extracted current phases, φ _{ and φ _{ respectively, in the omitted in the tracking. neighborhood of the microtron operating conditions.

040701 -3 KAZAKH VICH, PAVLOV, JEONG, AND LEE Ph s. Rev. ST Accel. Beams 12, 040701 (2009) affecting, as it will be shown below, the FEL operation in the beginning of the macropulse.

111. TRANSIENT STATE OF THE MICROTRON CAVITY AND INTRAPULSE STABILIZATION OF THE ACCELERATED CURRENT

A transient state of the microtron cavity has been computed based on the slowly varying envelope approximation (S VEA) [S] considering loading of the cavity caused by the electron beam under acceleration. The effect of the incremental emission current caused by pulsed overheating of the emitting surface by back-streaming nonsynchronous electrons [4] was included in this consideration.

V.. Γ /1 For the microtron cavity, the abridged equation for the transient state is [8]

FIG. 2. (Color) Normalized amplitudes of the loading current,

i _c , and the accelerated current extracted from 12th orbit, J _n ,

versus the accelerating voltage. In the inset, (2), the curves I _c ^■J oc and J i2 are plotted in detail its the neighborhood of the microtron 2QEC ^■ Ά oc operating parameters. I _c ^■ exp(i · <pc). (8)

The plots in Fig. 3, inset 2, show feat the dependence of Here Q _EC = (J, _:( / β and Q _LC - Q _oc /(i + β ) are the the phase of the loading current on V _c in the neighborhood external and loaded cavity quality factors, respectively, of the microtron operating conditions is quite weak beQoc— 9800 (measured value) is the cavity wall quality cause it is a result of contributions of all bunches on all factor, <!>oc is the circular eigenfrequency of the cavity, orbits and therefore it is a resulting phase averaged over all βς— 5.4 (measured value) is the cavity coupling coeffi orbits; in fact this is a collective effect. cient, s _c =—20 _{[ :} (ω— &> _oc )/&i _oc is the detuning pa¬

Unlike the weak dependence of the loading current rameter of the accelerating cavity, operating at the phase, φ. on V , the dependence of the phase of the frequency of ω, V are complex amplitudes of the oscilextracted current, φ _; , on V _c as shown in the inset is lation in the forward wave, <p _c is the phase of the complex much stronger. time-dependent amplitude V (t), R _sh = 1.08 MOhrn is the

This phenomenon is caused by a transient process in the effective shunt impedance of the accelerating cavity, and equilibrium phase establishment; it results in an additional Foe = 2fi _c /R _A = 1.0 X 10 ^~5 [1/Ohm] is ^' the external phase instability of the extracted bunches. This causes an waveguide conductance of the cavity. I _c is a complex additional intrapulse detuning of the FEL optical resonator function of V _c (r). It was calculated using the dependence

/ _C (V _C ) plotted in Figs. 2 and 3 and Eq. (5). The time- dependent normalized emission current, i ^' _c ( }, and I _i)C were obtained from measurements.

The time-domain computation of the accelerated macro- pulse current on the 12th orbit was based on simulation of the tracking; the data were used in the equation (8) for constant magnetron power and measured incremental emission current. The result is plotted in Fig. 4, curve 1.

Curve 1 shows that the amplitude of the accelerated current is reduced almost by half at the end of the macro- pulse because of an increase of the emission current, that causes the incremental beam loading in the accelerating cavity.

Compensation of the drop of the accelerated current was done by increasing the magnetron power during the macro-

V, fMVl pulse by tuning the modulator charging line to provide linear increments of the magnetron current by ~ 10%.

FIG. 3. (Color) Phases of the loading current, <x _/ „, and the Figure 5 shows the calculated shape of the accelerated extracted current, φ _ι , as functions of the accelerating cavity current, curve 2, for the measured incremental magnetron voltage, V _c . current, curve 1. The accelerated current, curve 3, mea-

040701 -4 MAGNETRON-DRIVEN MICROTRON INJECTOR OF A , Phys. Rev. ST Accel. Beams 12, 040701 (2009)

FIG. 4. Calculated shape of the accelerated current, curve I, in the forward wave, respectively, Y — 2.363 X

FIG. 5. (Color) Calculated, curve-: 2, relative units, and meaHere (i) i _A (t) is the normalized dimensionless time sured, curve 3, right scale, acceierated current at she 12th orbit

dent magnetr on anode current.

vs tire incremental magnetron current, curve 1, left scale. sured with an internal removable target shows satisfactory and (ii) y _M is the relative electron conductance.

agreement between the calculations and the measurements. The relative electron conductance y _M depends on the anode voltage U _A and the modulus of the magnetron cavity

IV. TRANSIENT STATE OF THE MAGNETRON- voltage V,v? as

MICROTRON CAVITY SYSTEM AND I RAPULSE STABILIZATION OF THE 'M - f(U _A ) ^■ g _M {V _M ) + i ^■ {ϋ _Α ) ^■ b _M (V _M ).

