Quasi-polygonal cross-section skeleton cct coil magnet and method of manufacturing the same

Abstract

The application discloses a kind of quasi-polygonal cross-section skeleton CCT coil magnet manufacturing method, comprising: the magnetic multipole field required in quasi-polygonal cross-section skeleton is associated with the continuous current density distribution on quasi-polygonal skeleton, and the ideal continuous current distribution of quasi-polygonal cross-section skeleton is obtained;Based on the ideal continuous current distribution, it is approximated using an inclined solenoid coil, and a quasi-polygonal cross-section skeleton CCT coil magnet is obtained.The quasi-polygonal cross-section skeleton CCT coil magnet manufacturing method disclosed by the application generalizes the traditional CCT magnet from a circular skeleton to a class of quasi-polygonal skeletons, and realizes the generation of any required magnetic multipole field inside the quasi-polygonal skeleton.

Description

Technical Field

[0001] The invention relates to a CCT coil magnet with a quasi-polygonal cross-section skeleton, belonging to the technical field of magnetic fields. Background Art

[0002] Canted-Cosine-Theta (CCT) coil magnets have attracted extensive attention and research from many accelerator laboratories (such as CASIMP, CERN, LBNL, PSI, etc.) due to their compact structure, simple winding process, superior magnetic field distribution, outstanding mechanical properties, and low processing cost.

[0003] The frames of existing oblique solenoid coil magnets are all circular. However, the actual beam is not circular. The oblique solenoid coil magnet with a circular frame does not correspond to the beam, which will result in a smaller lateral space for the beam.

[0004] In fact, the cross-sectional shape of the beam is determined by the ion source and the nonlinear forces during the transmission process. It can generally be characterized by a quasi-polygon. For example, the initial beam coming out of a laser plasma accelerator is cross-shaped in cross section, which is naturally suitable for quasi-square pipes and corresponding magnets. In ion implanters, the magnet good field region required for strip beam extraction is a flat, nearly elliptical space, and the beam trajectory in the FFAG accelerator drifts outward with acceleration, which is also suitable for magnets with flat elliptical apertures.

[0005] However, since the magnetic field optimization process is complicated when designing a magnet with a non-circular skeleton, a coil magnet with a CCT configuration cannot be realized in the prior art.

[0006] Therefore, it is necessary to conduct more in-depth research on CCT coil magnets to obtain CCT coil magnets with non-circular frames. Summary of the Invention

[0007] In order to overcome the above problems, the inventors conducted in-depth research and proposed a method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton, comprising the following steps:

[0008] The desired magnetic multipole field in the quasi-polygonal cross-section skeleton is linked to the continuous current density distribution on the quasi-polygonal cross-section skeleton to obtain the idealized continuous current distribution of the quasi-polygonal cross-section skeleton;

[0009] Based on the idealized continuous current distribution, the inclined solenoid coil is used to approximate it, and a CCT coil magnet with a quasi-polygonal cross-section skeleton is obtained.

[0010] In a preferred embodiment, by establishing the precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton, on the basis of the continuous current density distribution of the circular cross-section, the required magnetic multipole field in the complex quasi-polygonal cross-section skeleton is realized, which is associated with the continuous current density distribution on the quasi-polygonal skeleton.

[0011] In a preferred embodiment, the precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton is obtained by using conformal transformation.

[0012] In a preferred embodiment, the precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton obtained by using conformal transformation includes the following sub-steps:

[0013] Adopting complex variable z to represent the two-dimensional plane of the circular cross-section skeleton;

[0014] Using conformal transformation to map the circle in the z plane to the quasi-polygon in the ζ plane.

[0015] In a preferred embodiment, by constructing the mapping relationship as follows, the finite domain around the origin of the z plane is mapped to the whole domain in the ζ plane to generate the quasi-polygon skeleton, and the mapping relationship is represented as:

[0016]

[0017] Wherein, ζ represents the mapped plane, c controls the shape of the mapping and is used for adjusting the dimension, generally taking a constant 1, n represents the number of edges of the transformed quasi-polygon, and in particular, n = 2 represents a quasi-biangular polygon, i.e. an ellipse. Multiplying the mapping relationship as a whole by a constant or a complex number is also within the scope of use of the present patent.

