WITTE, Holger (Ewert HouseEwert Place,Summertown, Oxford Oxfordshire OX2 7SG, GB)
PEACH, Ken (Ewert HouseEwert Place,Summertown, Oxford Oxfordshire OX2 7SG, GB)
WITTE, Holger (Ewert HouseEwert Place,Summertown, Oxford Oxfordshire OX2 7SG, GB)
| Claims 1. A magnet for a particle accelerator comprising four concentric tubular coils, each of said coils comprising a plurality of turns, wherein each of said four coils has a different radius and wherein, apart from their respective radii, the path of the outer coil is the same as the path of the inner coil, and wherein, apart from their respective radii, the paths of the middle coils are the same as each other, and wherein the four coils are arranged to produce a magnetic field in which there is substantially no solenoid component of the magnetic field present, and wherein the aspect ratio of the magnet is less than 15:1. 2. A magnet as claimed in claim 1 wherein the number of turns is the same for all four of the coils. 3. A magnet as claimed in claim 1 or 2 wherein the winding pitch has the same value for all four of the coils. 4. A magnet as claimed in claim 1 , 2 or 3 wherein the coils are configured so that the current passing through all four of the coils has the same absolute value. 5. A magnet as claimed in any preceding claim wherein the coils are configured so that current passes through the middle two coils in the opposite direction to the current passing through the inner and outer coils. 6. A magnet as claimed in any preceding claim wherein the coils are configured so that the tilt angle for all four of the coils has the same magnitude. 7. A magnet as claimed in any preceding claim wherein the windings of the coils are arranged to provide a superposition of multipole magnets. 8. A magnet as claimed in any preceding claim wherein the windings of the coil are arranged to provide a superposition of multipole magnets whose coefficients vary along the length of the magnet. 9. A magnet as claimed in any preceding claim wherein the paths of the windings of the coils are arranged such that for the middle coils z = p(9) + f(9), where z is the coordinate along the axis of the coils, 9 \s the azimuthal angle, p(9) is a term representing the pitch of the turns, and f(9) is a term representing the multipole component(s), and for the inner coil z = ρ(θ) - f(9). 10. A magnet as claimed in claim 9 wherein at least one of ρ(θ) and f(9) is varied along the length of the magnet. 1 1 . A magnet as claimed in claim 9 or 10 wherein f(9) describes a superposition of multipole magnets. 12. A magnet as claimed in claim 1 1 wherein the superposition is a linear superposition. 13. A magnet as claimed in any of claims 9 to 12 wherein f(9) comprises the 14. A magnet as claimed in claim 13 wherein the coefficients, An, for each coil have the same value at each point along the length of the magnet. 15. A magnet as claimed in any of claims 9 to 14 wherein p(9) comprises the term h9/2 , where h is the winding pitch. 16. A magnet as claimed in any preceding claim wherein the winding pitch varies along the length of the magnet. 17. A magnet as claimed in any of claims 9 to 16 wherein the coils comprise a plurality of zones in which the coefficients are constant. 18. A magnet as claimed in claim 17 comprising a transition region in between each of the zones in which the coefficients vary. 19. A magnet as claimed in claim 18 wherein the transition region comprises ten or fewer turns, preferably five or fewer turns. 20. A magnet as claimed in any preceding claim wherein the coils are wound around at least one former. 21 . A magnet as claimed in claim 20 wherein a separate former is used for each coil. 22. A magnet as claimed in claim 20 or 21 wherein the or each former comprises a groove to receive the coil turns. 23. A magnet as claimed in any preceding claim wherein the cross-sectional shape of the coils is a circle or an ellipse. 24. A magnet as claimed in any preceding claim wherein the plurality of turns for each coil comprises between 100 and 400 turns, preferably between 200 and 300 turns, preferably between 240 and 260 turns. 25. A magnet as claimed in any preceding claim wherein the tilt angle is between 20 degrees and 80 degrees, e.g. between 40 and 70 degrees, e.g. between 60 and 70 degrees, e.g. approximately 65 degrees. 26. An accelerator comprising a magnet as claimed in any preceding claim. 27. An accelerator as claimed in claim 26 suitable for accelerating protons. 28. An accelerator as claimed in claim 26 suitable for accelerating carbon ions. 29. An accelerator as claimed in claim 26, 27 or 28 wherein the accelerator is a fixed field alternating gradient accelerator. |
This invention relates to magnets for bending and focussing moving charged particles, particularly in particle accelerators.
Traditionally very large scale particle accelerators have been used in scientific research as probing instruments to investigate the structure of matter. Equally important however is the use of much smaller accelerators in industry where they are used in a diverse range of applications such as ion implanters for
semiconductors, surface hardening, synchrotron radiation sources, and medical applications (radiotherapy, biomedical research and radioisotope production). This application is concerned particularly, but not exclusively, with smaller accelerators for medical applications, e.g. proton and carbon ion therapy.
Conventionally charged particles are accelerated in circular accelerators where the particles are kept in the accelerator for multiple revolutions. To keep the particles within the beam pipe of the accelerator, bending magnets are needed to make the particles follow a curved trajectory. Conveniently such accelerators have a circular particle trajectory, but this is not essential and other loop shapes are possible.
The Lorentz force, F=q(E + vxB), describes the force experienced by a charged particle with velocity v and charge q in an electric field E and magnetic field B. Considering when only a magnetic field is present, the force experienced by the particle is perpendicular to both the magnetic field and the component of its velocity perpendicular to the magnetic field. Therefore if the velocity of the particle is only in this direction, i.e. perpendicular to the magnetic field, the trajectory of the particle will be a circle if the magnetic field is homogeneous.
Therefore if a homogeneous magnetic field is created across the area of a circular particle accelerator, perpendicular to the plane of the accelerator and a supply of particles is injected into the magnet, they will circulate within the accelerator as long as the magnetic field is chosen correctly. A magnet able to perform this function is called a dipole magnet which has a homogeneous magnetic field over a certain region and bends particles in a circular path. Conventional magnets use a solid iron core around which a coil is wound to create the desired field, the core amplifying the magnetic field created by the coil. The maximum field obtainable with such a magnet is approximately 2 T, at which point the iron core saturates and only an insignificant increase in magnetic field is possible as the current in the coil is increased.
The magnetic rigidity of a charged particle describes the relationship between the radius of curvature in a magnetic field, which can be derived from balancing the Lorentz force with the centrifugal force to give Bp = p/q where B is the magnetic field, p is the radius of curvature, p is the particle's momentum and q is the particle's charge. For a given application particles of a certain energy, and therefore momentum, are generally required. For example in radiotherapy using protons, an energy of 250 MeV is required, e.g. to treat tumours at a maximum depth of 25 cm below the skin. This means that once the energy has been set, the magnetic field and radius are inversely proportional to each other, and therefore if an accelerator with a small radius is required, e.g. to fit into a confined hospital space, a large magnetic field is required.
The solution to providing a magnet which can create a magnetic field greater than 2T is to dispense with the iron core and to use electromagnets. In this respect superconducting magnets are very attractive as they require relatively little power, owing to the fact that the electrical resistivity is zero. Superconducting magnets routinely produce magnetic fields in excess of 22 T.
