GB2533334A

GB2533334A - Improved magnet

Info

Publication number: GB2533334A
Application number: GB1422397.8A
Authority: GB
Inventors: Marks Neil
Original assignee: Science and Technology Facilities Council
Current assignee: Science and Technology Facilities Council
Priority date: 2014-12-16
Filing date: 2014-12-16
Publication date: 2016-06-22
Anticipated expiration: 2034-12-16
Also published as: GB2533334B

Abstract

An electromagnet for steering a beam of charged particles comprising a ferromagnetic frame and a plurality of electrically conducting coils wound upon the frame for producing a magnetic field in and around the frame 112. The frame includes a plurality of limbs 114 connected at vertices 116 and arranged in a closed shape around a beam line space centred on a longitudinal axis 111; each limb extends along a limb axis joining adjacent vertices 116. The coils are wound onto each of the limbs to form a plurality of windings 130 that define an inner profile around the beam line space. The inner frame profile may be defined in part by portions of the limbs, wherein a first limb portion extends away from the limb axis towards the longitudinal axis and a second limb portion extends towards the limb axis and away from the longitudinal axis. The windings 130 may also include bevelled portions adjacent to the ends of the limbs. The ferromagnetic frame may comprise steel and it may possess four limbs.

Description

Improved Magnet [0001] This invention relates to an improved magnet, and, in particular, to an electromagnet that is particularly suitable for use as a corrector magnet in a particle accelerator.

BACKGROUND

[0002] In a circular particle accelerator, the usual means for deflecting charged particles around the accelerator comprise multiple "bending magnets" positioned along the beam pipe. A bending magnet is typically an electromagnet having a dipole configuration and, in circular particle accelerators, the dipole bending magnet is typically arranged so that one pole is disposed above the beam pipe (through which particles travel) and one pole is disposed below the beam pipe. Such an arrangement generates a vertical magnetic flux density across the beam pipe and has the effect of deflecting the path of a charged particle passing therethrough. To fulfill their required role, bending magnets are necessarily strong, typically producing a magnetic field strength of the order of 1.0 to 1.8 Tesla for a room temperature (i.e. non-superconducting) magnet. Additionally, bending magnets are required to produce a highly homogenous magnetic flux density across the beam pipe. In many applications, homogeneity of 1:104 is typically required. For electromagnet bending magnets, current carrying coils are wound on the dipoles to create the necessary magnetic flux density across the beam pipe.

These current carrying coils are usually arranged electrically in series, thereby ensuring a high degree of uniformity between multiple bending magnets [0003] In addition to dipole bending magnets, it is necessary to use weaker magnets, known as "corrector" or "steerer" magnets, to adjust the position of the beam around the complete circumference of the accelerator. Corrector magnets are needed for several reasons including variations in the Earth's magnetic field along the beam pipe, stray magnetic fields produced by local electrical cables and equipment, and the variance of the multiple main bending magnets. Additionally, certain experimental setups require the beam orbit to be positioned at specific locations within the beam pipe and so require "correcting". Corrector magnets are typically required to adjust the beam position to a precision of 0.1 mm or less. As the corrector magnets are required only to make small adjustments to the beam of charged particles, they are typically orders of magnitude weaker than the main bending magnets. The actual required magnitude of the corrector magnets is strongly dependent on many parameters, but, in a circular particle accelerator using room-temperature magnets, the required strength of the corrector magnets would seldom exceed a few percent of the strength of the main bending magnets. Additionally, since the size of the corrector magnets is often much less than that of the main bending magnets, the corrector magnets often provide much less than 1% of the bend of the bending magnets.

[0004] Since corrector magnets are much weaker than the main bending magnets, it is less critical for the corrector magnets to produce highly homogenous fields. Nevertheless, given that the purpose of corrector magnets is to correct field errors, it would be futile to adopt a design that significantly adds to beam disturbance. For corrector magnets, field homogeneity of around 1:102 is usually satisfactory, and anything that is significantly worse than this would likely be regarded as inadequate.

