BACKGROUND OF THE INVENTION

The inventor teaches in USSN 169,648 and in USSN 112,842 methods for forming a coherent beam and a coherent cluster beam of bosons having mass. In these applications which are incorporated herein by reference, it is disclosed that these beams may be charged by exposing them to charged particles and, as such, accelerated by an applied voltage. Cluster formation from gas, supersaturated gas and superfluid helium, coherency of helium (helium being comprised of bosons having mass) , and accelerating particles is well known in the art. The reader is referred to: U.S. Patent 4,755,344, Friedman, July 5, 1988, "Cluster-Impact Fusion" by P. M. Echenique, J.R. Mousin, R. H. Ritchie, Physical Review Letters, Vol. 64, No. 12, 19 March, 1990 pp 1413-1416; "Clouds of Trapped Cooled Ions Condense Into Crystals", Physics Today, Sept. 1988, pp. 17-20; "Cluster-Impact Fusion", R. J. Beuhler, J. Friedlander, and L. Friedman, Physical Review Letters. Vol. 63, No. 12, 18 September, 1989 pp. 1292-1295; "Phase-Diagram Considerations of Cluster Formation When Using Nozzle- Beam Sources", E. L. Knuth, W. Li, J. P. Toennies, copyright 1989, American Institute of Aeronautics and Astronauts, Inc. , International Symposium on Rarefied Gas Dynamics, p. 239, edited by M. Summerfield; "Cluster Ion Formation in Free Jet Expansion Processes at Low Temperatures", R. J. Beuhler and L. Friedman, copyright Verlog Che ie (mbH,D-6940 Weinheim, 1984) International

Symposium on Rarefied Gas Dynamics; "Influence of Surface Roughness on the Momentum Transfer by 350-KeV Hydrogen- Cluster Ions"; W. Keller, R. Klingelhofer, B. Krevet, H. O. Moser, and R. Ries, Rev. Sci. Instrum 55(4.. April 1984 pp.468-471; "New Type of Collective Accelerations," Charles W. Hartman, James H. Hammer, Physical Review Letters. Vol. 48, No. 14, 5 April, 1982 pp 929-932; "Experimental Demonstration of Acceleration and Focusing of Magnetically Confined Plasma Rings", J. H. Haniver, Charles W. Hartman, Jr. , L. Eddleman, Physical Review Letters, Vol. 61, No. 25, 19 December, 1988, pp. 2843- 2846, Japanese Patent 60-200448, Hitachi Seisakusho, K.K. , 10

- 3 -

September, 1985; Conference Paper on "Rarefied Gas Dynamics", H. Buchenau, R. Gotting, A. Scheidemann, J.P. Toennies (1986) 15th International Symposium on Rarefied Gas Dynamics, Vol. II, p. 197 (1986), edited by V. Boffi and L. Ceragnami; and "Dynamics of Atomic Collisions on Helium Clusters", Jurgen Gspann, R. Ries (28 October, 1986) Physics and Chemistry of Small Qusters edited by P. Jenna, B.K. Rao and S.N. Khanna, Nato ASI Series 158, 1986, p. 199.

In considering the introduction of charged particles into fluids, the principle of field emission is now considered.

The principle of field emission is that for a curved surface with radius "a" of curvature V at a potential V, the electric field E may be defined as V/r so that for a small enough radius, say r = lμm, and a potential of lkV, the electric field is IO ⁷ V/cm. With this large field outside an atom, an electron may readily tunnel through the potential barrier of the nucleus and become free. This technique has been used in transmission electron microscopes to generate an electron source of very high brightness. In these devices, the cathode is made of a tungsten wire with a 1/αn radius and then an extra f ne tip with a radius of lOOnm or less is electrolytically etched on the wire. For a brief description of this technology, see e.g. L. Reiner: Transmission Electron Microscope, 2nd Edition, Springer Valley (1989).

The characteristics of the electron source are

Until now, field emission techniques have been used to generate electrons. Now disclosed is the use of the field emission technique to charge liquids as well as gases, that is in fluids, to charge strongly coupled or coherent clusters, or alternatively a

Iiquid jet.

SUMMARY OF THE INVENTION

In accordance with the present invention there is provided a method of charging a beam comprising passing a fluid from an area of first pressure to an area of second pressure, the second pressure being lower than the first pressure, and charging said fluid so that particles of the fluid are accelerated in the area of second pressure so as to form a charged beam, wherein the charging imparts sufficient charge to the fluid so as to achieve a charge density greater than IO ¹⁶ charge per cm ³ within the fluid.

In another aspect, there is provided a method for forming charged liquid jet comprising: passing a liquid into a nozzle defining a nozzle mouth, said nozzle maintaining the liquid at a first pressure; introducing one of negatively or positively charged particles in the liquid by means of the respective one of field emission or field ionisation; directing the charged liquid out of said nozzle mouth into a second area of lesser pressure than the first area such that a charged liquid jet is created.

In another aspect, there is also provided a method for forming strongly coupled or coherent charged clusters comprising: passing a fluid comprised of liquid or gas, into a mozzle defining a nozzle mouth, said nozzle maintaining the liquid at a first pressure; introducing one of negatively or positively charged particles in the liquid by means of the respective one of field emission or ionisation; directing the charged liquid out of said nozzle mouth into a second area of lesser pressure than the first area such that of charged clusters is created.

Tie charged particles may be introduced by a process involving field emission

from a through a tip made from, for example, tungsten wire, a latham compound (LaB^, or other element with a low work function. Particularly of interest in this invention is the charging of a liquid as it is turned into clusters and doing so without destroying the strong coupling or coherency of that cluster.

It is preferable that these charges be introduced close to the nozzle mouth.

DESCRIPTION OF THE DRAWINGS

Figure 1 is a sectional view of a cryostat and nozzle for creating a charged beam.

Figure 2 is a diagrammatic depiction of the tungsten tip, nozzle mount, and skimmers of Figure 1.

Figures 3a through 3k are graphs of a computer simulation showing the field emission effects in a device such as shown in Figure 1.

Figure 4 is a diagrammatic view of a second embodiment of the nozzle portion of the invention, the tungsten wire being replaced by a photoelectric device.

Figure 5 is a diagrammatic view of a third embodiment of the nozzle portion of the invention, tungsten foil and an electron gun replacing the tungsten wire.

Figure 6 is a view similar to that of Figure 1, a tungsten wire being shown immersed in liquid.

Figure 7 is a diagrammatical view of apparatus for creating a neutral beam.

Figure 7a is a diagrammatical view of apparatus for creating a neutral beam.

Figures 8 through 8d are diagrammatical views of a nozzle for charging a liquid jet.

Figure 9 is a front view of a nozzle for charging a liquid jet.

DETAILED DESCRIPTION QF THE INVENTION

THEORETICAL BACKGROUND

To assist the reader in better understanding this invention, a theoretical description of the technology involved the production of cluster beams and liquid jet beams is first presented.