Conventional electromagnets for particle accelerators are constructed by arranging a number of coil segments around the coil bore, each of which carries a constant current, with the current running along the axis (z-direction) of the magnet. The net current is varied around the circumference of the bore to give the required distribution, e.g. for a dipole magnet this is a cosine theta distribution, i.e. J z ∞ cos(9), where J z is the z-component of the current and # is the azimuth angle, which results in the creation of a dipole magnetic field across the interior of the bore.
A further requirement for a small radius particle accelerator is that the magnets themselves have to be shorter in length to fit into the reduced circumference of the accelerator. Another important concern for particle accelerator magnets is the required beam aperture, which needs to be large enough to accommodate the beam. The beam aperture is determined by the optical lattice of the accelerator. For most magnets it is desirable to have a small aperture which minimises the cost, but for some accelerators, e.g. fixed field alternating gradient (FFAG) accelerators, the aperture is required to be relatively large to accommodate the large radial excursions of the particles in such accelerators.
However when a magnet has a large aperture and a short length, giving it a very small aspect ratio (ratio of length to radius of aperture), the effects of the ends of the coil, which return the current, become important. Conventional coil ends do not contribute to the useful magnetic field and thus reduce the available space for the 'useful' part of the magnet. A further disadvantage of the coil ends is that they can introduce field errors.
One suggested solution for reducing the field errors and to overcome the space issue is to use a technology commonly referred to as a helical coil or a so-called "double-helix" coil. A double-helix coil comprises two concentric solenoid coils wound in opposite directions - in other words the turns of the respective coils follow paths which are a reflection of each other in the plane which bisects the coils normal to the axis of the coils. For example in a dipole magnet this is two coils whose turns are each in a plane tilted at an angle away from the plane normal to the axis of the magnet, with the turns of each coil being tilted in the opposite direction to the other. If an equal current is now passed through each of the coils in different directions, the effect is that the solenoidal (axial) fields cancel, and the multipole fields add (e.g. for a dipole this field is perpendicular to the axis), giving a high quality multipole field. The multipole field generated by the double-helix magnet can have smaller errors than a conventional multipole magnet with coil segments because it is a better approximation to a cosine theta current density distribution. The coil ends are not artificial structures to return the current back through the coil but natural extensions of the main section of the coil, and the part of the coil contributing to the useful multipole field tends to be large in comparison to conventional designs. The integral field quality of double-helix coils is very good, as field errors (unwanted harmonics) tend to cancel out. The double-helix coil can be shown to give a current distribution of J z ∞cos(0), i.e. that needed to create a dipole field. This is because the tilted coils of the magnet trace a path in z of z °c sin(9) (making the assumption that the additional term to account for the winding pitch is small compared to the sin( Θ) term).
However the present inventors have appreciated that there are shortcomings with the proposed double-helix arrangement and the present invention aims to address these.
From a first aspect the present invention provides a magnet for a particle accelerator comprising four concentric tubular coils, each of said coils comprising a plurality of turns, wherein each of said four coils has a different radius and wherein, apart from their respective radii, the path of the outer coil is the same as the path of the inner coil, and wherein, apart from their respective radii, the paths of the middle coils are the same as each other, and wherein the four coils are arranged to produce a magnetic field in which there is substantially no solenoid component of the magnetic field present, and wherein the aspect ratio of the magnet is less than 15:1.
The inventors have realised that although the double-helix coil offers a significant improvement over a conventional coil in mitigating field errors and the space issue, there is still a residual component of the solenoid field along the axis of the coil and non-trivial higher order fringe fields which cannot be eliminated. This, they have realised, arises because the two coils which comprise the double-helix have slightly different radii owing to them being concentric and winding pitch effects.
In accordance with the present invention however, four coils in oppositely-wound pairs are provided, with the inner and outer coils having the same path (at slightly different radii of course) and the intermediate two coils following the mirror-image path (again apart from the different radii of the coils). This has been found to reduce the problem of the non-cancelling solenoid field in the double-helix coil significantly, particularly at the ends of the magnet, since when an equal current is sent through the coils (in one direction for the inner and outer coils and the opposite direction for the two middle coils), the solenoid field substantially cancels leaving a multipole field remaining. In a magnet with a short length and/or large aperture, i.e. an aspect ratio (the ratio of the coil length to the magnet aperture radius) of less than 15:1 , this design of magnet coil is therefore particularly suitable.
In short magnets, the end effects of the magnetic field become very important, as they make a proportionally more significant contribution to the magnetic field compared to a long magnet where the primary concern is having a uniform field along the majority of the length, and any small deviations from the uniform field towards the ends of the magnet are not important. However, in a short magnet it is most important to be able to control the end effects of the magnetic field as these become significant and will therefore have deleterious effects on a beam of particles passing through the magnet, e.g. loss of the particles from an accelerator, if they are not controlled and the deviations minimised as much as possible.
The four coil magnet of the present invention achieves substantial cancellation of the solenoid field all the way along the magnet, leaving only transverse multipole components, therefore significantly minimising the deviations from the desired field at the ends of the magnet where this is most important.
As well as achieving cancellation of the solenoid field for the primary multipole of the magnet, the four coil magnet also achieves cancellation of other order multipoles which may be present in a double-helix magnet, e.g. cancellation of the quadrupole component in a double-helix dipole magnet. These multipole components of other orders are often present towards the ends of the magnet and therefore would contribute to the "fringe field", which is therefore minimised by the arrangement set out in the present invention and enables a more uniform field along the whole length of the magnet to be produced.
As used herein the term 'axis' of a coil should be taken to be a line through the centre of the coil parallel to the sides of the coil.
The magnet provided by the present invention is suitable to be used in a number of different particle accelerators, e.g. fixed field alternating gradient (FFAG) accelerators which have a number of applications, such as in hospitals for radiotherapy treatment; in scientific research for neutrino factories, muon sources and proton drivers; in industry for accelerator driven subcritical reactors (ADSR). Preferably the number of turns is the same for all four of the coils. Preferably the winding pitch has the same value for all four of the coils. Preferably the coils are configured so that the current passing through all four of the coils has the same absolute value. Preferably the coils are configured so that current passes through the middle two coils in the opposite direction to the current passing through the inner and outer coils. Preferably the coils are configured so that the tilt angle for all four of the coils has the same magnitude. These features help to ensure that the magnet in accordance with the invention generates a magnetic field for which the solenoid field component is reduced as much as possible.
Owing to the thickness of the windings, the coils have a winding pitch which, although small compared to the sin(9) (or other order) term in the path of the coil, contributes to some distortion of the magnetic field (compared to the desired ideal multipole field). This distortion is more significant for shorter magnets (for which the present invention is particularly suitable) as the winding pitch (which can be of the order of 1 cm) is a greater proportion of the total length of the coil compared to that for a longer magnet. However, as has previously been described for the cancellation of the effects of the different radii of the coils in the double-helix magnet when providing a four coil magnet, the distortion effects owing to the winding pitch are generally cancelled when a four coil magnet is provided, compared to a double-helix magnet.