MAGNETRON FREQUENCY

The ano is equal to

Simulation of the intrapulse instability of the magnetron

frequency caused by variation of the magnetron current, for U _A (t)

and properties of the stabilizing microwave scheme emfor U _A {t)

ploying frequency pulling in the magnetron, was done

using the SVEA method for the system including coupled Here U = 0.8 · U _An is the threshold of the anode magnetron and microtron cavities. voltage.

The abridged equation for the transient state in the The typical values of and i- iV _/ the conducmagnetron cavity differs from Eq. (8) with the noise term tance and the susceptance of the magnetron cavity, respeconly | ]: tively, were taken in accordance with [9J. Figure 6 shows

040701 -5 KAZAKH VICH, PAVLOV, JEONG, AND LEE Phys. Rev. ST Accel. Beams 12, 040701 (2009)

time interval [10]. One can see that the magnetron fredependences of these values on the relative magnetron

quency deviations i fact follow deviations in the magnecavity voltage V _M /V _M .

The output power of the magnetron is equal to tron current because of the frequency pushing in the magnetron.

P = p - ^Y ° ^M . \ v i ² The simulation based on the measured time-dependent t M _a <ji — ¹ RM ^" . ^" ! ^V RM' · values of the magnetron pulse current and the pulse voltage shows agreemeni with the measured frequency deviations

The voltage of the reflected wave in the waveguide is

of the magnetron. The deviations at the incremental mag¬

^ RM " V _M — VpM- netron current are in the range of -« 0.8 MHz during the macropulse in operation with a passive load.

The expression for V _RM can be presented as The developed microtron-driven terahertz PEL utilizes an optical resonator with the length determined from the V RM - VRM ^* exp(i · <p _m ).

expression L — 52 - f- ~ 52 · , where A _b ~ c/f _b is the

The time-dependent deviations of the magnetron frequency wavelength of the accelerating voltage, and f _b is the bunch can be calculated from repetition rate of the accelerated current. For f _h ~

2.801 GHz, AL/Af _h « 26{ _b /f _b ) « 0.99 mm/MHz,

P 1 d ⁽ p _RM

r RM — ~ - i.e., the bunch repetition rate deviations in the range of

0.8 MHz are equivalent to the FEL optical resonator detun¬

In Fig. 7 are shown the calculated and the measured ing by ~ 0.8 mm during the macropulse. This value is intrapuise inagnetron frequency deviations for the magneinadmissibly large for the terahertz FEL operating in the tron loaded by a passive load ( V _FM — 0, so V _{R M} — V _M ). wavelength range of 0.1-0.35 mm.

Measured shapes of the pulse tops of the magnetron To provide intrapuise stability of the bunch repetition anode current and the magnetron anode voltage are plotted rate acceptable for lasing in the terahertz range, we develin curves (3) and (4), respectively. oped a simplified microwave scheme to stabilize the mag¬

The magnetron intrapuise frequency deviations were netron frequency. The scheme is based on the frequency measured using a heterodyne method. The magnetron pulling in the magnetron through the wave reflected from was loaded by the passive matched waveguide load. A the accelerating cavity; in other words, the accelerating directional coupler with directionality of ~ 20 ciB was cavity serves concurrently as an external stabilizing resoused to measure the deviation of the magnetron frequency nator for the inagnetron. The reflected wave passes through in the forward wave. The attenuated wave from the maga ferrite insulator, having limited inverse loss of ~ 18 dB netron was mixed with the 2.793 GHz signal of a syntheat the magnetron pulse power of 1,7-2 MW. Such loss sizer and periods of the difference frequency were provides an acceptable level of the passing wave for the measured during the macropulse with a 2 Gs/s digital frequency pulling in the magnetron. At that the microwave oscilloscope. The measured results were averaged over microtron system was optimized in length. A layout of the i 0 macropolses. The accuracy of the measured frequency microtron and the microwave system based on the MI- deviations with this method is ~ 3-5 kHz for the 100 ns 456A magnetron is shown in Fig. 8.

040701 -6 MAGNETRON-DRIVEN MICROTRON INJECTOR OF A , Phys. Rev. ST Accel. Beams 12, 040701 (2009)

FIG. 9. (Color) Calculated (solid lines) and measured (bold solid

To calculate the frequency in the coupled system of lines with error bars) deviations of the magnetron frequency in magnetron and accelerating cavities, we used additional the magnetroti-acceleratiag cavity system, left scale, at various equations that considered the power rel tionships between values of the magnetron-accelerating cavity detuning parameter, the magnetron and the microtron cavities through the e. I— e = 0.47, 2—e - 0.74, 3— ε - 0.93, and —p!ot of the voltages in the reflected and forward waves in the wavemeasured incremental magnetron current, right scale.

guide:

The calculated time -dependent deviations in the magne¬

V Vr - V f ^' C> V (13 ) tron frequency are shown in Fig. 9 by solid lines. The solid lines with error bars are the measured magnetron frequency

The voltages in the forward waves for the magnetron and deviations in the coupled system. Curve 4 is the measured the microtron cavities are expressed as incremental magnetron current.