1. Beam of Strongly Coupled or Coherent qusters

There are two kinds of beams made up of coherent clusters which arc charged. For neutral coherent clusters, there does not exist any interaction between any two clusters. However, if the clusters are charged, then the clusteis interact via Coulomb forces. In such a beam, the coupling of the clusteis can be separated into weakly coupled clusteis and strongly coupled clusters by their coupling factor (T) defined as

(1)

The charged cluster beam then can behave as r « 1 gas-like T - 1 liquid-like r » 1 superfluid or solid (2)

In Table I, the coupling for clusters with some charges, Z, are listed

Table I The Coupling of Charged Cluster Beam

The average distance "a" between clusters is defined by

— 4 π_r 3 n=l .

3

From Table 1, it is seen that for singly charged clusters with Z = 1, at 0.4 degrees kelvin, density n - IO ⁶ to IO ⁹ , the coupling factor (T) ranges from 1 to 7 so that the charged cluster beam is liquid-like. To have a crystalline cluster beam, it is convenient to have multiple charged clusters, say with Z « 10 for each cluster.

There are three binding energies that are important in considering the stability of strongly coupled cluster beams:

(1) the binding energy of electrons or ions to the atom (or molecule),

(2) the binding energy of one atom (molecule) with another atom (molecule) in the cluster, and

(3) the potential energy among the charged clusteis.

If these three energies are stronger than the perturbing source, such as from the external accelerating electric potential, or from the Coulomb repulsion among charges inside the cluster beam, then the cluster beam will preserve its character. Otherwise, the cluster beam will imdergo some qualitative changes. Let us discuss these binding energies and Coulomb repulsion forces one at a time.

Although the above discussion is largely concerned with dusters, similar considerations apply conncerning charges in neutral liquid, and in particular the deformation of the above described is applicable in such case.

2. Binding Energies

(i) The binding energy (B) of electrons and ions with atoms (or molecules). TJic binding energy of electrons to H or H ₂ to form H ^" and H ₂ " is 0.75eV,

which is about 20 times smaller than the binding energy of electrons in a neutral hydrogen molecule.

_9, (# ^~ ) = 0.7542«K (3)

(ii) The binding energy of an atom (molecule) in a cluster. Here, the binding energy can be estimated from the heat of vaporisation. The heat of vaporisation for liquid oxygen is 6812.3 J/mole. By molecule, the binding energy (B) is

B = ^68I2 - ^3y . 0.07 V (4)

° ^> όxlO ²³

where O ₂ is oxygen and όxlO ²³ is Avogadro's number. This binding energy is ten times smaller than the binding energy of electrons to the hydrogen atom. For helium, the heat of vaporisation is about 14 to 22 cal/mole depending on pressure, and the binding energy of the helium atom in liquid is in the range of

B _Bt = (6.1 to 9.6)xlθ rF

The potential energy between two neighbouring charged clusters inside a cluster beam is

_e γ _e - z ² → (5) a

= lMxlO^eVfor Z-l, a~-lμm

where again V is the potential, Z is the cluster charge, and a is the average distance between clusteis. Hence the potential energy between two neighbouring charged clusteis is smaller than the binding energy of the cluster (except in the case of helium clusteis). We then have the following inequality.

*. > *o ₂ > V _c (6)

The condition for accelerating a crystalline solid strongly coupled cluster without destroying the crystalline structure is

-* < - -- (7)

I a

where eV _c = the potential difference between two electrodes / = distance between two electrodes eV < eV _c so for

« _c =1.46xl0 ^'3 volt, a~-lμm, /=lcιw, eV<U.6 volt for Z=l eV<1.46 for Z ^~ ~10

Ticre are two important features for accelerating a crystalline charged cluster beam that separate it from those of an ordinary ion beam.

(1) The total beam intensity is greatly enhanced. IThe size of a cluster in a cluster beam may range from A-100 to A=5,000 atoms or more in any single cluster. TJie charges in each cluster may vary from Z=l to Z=10 or more. If we select dusters with a fixed number of atoms, say 200 atoms, and fixed charge, say Z=l, we only have a very small portion of all dusters in a duster beam. However, if the clusters are not strongly coupled, we can only accelerate dusters with the same A and Z, with a given potential. Qusters with different A's and Z's will travel at different speeds. The resulting cluster beam from acceleration through an applied electric field is a very weak beam for a weakly coupled cluster beam.

(2) The energy spread AE of the accelerated crystalline cluster beam is very small. It is only equal to the temperature T of the duster.

__£ - T

Since T~10 ^"4 eV for a helium cluster which was cooled to this temperature during expansion, the energy spread as a percentage of the final energy E of the cluster beam is extraordinarily small,

___? = I = W for E=lkeV E E

A very high quality beam is produced. It is clear that production of a charged crystalline solid strongly coupled cluster is advantageous. The inventor's earlier noted applications, all incorporated herein by reference, disclose the means for forming coherent clusters. These are clusters that are coherent within themselves and amongst themselves. As discussed above, adding charge to these clusters is tremendously advantageous and now disclosed is the detailed method of accomplishing this task. This method does not destroy the coherency of the clusters nor does it unduly heat the fluid from which the clusters are made. This is not true when electric arcing, (such as in the above-noted Friedman patent), microwaves or heating gas is used.

3. Method of Generating Charged Particles to Produce Strongly Coupled Clusters

The inventor teaches in the above-noted patent applications, incorporated herein by reference, the method of making coherent clusteis. These are created by passing bosons with mass (such as helium) through a nozzle of a higher pressure to an area of lower pressure (such as a vacuum). In this method, it is advantageous to have a high density of bosons and to keep the temperatures at room temperature or below. The forming of coherent helium and helium clusters is well-known in the art. The method of producing clusters is modified in this invention by charging the bosons with mass just before they exit the nozzle mouth into the area of lower pressure. Presenting the charge at this point and presenting it in a slow, low energy manner, prevents the heating of the bosons with mass, thus, preventing the undue heating of the fluid. It also prevents or minimises the destruction of any strongly coupled or coherent particles or clusters. Also clearly taught herein is forming clusters from a liquid as well as a gas.

4. Liquid Jet Beam and Molecular Binding Forces within a T .iqnid

In a neutral jet of liquid there exist molecular binding forces between the molecules forming the liquid. These binding forces provide a cohesion throughout the liquid which provides the ensemble of molecules with liquid characteristics.

If the kinetic energy of the molecules is increased the binding forces will be overcome and the liquid will dissociate into individual gas particles. This can be seen generally from the coupling factor (T) as defined above

If the molecules or particles forming the liquid are charged and introduced into the liquid jet, Coulomb repulsion between these particles/molecules, together with the diameter of the jet become relevant factors in determining whether the molecular binding forces within the liquid jet will be overcome and the individual molecules of the liquid dissodate to form clusters or a gas phase.

If the charge density n_ is small, the beam diameter not big, the electric field will not be strong enough to overcome the molecular binding among the molecules in the liquid. The liquid jet will remain a liquid jet. If the charge density n_ increases the electric field from Coulomb repulsion among the negative charges in the beam will overcome the adhesive forces among the molecules. The liquid jet will break into charged dusters.

The electric field around a cylinder is given by

f j i _Er*"d ass = = Q yljεε,. Oa)

where r is the radius of cylinder and n_ is the charge density inside the cylinder.