Although the invention is defined in terms of two intermediate coils, it should be understood that because these follow the same path, they can be thought of as a single coil with a double layer of turns or a single layer with turns of twice the radial thickness.
Although the invention has thus far been described in terms of four coils this should not be considered as limiting the claims to requiring only four coils; additional coils could be added, e.g. to provide improved cancellation of the solenoid field, to increase the magnetic field, or for some other reason. Preferably if additional coils are provided, these are provided concentrically in groups of four, i.e. a magnet with more than four coils would preferably have eight, twelve or sixteen coils, etc.
Preferably these groups of four coils would each be arranged in the same manner as the first-recited group, i.e. with the inner and the outer coils of each group following a first path and the middle coils following a second, preferably mirror- image path.
Although the invention has been described with reference to dipole magnets, this is not limiting and the invention can be applied equally to higher order multipole magnets. In other words, the path taken by the turns of the magnet coil in z can be generalised for higher orders to be z °c sin(n9), where n is an integer, and so for a dipole magnet, n = 1. When n = 2 this gives a quadrupole magnetic field, and when n = 3 this gives a sextupole magnetic field.
Higher order multipole magnets such as quadrupole and sextupole magnets are typically used in particle accelerators because the case of an ideal charged particle circulating in a dipole field does not exist. There are many systematic errors that result in the defocusing of the particle beam: radiation losses in the dipole magnets, gravity, field imperfections, ground motion, alignment of the accelerator, having a limited physical aperture, errors in the power supplies and calibrations resulting in errors in the magnet strength, and variations in the energy of the particles. As a result of these factors if purely dipole magnets were employed, particles in the accelerator would tend to spread out transversely and longitudinally and eventually get lost from the accelerator. Other magnets are therefore used to compensate for the spread in particles and so reduce the loss of particles from the beam pipe.
Quadrupole magnets produce a magnetic field which is able to correct for the transverse spreading of the particle beam by focusing the particles back towards the axis of the accelerator beam pipe. In practice, a lattice of quadrupole magnets is provided which alternately focuses and defocuses the particles in order to keep them centred within the beam pipe.
Sextupole magnets produce a magnetic field which is able to correct for the longitudinal spreading of the particle beam. Different particles within the beam will have different energies and therefore they are bent a different amount by the dipole magnets. This is comparable to chromatic aberration in optical lenses where different frequencies of light experience a slightly different refractive index and therefore are focused to a slightly different point, resulting in spreading of the image. Sextupole magnets are able to correct for this by deflecting particles with a higher energy an extra amount in order to keep the beam of particles collimated.
Sometimes it is necessary to include even higher order multipoles, e.g. octupole (having a path described with a sin(49) term), decapole (having a sin(59) term) magnets and further higher order multipoles still, in particle accelerators to keep the beam of particles within the beam aperture.
The windings of the coils are preferably arranged to provide a multipole magnet or a superposition of multipole magnets. The most basic example of this is a dipole magnet. As was shown previously, the path of the turns for a dipole magnet is z∞ sin(9) where z is the coordinate along the axis of the coil. This can be generalised for higher orders to be z x sin(nO), where n is an integer, and so for a dipole magnet, n = 1. When n = 2 this gives a quadrupole magnetic field, and when n = 3 this gives a sextupole magnetic field, etc. For a dipole magnet when the coil is a circular cylinder, the path followed by the turns of the coil is an elliptical helix in which the turns are tilted at an angle to the plane normal to the axis of the cylinder, but for higher orders this produces a more complicated sinusoidal path. However if the axis of the coil is not straight, or the transverse cross section is not circular, the paths of the windings cannot easily be described by simple sinusoidal terms.
In some accelerator designs the magnetic field required from a single magnet is a mixture of the fields produced from different multipoles, e.g. mostly a dipole field with a smaller component of a quadrupole field. Such a type of magnet is known as a combined function magnet. This can be achieved in accordance with the present invention by having coils that follow a path which is a combination of the different terms for the different multipole fields, e.g. for a magnet with both dipole and quadrupole components the path followed would be z = A 1 sin(9) + A 2 sin(29), where A 1 and A 2 are constants which are chosen to give the appropriate amount of dipole and quadrupole fields respectively. This therefore produces a magnetic field which is a superposition of the fields from the different multipoles included in the path of the coil turns. As well as having the windings of the coils arranged to provide a superposition of multipole magnets, where the coefficients, A 1 and A 2 (and further coefficients if more components are included in the superposition), of the multipole components are constant, in some embodiments it may be advantageous to vary these coefficients along the length of the magnet, i.e. the windings of the coils are arranged to provide components of at least two multipole magnets with the proportions of the respective components varying along the length of the magnet.
As well or instead of varying the multipole components along the length of the magnet, in some embodiments the winding pitch could be varied along the length of the magnet, for example to produce different magnetic field shapes. In other embodiments the winding pitch could be kept constant along the length of the magnet.
In one set of embodiments this superposition of the multipole magnets, with either the coefficients and/or the winding pitch varying along the length of the magnet and the solenoid field being substantially cancelled, can be achieved by arranging the paths of the windings of the coils such that for the middle coils z = p(9) + f(9), where z is the coordinate along the axis of the coils, 9 \s the azimuthal angle, p(9) is a term representing the pitch of the turns, and f(9) is a term representing the superposition of the multipole components, and for the inner coil z = ρ(θ) - f(9). Preferably, at least one of ρ(θ) and f(9) is varied along the length of the magnet.
This arrangement of the paths of windings of the middle coils being inverted, i.e. z = f(9), as compared to the path of the windings of the inner coil (z = - f(9), ignoring the term for the winding pitch) is not limited to a magnet in which the coefficients of the multipole components vary along the length of the magnet or even limited to a combined function magnet, and is equally applicable when the coefficients are constant along the length of the magnet or for a single multipole magnet, i.e. as in previously described embodiments.
This arrangement of varying multipole components and/or the winding pitch is novel and inventive in its own right and therefore when viewed from a second aspect the invention provides a magnet for a particle accelerator comprising at least first and second concentric tubular coils, each of said coils comprising a plurality of turns, wherein the paths of the windings of the of the coils are arranged to minimise the solenoid component of the magnetic field such that for the first coil z = ρ(θ) + f(9), where z is the coordinate along the axis of the coils, 9 \s the azimuthal angle, ρ(θ) is a term representing the pitch of the turns, and f(9) is a term representing the multipole component(s), and for the second coil z = ρ(θ) - f(9), and wherein at least one of ρ(θ) and f(9) is varied along the length of the magnet.
Therefore, for example, if one coil follows the path (in z, the coordinate along the axis of the coil) z = h9/2 + A 1 sin(9) + A 2 sin(29), the other coil follows the path z = h9/2 - A 1 sin(9) - A 2 sin(29), with either h, A 1 or A 2 (or any combination thereof) varying along the length of the magnet. As will be seen below, the paths in x and y, the coordinates in the plane normal to the z-axis, are also reversed.
The inversion of the path of the windings of the first coil (ignoring the term, ρ(θ), for the pitch of the windings) to give the path of the windings of the second coil, i.e. z = ρ(θ) + f(9) to z = ρ(θ) - f(9), acts to minimise the solenoid component of the magnetic field.