For the measurements, the magnetron was loaded by the accelerating cavity through the ferrite insulator. The frequency deviations were measured in the forward wave with the directional coupler. The measurements were done using the heterodyne method as described above at an accel on 12th

Π ¼) The calculated and measured frequency oscillations in the magnetron-accelerating cavity system, having a period of ~ 0.6-0.7 μα and a relative amplitude of ~ 10 ^-3 , are in-phase with the ripple in the magnetron current, Fig. 9,

(15b) curve 4, and are caused by deviations of the magnetron current during the macropulse with relative amplitudes of - 1.5% (corresponding to <0.2% in the modulator pulse

Calculation of the frequency deviations in the coupled voltage).

system of the magnetron and the microtron cavities was Comparison of the measured drift of the magnetron done using Eqs, (S), (9), (15a), and (15b) for various frequency during the macropulse with the computed fredetuning parameters of the microtron cavity. Note that quency drift of the accelerating voltage shows that the the equations include the frequency drift in the stabilizing stabilizing scheme in fact suppressed the magnetron fre(accelerating) cavity caused by variation of the beam quency drift up to the value of the frequency drift of the loading. accelerating voltage. This drift, is caused by the back-

040701 -7 KAZAKH VICH, PAVLOV, JEONG, AND LEE Phys. Rev. ST Accel. Beams 12, 040701 (2009) streaming electrons overheating the cathode surface resulting in incremental beam loading in the accelerating cavity

[4], Thus it becomes necessary to minimize the emission

current increment for the micro tron employing internal

injection and intended to drive a terahertz FEL.

V, VARIATION OF THE EQUILIBRIUM PHASE

UNDER TRANSIENT PROCESS IN THE MICROTRON CAVITY

The amplitude and the phase of the extracted current,

computed as functions of the amplitude of the accelerating

voltage, allow one to compute in the time domain the

deviation of the phase of the extracted current caused by

variation of the equilibrium phase during the transient

process.

The cavity voltage can be written in following form: FIG. 10. (Color) B— deviations of the frequency in the micro¬

V _c (t) = V _c (t) ^■ expj · ip _c (f)]. (16) tron accelerating cavity. C— bunch repetition rate deviations of the extracted current.

Here Vci ) is the time-dependent modulus of the cavity

voltage and <p _c {t) is the time-dependent phase of the cavity

of ~ 30 kHz, that is ~ 10 ^" ° of the magnetron frequency, voltage. The extracted current is proportional to the time- are caused by ripples of the magnetron current because of dependent emission current, the dimensionless amplitude

the frequency pushing in the magnetron during the macro- of the accelerated current from the 12th orbit, depending

pulse as was noted above. Oscillations in the bunch repeon V _c (f), and depends on the phase, ψα(ή- The phase of the

tition rate, curve C, in the beginning of the macropulse are bunch at the entrance of the extracting channel depends on

caused by variation of the equilibrium phase during the time as

transient process. The effect results in an additional modu¬

C17 ^' ) lation of the repetition rate of the bunches extracted from the microtron and transported into the FEL undulator.

Deviations of the frequency in the microtron acceleratThe establishment of the equilibrium phase is continued ing cavity during the tnacropulse are computed using the during the increase of the V _c amplitude from a minimum following expression: value, acceptable for acceleration of the electrons over all orbits in the microtron and corresponding to 0.556 MV,

AF _c (t) (18) to the optimum operating value, corresponding to ≤ 0.572 MV, as is shown in Fig. 3, inset 2.

it is obvious that the input microtron cavity voltage and the

magnetron frequency have the same deviations.

VL OPTIMIZATION OF THE MAGNETRON-

Deviations of the bunch repetition rate caused by the

DRIVEN MICROTRON INJECTOR OF THE

phase motion of the extracted bunches are computed as

TERAHERTZ FEL

(19) Regimes of the magnetron-driven microtron injector

2TT dt employing intrapulse stabilization of the accelerated cur¬

The time-dependent deviations of the repetition rate of rent and the magnetron frequency have been optimized for the extracted bunches computed for the accelerating cavity maximum macropulse lasing energy to user applications. detuning parameter, ε— 0.74, are shown in Fig. 10 as The optimization at a given accelerated current included curve C. For comparison in Fig. 10, curve B shows deviaminimization of the microtron cathode current to decrease tions of the accelerating frequency caused by phase deviathe magnetron frequency deviation. The minimization protions of the current loading the accelerating cavity during longs the cathode life time that is also important for users. the maeropu!se. In particular, these deviations determine Consideration of the beam dynamics shows that the the stability of the frequency of the accelerating voltage in range of variation of the equilibrium phase has a strong the microtron-FEL injector. dependence on the detuning parameter when the accelerat¬