[0018] In a preferred embodiment, the part of the arc segment of the circle with a radius of ρ on the z plane before mapping is cut and removed, so that the curve on the ζ plane after mapping becomes closed and does not intersect itself. According to the required magnetic multipole field in the quasi-polygon skeleton, the idealized continuous current distribution on the quasi-polygon skeleton is obtained through conformal transformation theory.

[0019] In a preferred embodiment, based on the idealized continuous current distribution, the quasi-polygon cross-section skeleton CCT coil magnet is obtained by approximating it with an inclined solenoid coil, including the following sub-steps:

[0020] Regarding the differential current element as a vector, it is decomposed into a longitudinal component and a transverse component;

[0021] By uniformly distributing the line current on the micro-surface area where the current element is located, the longitudinal surface current density and the circumferential surface current density are obtained;

[0022] Based on the idealized continuous current distribution, the CCT coil path on the quasi-polymorphic skeleton is set;

[0023] Winding is performed according to the CCT coil path to obtain a CCT coil magnet with a quasi-polygonal cross-section skeleton.

[0024] In a preferred embodiment, the longitudinal surface current density Expressed as:

[0025]

[0026] The annular surface current density Expressed as:

[0027]

[0028] Where I is the conductor current and w is the longitudinal turn spacing after the coil is wound one circle.

[0029] In a preferred embodiment, the CCT coil path on the quasi-polymorphic skeleton is expressed as:

[0030]

[0031] in, represents the real part of the mapping function, represents the imaginary part of the mapping function; ζ(z=(ρ0,θ)), namely ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of periods of the trigonometric function, |ζ ′ (z)| is the derivative modulus of ζ(z), s represents the projection of the path onto the cross section, X, Y, and Z represent the Cartesian coordinates of the coil path, w is the longitudinal turn spacing after one coil turn, ρ0 is the radius of the circular skeleton in the z plane before mapping, which controls the specific shape of the quasi-polygonal skeleton in the ζ plane after mapping, and θ is the polar angle coordinate of the circular skeleton before mapping. In a preferred embodiment of the present invention, CCT winding is performed by selecting a trigonometric function with a period of m to generate a positive 2m-pole magnetic field.

[0032] The present invention also discloses a CCT coil magnet with a quasi-polygonal cross-section skeleton. The CCT coil path of the coil magnet is:

[0033]

[0034] in, represents the real part of the mapping function, represents the imaginary part of the mapping function; ζ(z=(ρ0,θ)), namely ζ(z) or ζ, represents the mapping relationship; A mis the amplitude of the winding trigonometric function, m represents the number of periods of the trigonometric function, |ζ ′ (z)| is the derivative modulus of ζ(z), s represents the projection of the path on the cross section, X, Y, and Z represent the Cartesian coordinates of the coil path, w is the longitudinal turn spacing after the coil is wound one circle, ρ0 is the radius of the circular skeleton in the z plane before mapping, which is used to control the specific shape of the quasi-polygon after mapping, and θ is the polar angle coordinate of the circular skeleton before mapping. In the present invention, the CCT coil path is designed to generate a positive multipolar magnetic field. The generation of the skew multipolar field can be achieved by appropriately modifying the sine and cosine functions. In some embodiments, even in order to generate a single positive multipolar field, the superposition of multiple winding trigonometric functions may be required, which is different from the conventional circular cross-section skeleton CCT coil.

[0035] The beneficial effects of the present invention include:

[0036] (1) The traditional CCT magnet is extended from a circular skeleton to a quasi-polygonal skeleton. On the one hand, the advantages of the CCT magnet such as superior magnetic field quality, outstanding mechanical properties, simple winding process, and low processing cost are maintained. On the other hand, the aperture is extended from the traditional circular to quasi-triangular, quasi-square and other quasi-polygonal shapes.