The repulsive force F _r on a charge e by this electric field is

= ) (L) (3c)

^{?r =} [a ² ] 2R J

α =

4πε _Λ 137

where R is the ratio between neutral and charge density

ⁿ _,

R = - n_

and a is the radius of the volume occupied by one molecule

— 4π α ₃ = 1 , (4)

3

Ηiis repulsive force is being counter-balanced by the attractive force between molecules:

F -- ---- - --- (5) dr a

where ε _M = molecular binding energy = 58 meV for liquid nitrogen

For the liquid jet not to be broken up by Coulomb repulsion, we require

F _r ≤ , (6)

or

(a) 3 t _u where

α

-± - IO ^'2 for LN, (8) ε,_

- 14 -

The numerical factor (*τ_) is reduced to 1, if we are not considering a cylindrical liquid jet beam with beam radius r, but a spherical liquid drop with radius r. We tabulate the typical values for liquid nitrogen in the following table (1). The equation (7) is modified if we regard it as necessary to break all the molecular binding in the cross- section to become

where N _C ^M is the number of molecules of which the bonding must be broken.

Table 1

N _c = number of molecules in a spherical charged cluster Z _j . = number of negative charges in the cluster calculated from eq. (7) and not (9a).

5. Formation of a Liquid Jet

To form a liquid jet it is necessary to have a suitable nozzle or hole through which liquid must pass without forming spray or turbulence. Quantitatively the most important scale variable that determines the formation of a liquid jet is its Reynold number defined by

Ώ - ^{uD R} - —

where u is the velocity of the liquid jet, D the diameter of the nozzle, or hole, and v the kinetic viscosity of the liquid. The velocity is related to the pressure by

u =

P p ₀ = pressure of the liquid at the nozzle p = density of the liquid

If the Reynolds number is smaller than a minimum number, R ₀ <R _ιmi „ liquid just seeps through to form droplets. Also if the Reynolds number is bigger than some maximum number R ₀ >R _{o m} _-, turbulence will develop and magnify itself so that a stable jet can not be formed. Probably spray-type formation occurs. In the range R _{o mi-} <R _OB -_, we have a liquid jet.

It has been found by M. Faubel, S. Schlemma and J.P. Toennies, Z-Phys. D-

Atoms, Molecules and Qusters 1Q, 269-277 (1988) that a water jet passing through a nozzle of diameter D = 5μm with thickness 20 m, will form a liquid jet in the range

250 < R _Φ < 1200

The upper limit is only an experimental finding spedal to the set-up of this particular experiment. If the Reynolds number is very large, laminar flow will be observed within the nozzle, in particular within a long pipe with a Reynolds number 50,000. For a detailed discussion, see LD. Landau and E.M. Iifshitz. Fluid Mechanics, Pergamon Press 1959, P. 111-114. Even the discussion there refers to a pipe with infinite length. In the present invention, the length of the nozzle may be of the same order as the diameter.

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Two cases are now discussed, one for liquid nitrogen, and another one for liquid helium.

(1) Liquid nitrogen:

The kinetic viscosity for liquids are v = 0.0272 cm ² /sec (liquid nitrogen) = 0.010 (water) = 0.022 (alcohol)

The Reynolds numbers for different pressures are tabulated in Table (2) for a nozzle diameter D = 5Qκm.

Table 2

The pressure can come from two sources:

P = Pc ⁺ P.

where p ₀ is the pressure applied to the liquid nitrogen externally, say, through a nitrogen gas tank, and p_ is the pressure due to the charges being accelerated from the tip to the nozzle by externally applied electric field given by

P- eV

n _o R R = n n ₀ -i _t , = 1.74xl0 ²² /cm ³ for liquid nitrogen

For eV = leV, we have p = 2.78xl0 ⁹ Pa. Here if we take V = 5kV, and for various charge density n_, we calculate n_ from p_ by setting p ₀ = O, p = p_. The values of charged densities obtained thus are listed at the last column of Table (2).

(2) Liquid helium

The kinetic viscosity varies with temperature:

For tabulation purposes, we choose to express

v = lO^v

where v is of the order 1 in the range of T = 1.0 to 2.1 ^β K. For a nozzle diameter D = 5μm, we calculate the Reynolds number R _o , and it is tabulated in Table (3).

Table 3

6. Method of Generating Charged Particles to Produce A charged T -iqiiiri Jet Similarly to the method of generating charged particles to produce strongly coupled dusters, the method of producing a charged liquid jet is facilitated by charging molecules or atoms which form the liquid just before they exit the nozzle mouth into the area of lower pressure. Presenting the charge at this point and presenting it in a slow, low energy manner, prevents the heating of the molecules, thus, preventing the undue heating of the liquid. It also prevents or minimises the destruction of molecular binding forces existing between the molecules forming the liquid.

The apparatus used to fadlitate the charging of the fluid to form either the strongly coupled cluster beam or the liquid jet beam is shown in Figure 1. Cryostat (100) defines within itself a reservoir (102) in which liquid nitrogen is held. Instead of liquid nitrogen, other elements for cryogenic cooling may be used. Some of these are liquid helium, liquid hydrogen, etc. At the top of cryostat (100) is inlet pipe (104) through which the liquid nitrogen is introduced into reservoir (102), and outlet pumping connection (106) which communicates with reservoir (102). Also shown is tube (108) which passes through cryostat (100) and reservoir (102). It is

through tube (108) that the fluid which is to be charged in the nozzle is fed. This fluid is usually in the form of a gas and preferably a purified gas, when introduced near the top of cryostat (100) into tube (108). However, as the gas passes down tube (108) and thus through reservoir (102), it is cooled by the liquid nitrogen surrounding tube (108) and becomes a liquid. The liquid contemplated herein is comprised of bosons having mass such as water, hydrogen, nitrogen, deuterium, helium, etc. Cryostat (100) is connected through attachment means (110) to nozzle cell (112) which forms a portion of nozzle used to spray the liquid into the lower pressure area. Tube (108) passes through cryostat (100), attachment means (110), and into the cavity defined by nozzle cell (112). Here the gas turned liquid which is passes through tube (108), empties. The back of nozzle cell (112) attaches to a plug (114) whose electrical wires are diagrammatically depicted as "a" and "b". At one end outside of nozzle cell (112), wires "a" and "b" are attached to a voltage device which is not shown. At another end, wires (a, b) pass through plug (114) and are electrically connected to tungsten wire (122) held in adjustable mounting (116). Screws (118) or other adjustment means are shown in adjustable mounting (116) and attach adjustable mounting (116) to nozzle face (120). Adjustment of screws (118) enables the displacement of adjustable mounting (116), tungsten wire (122) and its tip (124) with respect to the back of the nozzle cell (112) and nozzle face (120). As can be seen in Figure 1, nozzle face (120) connects to nozzle cell (112) opposite of the back of nozzle cell (112). Some details concerning tungsten wire (122) and its tip (124) are discussed herein in the Background of Invention section and the reader may wish to review this section. Tip (124) lies preferably behind and centrally of nozzle mouth (126) defined in nozzle face (120). The distance between tip (124) and nozzle mouth (126), and the size of the tip (124) are significant in terms of the results obtained and are discussed further herein.