Analysis of these plots shows that the average increment ing cavity is well matched with the loading beam. An in both curves is approximately the same and caused by increase of the detuning parameter increases the amplitude incremental loading of the accelerating cavity because of a of the equilibrium phase deviation that increases the amback bombardment of the cathode surface by nonsynchro- plitude of the frequency modulation of the extracted nous electrons. The oscillations in curve B with amplitude bunches. The effect has been studied by measuring the

040701 -8 MAGNETRON-DRIVEN MICROTRON INJECTOR OF A , Phys. Rev. ST Accel. Beams 12, 040701 (2009) intrapulse bunch repetition rate deviations at various values optical resonator. The phenomenon was studied in operaof the detuning parameter. tion of the terahertz FEL [ 1 1 ]. For that we have measured

To measure the intrapulse bunch repetition rate, the the terahertz FEL power signal varying the detuning electron beam extracted from the 12th orbit was transparameter.

ported through a low Q-factor measuring cavity integrated During the measurements the modulator charging voltinto a beam line [10]. The cavity signal containing inforage was kept constant. The accelerated current also was mation about the bunch repetition rate has been measured kept, constant with accuracy better than 3.5% to keep a using a heterodyne method in the manner described above. constant current at the entrance of the FEL undnlator. The The microtron parameters were optimized to provide a accelerated beam injected into the FEL undulator was macropulse current of 40-42 mA in the beam line at a extracted from the 12th orbit of the microtron and the minimized increment of the emission current and an a verFEL was tuned for lasing at A = 110 μτα. The microtron age emission current of ~ 1.1 A. The modulator charging operating parameters were optimized to get minimal incresystem provided constant charging voltage with accuracy ments of the emission current at the accelerated macrobetter than 0.1 %. pulse current of 42 mA. The lasing macropulse power was

Results of these measurements for various detuning measured by a wideband Schottky-barrier detector [12]. parameter values are shown in Fig. 11 by bold solid lines Figure ! 2Ca) shows the measured lasing pulse shapes for with error bars. The detuning parameter was varied by various values of the magnetron-accelerating cavity detunmechanical tuning of the magnetron. For comparison in ing parameter.

this figure, the measured intrapulse magnetron frequency Plot b in Fig. 12 shows the measured drop of the lasing deviations are plotted by dots with the same color. energy with an increase of the detuning parameter. The

The plotted curves show thai the measured deviations of drop is a result of the additional frequency modulation in the magnetron frequency, with a period of—0.6 μ$ and an the bunch repetition rate that is caused by variation of the amplitude of—30 kHz, are in fact similar in shape for ail equilibrium phase during the transient process.

considered values of the detuning parameter. However, the The plots in the inset (a) show a noticeable growth of the measured repetition rate of the extracted bunches in the buildup time with an increase of the detuning parameter. first half of the accelerated macropulse current demonSince the last one determines the value of the maximum strates an additional oscillation noticeably different from accelerated current, the microtron parameters have to be deviations of the magnetron frequency. The amplitude of optimized for minimum detuning in the system magnetron- the oscillation strongly depends on the detuning parameter, accelerating cavity at a given accelerated current injected as was noted above, in agreement with the beam dynamic into the FEL, In this case, one can provide maximum consideration. energy in lasing and maximum lasing macropulse duration.

The additional bunch repetition rate oscillation does not

affect the microtron operation in the considered range of

9

Time [us] FIG. 12. (Color) (a) Variation of the lasing macropulse shape vs the magnetron-accelerating cavity detuning (left scale). 1— e—

FIG. 11. (Color) Measured deviations in the bunch repetition 0.52; 2— ε - 0.69; 3— e - 0,74; 4— e - 0.88; 5— shape of the rate (bold solid lines with error bars) and in the magnetron beam line current, (b) Variation of the lasing macropulse energy frequency (dots) for various values of the detuning parameter, e. at wavelength of 1 10 μ.τιι vs the detuning parameter.