[0037] (2) It is possible to generate any desired magnetic multipole field inside the quasi-polygonal skeleton. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A schematic flow chart of a method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to a preferred embodiment of the present invention is shown;

[0039] Figure 2 1. A quasi-polygonal figure is shown after a circle in the z plane is mapped to the ζ plane in a method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to a preferred embodiment of the present invention;

[0040] Figure 3 1. A graph showing a method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to a preferred embodiment of the present invention, wherein a circle in the z plane is mapped to the ζ plane by quasi-triangular mapping at different radii;

[0041] Figure 4 1. A graph showing a method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to a preferred embodiment of the present invention, wherein a circle in the z plane is mapped to the ζ plane by quasi-square mapping at different radii;

[0042] Figure 5A method for making a quasi-polygonal cross-section skeleton CCT coil magnet according to a preferred embodiment of the present application is shown, in which a circle in the z plane is mapped to a quasi-triangle in the z plane at different radii, and then the curve after cutting and domain constraint;

[0043] Figure 6 A method for making a quasi-polygonal cross-section skeleton CCT coil magnet according to a preferred embodiment of the present application is shown, in which a circle in the z plane is mapped to a quasi-square in the z plane at different radii, and then the curve after cutting and domain constraint;

[0044] Figure 7 A CCT coil path diagram obtained in Example 1 is shown;

[0045] Figure 8 Results of verifying the CCT coil using the Biot-Savart law in Example 1 are shown;

[0046] Figure 9 A CCT magnet winding with an elliptical (i.e. bi-polygonal) cross-section skeleton generating a bi-pole magnetic field according to the present application is shown;

[0047] Figure 10 A CCT magnet winding with a quasi-square (i.e. quad-polygonal) cross-section skeleton generating a quad-pole magnetic field according to the present application is shown;

[0048] Figure 11 A CCT magnet winding with a quasi-triangle (i.e. tri-polygonal) cross-section skeleton generating a hexa-pole magnetic field according to the present application is shown. DETAILED DESCRIPTION

[0049] The present application is further described through the accompanying drawings and examples. The features and advantages of the present application will become more apparent from the detailed description, when taken in conjunction with the accompanying drawings.

[0050] The term "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations. Unless specifically stated otherwise, the drawings are not drawn to scale and the disclosure is not limited to the specific embodiments illustrated in the drawings.

[0051] A method for making a quasi-polygonal cross-section skeleton CCT coil magnet according to the present application is provided, as shown in Figure 1 comprising the following steps:

[0052] S1, associating the required magnetic multi-pole field in the quasi-polygonal cross-section skeleton with a continuous current density distribution on the quasi-polygonal skeleton, to obtain an idealized continuous current distribution of the quasi-polygonal cross-section skeleton;

[0053] S2. Based on the idealized continuous current distribution, an inclined solenoid coil is used to approximate it, and a quasi-polygonal cross-section skeleton CCT coil magnet is obtained.

[0054] At present, there is no effective method to obtain quasi-polygonal continuous current distribution. In the present invention, in S1, by establishing a precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton, on the basis of the continuous current density distribution of the circular cross-section, the required magnetic multipole field in the complex quasi-polygonal cross-section skeleton is realized, which is connected with the continuous current density distribution on the quasi-polygonal skeleton.

[0055] Furthermore, the circular cross-section continuous current density distribution is obtained by the following steps:

[0056] Assume a magnet with no longitudinal variation, which satisfies Poisson's equation:

[0057]

[0058] Among them, A z represents the longitudinal component of the magnetic vector potential, μ0 represents the vacuum permeability, J z represents the longitudinal current density, is the Laplace operator.

[0059] Solving in polar coordinates yields:

[0060]

[0061] in, represents the magnetic induction intensity, represents the polar direction in polar coordinates, represents the polar direction in polar coordinates, ρ represents the polar diameter in the z plane, and θ represents the polar angle in the z plane.

[0062] Obtain the magnetic potential and current distribution of a circular cross-section skeleton:

[0063]

[0064] Among them, normal represents the positive magnetic field generated by the circular cross-section skeleton, skew represents the oblique magnetic field generated by the circular cross-section skeleton, and relation represents the relationship between the magnetic fields inside and outside the circular cross-section skeleton. represents the magnetic potential within the skeleton, represents the magnetic potential outside the skeleton, a i represents the magnetic potential coefficient within the skeleton, a o represents the magnetic potential coefficient outside the skeleton, N represents the order of the magnetic multipole field, which is an integer variable, and J N represents the current density distributed on the circular skeleton, and ρ0 represents the radius of the circular cross-section skeleton.