Hie diameter of nozzle mouth (126) should be in the range of approximately

5 microns to 1 millimeter. Located near nozzle mouth (126) and emanating therefrom are skimmers (128) attached to variable position mount (130). Variable position mount (130) is adjustably connected to nozzle face (120) to enable movement of

skimmers (128) toward or away from nozzle mouth (126). Whilte skimmers (128) are indirectly connected to nozzle face (120) they are insulated therefrom so that the voltage between skimmers (128) and nozzle mouth (126) can be varied. The manner of achieving such insulation is evident to one skilled in the art. In Figure 1, insulated elements (132) are shown as part of variable position mount (130), and conductive elements (134) also part of variable position mount (130), connect to voltage means (not shown) for charging skimmers (128). While electrical connections to skimmers (128) and nozzle mouth (126) are not shown, the manner of attending to such is known in the art and is contemplated herein to achieve the voltage variation discusses. Similarly, while tip (124) is indirectly connected to nozzle face (120) by adjustable mount (116), it is insulated therefrom so that again a voltage difference between tip (124) and nozzle mouth (126) is possible.

It is to be understood that the pressure in nozzle cell (112) is at one level while the pressure around skimmers (126) is at another level. In the ipesent example, skimmers (126) are located in a vacuum chamber while the pressure inside nozzle cell (112) is at a higher level.

With the apparatus of Figure 1, the fluid introduced through tube (108) into nozzle cell (112) will exit nozzle mouth (124) into an area of lower pressure such as a vacuum chamber. Prior to exiting, however, the gas turned liquid will be charged by a veiy low voltage emitted from tip (124) of tungsten wire (122). Tip (124) is then at one voltage level, nozzle mouth (126) is at another voltage level, and skimmers (128) are at a voltage level different from that of nozzle mouth (126). Review of Figure 2, is of use in this instance.

In Figure 2, tip (124) emits a charge of negative 13 kilovolts. Nozzle mouth (126) is at ground and skimmers (128) arc at positive 5 kilovolts. Alternatively, tip (124) could be at positive 5 kilovolts, nozzle mouth (126), at ground, and skimmers (128) at negative 5 kilovolts.

Once the liquid near tip (124) in nozzle cell (112) is charged by electrons slowly emitted from tip (124), the charged liquid is attracted and accelerated toward and through the positively biased nozzle mouth (126). Some of the electrons may also combine with the molecules in the liquid to form negative ions such as N ₂ ^" . The liquid with electrons passes through nozzle mouth (126) and enters the vacuum chamber where skimmers (128) are located. If the voltage in tip (124) is reversed so that it is positive, say 5 kilovolts voltage with respect to nozzle mouth (126), then the strong positive filed near the surface of tip (124), will ionise the atoms or molecules in the liquid. Electrons will flow into the tungsten wire (122) and positive ions such as ions H ⁺ , N ⁺ , d ⁺ , or He*, (if the liquid is composed of hydrogen, nitrogen, deuterium, or helium), will travel toward the relatively negatively biased nozzle mouth (126). The liquid containing these positively charged ions then flows into the vacuum chamber.

Tip (124) is preferably placed within nozzle cell (112) and within the liquid to be formed into clusters. It is also preferably placed near nozzle mouth (126).

If field emission method is used to inject electrons or ions in liquid, due to small mobility of charged particles in liquid, they tend to travel slowly. In fad, the velo ty (u) is

U = μ E (9)

where μ is the mobility and E the electric field at that point. For a spherical symmetric configuration where tip (124) is at the center with applied potential V, the electric field due to the applied external potential without counting the contribution from charges in the liquid drops off as 1/r ² where r is the distance from the center. So, if the charged ions in the liquid are under the influence of an external electric field alone, they will travel at a slower speed as they move further from tip (124). This is quite difference from the case in a vacuum. However, since charges are continuously

being emitted from tip (124), Coulomb repulsion forces will push the charged ions causing them to move faster away from tip. The three equations that govern the behaviour of charged particles in liquid are the continuity equation, the Poisson equation, and the Lorentz force equation:

where

V • (mi) = 0 (10)

φ ^* = Aπen dD

where n = charge density φ = electric potential V = gradient u = velodty μ = mobility e - electron charge

Solving these in the spherical symmetric case leaves only the radial velodty, or

u _Λ - u. - 0 (13)

The continuity equation becomes

j- i<→ -° (14)

The Poisson equation reduces to

(15) dr (r ² dr - 4πenr ²

The Lorentz equation is

u _r = μV.φ = μ (16)

Putting (16) into (14) results in

£ -f)- (17)

or

θφ ₌ (18) dr r ² nμ where c, is a constant.

Together with (15), one can solve for the charge density

where n,, is the charge density at the surface of tip r = r ₀ . At r = r ₀ , the electric field is _v, from (18), one gets

-c, ⁿ c - (20) γ;μ*.

and at the outer surface r = R, the electric field is E(R); then

-c n(R) = (21)

R ² μE(R)

which form (19) is also equal to

1 + %cn ₀ R (22) n(R)

3c,

Equating (21) and (22), one can solve for c .

A numeral method to solve these equations may be used. With realistic values of the radius of tip (124) being 100 nm, the distance between tip (124) and nozzle mouth (126) being 1 mm, and the voltage between tip (124) and nozzle mouth (126) being 2 kV, the current density is found to be fore the negatively charged case 3 x 10 ^s amp/cm ² . The electron density at the center of nozzle mouth (126) is 4 x 10 ¹⁵ /cm ³ , and decreases to 10 ¹ /cm ³ near the edge of nozzle mouth (126). Figures 3a through 3k illustrate this. In these graphs, as in this discussion, we have

a = tip size b = the distance between tip and nozzle mouth mu = mobility

E _f = feπnion energy, a characteristic of the tungsten W ss work function, a characteristic of the tungsten J ₀ = electron current density Ii- = electric field n- = charge density r(m) = distance from tip to area measured (electric field, current density, potential, etc.)

Figure 3a shows a charge density (1/m ³ ) at tip (124) as a fundion of the bias voltage (volts) between tip (124) and nozzle mouth (126). The maximum density cna be as high as (5 x IO ²⁴ ) m ³ .

In Figure 3b, the current density J ₀ at tip (124) as a function of the bias voltage between tip (124) and nozzle mouth (126) is depided. It is in the range of about IO ⁹

- 25 - to approximately 10" amps/m ² .

In Figure 3c, the electric field at the surface of tip (124) as a function of the bias voltage is illustrated. It is basically 2 x 10 ⁹ volts/m and is not sensitive to the bias voltage.

One can change the distance between tip (124) and nozzle mouth (126) to 100 micro meters and calculate the charge density, the current density, and the electric field as a function of the bias voltage. This has been done by the inventor and the results are found in Figures 3d through 3f.

One can also change tip size (a) as well as alter the distance (b) between tip (124) and nozzle mouth (126) and see varied results. This again has been done by the inventor and is depicted in Figures 3g through 3i. These figures illustrate, charge density, current density, and electric field at the surfacr of the tip (124) with the tip being 0.5 micron and the distance between the tip and nozzle mouth being 1 milli meter. In Figures 3j and 3k the tip size is increased to 100 nano meters while the distance between the tip and nozzle mouth is kept at 1 milli meter. The charge density and potential are shown as a function of the distance r from the surface of tip (124).