040701 -9 KAZAKH VICH, PAVLOV, JEONG, AND LEE Phys. Rev. ST Accel. Beams 12, 040701 (2009)

Optimizing the microtron parameters and minimizing institute and by Fermi Research Alliance, LLC under the detuning parameter, we provided operation of the Contract No. DE-AC02-07CH1 1 359 with the United microtrt -driveii terahertz FEL with a measured extracted States Department of Energy.

macropulse lasing energy of ~ 0.2 in J at a macropulse

power of 40-50 W in the range of 1.5- 3 THz. The measured mis deviation in the lasing macropulse energy was

less than 9% for long-time (few hours) measurements [4] , [1] G. M. Kazakevitch, S. O. Cho, Y. U. Jeong, B. C. Lee,

J. Lee, V. P. Belov, and N, G. Gavriiov, in Proceedings

ΥΪ1. SUMMARY of the Particle Accelerator Conference, Chicago, IL, 2001, edited by P. Lucas and S. Webber (IEEE, New York,

A compact and inexpensive high-current magnetron- 2001), pp. 2739-2741.

driven classical microtron has been developed as an injec[2] Y. Li. Jeong, G. M. Kazakevitch, B. C. Lee, S. O. Cho, tor of the widely tunable ierahertz FEL. Computations J. Yoo, N. G. Gavriiov, and V. V. Kubarev, Noel, lnstrum. based on 2D tracking and transient process simulation Methods Phys. Res., Sect. A 507, 125 (2003).

have been done to calculate in the time domain the micro[3] S. P. Kapitza and V. N. Meiekhin, in The Microtron, edited tron accelerated current, deviations of the frequency of the by E. M. Rowe (Har ood Academic Publishers, London, accelerating voltage, and deviations of the repetition rate of 1978), Vol. L p, 6-12.

the bunches feeding the FEL. The calculations validate [4] G. M. Kazakevich, V.M. Pavlov, G. I. Kuznetsov, Y. U.

Jeong, S. H. Park, and B. C. Lee, J. Appi. Phys. 102, simple in realization concepts and techniques for the intra-

034507 (2007).

pulse stabilization of the accelerated current and the bunch

[5] G. M. Kazakevitch, Y. U. Jeong, V. M. Pavlov, and B. C. repetition rate in the microtron-FEL injector. The realized Lee, Nucl. Instnrrn. Methods Phys. Res., Sect. A 528, 11.5 concepts allowed the development of the laboratory-sized, (2004).

inexpensive, and reliable terahertz FEL. The effect of the [6] L. B. Lugansky and V. N. Meiekhin, in High Power equilibrium phase variation during the transient process Electronics, edited by P. L. Kapitza and L. A. Vainstein has been studied through computations and experiments (Nauka, Moscow, 1965), Vol. V, pp. 238-256 (it) Russian). that allowed optimization of the microtron-FEL injector [7] A. Takafuji, K. Sugiyama, K. Kuroc'a, K. Koyanagi, and operation. Long-time operation of the facility demonM. Nishimura, IEEE Trans. Nucl. Sei. 44, 1677 (1997). strated that the microtron provides operation of the FEL [8] D. PL Whittum, Frontiers of Accelerator Technology, in the range of 1-3 THz with extracted lasing power of 30- U.S.-CERN-Japan International School, Japan, edited by

S. I. Kurokawa, M. Month, and S. Turner (World 50 W in the macropulse having durations of 2.5-4 /A S. The

Scientific, Singapore, London, 1996), pp. 1-135.

standard deviations of the lasing macropulse energy are

[9] V. N. Zavoiotilo and O. S. MUovanov, Accelerators less than 9% for long-term operation. The widely tunable (Atomizdat, Moscow, 1977), Vol. XVI, pp. 34-37 (in ieraliertz FEL based on the magnetron-driven classical Russian).

microtron injector has demonstrated stable and reliable [10] G. M. Kazakevitch. Y U. Jeong. B. C. Lee. and J. Lee, operation for users for more than 5 years. Nucl. lnstrum. Methods Phys. Res., Sect. A 483, 331

(2002) .

ACKNOWLEDGMENTS [11] G. M. Kazakevitch, Y. U. Jeong, B. C. Lee, N. G. Gavriiov, and M. N. Kondaurov, Nucl. lnstrum. Methods Phys. Res.,

We are very thankful to Dr. R. Thurman-Keup for fruitSect. A 507, 146 (2003).

ful discussions. This work was supported in frames of [12] V. V. Kubarev, G. M. Kazakevitch, Y. U. Jeong, and B. C. scientific collaboration between Budker institute of Lee, Nud. lnstrum. Methods Phys. Res., Sect. A 507, 523 Nuclear Physics and Korea Atomic Energy Research (2003) .