It will therefore be appreciated that this aspect of the invention, if f(9) is varied along the length of the magnet, allows a combined function magnet with different multipole components to be provided, with the windings of the coils arranged to vary the coefficients of these multipole components along the length of the magnet. This is advantageous as, for example, it allows two or more multipoles (or superposition of multipoles) to be provided adjacent to each other in a single magnet, instead of needing two separately wound magnets to be provided one after each other along a particle accelerator, or nested within each other, resulting in a significant gap between the magnets. Therefore it can be seen that in some embodiments, f(9) describes a superposition of multipole components. In a preferred set of embodiments, f(0) describes a superposition of multipole components whose coefficients vary along the length of the magnet.
This aspect of the invention therefore allows such gaps between the different multipoles (or combination of multipoles) to be eliminated enabling matching of the fringe field extent, i.e. previously with two adjacent magnets it was extremely difficult to match the magnetic field at the ends of each of the magnets resulting in an unstable beam and therefore subsequent loss of particles from the accelerator, whereas the aspect of the invention set out above allows seamless matching between the different multipole components of the magnet thereby creating a stable tune for the particle accelerator which prevents blow up of the particle beam and the subsequent loss of particles from the accelerator. One example of where this might be required is in a fixed-field alternating gradient particle accelerator.
This seamless matching between the different multipole components of the magnet is difficult to achieve in one layer with previous electromagnets, e.g. conventional cosine theta magnets with blocks of constant current density, as for two different multipole magnets the longitudinal current has a completely different angular distribution and therefore there is nowhere for the current to go if the two magnets were to be connected. However in the present invention the windings of the coils are arranged so that the multipole components can vary along the magnet and therefore the current distribution is also varied likewise to avoid the discontinuities present in the previous electromagnets.
The second aspect of the invention, if ρ(θ) is varied along the length of the magnet, allows the pitch of the windings of the coils to be varied along the length of the magnet. This allows greater flexibility in the design of a magnet, whether it is a single multipole or a superposition of multipoles, as the field can be shaped and therefore better performance can be obtained.
In one set of embodiments, the density of turns can be increased at the ends of the coils. This is usually the region where the peak field on the wire tends to be lower in comparison to the middle of the coils, so the density of turns can be increased in this area to get more performance.
For a cylindrical coil with a circular cross section, the path of the turns around the axis of the inner and outer coils is described in 3D Cartesian coordinates by the following equations:
χ(θ) = R cos(0)
y(0) = R sin(0) ζ(θ) = ιθ/2π + R sin(n0)/tan(a)
where # is the azimuthal angle, R is the coil radius, h is the pitch of the turns, n is the multipole order and a is the tilt angle of the coil, which is the minimum angle between the plane in which the turns of a dipole coil lie and the axis of the coil.
When described in this manner for the embodiments of the invention which have the path of the windings for the two middle coils being the reflection of the path for the inner and outer coils, the equations describing the path for the two middle coils are:
χ(θ) = - R cos(0)
y(0) = - R sin(0)
ζ(θ) = - Ιιθ/2π- R sin(n0)/tan(-a)
Thus the tilt angle for the two middle coils is in the opposite direction to the tilt angle of the inner and outer coils. The negative sign in the equations for the two middle coils reflects the reversing of the current in the coils.
The tilt angle is an observable variable in the coils of the different multipole magnets, which is especially apparent for the case of the dipole when it is the angle at which the turns of the coils are tilted away from the x-z plane. For each of the different multipoles the tilt angle can be varied to optimise the magnetic field produced by the coils.
Preferably the tilt angle is between 20 degrees and 80 degrees, e.g. between 40 and 70 degrees, e.g. between 60 and 70 degrees, e.g. approximately 65 degrees. The multipole field increases and the solenoid field decreases as the tilt angle is reduced because more current is flowing in a longitudinal direction, but a large tilt angle enables more turns to be wound in a given space which increases the magnetic field. In one embodiment a tilt angle of approximately 65 degrees enables a high quality field to be maintained for a small aspect ratio, i.e. a short magnet with a large aperture. However the tilt angle may vary depending on the order of the multipole and also whether the accelerator is for protons or carbon ions. It has been found that a larger tilt angle is more suitable for coils with a larger radius, e.g. if a number of different multipole coils are nested within on another, then a tilt angle of 60 degrees is suitable for the inner coil and 70 degrees for the outer coil. The superposition of the different multipole components could be a non-linear superposition, e.g. when using iron in the magnet design for shielding purposes, but in a preferred set of embodiments the superposition is a linear superposition. In general terms for all aspects of the invention, the path followed by the windings of the first or inner coil for a multipole magnet can, excluding the term for the pitch of the turns, be expressed as
z =∑ sin(rc#)
The path followed by the windings of the two middle coils for the first aspects of the invention, or the second coil for the second aspect of the invention, can be expressed as
z = -∑ sin(rc#)
For a single multipole there is only one multipole component, i.e. A n = O for all n apart from the value of n which gives the order of multipole required, e.g. n = 2 for a quadrupole magnet. For a combined function magnet at least two coefficients of A n are non-zero. Therefore for a combined function magnet, in accordance with the invention, in which the coefficients can vary along the length of the magnet, it is the coefficients A n which vary with z, the coordinate along the axis of the magnet. The coefficients for each coil could be different for each different coil, but in a preferred set of embodiments the coefficients for each coil have the same value at each point along the length of the magnet. Similarly, the pitch of the turns for each coil could be different for each coil, but in a preferred set of embodiments the values of the pitch for each coil have the same value at each point along the length of the magnet.
Therefore it can be seen that the path of the two middle coils (for the first aspect of the invention) or the path of the outer coil (for the second aspect of the invention) is an inversion of the path of the inner coil, or equivalently a rotation of each of the multipole components by τι/η (since sin(n(9+7i/n)) = -sin(nO)), when the function f(9) is expressed as a linear superposition of sinusoidal terms. For the combined function magnet in which the coefficients can vary along the length of the magnet, this reversal or rotation happens locally as the coefficients are changing along the length of the coil so some multipole components can appear or disappear, i.e. the coefficients become zero or non-zero from zero at different points along the length of the coil.
In the second aspect of the invention the magnet could comprise two concentric coils as in a double helix magnet, but preferably the magnet comprises third and fourth concentric tubular coils as in the first aspect of the invention. In a preferred set of embodiments the coils of the four coil magnet are arranged such that apart from their respective radii, the path of the first coil is the same as the path of the fourth coil, and wherein, apart from their respective radii, the paths of the second and third coils are the same as each other.
For the combined function magnet with varying coefficients, the components of the multipole magnets could be present as a number of zones along the magnet in which the coefficients are constant, e.g. one zone of the magnet could provide a dipole field and the other zone could provide a quadrupole field. In one set of embodiments the change between the different zones is a step change, e.g. the path of the windings of the coils changes immediately from that for a dipole to that for a quadrupole. However in a preferred set of embodiment the varying of the coefficients between each of the different zones is provided in a transition region, i.e. the windings of the coils change gradually between providing one type of multipole (or superposition of multipoles) to providing a different type of multipole. The transition region could comprise only a few turns (in the most extreme case of the transition region being zero turns long, this is the previous case of a step change) or the transition region could comprise the entire coil, i.e. the windings of the coils start at one end of the coil in one multipole configuration and gradually change along the whole length of the coil into a different multipole configuration at the other end of the coil. Preferably the transition region comprises ten or fewer turns, preferably five or fewer turns.