As the beam is formed outside nozzle face (12) in the vacuum region, it is negatively charged by the excess electrons in it.

In order to enhance the current emitted, it may be advantageous to heat up the tungsten wire (122) connected to tip (124) by passing electric current rhough it. This generally vaporises the liquid surrounding it to create a thin film of vapour around it.

The vapour, however, serves as insulation to prevent the transmission of too much heat to the liquid. The power is of the order of 0.1 watts or less.

As an alternative to heating up the tungsten wire 122 in order to increase the

total current generated, many such tips 124 may be utilised. In the limit of an infinite number of tips arranged in two dimensions, a substantially line-like structure such as the edge off of a wedge-shaped structure will be formed. An edge may therefore replace a single tip or plurality of tips to provide a large current with a high current density, as is shown below.

The electric field at a tip, Eμ without space charge effect can be estimated from a sphere of radius r,. This is

V = potential of the tip

The electric field at an edge Eψ can be estimated from that of a long, straight wire with radius r,. Applying Gauss's law to a closed cylindrical surface of radius r and length /, we have

E _w x 2πrZ = -^ O

E * ^* * - - ^w 2πe _Λ rl

The potential difference between the surface of the wire at radius r _w and the anode at radius r ₂ is

o the electric field at the edge surface of the wedge is

The electric field at the surface of the edge as compared with that at the surface of the tip is reduced by only a logarithmic factor of ln^r,,) if r _w =τ _t . So the reduction is not severe at all. For sufficient electrons to be emitted, it is necessary to have Bψ ≥ 2 x 10 ⁷ volt cm. For an edge thickness 2r _w , we can estimate the voltage required to have a high current density emitted: For r _w = 0.5μm, r ₂ = 2.5μm V = 1.6kV r ₂ = 10 m V = 3kV r ₂ = 25μm V = 3.91kV

Let us now compare the total current emitted from a sphere of radius r, and a long wire with radius r _w and length /. The current I, from the tip is

/. = 4 j

and the current from the long wire is

_V = 2-τr^j

The amount of increase is

If the edge of the wedge is formed as an ark of a circle, and / = %D, which is equal to half a circle with diameter D, we have

Λ _p _ — _ 1- D

-w — —

4 r.

Some numerical values are:

D = lOtαn, r _w = 03 m R _w = 15.7 D = 25 m, r _w = 0.5 m R _w = 39.3

Such a field emission wedge can be incorporated into the nozzle cells for charging up fluid as it passes through the nozzle. This is illustrated in Figure 8. In Figure 8a, we schematically outline the liquid jet 200 coming out from the nozzle 204. The nozzle 204 is basically made up of an insulator 206, as shown in Figures 8b and 8c, with a metal layer or edge 210, such as molybdenum tungsten, or silver deposited on the insulator 206. The insulator 206 can be glass, epoxy, or silicon. Metal layer 210 is deposited on the insulator 206, with a thickness of 2r _» , either on the inside of the cell 202 as depicted in Figure 8b, or just outside the cell as in Figure 8c. The insulator 206 is only partly covered with the metal layer 210, as can be seen from Figure 8d. In this case the metal layer 210 extends around half of the nozzle hole 212, and covers the left side of the nozzle 204 as shown. An anode, in the form of a metallic plate or wire 214 may be attached to the right side of the nozzle 204 such that a potential difference may be applied between the plate 214 and the layer 210 to induce field emission from the metal layer 210. As electrons are emitted from the metal layer 210 on the left, they will travel across the nozzle hole 212 to the right and, prior to reaching the plate 214 a substantial portion of the electrons will be carried out of the nozzle 204 by out flowing fluid.

If even more current is required, the nozzle 204 may instead be formed so as to maximise the area over which the edge of the metal layer 210 extends, such as by the arrangement shown in Figure 9. In this case a central disc will form an anode 216, and electrons will flow from the wedge-shaped edge 218 of the metal layer 210 which concentrically surrounds the anode 216, towards the anode 216. The anode 216 is secured in position by insulating blocks 222 so as to define a hole 220 between the anode 216 and the surrounding metal layer 210, through which fluid may pass. As electrons are emitted from the wedge-shaped edge 218 and moved across the hole 220 to the anode 216, they will be carried by the fluid that flows through the hole 220, out of the nozzle 204.

Therefore, the above mentioned nozzle construction incorporating a field emission/ionisation edge may be used to more effectively charge fluid as it passes

- 29 - from nozzle cells, than the previously described method of generating field emission from a tip.

The electron density at the nozzle mouth is given for either of the above techniques for charging the fluid exiting the nozzle cell as

Λ_ _ = _ J J (23) cv.

which is inversely proportional to the velocity of the electron v _e desired so as not to disturb the molecular binding. As the current density (j) is conserved, the follow equality results.

(j) before nozzle mouth = Q) after nozzle mouth (24)

n ' v ' — n v

n.' = electron density before nozzle mouth n _e ^l = velocity of electron before nozzle mouth n. ^* = electron density after nozzle mouth v _c = velocity of electron after nozzle mouth

So the density of excess eledrons n-' in the beam after exiting the nozzle is increased by a factor of the ratio of v.'/v,, the velocity of electrons in the liquid before the nozzle and after leaving the nozzle. This fador can be as much as 10 ³ .

In order to have a large n^ it is better to discharge the electrons slowly near the nozzle mouth. The ratio of the electron density to the neutral density is R _j where

R _t = — (25)

n„ - density of atoms in the liquid - 2xl0 ²³ /cm ³ (He).

- 30 -

TTie energy per atom E, in the liquid jet after passing through the nozzle is given by

where Φ is the accelerating voltage after the beam emerges from nozzle. For the case in which the beam is formed of clusters, some values of energy per atom are listed in the tabel below.

Table II

where

V _e is the velodty of the electrons after expansion is electron density at nozzle mouth

R, is the ration of electron density to neutral density

E. is energy per atom after expansion through nozzle mouth

For a greater number of beams of charged particles, a plurality of nozzle mouths (126) with a plurality of centrally located tips (124) may be provided in one nozzle cell. These tips (124) would preferably be separated from each other but would all communicate with nozzle cell (112) for a common source of liquid. Since

the size of tip (124) cannot be enlarged without diminishing the field emission effect, a way of increasing current is to have many tips with many nozzle mouths (126) defined in one nozzle face (120).

For the case in which the nozzle is dimensioned to form a liquid jet, and provided the neutral to charged ratio R in the liquid jet is small enough so that, for a narrow liquid jet, the Coulomb repulsion is not enough to break up the cohesive force of the liquid, then the beam will form a charged liquid jet, and the accelerated charges will effect an acceleration of the jet itself. Under such an acceleration the jet will eventually break into smaller droplets which, in a vacuum, will freeze to form solid droplets ormicroparticles, having a diameter of the order 10 μm which then form the beam. For R = IO ⁷ or charge density n - 2 x lO^/cm ³ , and neutral density n. * 2.2 x lO^/cm ³ , a liquid nitrogen beam with radius 20μm will remain as a liquid jet prior to acceleration. Normally, in high energy accelerators, the ions forming ion beams behave like gas particles, and a density lOVcm ³ (or at most 10 ¹⁰ /cm ³ ) is necessary to avoid space charge effect. In a charged liquid jet, we have

(1) The charged density is at least five orders of magnitude larger than an ordinary ion beam.