[0005] In order for the beam position to be fine-tuned around the entire circumference of the accelerator, it is necessary for the corrector magnets to be independently powered and controlled and produce magnetic flux density in both horizontal and vertical planes. Depending on the criticality of the available space in the magnet lattice, the horizontal and vertical correctors may be separate devices or the required functions may be combined into the same single magnet. In a corrector magnet capable of producing magnetic flux density in both horizontal and vertical directions, it is necessary to separately control the magnitude of horizontal magnetic flux density relative to the magnitude of vertical magnetic flux density.

[0006] Figure 1 shows a cross-sectional view of an example of a known electromagnet 10 used as a corrector magnet in particle accelerators. The electromagnet 10 of Figure 1 adopts a so-called "window frame" configuration and includes a square frame 12 that surrounds a central beam line space that is centered on a longitudinal axis 11 (which is perpendicular to the page).

Typically, a beam pipe comprising a vacuum tube passes through the beam line space and provides a conduit for travelling charged particles.

[0007] The frame 12 is made up of four limbs 14a,14b,14c,14d upon each of which is wound an electrically conducting coil that forms a winding 30a,30b,30c,30d. The limbs 14a,14b,14c,14d define an inner frame profile 24 that has a square shape centered on the longitudinal axis 11 and surrounding the beam line space. Similarly, the windings 30a,30b,30c,30d define an inner winding profile 32 that has a square shape centered on the longitudinal axis 11 and surrounding the beam line space. The limbs 14a,14b,14c,14d are substantially identical to one another. Similarly, the windings 30a,30b,30c,30d are substantially identical to one another. Each winding 30a,30b,30c,30d is bevelled at its ends (at a 45° angle) to accommodate the adjacent windings 30a,30b,30c,30d inside the frame 12.

[0008] The magnet 10 of Figure 1 is capable of producing magnetic flux in both horizontal (i.e. parallel to the x-axis indicated) and vertical (i.e. parallel to the y-axis indicated) directions, where bottom and top windings 30a,30c produce magnetic flux in a horizontal direction (i.e. parallel to bottom and top limbs 14a,14c) across the beam line space and left and right windings 30d,30b produce magnetic flux in a vertical direction (i.e. parallel to left and right limbs 14d,14b) across the beam line space.

[0009] Figure 2 shows the fractional variation in vertical flux density distribution along the x-axis (i.e. {B(x)-B(0)}/B(0))across the beam line space defined between the windings 30a,30b,30c,30d for the magnet of Figure 1. The data of Figure 2 assumes that the windings 30a,30b,30c,30d define a square aperture of ±26 mm relative to the longitudinal axis (i.e. 52 mm in total), where x=0 and y=0 at the longitudinal axis 11. As Figure 2 shows, there is a variation of 7% across the aperture. Acceptable flux density (for a corrector magnet) is only produced across 14 mm of the aperture in comparison to 52 mm of other known corrector magnets that serve to only correct in a single direction (i.e. horizontal or vertical, but not both).

It is therefore clear that in attempting to incorporate both horizontal and vertical steering capability into the same magnet, prior art arrangements are unable to produce acceptably homogenous magnetic flux density over a large extent of the aperture in a magnet of reasonable size and cost. Indeed, it may be possible to produce the required flux density quality using the arrangement of Figure 1, however, such a magnet would need to be much larger (in order to increase the aperture size) thereby increasing capital and running costs.

[0010] There therefore exists a need for an improved magnet that may produce magnetic flux in both horizontal and vertical directions and produce improved homogeneity of magnetic flux density over a larger extent of the aperture of the magnet.

[0011] It is an object of certain embodiments of the present invention to provide a magnet that overcomes one or more disadvantages associated with the prior art.