It is envisaged that any number of different combinations of multipole magnets could be provided in one set of coils, as well as any number of different superpositions of multipoles, e.g. the windings of the coils could change along the length of the magnet from providing a superposition of a dipole and a quadrupole (in any ratio of relative strength) to a superposition of a sextupole and a quadrupole to a superposition of a dipole and an octupole. Thereby different multipoles can be effectively turned on and off at different points along the magnet so that a particle travelling through the magnet experiences the different multipoles as it travels through, but with no discernible gap between the different components.
In the set of preferred embodiments in which a transition region is provided for changing between the different multipole magnets, the function of the path of the windings in the transition region could be any function which provides the necessary transition between the paths of the windings on either side of the transition region.
Therefore there are many different ways, i.e. functions, in which the windings can change in the transition region between the different multipole configurations. The function of the path in the transition region could comprise a linear function of the coefficients of the different multipole terms in the windings of the coil either side of the transition region, i.e. a linear interpolation across the transition region between the different values of A n as for the above formula. However different interpolation functions could also be used, e.g. a polynomial interpolation or a spline
interpolation.
However for the type of combined function coil discussed above the ratio of the multipole fields is hardwired into the coil (by the values of the different coefficients for the components of the different multipole components) thus eliminating one degree of freedom. In an alternative set of embodiments of the first aspect of the invention, when a combined function magnet is required, a plurality of different discrete multipole magnets concentric to each other can be provided. For example, this type of combined function magnet could have four coils creating a dipole field which could be concentric with a higher order multiple comprising four additional coils. The magnetic field produced in such embodiments is a superposition of the fields created by each multipole, thus allowing the different multipole terms to be achieved, but with a separate set of coils for each different discrete multipole. The path of the turns for each of these multipoles and the current passing through them can be chosen to give the desired ratio between the strength of the different multipoles which are included in the magnet. As each of the multipoles is effectively a separate magnet, the current passing through the coils can be fine- tuned individually to give the desired balance between the different multipoles once the magnet is in operation which is not possible with a "hardwired" combined function magnet, and therefore such an arrangement gives greater flexibility in this regard.
The different multipole magnets can be arranged in arbitrary order, but usually it is preferred to position the multipole which produces the highest magnetic field as the innermost magnet. This helps to minimize the air volume the particular magnet has to magnetise.
As has been explained previously, different multipole magnets are used in a particle accelerator to keep the beam of particles within the accelerator. There may be a further requirement that the magnets are arranged for focusing and defocusing. Focusing and defocusing magnets are typically arranged in a lattice along the beam line of a particle accelerator, alternating between focusing and defocusing magnets. The alternate focusing and defocusing magnets converge and diverge the beam of particles in the accelerator respectively and, like an array of optical lenses, help to collimate the beam of particles in the accelerator and confine the particles within the aperture of the magnets. Without both focusing and defocusing magnets present, the particle beam would quickly be lost from the accelerator.
Focusing and defocusing magnets have different magnetic polarities, so either the coils are rotated through 180/n degrees with respect to the accelerator beam line, where n is the multipole order, or the current direction is reversed to change from one type of magnet to the other. In practice focusing and defocusing magnets may differ in their magnetic field strength, depending on the design of the lattice of the accelerator in order to provide the necessary forces on the particle beam.
Therefore the magnet parameters, e.g. number of turns, tilt angle, winding pitch, etc. may differ between focusing and defocusing magnets, or it may be possible to use the same magnet design for both types of magnets but with different currents. As multipole magnets focus in one plane and defocus in the other, the magnets in accordance with the present invention are suitable for use as both focusing and defocusing magnets. Preferably in all aspects of the invention the coils are wound around at least one former. This facilitates production of the coils. In exemplary embodiments the former is as thin as possible whilst retaining sufficient strength to support any pre- stress applied during winding as well as supporting the coil during operation from the Lorentz forces generated when current is passed through the coil.
In one set of embodiments only one former is used, i.e. for the inner coil winding with the outer windings being wrapped around the inner coil. In an alternative set of embodiments a separate former is used for each coil. This affords the advantage that each coil is mounted on a former and therefore this helps to improve the alignment of the path the turns of each coil take. The former supporting the innermost coil will of course typically define the maximum aperture of the particle accelerator.
In some embodiments it is envisaged that pins pushed radially into the former at appropriate positions are used to position the coil turns, but preferably the former comprises a groove to receive the coil turns. Having a groove in the former provides a predefined path on the former for the turns and therefore allows the turns to be accurately positioned on the former in order to produce the required magnetic field as well as giving the turns longitudinal support which is particularly important for the higher order multipoles in which the path of the turns is highly curved in the axial direction. The Applicant has found that using a groove produces a better alignment tolerance for the coil turns and therefore a higher quality magnetic field compared to using pins to locate the turns. Having a groove is particularly advantageous with a multipole with equal or higher order than a quadrupole as the coil turns for these magnets follow a sinusoidal path around the axis of the coil, as opposed to the turns of a coil for a dipole which remain in the same (tilted) plane around axis of the coil.
Possible materials out of which to make the former include aluminium, e.g. AI-6063- T6, an epoxy glass fabric laminate, e.g. 10G/40, or stainless steel, e.g. austenitic steel AISI 316L. All of these materials are non-magnetic and strong which therefore provides a good structure onto which the coil windings can be formed to create an accurate path for the turns, without influencing the magnetic field. In embodiments which have a groove on the former, these materials provide a good basis for machining the groove. These materials are also suitable to be used with a cryogenic cooling system which is used to cool the coil windings to cryogenic temperatures, which is necessary if the magnet is superconducting.
In some embodiments according to all aspects of the invention the axis of the coils is a straight line. The transverse cross-sectional shape of the coils may take a number of different forms, but preferably the cross-sectional shape is a circle or an ellipse. In another set of embodiments the axis of the coils is curved. Again the cross section may also take a number of different forms, e.g. a circle or an ellipse. In some of these embodiments therefore the magnet could be part of a torus. As explained previously a dipole magnet deflects a charged particle travelling through the magnetic field, so sometimes coils in the form of a curved tubes will be advantageous. However when using curved tube coils it is more difficult to produce pure multipole fields, e.g. a when trying to create a dipole, the magnet would often include a small component of a quadrupole. These higher order field components can be compensated by adding a separate multipole coil to create a combined function magnet or by hardwiring extra multipoles into the coil as previously described.
As was mentioned previously, magnets in accordance with the invention could be suitable to be used in medical applications such as for radiotherapy using protons or carbon ions. In one set of embodiments, e.g. suitable for accelerating protons, the coils have a length of between 30 and 80 cm, e.g. between 50 cm and 60 cm, e.g. approximately 55 cm.