Available online at www.sciencedirect.c

NUCLEAR INSTRUMENTS

& METHODS IN PHYSICS

RESEARCH

ELSEVIER Nuclear Instruments and Methods in Physics Research A 528 (2004) 115-119 ^Sec " ^{on A}

www.elsevier.com/locate/nima

Stabilization of the microtron-injector for a wide-band

compact FIR FEL

Grigori M. Kazakevitch ^a '*, Young Uk Jeong ^a , Viatcheslav M. Pavlov ^b ,

Byung Cheol Lee ^a

a Laboratory for Quantum Optics, Korea Atomic Energy Research Institute, P. O. Box 105, Yusong, Taejon 305-600, South Korea b Budker Institute of Nuclear Physics RAS, Academician Lavrentyev 11, Novosibirsk 630090, Russia

Abstract

To provide parameters of a simple and inexpensive magnetron-driven microtron-injector acceptable for a wide-band FIR FEL, the microtron has been improved through stabilization of the beam current and the magnetron frequency. The beam current was stabilized during the macro-pulse by increasing the magnetron anode current. The pulse stabilization of the emission current makes possible the microtron operation with the maximal accelerated current, without risk of break-downs in the cavity and keeps the instability of the accelerated current at approximately 1 % during long-time experiments. The magnetron frequency was stabilized using the microtron accelerating cavity as a stabilizing external resonator in a simple scheme that involved the cavity loading of the magnetron through a ferrite insulator. The scheme provides stabilization of the magnetron frequency with a coefficient of 3.5. The stabilization of current and the frequency at the microtron FIR FEL-injector provides satisfactory intrapulse stability of the extracted lasing power of 40-50 W in the FIR macro-pulse having duration of 3-4 μβ and a long-time pulse-to-pulse instability of the FIR pulse energy in the range of < 10%. Results of simulations of the stabilization based on the microtron operating parameters and measured results are presented and discussed.

© 2004 Elsevier B.V. All rights reserved.

PACS: 41.60.Cr; 07.57Hm; 29.20. -c

Keywords: Microtron; Magnetron; Stabilization; Frequency pulling; Free electron laser; Deviations

1. Introduction internal cathode provides good bunching properties for the electron beam, and this makes it

An inexpensive, simple, reliable magnetron- acceptable as an injector for a FIR FEL [1]. The driven, 12-turn classical microtron having an microtron has been upgraded to increase the accelerated current up to 50-70 mA in the macro- pulse having duration of 6 for a wide-band FIR

^■ "Corresponding author. Tel.: + 82-42-868-8253; fax:

42-861-8292. FEL. By such parameters of the accelerated

E-mail address: gkazakevitch@yahoo.com beam the emission current of the microtron has (G.M. Kazakevitch). an increase of 25-30% during the macro-pulse

0168-9002/$ - see front matter © 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.nima.2004.04.030 116 G.M. Kazakevitch et al. I Nuclear Instruments and Methods in Physics Research A 528 (2004) 115-119 because of the back-streaming electrons overamplitude of the first-time harmonic of the loading heating the cathode. This phenomenon causes an current, and q> _c is the phase of the complex abatement of the accelerated current. We stabilize amplitude of Vc(t). By simulation of the transient the current by increasing the magnetron power, state of the microtron cavity, the cardinal problem increasing the magnetron current during the macro- is the calculation of the loading current J [3]: pulse [2]. Respective deviations of the magnetron

1

frequency are stabilized with a simplified scheme Jc = J\ (t, r) e(r)d V (2) using a frequency pulling in the magnetron through

the wave reflected from the accelerating cavity. An where e(r) is he normalized cavity electric field additional stabilization of the pulse emission distribution, J\ (t, r) is the first-time harmonic of current in the microtron provides a pulse-to-pulse the current density, which depends on the emission instability of the lasing energy in the range of current ¾( ^an <3 coordinates and velocities of the ≤ 10% during a long-time operation. electrons passing through the cavity, w* =

Ideas, methods and measured results permitting / ₂ e _z (r ± = 0, z) _e - ^imo(z M dz. Here L is the cavity us to develop the inexpensive, stable, wide-band length, and vo is the average velocity of the tunable FEL, having tens of Watts in the extracted electron.

FIR macro-pulse power, based on the cheap, Note that the loading current J expressed by simple and reliable microtron-injector are preEq. (2) was calculated as a sum of the currents for sented and discussed. all of the electrons simultaneously passing through the cavity from all of the orbits. The current on each of the orbits was calculated using 2-D

2. Intrapulse stabilization of the accelerated current tracking simulating the motion of the electrons.

The Lorentz-force equation in the dimensionless

The effect of the incremental emission current variables [4] was used for the tracking. This on the shape of the accelerated current was method allows us to take into account the loading investigated using a numerical simulation of the current of all the accelerated electrons, synchrocoupled magnetron-microtron cavity system connous and non-synchronous as well.

sidering the motion of the electrons in the median The result of the calculation of the accelerated plane. current for the 12th orbit is shown in Fig. 1 , curve

As a first step of the simulation we calculated 2. As follows from the curve, the accelerated the shape of the accelerated current for the current has a decrease of up to half during the measured time-dependent emission current by w