BRIEF SUMMARY OF THE DISCLOSURE

[0012] In accordance with a first aspect of the present invention there is provided an electromagnet for steering a beam of charged particles, the electromagnet comprising a ferromagnetic frame and a plurality of electrically conducting coils wound upon the frame for producing a magnetic field in and around the frame, where the frame includes a plurality of limbs connected at vertices and arranged in a closed shape around a beam line space centred on a longitudinal axis, each limb extends along a limb axis from a first end to a second end defined by an adjacent pair of the vertices, and the limbs define an inner frame profile around the beam line space and the inner frame profile defined by each limb is not parallel to the respective limb axis of the limb; and wherein the coils are wound onto each of the limbs to form a plurality of windings that define an inner winding profile around the beam line space, and the inner winding profile defined by each winding is not parallel to the respective limb axis of the limb on which the winding is 35 disposed.

[0013] The inner frame profile may be at least in part defined by a first limb portion and a second limb portion of each limb, where each first limb portion increasingly extends away from the respective limb axis and towards the longitudinal axis along a direction from the first end towards the second end, and each second limb portion increasingly extends towards the respective limb axis and away from the longitudinal axis along a direction from the first end towards the second end. For each limb, the first limb portion and the second limb portion may meet at a point that is perpendicular to the middle point of the respective limb axis. For each limb the first limb portion may be disposed between the first end and the second limb portion.

For each limb each of the first limb portion and second limb portion may be curved relative to the respective limb axis.

[0014] Optionally, the inner winding profile may be at least in part defined by a first winding portion and a second winding portion of each winding, where each first winding portion increasingly extends towards the respective limb axis along a direction from the first end towards the second end, and each second winding portion increasingly extends away from the respective limb axis along a direction from the first end towards the second end. For each winding the first winding portion and the second winding portion may meet at a point that is perpendicular to the middle point of the respective limb axis. For each winding the first winding portion may be disposed between the first end and the second winding portion. For each winding each of the first winding portion and second winding portion may be curved relative to the respective limb axis.

[0015] Each winding may include a first bevelled portion adjacent the first end of the respective limb and a second bevelled portion adjacent the second end of the respective limb. Each of the first bevelled portions and second bevelled portions may have an angle of inclination relative to the respective limb axis of substantially (360/2N)°, where N in the total number of limbs. The first winding portion and second winding portion may each be disposed between the first bevelled portion and the second bevelled portion.

[0016] The ferromagnetic frame may have a magnetic permeability of at least lOpo, preferably at least 100po, or preferably at least 1000po, where po is the permeability of free space.

[0017] The ferromagnetic frame may comprise steel.

[0018] The electromagnet may comprises four limbs. In alternative embodiments, any suitable number of limbs forming a closed shape around a beam line space centred on a longitudinal axis may be present.

[0019] In accordance with a second aspect of the present invention, there is provided a particle accelerator including one or more electromagnets according to any preceding claim.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Embodiments of the invention are further described hereinafter with reference to the accompanying drawings, in which: Figure 1 is a cross-sectional view of an example of a prior art corrector magnet; Figure 2 is a plot of fractional variation in vertical flux density distribution across the aperture of the magnet of Figure 1 along the x-axis; Figure 3 shows a cross-sectional view of a magnet according to an embodiment of the present invention; Figure 4 is a detailed view of a selected part of the magnet of Figure 3; Figure 5 is a plot of fractional variation in vertical flux density distribution across the aperture of the magnet of Figure 3 along the x-axis; and Figure 6 is a detailed plot of fractional variation in vertical flux density distribution across a portion of the aperture of the magnet of Figure 3 along the x-axis.

DETAILED DESCRIPTION

[0021] Figure 3 shows a cross-sectional view of an electromagnet 110 in accordance with an embodiment of the present invention. The electromagnet 110 of Figure 3 includes a frame 112 that surrounds a central beam line space that is centered on a longitudinal axis 111. The cross-sectional view is across an x-y plane where the x-and y-axes are indicated on Figure 3. The longitudinal axis 111 is perpendicular to the x-y plane and intersects the x-y plane at x=0, y=0.