(2) The neutral density n. * 2.2 x KP/cm ³ is IO ¹² or one trillion times denser than that of an ion beam.

(3) Because it is charged, it can be accelerated to higher energy as well.

The following set of parameters can be set at the source where the charged liquid nitrogen jet is created

r, = 5μm = radius of the tip l _t = 20μm = gap between the tip and the nozzle V _t = 30tv = voltage between the tip and the nozzle D = 20μm = diameter of the nozzle

The resulting electric field E„ current density j„ charge density n(r,), and current I at

the tip are calculated to be

E, = 1.67 x 10 ⁷ V/cm j, ^* = 2.28 x 20 ³ Amp/cm ² n. (r,) = 1.06 x 10 ¹⁷ /cm ³ n_ (lg) ■ 2.5 x 20 ^It5 /cm ³ = charge density at the nozzle

I = 0.9 mA

R = n _o (Ig)/n.(Ig) = 10 ⁶

The charged droplets or microparticles of the liquid jet can further be accelerated by a linear accelerator to eVo = 10 GeV. The power in one such beam is

P _j s Wo = IO ⁷ watts

Requirement for magnetic fusion is

P = 50 - 70 MW

The number of liquid jet beams is

P

N = — « 7 beams ^b

These N _b beams can be easily created by having N _b tips and N _b nozzles, the beams being together accelerated in the same cavity of the linear accelerator. The length / of the linear accelerator depends on the accelerating gradient Eo. If Eo = 20 MeV/m, then

Vo I = — * 500 meters Eo

The energy per nitrogen molecule Ε^ at the end of acceleration is

E _m ^~ ~ — ^~ - lOtøF r

To form the increased number of liquid jet beams, a plurality of nozzle mouths (126) with a plurality of centrally located tips (124) may be provided in one nozzle cell. These tips (124) are preferably be separated from each other but would all communicate with nozzle cell (112) for a common source of liquid. Since the size of tip (124) cannot be enlarged without diminishing the field emission effect, the way to increase current is to have many tips with many nozzle mouths (126) defined in one nozzle face (120).

Turning now to Figure 4, a second embodiment of the invention is shown. In this graphic depiction, cryostat (100) and attachment means (110) have been omitted for the sake of simplidty. Instead, Figure 4 shows on tube (108) as it enters nozzle cell (112). In this embodiment, nozzle cell (112) again includes nozzle face (120) and nozzle mouth (126). Skimmers (128) are diagrammatically depided in the area of lower pressure. The dimensions of nozzle mouth (126) are the same as that noted above, that is from about 5 microns to 1 millimeter. Absent from Figure 4, is plug (114), adjustable mount (116) and tungsten wire (122) and its tip (124). These are replaced by a photoelectric device now described.

Resting generally normally of, connected to, but insulated from nozzle mouth (126) is photocathode (140). This cathode is seen to extend inwardly from nozzle mouth (126) inside of nozzle cell (112). In communication with photocathode (140) is optical fibre (142) which passes outside of nozzle cell (112) to receive light waves transmitted through lens (144) by means of light source (146). In Figure 4 a photoelectric effect is used to charge the liquid surrounding photocathode (140) prior to the liquid exiting the nozzle into the lower pressure area where skimmers (128) are located. This means of charging the liquid is advantageous since it may be used at low temperature. This facilitates maintaining the liquid at a cold temperature, and since it generates a high number of emitted electrons, a high current results. Commercially available cathodes of this type have the following characteristics:

Table 3

However, the Ceasium (Cs) is easily damaged by impurities each as oxygen in the liquid. A more robust cathode will be a tungsten foil which has a work function φ = 4.5 eV, as compared with φ = 2.14 eV for Cs. The light source shown in Figure 4 may well be a laser source or a mercury lamp to generate ultraviolet light. This source may be pulsed or shown continuously on the cathode. A much stronger laser pulse is needed if tungsten foil is used because the quantum efficiency of tungsten is many orders of magnitude smaller than for Cs. The intensity of the laser beam is determined by the foil material and the degree of strong coupling desired. Preferably, this should be of the order of 100 watts or more.

The electrons emitted from the cathode generally have the kinetic energy T equal to the difference of photon energy _ and the work fundion of the metal

ω = frequency of the photon

So the kinetic energy of the electron is generally of the order leV, unless the photon energy is tuned to be just above the work fundion. If the photocathode (140) is immersed in the liquid, such as helium, and as shown in Figure 4, then the electrons can be cooled off immediately to the temperature of the liquid. The kinetic energy of the electrons will be distributed throughout the liquid while only a small portion of the liquid will be squeezed off by pressure to nozzle. The electrons will be further attracted to nozzle mouth (126) by the external electric field applied by voltage (V).

This is shown in Figure 4. The maximum charge density at nozzle mouth (126) is

« _* ___ = / 4) (28)

I = current from photoelectric effect d = diameter of nozzle mouth v = velocity of the cluster at nozzle mouth

which is obtained by assuming that all of the electrons eventually will pass out of the nozzle only through the nozzle mouth (126). The velocity v of the beam at the nozzle mouth (126) depends on the pressure applied to the liquid, for example helium. If we take v = lϋ~cm/sec, d - 5μm, I = 1mA, the maximum possible electron density is __„,„ = 3.2xl0 ¹⁹ /cm ³ . This is quite a large number. At T = lCV liquid helium temperature, the coupling T is 7.5x10 ^s . Hence, when the beam is formed outside the nozzle, it is to be expected that the molecular binding will be greater than the Coulomb repulsion for the case in which the beam is a liquid jet, or alternatively the clusters will be strongly coupled clusters for the case in which the beam is a cluster beam. The photoelectric effect can only produce electrons, and cannot produce positively charged ions.

Reference is now made to Figure 5. Here, as in Figure 4, the cryostat (100) and attachment means (110) are omitted for the sake of simplidty. Tube (108) which initially was charged with a gas, preferably a purified gas, at the top of cryostat (100), is again shown in its connection with nozzle cell (112), at which point the gas has condensed into a liquid and empties into nozzle cell (112). Nozzle face (120) connects to nozzle cell (112) and defines as before, nozzle mouth (126). Nozzle mouth (126) has the same dimensions noted above. As in Figure 4, absent from Figure 5 is plug (114), adjustable mounting (116), tungsten wire (122) and tip (124). Instead, Figure 5 illustrates an electron beam to charge the liquid in nozzle cell (112) which is now described. An ion beam may be used instead of an electron beam.

Opposite nozzle mouth (126) is tungsten foil (150) which forms a dividing wall

of nozzle cell (112). Connected to nozzle cell (112) and tungsten foil or film (150) is a vacuum tunnel (152). As can be seen in Figure 5, vacuum tunnel (152) is isolated from nozzle cell (112) such that the pressure in nozzle cell (112) is not affected by the vacuum in vacuum tunnel (152). An electron gun (154) familiar to those skilled in the art, is connected to and communicates with vacuum tunnel (152). Electrons arc fired from electron gun (154) in pulses or continuously through vacuum tunnel (152) and against tungsten foil (150). The electrons are insulated by vacuum tube (152) from nozzle cell (112). The electrons are shot at film (150) as liquid is pumped through nozzle cell (112), out of nozzle mouth (126), and into the vacuum area where skimmers (126) are situated. Nozzle mouth (126) is again positively biased by known means. Connecting skimmers (128) to a voltage source is agains also contemplated.