Here, τ = t/ co, fco is the fill -time of the cavity,

Time, p,s

<2o is the wall quality factor, coo is the circular

eigen frequency of the cavity, i _c is the cavity Fig. 1. 1— Measured macro-pulse emission current, vert, scale coupling coefficient, VQ and pc are complex is 250mA/div., 2— calculated shape of the accelerated current by a constant magnetron current during the macro-pulse, 3— amplitudes of the oscillation in the cavity and in calculated shape of the accelerated current by the incremental the forward wave, respectively, ¾h is the shunt magnetron power, 4— measured accelerated current by the impedance of the cavity, J is the complex incremental magnetron power, vert, scale is lOmA/div. G.M. Kazakevitch et al. I Nuclear Instruments and Methods in Physics Research A 528 (2004) 115-119 117 macro-pulse versus an increase of the emission The result of the numerical simulation for the current, Fig. 1 , curve 1. The increase causes an measured increase of the magnetron anode current additional loading in the accelerating cavity and as is shown in Fig. 1, curve 3. The result has a a result, the abatement of the accelerating field satisfactory coincidence with the measured shape causing the abatement of the current. That makes of the accelerated current, Fig. 1, curve 4. a serious problem with the FEL operation in the Increasing the magnetron anode current during full scale of the macro-pulse duration. To avoid the macro-pulse provides a full-scale FIR FEL that and to compensate for the effect of additional operation during the beam current.

loading in the cavity because of the increase of the

emission current, we stabilized the accelerated

current by increasing the magnetron power during 3. Stabilization of the magnetron frequency the macro-pulse. For that the modulator charging

line was tuned to provide linear enhancement of The stabilization was developed for lasing to the magnetron current for ¾ 10% during the provide acceptable stability of the bunch repetition macro-pulse [2]. rate during the macro-pulse with a simple, reliable

The shape of the accelerated current for and inexpensive magnetron generator, which feeds measured time-dependent magnetron and emission the microtron cavity. The electron frequency drift currents, was calculated using the equation system caused by the incremental anode current in the including the abridged equation for the acceleratmagnetron and deteriorating the bunch repetition ing cavity (1) and a similar one, which described rate stability was suppressed by means of a the transient state in the magnetron this equation simplified scheme. The scheme is based on the differs from Eq. (1) with the noise term [5]. The frequency pulling in the magnetron through the loading current for the microtron cavity was wave reflected from the accelerating cavity, which calculated by the tracking in the median plane up also serves as an external stabilizing resonator. to 12th orbit. The magnetron current was meaThe reflected wave passes through a ferrite sured using a calibrated wide-band current transinsulator, having inverse losses of ¾ 18 dB by the former. The measured shape of the top of the power of 1.7-2 MW, providing an acceptable level magnetron macro-pulse current is shown in of the passing wave for the frequency pulling. The Fig. 2(c). microtron-microwave system has been optimized in the length.

To determine the coefficient of the magnetron frequency stabilization, the simulations and the measurements have been conducted for both cases of the magnetron load: with the accelerating cavity loaded by the electron current and with a passive matched waveguide load. For the simulations we used the considered abridged equations system describing the transient state in the magnetron and in the microtron cavity and measured time- dependent magnetron and emission currents.

Results of the simulations for the magnetron- microtron cavity system and the magnetron

Time, μβ

feeding the passive matched load are plotted in

Fig. 2. Magnetron frequency deviations with (a) and without Fig. 2 by solid lines (a) and (b), respectively. (b) stabilization by the frequency pulling. Curves (a) are Measurements of the magnetron frequency respective to the accelerating cavity loading of the magnetron,

curves (b) are respective to the passive matched load. Curve (c) deviations during the macro-pulse in the coupled demonstrates the shape of the top of the magnetron pulse magnetron-microtron cavity system and the magcurrent (relative units). netron-passive load system were done using a 118 G.M. Kazakevitch et al. I Nuclear Instruments and Methods in Physics Research A 528 (2004) 115-119 temporal heterodyne method [6], providing the on a fast ADC measuring the emission pulse relative inaccuracy of ¾ 10 ^~6 in the time interval current. The system averages the data for a few of ¾ 100 ns. The deviations were measured in the pulses, analyzes the data and tunes the cathode forward wave using the 20-dB directional coupler. filament stabilizer. By the randomized stripping of The results are shown in Fig. 2 by dotted lines (a) acceleration, the stabilization system tunes the and (b), respectively. The shape of the top of the cathode filament stabilizer to prevent breakdowns. magnetron macro-pulse current is plotted in The system provides long-time pulse-to-pulse Fig. 2(c) in relative units. instability of the emission current ≤ 1 % . The

In both cases, the simulated and measured instability in the accelerated current is approxiresults have good coincidence and demonstrate mately the same. Measured pulse-to-pulse instabilcorrectness of the simulations and measurements. ity of the extracted current has a level of < 2.5% The value of the stabilization coefficient of « 3.5 by operation of the stabilization system.