[0022] The frame 112 is made up of four limbs 114a,114b,114c,114d upon each of which is wound an electrically conducting coil that forms a winding 130a,130b,130c,130d. The frame 112 is made of a ferromagnetic material, and may comprise steel, for example. In alternative embodiments, other materials may be used. In particular, other highly magnetically permeable materials may be used, and may, for example, have a magnetic permeability of at least 10p0, preferably at least 100po, or further preferably at least 1000po, where po is the permeability of free space (1.25663706 x 10-6 m kg S-2 A-2).

[0023] The limbs 114a,114b,114c,114b are substantially identical to one another and are connected to one another at vertices 116 to form a closed shape around the beam line space and each define a part 124a,124b,124c,124d of an inner frame profile 124 around the beam line space. Similarly, the windings 130a,130b,130c,130d are substantially identical to one another and each define a part 132a,132b,132c,132d of an inner winding profile 132 around the beam line space. The features of each limb 114a,114b,114c,114d and each winding 130a,130b,130c,130d may therefore be understood from the following description of a single limb 114a and single winding 130a with reference to Figure 4.

[0024] Figure 4 shows part of the magnet 110 of Figure 3 that includes a single limb 114a and single winding 130a. The limb 114a extends along a limb axis 118a from a first end 120a coincident with one of the vertices 116 to a second end 121a coincident with an adjacent vertex 116. The part 124a of the inner frame profile 124 is defined by a first limb portion 126a and a second limb portion 128a of each limb 114a, where the first limb portion 126a increasingly extends away from the limb axis 118a and towards the longitudinal axis 111 along a direction from the first end 120a towards the second end 121a, and each second limb portion 128a increasingly extends towards the limb axis 118a and away from the longitudinal axis 111 along a direction from the first end 120a towards the second end 121a. In particular, in the embodiment shown in Figures 3 and 4, the first limb portion 126a and the second limb portion 128a meet at a point that is perpendicular to the middle point of the limb axis 118a.

Additionally, the first limb portion 126a is axially disposed between the first end 120a and the second limb portion 128a. In alternative embodiments, other arrangements are possible in which the inner frame profile 124 defined by each limb 114a,114b,114c,114d is not parallel to the respective limb axis 118a,118b,118c,118d of the limb 114a,114b,114c,114d but does not necessarily correspond to the precise shape shown in Figures 3 and 4. Returning to the specific non-limiting embodiment shown in Figures 3 and 4, each of the first limb portion 126a and second limb portion 128a is curved relative to the limb axis 118a. In other embodiments within the scope of the present invention, non-curved arrangements are possible.

[0025] The part 132a of the inner winding profile 132 is defined by a first winding portion 134a and a second winding portion 136a, where the first winding portion 134a increasingly extends towards the limb axis 118a along a direction from the first end 120a towards the second end 121a, and the second winding portion 136a increasingly extends away from the limb axis 118a along a direction from the first end 120a towards the second end 121a.

[0026] In particular, in the embodiment shown in Figures 3 and 4, the first winding portion 134a and the second winding portion 136a meet at a point that is perpendicular to the middle point of the limb axis 118a. In alternative embodiments, other arrangements are possible in which the inner winding profile 132 defined by each winding 130a,130b,130c,130d is not parallel to the respective limb axis 118a,118b,118c,118d of the limb 114a,114b,114c,114d but does not necessarily correspond to the precise shape shown in Figures 3 and 4. Returning to the specific non-limiting embodiment shown in Figures 3 and 4, the first winding portion 134a is wound around the limb axis 114a between the first end 120a and the second winding portion 136a. The first winding portion 134a and/or second winding portion 136a may be, but are not necessarily, curved relative to the limb axis 118a. The limb axes 118a,118b,118c,118d collectively define a polygon surrounding the beam line space.