The energetic electron beam (which can be substituted by an ion beam of He+ or Ar+) is generated in the electron gun and injected into the liquid, such as helium, through the thin tungsten film (150). A tough thin metallic film, like tungsten film (150), is necessaiy to separate the vacuum tube (152) through which the electron/ion beam must travel to the liquid helium. The kinetic energy of the electron/ion beam must be high enough to penetrate the tungsten film (150). The electron range is given by:

A = 035 mg (cm ² keV) B = 0.984 C = 0.003 keV ¹

T = kinetic energy of the eledron in keV

where a, A, B, and C are parameters as found in "Review of Particle Properties", Physic. Letteis, Vol 170B, April 1986.

Numerically, they may have the values

For a tungsten foil of thickness d=5μm, density 4.5 mg/cm ³ , the range is 2.25 mg cm ² . So an electron beam of 40 keV can then penetrate through a 5μm foil and still inonize the liquid helium to produce both electrons and He ⁺ . Provided that an electric field is applied by voltage (V), the electron and positive ion He ⁺ produced from ionization will no recombine. For each highly energetic electron, we shall have more than one electron and ion at liquid helium temperature may be produced.

The foil (150) should be as close to nozzle mouth (126) as possible with the space therebetween being about 30 microns to 1 mm. The space between the foil (150) and the nozzle mouth (126) (the gap (g)) should be wide enough that the liquid which lies therebetween is able to stop electrons emanating from the foil (150) so that the electrons do not pass out of the nozzle mouth (126) without stopping.

g > (R - R _w ) /p (30)

where

R„ = decrease of range due to tungsten p = density of liquid helium R = range of eledrons

For numerical example given above, g > 30 micro meters. Then, all of the eledrons will be stopped between the nozzle mouth (126) and foil (150). The electrons and ions as they are emitted from the foil are also very close to nozzle mouth (126).

An external voltage of, say, 5kV or more is maintained between nozzle mouth (126) and tungsten foil (150). If nozzle mouth (126) is maintained at a positive

voltage with respect to tungsten foil (150), electrons will be attracted toward nozzle mouth (126). The beam formed beyond nozzle mouth (126) will contain excessive electrons and will be negatively charged. If the polarity is reversed so that nozzle mouth (126) is negative with respect to foil (150), ions will be attracted to nozzle mouth (126). The beam will be positively charged.

The same kind of effect can be obtained by replacing the electron beam with an ion beam. Generally, the electron beam should be at least 1 micro Amp to 1 milli

Amp in intensity and it should be focused on the foil to a point of no less than 1 millimeter. The exact intensity of the beam depends upon the type of coupling between the molecules desired. The stronger the beam, the stronger the coupling.

A last method of charging the liquid is depicted in Figure 6. Here thermionic emission of electrons is used. A tungsten wire (122) is used to generate electrons in the liquid before the liquid passes through nozzle mouth (126). In this instance, the tungsten wire (122) of approximately .005" thickness is immersed in the liquid, such as liquid nitrogen. Electric current is then passed through the wire (122) and heat is thereby generated heating the wire (122). Due to the poor conductivity of the liquid nitrogen, the liquid around the wire (122) will be heated and a gas bubble will form around the wire. There will then be a temperature gradient between the gas bubble and the surrounding liquid nitrogen. Electrons will be emitted by the normal thermionic emission, and will be attracted by the positively biased potential maintained at nozzle mouth (126). For this method, the set up shown in Figure 1 is generally applicable, the tungsten tip (124) as well as adjustable mounting (116) being replaced by a simple non insulated tungsten wire (122). Thermionic emission is shown to work in superfluid helium to yield a total current of one microamp. The reader may wish to review Glen E. Spangler and F.L. Hereford: "Injection of electrons into Hell from an Immersed Tungsten Filament". Phys. Rev. Lett. V.2Q 1229 (1968). The tungsten wire can also be substituted by a latham compound such as LaB ₆ or other electrical element with a low work function.

The above described method may be practical such that the liquid within the nozzle cell 112 is charged by tip 124, and forced to pass through the nozzle mouth 126 into a vacuum to form a liquid jet or beam, or otherwise such as to form a cluster beam. The vacuum is, however, not an essential feature, and the liquid may instead be forced through the nozzle mouth 126 into an atmosphere, provided the atmospheric pressure is lower than that existing within the nozzle cell 112.

Using the above described method of forming liquid jets or clusters, it is possible to combine two oppositely charged jets or beams of liquid droplets or microparticles formed therefrom or cluster beams to form a neutral beam such as shown in Figure 7, wherein the cells are similar to those previously described. For simplicity, only the section depicting the nozzle and skimmers is shown.

As described above, beams of opposite charge may be formed by the introduction of positive ions generated, for example, by field ionisation from a tip 158, into a fluid as it exits the cell 165 through nozzle 162 to form a positively charged beam 150. A further cell 167 similar to those used in previous embodiments may be used to generate a negatively charged beam 152. The two beams 150, 152 pass through skimmers 154 and 156 respectively.

The path of the beams 150, 152 may be altered by a series of electrically charged elements 170 and further electrically charged elements 172. The elements 170, 172 are effective to direct the charged beams 150, 152 so as to converge whilst maintaining motion of the beam away from the cells 165,167. The charge associated with one beam will cancel with the opposite charge assodated with the other beam such that, on combination, a neutral beam 180 will result.

Since the resultant beam 180 is neutral, it cannot be accelerated, and it is therefore necessary to accelerate the individual charged beams up to the required energy prior to combination into beam 180.

Alternativcly, a charge beam may be neutralised by introducing into the beam, low energy ions having a charge sign opposite to that of the beam. This method is depicted in Figure 7a, wherein a charge beam 182 is formed in a vacuum 186 after passing from a nozzle cell 184. The beam 182 passes between an ion generated 188 and an electrode 190. The ion generator 188 may in the form of a heated element 192 which emits low energy electrons. The electrons arc accelerated toward the electrode 190, which, in the case that the generator is emitting electrons, is an anode. The beam 182 is in this instance positively charged, and generator 188, and element 192 are arranged about the beam 182 so that electrons accelerated from the generator 188 can will pass into the beam 182, whereat the negative charge of the electron will cancel a corresponding positive charge of the beam 182. In this manner, neutralisation of the beam will result, upon the introduction of sufficient electrons to the beam 182.

The above described method of neutralising a beam may also be applied in the case where the beam is negatively charged by providing an ion generator 188 which produces positive ions for introduction into the beam.

It is also desirable, if charged beams are accelerated in a vacuum, to ensure that solidification of the fluid does not occur prior to combination.This can be achieved by having a low pressure present in the acceleration region, ensuring the rate of heat evaporated from the fluid is reduced, the fluid thereby remaining in the fluid state rather than cooling to a solid.

If liquid helium is used in the nozzle cell, the liquid jet may be formed of superfluid helium, the beam then consisting of coherent helium, and nuclear fusion can proceed via a coherent mechanism as well.