As previously explained the radii of the coils differ from one to another. The mean radius is in one set of embodiments however between 5 cm and 40 cm, e.g.
between 10 cm and 30 cm, e.g. between 10 cm and 25 cm or 15 cm and 30 cm.
In a set of embodiments, e.g. suitable for accelerating carbon ions, the coil length is between 80 cm and 150 cm, e.g. between 90 cm and 140 cm, e.g. between 100 cm and 130 cm, e.g. approximately 1 15 cm.
Thus it can be seen that according to all aspects the invention can be implemented by a magnet which is short with a large aperture and is therefore suitable for small radius particle accelerators, e.g. of radius approximately 6 m, where a large aperture is required to conserve a large proportion of the injected particles.
However it will be appreciated that for the embodiments according to the first aspect of the invention in which multipole magnets of different orders are nested within each other, e.g. with a dipole in the centre inside a quadrupole which is in turn inside a sextupole, etc., the radii of the coils will be different for the different multipole coils. This contrasts to the length of the coils which will be relatively similar for all the different order multipoles.
The invention is applicable where the ratio of the coil length to the magnet aperture radius (the "aspect ratio") is less than 15:1. In one set of embodiments, e.g.
suitable for accelerating protons, the ratio is less than 5:1 , e.g. less than 4:1 , and e.g. less than 3:1. This is small compared to the typical corresponding ratio for a known double-helix magnet. In another set of the embodiments suitable for accelerating carbon ions the coils are longer and therefore for example the coil aspect ratio is less than 8:1 , e.g. less than 7:1 , e.g. less than 6:1. For magnets with a small aspect ratio, the end effects of the magnetic field become very important, and thus it can be seen that the present invention gives a magnetic field which is particularly suitable for magnets with these dimensions.
Magnets in accordance with all aspects of the invention could be conventional electromagnets, superconducting or hybrid magnets. Where it is a conventional electromagnet, if cooling is required, the coils may be e.g. cooled by water. In one set of embodiments the wires are made from NbTi superconductor. The copper to superconductor ratio may be as high as 20:1 , but preferably the copper to superconductor ratio is between 1 .2:1 and 2.1 :1 , preferably approximately 1.35:1. Superconducting wires allow high magnetic fields to be reached which are not possible using a conventional electromagnet.
In one set of embodiments the wire used to wind the coils is a single filament wire, e.g. a superconducting NbTi wire with 54 NbTi filaments embedded in a Cu matrix, for example a single filament rectangular wire. In another set of embodiments the wire used to wind the coils is a Rutherford cable (a multi filament wire), e.g. with 5 strands each with a diameter of about 1 mm giving outer dimension of about 3 mm x 2 mm. ln the embodiments in which superconducting wires are used, the coils can be cooled below the critical temperature of the superconductor using a bath cryostat, but many other methods known to those skilled in the art for realising the cryostat could alternatively be used. For a superconductor made of NbTi the critical temperature is approximately 9.4 K.
Preferably the plurality of turns for each coil comprises between 100 and 400 turns, preferably between 200 and 300 turns, preferably between 240 and 260 turns. Providing a large number of turns for a coil helps to provide a high, uniform magnetic field. The number of turns will vary depending on a number of factors including the desired magnetic field, the type of wire used and what sort of particles the accelerator including the magnet is designed to accommodate.
Preferably a combined function magnet made up of four coil magnets in accordance with the first aspect of the present invention is arranged to deliver a peak magnetic field between 1 T and 8 T, e.g. between 2 T and 6 T, e.g. between 4 T and 5 T, e.g. about 4.5 T. As described previously a combined function magnet is a
superposition of a number of different multipoles which each have a different value for their peak magnetic field. Examples of such values for the different multipoles for a lattice of magnetic length 314.4 mm, with the peak fields calculated at a radius of 0.14 m are: 1.95 T for a dipole, 1.65 T for a quadrupole, 0.71 T for a sextupole, and 0.19 T for an octupole. The combined field of all these multipoles in such a combined function magnet varies across the horizontal direction, i.e. x, from 0.8 T to 4.5 T.
A magnet capable of delivering high strength magnetic fields set out above is suitable for inclusion in a small radius particle accelerator, e.g. of radius 6 m where a large magnetic field is needed to bend protons with an energy of approximately 250 MeV. As with many of the other dimensions and values which describe the magnet coil, the peak magnetic field differs between different multipoles and whether the magnet is being used for proton or carbon acceleration.
From a further broad aspect the present invention provides a magnet for a particle accelerator comprising at least four concentric tubular coils, each of said coils comprising a plurality of turns, wherein each of said four coils has a different radius and wherein, apart from their respective radii, the path of the outer coil is the same as the path of the inner coil, and wherein, apart from their respective radii, the paths of the middle coils are a reflection of the path of the inner coil in a plane which bisects the coils normal to their common axis.
Although it is presently considered most convenient that the paths of the turns of the second and third coils are a mirror image of those of the first and fourth coils, as is set out in the above aspect of the invention, this is not necessarily essential. Functionally it is possible to achieve the same effect, i.e. cancelling the solenoid fields created by the coils in opposite directions, by altering the current through the coils and the winding pitch of the coils.
Therefore from another broad aspect the invention provides a magnet for a particle accelerator comprising four concentric tubular coils, each of said coils comprising a plurality of turns, wherein each of said four coils has a different radius and wherein, apart from their respective radii, the path of the outer coil is the same as the path of the inner coil, and wherein, apart from their respective radii, the paths of the middle coils are the same as each other, and wherein the four coils are arranged to produce a magnetic field in which there is substantially no solenoid component of the magnetic field present.
Certain preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings in which:
Fig. 1 shows an arrangement of four coils in accordance with an
embodiment of the invention;
Figs. 2a, 2b and 2c show the structure of the coil turns for a dipole magnet and the resultant magnetic field for two coils with an opposite tilt angle;
Fig. 3 shows the wire of a coil winding being wound onto a former with a groove;
Fig. 4 shows the winding structure for a quadrupole magnet;
Fig. 5 shows a combined function magnet which includes several different concentric multipole magnets; Fig. 6 shows a cross section and the individual multipoles which make up a combined function magnet;
Fig. 7 shows the winding path for one coil of a combined function magnet with varying components of multipoles along the length of the magnet;
Fig. 8 shows a plot of the varying coefficients of the multipole components at a reference radius r 0 along the length of the magnet shown in Fig. 7;
Fig. 9 shows a plot comparing the horizontal magnetic field of a double-helix dipole with that of a four coil magnet in accordance with an embodiment of the invention;
Fig. 10 shows a plot of the quadrupole component of the magnetic field of a quadruple-helix dipole magnet; and
Fig. 1 1 shows a lattice of magnets forming part of a particle accelerator.