[0027] In order to maximize the extent of the windings 130a,130b,130c,130d around the beam line space whilst ensuring that each winding 130a,130b,130c,130d is substantially identical to each another, the windings each have bevelled portions to accommodate adjacent windings within the frame 112. Considering the winding 130a, a first bevelled portion 138a is adjacent to the first end 120a of the limb 114a and a second bevelled portion 140a is adjacent to the second end 121a of the limb 114a with the first winding portion 134a and second winding portion 136a being axially disposed between the first bevelled portion 138a and the second bevelled portion 140a. The windings 130a,130b,130c,130d may be arranged within the frame 112 such that the first bevelled portion of one winding is adjacent to and arranged closely to the second bevelled portion of an adjacent winding. In the case of a frame 112 made of four limbs, each winding is arranged orthogonally relative to adjacent windings. As such, the angle of the first and second bevelled portions relative to the respective limb axis is 45°. In alternative embodiments of the invention, the frame 112 may be made of other numbers of limbs forming a closed shape. For a frame 112 made of N limbs, the angle (in degrees) of the first and second bevelled portions of each limb relative to the respective limb axis may be equal to or about 360/2N. In any embodiment, the frame 112 may be integrally formed or may be assembled from multiple parts. For example, each limb may be separately formed and subsequently assembled together to form the frame 112.

[0028] In one particularly preferable embodiment, the part 132a of the inner winding profile 132 may be the inverse shape of the part 124a of the inner frame profile 124. That is, along a direction parallel to the limb axis 118a, the part 132a of the inner winding profile 132 may increasingly extend towards the limb axis 118a by the same amount that the part 124a of the inner frame profile 124 increasingly extends away from the limb axis 118a. Similarly, along a direction parallel to the limb axis 118a, the part 132a of the inner winding profile 132 may increasingly extend away from the limb axis 118a by the same amount that the part 124a of the inner frame profile 124 increasingly extends towards the limb axis 118a. In the same or an alternative embodiment, the inner winding profile 132 may have any shape provided that it is not parallel to the inner frame profile 124 and the limb axis 118a.

[0029] In certain embodiments, the part 132a of the inner winding profile 132 may be configured to, at least in part, compensate for current lost as a consequence of the bevelled portions 138a,140a that are used to facilitate multiple windings in inhabiting a restricted space within the frame 112.

[0030] In certain embodiments, such as the one illustrated in Figure 3, the winding 130a may narrow at its centre. Amongst other advantages, adopting this inner winding profile 132 increases the aperture between the windings 130a,130b,130c,130d on the major x-and y-axes at the centre of the magnet (i.e. through the longitudinal axis 111). Such a profile may also permit space savings if the inner winding profile 132 corresponds to the outer profile of a vacuum tube in the beam line space.

[0031] The skilled reader will appreciate that whilst the winding 130a is illustrated in the Figures as a solid component, in reality, the winding 130a is made of a continuous winding of electrically conducting coils. The solid component shown in the figures is therefore representative of the cross-sectional profile defined collectively by the wound coil. The "thickness" of the winding 130a (i.e. the extent of the winding in directions orthogonal to the limb axis 118a) is determined by how many times the coil is stacked upon itself through multiple windings around the limb 114a.

[0032] Given that the winding 130a is made of electrically conducting coils wound upon the limb 114a about the limb axis 118a, the winding 130a inherently defines an outer winding profile 142a radially outward of the frame 112 relative to the longitudinal axis 111. The precise form of the outer winding profile 142a may not be considered to be critical to contributing to the advantageous effects of the present invention. Nevertheless, the outer winding profile will be, at least in part, determined by the form of the inner winding profile 132a given that the winding 130a is formed by continuous coils.

[0033] In use, each of the windings 130a,130b,130c,130d may be individually energized (i.e. dc or ac electric current may be passed therethrough) so as to generate magnetic flux in and around the frame 112. The electromagnet 110 is configured such that the magnetic flux passes across the beam line space and can therefore deflect charged particles passing therethrough with a velocity component that is parallel to the longitudinal axis 111. In particular, the windings 130b,130d on limbs 114b,114d generate vertical magnetic flux in the beam line space (i.e. substantially parallel to the y-axis). Similarly, the windings 130a,130c on limbs 114a,114c generate horizontal flux in the beam line space (i.e. substantially parallel to the x-axis).