[0065] In particular, N = 0, that is, the current of the circular cross-section skeleton is equal everywhere, then:

[0066]

[0067] Among them, A arbi is an arbitrary constant, indicating that there is no magnetic field inside the circular cross-section skeleton. Generally, the A arbi Take 0.

[0068] Traditionally, the correspondence between two-dimensional structures is typically solved by solving a planar potential function under specific boundary conditions, typically using separation of variables or integral solution formulas. However, the structural differences between quasi-polygonal and circular cross-section skeletons are significant, and the boundary geometry is highly complex, making traditional methods incapable of obtaining such a correspondence. The difficulty of this invention lies in obtaining a precise correspondence between these two cross-section skeletons.

[0069] In the present invention, an accurate correspondence between a quasi-polygonal cross-section skeleton and a circular cross-section skeleton is obtained by using conformal transformation.

[0070] The conformal transformation, also called conformal mapping, converts from the z plane to the ζ plane. If this transformation is analytical, that is, it satisfies the Cauchy-Riemann condition, then the physical laws in the original z plane (such as Poisson's equation) will maintain the same form in the new plane ζ plane. Note that during the transformation, the strength of the source in the Poisson equation needs to be scaled. The linear distribution source 1 in the z plane becomes |ζ in the ζ plane. ′ (z)| -1 , which means that when the thin current shell skeleton on the z plane is converted to the ζ plane, the current intensity becomes the original |ζ ′ (z)| -1 .

[0071] Furthermore, the method of obtaining the precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton by using conformal transformation includes the following sub-steps:

[0072] S111, using the complex variable z to represent the two-dimensional plane of the circular cross-section skeleton;

[0073] S112. Use conformal transformation to map the circle in the z plane to a quasi-polygon in the ζ plane.

[0074] Existing conformal transformations do not have a known mapping that can directly map a circle to a quasi-polygon. Through extensive research, in the present invention, the following mapping relationship is constructed to map the finite domain around the origin of the z plane to the full domain in the z plane, generating a quasi-polygon skeleton. The mapping relationship is expressed as:

[0075]

[0076] Among them, ζ represents the plane after mapping, c controls the shape of the mapping and is used to adjust the dimension, which is generally taken as a constant 1, and n represents the number of sides of the quasi-polygon after transformation. In particular, n=2 represents a quasi-dilateral polygon, i.e., an ellipse.

[0077] In particular, multiplying the right side of the mapping relationship equation by a constant or a complex number is also within the scope of this patent.

[0078] In the above mapping, the quasi-polygon of the next equation is the result of rotating the previous equation by a certain angle, such as Figure 2 As shown, Figure 2 (a) is the mapping result of the above formula, Figure 2 (b) is the mapping result of the next formula. In the figure, from the outside to the inside, the quasi-hexagon, quasi-pentagon, quasi-quadrilateral (i.e., square), quasi-trilateral and quasi-dilateral (i.e., ellipse) obtained by mapping the circle are shown in order.

[0079] For example, the mapping relationship from a circle in the z plane to a quasi-triangle in the ζ plane can be set as:

[0080]

[0081] The mapping relationship from the circle in the z plane to the quasi-square in the ζ plane can be set as:

[0082]

[0083] Furthermore, the study found that when the circle in the z plane expands outward from the origin, the corresponding closed curve in the ζ plane shrinks inward from the infinite circle. This closed curve in the ζ plane will intersect with itself and have some knotted parts. For example, in the mapping of a quasi-trilateral, the more it shrinks inward, the more it resembles a quasi-trilateral. When the radius ρ increases by more than 2 -1 / 3 c, the corresponding curve in the ζ plane becomes self-intersecting, such as Figure 3 As shown, for example, in the quasi-square mapping, when the radius ρ increases beyond 3 -1 / 4 When c, the curve in the ζ plane intersects itself as Figure 4 As shown, Figure 4 (a) shows the curve in the ζ plane after mapping, Figure 4 (b) shows the circular curve in the z-plane before mapping.