Liquid jets and the resultant beams, as described here, may be used in nuclear fusion processes, with the advantage over present techniques of laser implosion and inertia confinement fusion (ICF) of not preheating the deuterium target, since there are no accelerated electrons as resulting from a laser-deuterium interaction. A

deuterium-deuterium collison does not break loose electrons and create ionised plasma. The electrons are ionised only when whole deuterium under great pressure heats up together adiabatically.

Further, because of the extremely high intensity of the liquid jet, it can be used alone to assist the nuclear fusion process in magnetic confinement schemes such as in Tokamak.

Beams generated with charged clusters as discussed herein have three distinct applications:

(1) Cutting Steel or Other Hard Objects. When liquid nitrogen is used in nozzle cells, it can be expanded into the ordinary atmospheric environment with some applied pressure. If the energy per nitrogen atom is above 0.1 eV, which is equivalent to one thousand degree IO ³⁰ !., the nitrogen cluster can cut all kinds of objects: metal, steel, rock, human tissues, or even diamond. The power consumption is small. For a current of 1 mA and applied voltage φ ₀ = lOkV, the power needed is 10 watts. This is to be compared with lasers, which consume kilowatts, or kW above, in power. Liquid nitrogen is readily available and very economical. Liquid nitrogen is also cold.

For many applications where high temperature beams such as those composed of flames, ions or plasma are to be avoided, this method is useful.

(2) For energy per atom E. above 6eV, which is equivalent to 2MB pressure when stopped, a liquid hydrogen cluster beam can be used to create metallic hydrogen. Six beams of liquid hydrogen can be shot together to a cube of solid hydrogen. The cube under extreme pressure from these six beams will form metallic hydrogen. The metallic hydrogen is superconducting at room temperature.

(3) For energy per atom E. above lOOeV, and preferably 1 keV, deuterium cluster beams formed from liquid deuterium, or helium cluster beams formed from

liquid helium can be used to create nuclear fusion. Six beams can be arranged to impact on a solid cube of deuterium.

Strongly coupled clu„ er beams, as described here, have advantages over laser implosion technique on inertia confinement fusion (ICF) because they do not preheat the deuterium target since there are no accelerated electrons as resulting from a laser- deuterium interaction. A deuterium-deuterium collision does not break loose electrons and create ionised plasma. The electrons are ionised only when whole deuterium under great pressure heats up together adiabatically.

Further, because of the extremely high intensity of the strongly coupled cluster beam, it can be used alone to assist the nuclear fusion process in magnetic confinement schemes such as in a Tokamak.

If the liquid helium in nozzle cell is superfluid helium, the helium clusters then consist of coherent helium and nuclear fusion can proceed via a coherent mechanism as well.

The inventor teaches the creation of clusters that are strongly or weakly coupled, that are coherent, and that are neutral or charged, these clusteis being formed from either a liquid or a gas, that is a fluid. While throughout this description, the term liquid is most often used when describing this invention, it is to be understood that the invention is equally applicable to gases. It is merely that the prior art does not disclose the formation of clusters from liquids, that the present disclosure has been written to draw the attention of the reader to the fact that this invention contemplates cluster formation from liquids as well as gases. The two may be generally referred to as fluids.

In the prior art known to the inventor, and in particular that disclosed by Friedman and in the Brookhaven experiments, the use of liquid for forming clusters is not disclosed and the forming of charged clusters prior to to during their formation

in a fashion that does not destroy the coupling or coherency of the clusters is not disclosed. The known art forms clusters from gases, super saturated gases, or superfluid helium and either charges the clusters significantly after formation or if it charges the clusters before formation, does so with electric arcing which disturbs the coupling of the clusters. To charge a fluid, that is a liquid or a gas, as taught by applicant, an element with a low work function is used to slowly emit the desired charge so that the coupling of the clusters is not disturbed.

Some of the fluids the inventor uses to form clusters, are water (H ₂ 0), heavy water (D ₂ O), liquid nitrogen, liquid deuterium, liquid helium, liquid oxygen, and liquid hydrogen. The advantages of forming each of these liquids into clusteis are enumerated below. The advantage of forming the clusters from a liquid rather than a gas is that the density of liquid (except liquid helium) is generally 800 to 10,000 times more than the density of the liquid in a gaseous state at boiling point. Thus clusteis formed from a liquid as disclosed herein, are larger in both size and number.

With such an increase, a much more intense cluster beam is created as the liquid formed clusters are sprayed out of the nozzle mouth. Quster beams from said spraying have been measured in intensity of 0.1 eV per atom which is equivalent to tens of kilobars of pressure or one IO ⁴ atmospheres of pressure. With the exception of liquid helium, the pressure in the nozzle cell need only be about 1 atmosphere or above. For liquid helium the pressure should be 10-100 atmospheres or above. The formation of helium clusters from superfluid helium is known in the art and not elaborated upon here.

a) Water

This is the cheapest and most easily obtainable commodity. When water clusters are accelerated to an energy per molecule of E _t > 0.1 eV. Accelerated in this fashion, the clusteis can be used to cut metal or drill holes in rock. Further, the pressure used outside of the nozzle mouth in the above examples does not have to be a vacuum, as long as the initial pressure on the water in nozzle cell is significantly above one atmosphere. The water can be at room temperature or below when passing

it from the nozzle cell to the outside area of lower pressure. The water should preferably be pure so that it does not clog nozzle mouth (126).

b) Heavy Water

Replacing hydrogen by deuterium in water increased the cost enormously. But at sufficiently high energy, E. > 300 eV, these heavy water clusters can ignite fusion as the Brookhaven group has shown. Again, as above, the heavy water may be at room temperature or below and the pressure outside nozzle mouth in the area of skimmers need not be vacuum pressure.

c) Liquid Nitrogen

Liquid nitrogen is very cold when compared with water. In industrial situations where cold treatments are preferable, liquid nitrogen can be substituted for water. Liquid nitrogen is still relatively inexpensive, and can be handled cyrogenically rather easily. Vacuum pressure is required outside of the nozzle mouth to keep the nitrogen cool.

d) liquid Hydrogen

Energetic hydrogen clusters (E _t > 20 eV, or pressure > 2MB [megabar]) formed from liquid hydrogen can be used to create superconducting metallic hydrogen. Vacuum pressure is required outside of the nozzle mouth.

e) Liquid Deuterium liquid deuterium is far purer than heavy water as it contains only deuterium atoms. In some applications, pure deuterium clusters formed from liquid deuterium may be preferable to ignite nuclear fusion. Vacuum pressure is required outside of the nozzle mouth.

f) Liquid Helium Coherent helium cluster can be obtained from liquid helium in the source nozzle cell and hence are very valuable as research tools as well as for industrial

application. Vacuum pressure is required outside of the nozzle mouth.

Charged cluster beams formed as disclosed herein may be accelerated by an external electric field. This field will not destroy the strong coupling of the clusters. The result will be an extremely intense, energetic, strongly coupled cluster beam having a low energy spread.

The described arrangement has been advanced by way of explanation only and many modifications may be made thereto without departing from the spirit and scope of the invention as defined in the appended claims.