[0034] Figure 5 shows the fractional variation in vertical flux density distribution along the x-axis across the beam line space defined between the windings 130a,130b,130c,130d for the magnet of Figure 3. The data of Figure 5 assumes that the windings 130a,130b,130c,130d define an aperture in the x-y plane of ±26 mm relative to the longitudinal axis (i.e. 52 mm in total), where x=0 and y=0 at the longitudinal axis 111. Figure 6 provides further detail across a ±16 mm portion of the aperture defined between the windings 130a,130b,130c,130d.

[0035] A comparison of Figure 5 with Figure 2 demonstrates the advantages associated with magnets according to embodiments of the present invention. Table 1 below provides a tabulated comparison of the data sets of Figure 2 and 5.

Aperture (mm) Homogeneity of magnetic flux Homogeneity of magnetic flux density of density of magnet of Figure 1 (prior magnet of Figure 3 (according to an art) embodiment of the present invention) ±26.0 ±0.035 (±3.5%) ±0.01 (±1%) ±21.0 ±0.025 (±2.5%) ±3 x 10- (±0.3%) ±16.0 ±0.015 (±1.5%) ±4 x 10-4 (±0.04%)

Table 1

[0036] The magnet according to an embodiment of the present invention and shown schematically in Figure 3 provides a much greater region of better quality magnetic flux density than the prior art arrangement shown in Figure 1. In particular, considering a required homogeneity of ±1%, the magnet of Figure 3 is able to satisfy this requirement across ±26 mm.

In contrast, the magnet of Figure 1 satisfies this requirement over ±13.5 mm only. If the magnet of Figure 1 was scaled up to produce a homogeneity of ±1% across ±26 mm, the resulting magnet would need to be 1.9 times the size of the magnet of Figure 3. As a further example, the magnet of Figure 3 is able to provide a required homogeneity of ±0.2% across ±19 mm. The magnet of Figure 1 satisfies the same requirement over ±6 mm only. If the magnet of Figure 1 was scaled up to produce a homogeneity of ±0.2% over ±19 mm, the resulting magnet would need to be over 3 times the size of the magnet of Figure 3.

[0037] Therefore, embodiments of the present invention provide magnets in which the inner frame profile and inner winding profile are such that significantly better homogeneity of magnetic flux density can be achieved without significantly increasing the overall dimensions of the magnet. As such, the present invention facilitates good quality magnets that are capable of providing the ability to steer a beam of charged particles in two orthogonal directions and that may be produced and operated at reasonable costs, in comparison to prior art magnets. In certain embodiments, the precise form of the inner frame profile and inner winding profile may be optimized by use of finite element software to achieve a desired homogeneity.

[0038] Whilst the magnet of Figure 3 shows an exemplary embodiment of the present invention, other configurations of inner frame profile and inner winding profile may be adopted within the scope of the present invention. Additionally, within the scope of the present invention, the magnet may include a number of limbs other than four. For example, embodiments of the present invention may include higher order magnets, e.g. quadrupole or sextupole. Additionally or alternatively, the limbs may not all be of equal length to one another. In particular, embodiments of the present invention may relate to a magnet having a non-square rectangular frame, e.g. where the horizontal width is greater than the vertical height. Such an arrangement may be advantageous in an accelerator where vertical height is restricted relative to the horizontal space on either side of the beam line.For the avoidance of doubt, the above description relating to limb 114a and winding 130a may be equally applied to the remaining limbs 114b,114c,114d and windings 130b,130c,130d of the magnet 110 whether in respect of the specific magnet of Figure 3 or other magnets in accordance with embodiments of the present invention.