Fig. 1 shows an embodiment of the present invention comprising a four coil magnet design which, in this example, generates a magnetic dipole field. The magnet comprises four cylindrical coils 2, 4, 6, 8 which are arranged concentrically within each other. Each coil has a plurality of turns which have been omitted for clarity. These each follow a helical path around the axis 5 of the coil, e.g. like a
conventional solenoid coil, but with the plane of each turn tilted at an angle to the axis 5. A first inner coil 2 has turns which follow a first path. A second coil 4 is concentrically outside the first coil 2 and has turns which follow a second path. The second path is a reflection of the first path in a plane 3 which is normal to the axis 5 of the cylindrical coils. A third coil 6 is concentrically outside the first and second coils 2, 4 and has turns which follow the second path, which is the same as for the second coil 4 (albeit at a marginally greater radius). A fourth coil 8 is concentrically outside the first, second and third coils 2, 4, 6 and has turns which follow the first path, i.e. the same as that followed by the first coil 2. The radius of each coil is slightly different, increasing from the first coil to the fourth coil to allow the coils to nest inside each other concentrically as described. Typically there is a radial gap of 1 mm between each layer of conductor to accommodate a former.
The winding paths of the coils for a four coil dipole magnet are shown in more detail in Figs. 2a, 2b and 2c. As an illustrative example, the first and second coils 2, 4 are shown in Figs. 2a and 2b each mounted on a former 10. Each coil comprises a plurality of turns 12, 14 which are wound round the former, each turn of the winding being in a plane which is at an angle a to the axis of the cylinder. The turns 12 of the first coil 2 are tilted in the opposite direction to the turns 14 of the second coil 4, but both coils tilted at equal angles. For a higher order multipole the coil turns would follow a path described by the general sinusoidal equations described previously.
Only the first two coils are shown for illustrative purposes; when the magnet is fully assembled with all four coils, either a single inner former 10 is used on which to mount the first coil 2 with the second 4, third 6 and fourth 8 coils then mounted on the previous coil respectively to give the arrangement shown in Fig. 1 , or a thin former is provided on which each individual coil is mounted.
Again for illustrative purposes, the first two coils are shown in Fig. 2c on the same former 10, with the second coil 4 arranged concentrically outside the first coil 2, as the coils would be arranged in the four coil dipole magnet, i.e. as shown in Fig. 1. The paths the coils follow is a mirror image of each other about a plane 3 which bisects the coils and is normal to the axis 5 of the coils.
To create the arrangement of the four coil dipole magnet a third coil would be wound concentrically outside of the second coil 4, with the turns of the third coil following the same path as the second coil 4. A fourth coil would be then wound concentrically outside of the third coil, with the turns of the fourth coil following the same path as the first coil 2.
Fig. 3 shows a wire 30 being wound onto a former 10. The former 10 includes a groove 32 which has been cut into the former. The groove 32 defines the path that the coil winding takes. To form the coil winding the wire 30 is placed in the groove and wrapped around the former 10 so that the wire 30 follows the path of the groove 32 thus forming a coil winding with the desired path. As the wire is being wound round the former, a tension is applied to the wire in order to keep the wire in the groove. After winding the coil it is usually impregnated with epoxy resin to keep the wire in place and to aid electrical insulation. Alternatively a pre-impregnated fibre cloth can be used. The wire 30 can either be a single filament wire such as a rectangular 54 filament wire with a copper to superconductor ratio of 1.3:1 (obtained from Oxford
Instruments Superconducting Technology, 600 Milik Street, PO Box 429, Carteret, NJ, 07008, USA), or a Rutherford cable which comprises a number of individual strands. With either the single filament wire or the Rutherford cable, the wire 30 is usually insulated before being wound onto the former 10.
To produce the former 10, a groove 32 is milled into either an aluminium former or into a layer of epoxy glass fabric laminate which is embedded in a steel or aluminium tube. Although the latter approach is more labour intensive, the epoxy glass fabric laminate provides insulation between the wire and the former in case the insulation on the wire 30 is damaged. Typically the former 10 has a radial thickness of 1 mm and the distance of the wall 34 between adjacent turns is 0.5 mm.
The operation of the four coil dipole magnet shown in Figs. 1 and 2 will now be described. A current J is passed through the turns 12, 14 of the coils 2,4, the current being of equal magnitude for both coils, and indeed the same magnitude for all four of the coils. The current is passed in one direction (e.g. left to right in Fig. 2a) for the first coil 2 and in the opposite direction (right to left in Fig. 2b) for the second coil 4. The current in the third coil is passed through the turns of the coil in the same direction as the current for the second coil, and the current in the first coil is passed through the turns of the coil in the same direction as the current for the fourth coil.
Passing these currents through the coils results in a net overall magnetic field B in each coil as shown in Figs 2a and 2b. Owing to the tilt of the turns, the magnetic field from each coil has one component B s along the axis of the cylinder which is equivalent to a solenoid field, and another component B d perpendicular to the axis which is equivalent to a dipole field. The solenoid fields created in the two oppositely tilted coils are in opposite directions and therefore cancel, and the dipole fields are in the same direction and therefore add. This results in just a dipole field (B = 2B d ) as shown when the two coils are on the same former 10 as shown in Fig. 2c. However, as has been explained previously, especially when short coils with a large aperture are used, the magnetic fields at the ends of the coil resulting from having two concentric coils with slightly different radii mean that the solenoid fields, B s , do not exactly cancel and so the magnetic field is perturbed by the solenoid field which leads to contributions to the horizontal and/or vertical magnetic field. Providing four coils in the arrangement shown in Fig. 1 gives better cancellation of the solenoid field resulting in smaller local deviations in the dipole field at the ends of the magnet.
Fig. 4 shows two differently rotated views of the winding structure for the coils 22, 24 of a four coil quadrupole magnet. For clarity, only a few turns of the coils are shown, in practice there are many more than this. It can be seen that the turns of the coils follow the paths in the z-direction (the direction along the axis of the coil) of ζ(θ) = Ιιθ/2π + R sin(20)/tan(a) for one coil 22 and ζ(θ) = - Ιιθ/2π- R sin(20)/tan(-a) for the other coil 24, where the terms have previously been defined. This gives a sinusoidal variation of the turns around the coil which have a period of π, with one coil having turns in anti-phase to the other, i.e. the second path is a reflection of the first path in a plane 3 which is normal to the axis 5 of the cylindrical coils, as for the dipole magnet.
Only two coils are shown for clarity, but the magnet is provided with four coils as previously described, the first coil being the innermost, with the second, third and fourth coils being arranged respectively concentrically outside of each other. The turns of the first and fourth coils follow a first path and the turns of the second and third coils follow a second path with the opposite sinusoidal term, i.e. a reflection of the first path in the plane which bisects the coils and is normal to the axis of the coils.
In operation the quadrupole magnet shown in Fig. 4 functions in the same manner as the dipole magnet. Current is passed through the first and fourth coils in one direction and the second and third coils in the opposite direction. This has the same effect as for the dipole magnet in that the solenoid fields cancel, but this time, the quadrupole fields add to give, overall, a quadrupole magnetic field which has very small local deviations from the ideal field at the ends of the magnet. Fig. 5 shows a combined function magnet 47 which has a number of different multipoles nested concentrically, each of them comprising four concentric coils. Innermost is a four coil dipole magnet 40, then a quadrupole 42, then a sextupole 44, and outermost an octupole 46. As described previously different multipoles have different bending and focusing capabilities and in a particle accelerator it is sometimes necessary to have magnets which have a combined function of more than one multipole. The combined function magnet 47 shown has been designed to provide all the functions of the different multipoles in one magnet. The parameters of each individual magnet are chosen, along with the magnitude of the current passed through the coils during operation, to provide the desired effect, i.e. forces acting on the particle beam passing through the magnet, from each of the component multipole magnets.