was determined from the obtained results. As

shown in Fig. 2, the deviations of the magnetron

frequency retrace the curve of the shape of the 5. Effect of the microtron stabilization on a lasing magnetron current, but with the developed stabilization using the accelerating cavity as the The effect of stabilization on the FIR lasing has stabilizing resonator they are noticeably supbeen investigated with parameters of the micropressed. tron optimized for long-time operation of the

In Fig. 2 one can see that the "slow" oscillation wide-band FIR FEL. The initial magnetron- of the magnetron frequency, having the period of microtron cavity detuning was chosen to provide «Ο.ό μβ, takes place in both cases: in the minimal range of the bunch repetition rate magnetron-microtron cavity system, and by the deviations by the accelerated current at the 12th passive load of the magnetron. This phenomenon orbit of ¾ 45 mA in the macro-pulse. The range of is caused by the oscillation in the magnetron the bunch repetition rate deviations measured by current. The magnetron current oscillation has a the temporal heterodyne method with the monrelative value of s i % in the amplitude, that itoring cavity [6] had a relative value of≤8 x l0 ^~5 . corresponds to the oscillation in the magnetron The emission current was chosen to provide pulse voltage with the level of ≤0.2%, and causes operation in the neighborhood of the maximum the "slow" oscillation in the magnetron frequency of the microtron volt-ampere characteristic. This with the relative value of ¾ 10 ^~5 and «4 x 10 ^~5 by provides the value of the beam current in the operation with the stabilizing cavity and the beamline at the undulator entrance in the range of passive load, respectively. 40-42 m A by extraction of electrons from the 12th orbit and in the range of 44-46 mA by extraction from the 10th orbit. Measured pulse-to-pulse

4. Pulse stabilization of the emission current instability of the current had a value of ≤ 1 mA.

Note that the values of the macro-pulse current

To provide maximal accelerated current by the provide deep saturation of the FIR FEL generamaximal capture coefficient, we are forced to tion, small dependence of the FIR macro-pulse operate on the left slope of the microtron volt- energy on the current and, as result, stable enough ampere characteristic in a neighborhood of a main FIR power during the macro-pulse. Measured maximum. In this case, a small decrease of the dependence of the FIR macro-pulse energy on the emission current leads to a stripping of the beamline current and the FIR power shape by the acceleration, a leap of the cavity voltage and FIR radiation wavelength of ¾ 110 μιη are shown break-downs in the cavity. in Figs. 3(a) and (b), curve 2, respectively. The

To avoid this problem, we developed stabilizameasurements were done using the pyroelectric tion of the pulse emission current using a detector and the wide-band Schottky-barrier computer-controlled system. The system is based detector. G.M. Kazakevitch et al. I Nuclear Instruments and Methods in Physics Research A 528 (2004) 115-119 119

6. Summary

Simple, inexpensive and reliable classical magnetron-driven microtron has been upgraded to use as an injector of the compact wide-band FIR FEL. The developed stabilization of the microtron operation provides long-time stability in the lasing iZ

_4 6 8 with a radiated power of 40-50 W in the macro-

! ime, s

0.0 pulse having a duration of 3^1 in the wide-band

32 36 38 40 42 range of the wavelength.

Beamiine current, rnA

Fig. 3. (a) Dependence of the macro-pulse FIR energy on the

beam current at the undulator entrance, (b) 1— The macro- References

pulse shape of the beamline current, vert, scale is 20mA/div.;

2— the macro-pulse shape of the FIR power, vert, scale is in

[1] G.M. Kazakevitch, et al., Nucl. Instr. and Meth. A 475 arbitrary units.

(2001) 599.

[2] G.M. Kazakevitch, et al., Proceedings of the 2001 Particle Accelerator Conference, V4, 2001, pp. 2739-2741.

By the optimized parameters of the microtron, [3] Joint US-CERN-JAPAN International School on Fronthe pulse-to-pulse instability of the FIR energy tiers in Accelerator Technology, 9-18 September 1996, measured using the pyroelectric detector has a World Scientific, Singapore ISBN 981-02-3838-X.

range of ≤ 10% during long-time operation [4] L.B. Lugansky, V.N. Melekhin, High Power Electronics, and the FIR FEL provides a radiated power Nauka, Moscow, 1965, pp. 238-256 (in Russian).

[5] V.N. Zavorotilo, O.S. Milovanov, Accelerators, Vol. 16, of 40-50 W during the macro-pulse having a 1977, Moscow, Atomizdat., pp. 34-37 (in Russian). duration of 3-4 μβ in the wavelength range of [6] G.M. Kazakevitch, et al., Nucl. Instr. and Meth. A 483 100-200 μπι. (2002) 331.