[0039] Throughout the present application, data relating to variations in flux density is derived from OPERA 2D, which is a two dimensional, non-linear, finite element, electro-magnetic modeling code produced by Cobham Vector Fields of Network House, Langford Locks, Kidlington, Oxfordshire, OX5 1GA, UK.

[0040] Throughout the description and claims of this specification, the words "comprise" and "contain" and variations of them mean "including but not limited to", and they are not intended to (and do not) exclude other moieties, additives, components, integers or steps. Throughout the description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular, where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise.

[0041] Features, integers, characteristics, compounds, chemical moieties or groups described in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

[0042] The readers attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference.

Claims

CLAIMS1. An electromagnet for steering a beam of charged particles, the electromagnet comprising a ferromagnetic frame and a plurality of electrically conducting coils wound upon the frame for producing a magnetic field in and around the frame, where the frame includes a plurality of limbs connected at vertices and arranged in a closed shape around a beam line space centred on a longitudinal axis, each limb extends along a limb axis from a first end to a second end defined by an adjacent pair of the vertices, and the limbs define an inner frame profile around the beam line space and the inner frame profile defined by each limb is not parallel to the respective limb axis of the limb; and wherein the coils are wound onto each of the limbs to form a plurality of windings that define an inner winding profile around the beam line space, and the inner winding profile defined by each winding is not parallel to the respective limb axis of the limb on which the winding is disposed.
2. An electromagnet according to claim 1, wherein the inner frame profile is at least in part defined by a first limb portion and a second limb portion of each limb, where each first limb portion increasingly extends away from the respective limb axis and towards the longitudinal axis along a direction from the first end towards the second end, and each second limb portion increasingly extends towards the respective limb axis and away from the longitudinal axis along a direction from the first end towards the second end.
3. An electromagnet according to claim 2, wherein for each limb the first limb portion and the second limb portion meet at a point that is perpendicular to the middle point of the respective limb axis.
4. An electromagnet according to claim 2 or 3, wherein for each limb the first limb portion is disposed between the first end and the second limb portion. 30
5. An electromagnet according to any of claims 2 to 4, wherein for each limb each of the first limb portion and second limb portion is curved relative to the respective limb axis.
6. An electromagnet according to any preceding claim, wherein the inner winding profile is at least in part defined by a first winding portion and a second winding portion of each winding, where each first winding portion increasingly extends towards the respective limb axis along a direction from the first end towards the second end, and each second winding portion increasingly extends away from the respective limb axis along a direction from the first end towards the second end.
7. An electromagnet according to claim 6, wherein for each winding the first winding portion and the second winding portion meet at a point that is perpendicular to the middle point of the respective limb axis.
8. An electromagnet according to claim 6 or 7, wherein for each winding the first winding portion is disposed between the first end and the second winding portion. 10
9. An electromagnet according to any of claims 6 to 8, wherein for each winding each of the first winding portion and second winding portion is curved relative to the respective limb axis.
10. An electromagnet according to any preceding claim, wherein each winding includes a first bevelled portion adjacent the first end of the respective limb and a second bevelled portion adjacent the second end of the respective limb.11 An electromagnet according to claim 10, wherein each of the first bevelled portions and second bevelled portions have an angle of inclination relative to the respective limb axis of substantially (36012N)°, where N in the total number of limbs.12. An electromagnet according to claim 11 or 12 when dependent on claim 6, wherein the first winding portion and second winding portion are each disposed between the first bevelled portion and the second bevelled portion.13. An electromagnet according to any preceding claim, wherein the ferromagnetic frame has a magnetic permeability of at least lOpo, preferably at least 100po, or preferably at least 1000po, where po is the permeability of free space.14. An electromagnet according to any preceding claim, wherein the ferromagnetic frame comprises steel.15. An electromagnet according to any preceding claim, comprising four limbs.16. A particle accelerator including one or more electromagnets according to any preceding claim.17. An electromagnet for steering a beam of charged particles substantially as hereinbefore described with reference to Figures 3 to 6.