Fig. 6 shows a cross section of the combined function magnet 47 shown in Fig. 5. The individual multipoles (dipole 40, quadrupole 42, sextupole 44 and octupole 46) which are nested concentrically can each be seen to have four layers, each layer representing one coil of the multipole. The individual multipoles are also shown separately from which the different sinusoidal paths of the coil windings can be seen.
Fig. 7 shows the winding path for one coil 70 of a combined function magnet with respective different multipole components varying along the length of the magnet. The vertical axis 72 denotes the distance along the coil and the horizontal axis 74 denotes the circumferential distance around the coil (i.e. the coil has been
"unrolled"). To produce the combined function magnet in such a way as to minimise the solenoidal field another coil would be provided to produce a double helix magnet as has been previously discussed. Providing another coil acts to add to the multipole field generated by the first coil 70 and minimise the solenoid field, i.e. the multipole field of the second coil is arranged to be in the same direction and the solenoid field in the opposite direction. Alternatively three more coils can be added to form a four coil magnet with the inner and the outer coils following the same path and the middle coils following the same path as previously described.
The lower part 76 of the coil has a plurality of turns which are of the form sin(9) and therefore produces a dipole magnetic field. The upper part 78 of the coil has a plurality of turns which are of the form sin(29) and therefore produces a quadrupole magnetic field. The middle part 80 of the coil has five turns which form a transition region to connect the lower part 76 of the coil with the upper part 78 of the coil. The function of path of the windings in the transition region 80 is a linear function of the two coefficients for each of the dipole and the quadrupole windings. E.g. the lower part 76 of the coil has turns which follow the path A 1 sin(9) and the upper part 78 of the coil has turns which follow the path A 2 sin(29) therefore giving the transition region 80 turns which follow the path A 1 sin(9) + A 2 sin(29) with the values of A 1 and A 2 being varied in a linear manner across the transition region 80 so that they match the values of A 1 and A 2 either side.
To produce a double helix or four coil magnet that generates a dipole field at one end and a quadrupole at the other end, as shown in Fig. 7 requires the addition of at least one or three more coils. For the simpler case of the double helix magnet, the other coil needs to have windings which, as well as reversing the path in x and y (as indicated in previous equations), follow a path in z of -A f Sin(9) in the lower part of the coil, -A 2 sin(29) in the upper part of the coil, and -A f Sin(9) - A 2 sin(29) in the transition region between the lower and upper parts so that these different parts of the coil complement the coil shown in Fig. 7 to minimise the solenoid field of the magnet, i.e. the values of A 1 and A 2 are the same for the two coils at all points along the length of the coils, even though these values vary along the length of the magnet.
Fig. 8 shows a plot of the coefficients of the multipole components of a combined function magnet which includes a coil as shown in Fig. 7, i.e. comprising both dipole and quadrupole components. The vertical axis 82 denotes the value of the multipole coefficients at a reference radius r 0 and the horizontal axis 84 denotes the distance along the coil. Starting from the bottom of the coil (as viewed in Fig. 7) and from the left hand side of the plot in Fig. 8, the magnitude of the dipole coefficient 86 increases rapidly to a constant value, corresponding to the lower part 76 of the coil in Fig. 7. Travelling upwards through the magnet, the transition region 80 in Fig. 7 is encountered and here the coefficients undergo a transition 90 in which the dipole coefficient 86 is reduced to zero to the quadrupole coefficient 88 is increased from zero. The linear nature of the transition region 80 creates a smooth transition 90 between the dipole coefficient 86 being reduced to zero and the quadrupole coefficient 88 (corresponding to the upper part 78 of the coil in Fig. 7) increasing to a constant value where it remains until the end of the magnet.
As described previously the four coil magnets described above are suitable for use in a particle accelerator which is used for medical applications, e.g. proton and carbon ion therapy. Table 1 shows typical design specification values for different parameters of a dipole, quadrupole, sextupole and octupole coils for four coil magnets suitable to be used in a proton accelerator.
Table 1 : Proton accelerator coil specification values using a single filament wire. The equivalent vertical magnetic field is calculated for the magnetic length of the lattice, which is 314.4 mm.
Table 2 shows typical design specification values for different parameters of a dipole, quadrupole, sextupole and octupole coils for four coil magnets suitable to be used in a carbon ion accelerator.
Dipole Quadrupole Sextupole Octupole
Inner radius 170 mm 215 mm 240 mm 255 mm
Outer radius 210 mm 235 mm 250 mm 265 mm
Length 1 150 mm 1 160 mm 1 180 mm 1 160 mm
Tilt angle 60 65 degrees 65 65
degrees degrees degrees
Equivalent vertical magnetic 2.62 T 1.76 T 0.60 T 0.13 T field at x = 150 mm, y = 0 mm Table 2: Carbon ion accelerator coil specification values. The equivalent vertical magnetic field is calculated for the magnetic length of the lattice, which is 633 mm.
Fig. 9 shows a plot of the horizontal magnetic field for both a double-helix magnet 60 and a four coil magnet 62. The component of the magnetic field in the horizontal direction is zero for a pure dipole field, so any deviation from this is unwanted. The deviations shown in the plot arise from the non-cancellation of the solenoid field. It can be seen that there is a reduction by a factor of about 10 in the deviations in the horizontal magnetic field when using a four coil magnet in accordance with the invention compared to the double-helix magnet. The magnitude of the local deviations in the magnetic field obtained when using a four coil dipole magnet in accordance with the invention can therefore be significantly reduced in comparison to a double-helix magnet.
Fig. 10 shows a plot of the normalised quadrupole component of a quadruple helix dipole magnet, as a function of the length of a magnet in accordance with the invention. The plot shows the quadrupole components 92, 94 for both of the double helix magnets in the quadruple helix magnet, i.e. the double helix magnet which comprises the inner and outer coils and the double helix magnet which comprises the two middle coils. This shows that there is often a residual component of higher order multipoles in a lower order multipole magnet, and in this magnet the quadrupole components are significant towards the ends of the magnet. However, in a quadruple helix magnet in accordance with the present invention, these quadrupole components 92, 94 arising from each of the nested double helix magnets cancel, leaving a quadrupole component 96 which is zero along the length of the quadruple helix magnet.
Fig. 1 1 schematically shows a typical lattice of magnets arranged around the beam line 54 of a particle accelerator in accordance with the invention. The magnets are alternatively focusing 50 and defocusing 52 magnets. In operation the lattice of alternate focusing 50 and defocusing 52 magnets acts on the beam of particles passing through the lattice to converge and diverge the beam in order to keep the beam collimated within the aperture of the magnets. It will be appreciated by those skilled in the art that many variations and modifications to the embodiments described above may be made within the scope of the various aspects of the invention set out herein. For example more than four coils could be employed even to produce a single magnet of given order. Also it is not essential for the oppositely-directed coils to have similar paths, their pitch and currents could be manipulated instead to give a similar result.