[0084] In the present invention, the arc segments on the circle with a radius ρ before mapping are clipped and removed, so that the mapped curve becomes closed and does not intersect with itself.

[0085] Furthermore, since the inverse mapping from ζ to z is complex and does not produce a unique solution, in the present invention, a domain is established in the z plane so that the mapping is one-to-one.

[0086] In the present application, the skilled person can perform the clipping and domain establishment according to the actually obtained mapped curve, which is not particularly limited herein.

[0087] For example, in the quasi-triangular mapping, the clipping and domain constraint of the curve in ζ is represented as:

[0088]

[0089] The curve after clipping and domain constraint is shown in FIG. 2, wherein Figure 5 (a) shows the curve in the ζ plane after mapping, and Figure 5 (b) shows the circular curve in the z plane before mapping. Figure 5

[0090] For example, in the quasi-triangular mapping, the clipping and domain constraint of the curve in ζ is represented as:

[0091]

[0092] The curve after clipping and domain constraint is shown in FIG. 2, wherein Figure 6 According to the present application, when performing the mapping, the cross-sectional radius p0 of the circular cross-sectional skeleton should not be too large, otherwise the quasi-polygonal skeleton obtained by mapping will no longer satisfy the convex polygon property, and the cross-sectional radius p0 of the circular cross-sectional skeleton should not be too small, otherwise the corresponding quasi-triangular skeleton tends to be circular, and the polygonal shape is not obvious. The skilled person can reasonably select the cross-sectional radius p0 of the circular cross-sectional skeleton according to actual needs.

[0093] According to the present application, on the basis of the continuous current density distribution of the circular cross-section, the precise correspondence between the quasi-polygonal cross-sectional skeleton and the circular cross-sectional skeleton can be applied, so as to obtain the ideal continuous current distribution of the quasi-polygonal cross-sectional skeleton.

[0094] According to a preferred embodiment of the present application, the quasi-square skeleton is selected as the quasi-polygonal cross-sectional skeleton, and more preferably, the following mapping is performed:

[0095]

[0096] The circular skeleton in the z plane, after mapping and transformation, the quasi-square skeleton in the ζ plane can be obtained:

[0097]

[0098]

[0099] wherein ζ0 represents the quasi-square skeleton in the mapped plane, and i represents the unit imaginary number.

[0100] ​​For example, if the magnetic field inside the quasi-square frame is required to be a positive octupole magnetic field, the vector potential inside the frame in the ζ plane can be expressed using the parameters in the z plane as:

[0101]

[0102] Where P represents the polar diameter of the ζ plane after transformation, Θ represents the polar angle of the ζ plane after transformation, represents the real part of the function, ρ and θ in this formula represent the polar coordinates of the z plane before transformation, and ρ0 is the radius of the circular cross-section skeleton specified in the z plane.

[0103] According to the above formula about the negative power ρ -4 , and combined with the corresponding relationship between the magnetic vector potential outside the circular skeleton in the z plane and the current on the circular skeleton, the current distribution can be obtained:

[0104]

[0105] Among them, ~ represents a proportional relationship, |ζ ′ (z)| is the derivative modulus of ζ(z), J z is the current distribution on the circular skeleton ρ0 in the z plane, is the current distribution on the quasi-square skeleton ζ0 corresponding to the ζ plane.

[0106] The uniqueness of the CCT coil lies in its winding path. By introducing periodic trigonometric functions, the original longitudinal spiral path is modulated, thereby creating a unique spiral winding trajectory. However, another difficulty of the present invention is how to average the current density distribution on the surface of the CCT coil based on its specific winding path.

[0107] S2 includes the following sub-steps:

[0108] S21. Treat the differential current element as a vector and decompose it into longitudinal and transverse components;

[0109] By evenly distributing this line current over the tiny surface area where these current elements are located, the longitudinal surface current density and the circumferential surface current density are obtained;

[0110] S22, setting the CCT coil path on the quasi-polymorphic skeleton based on the idealized continuous current distribution;

[0111] S23 , winding the coil according to the CCT coil path to obtain a CCT coil magnet with a quasi-polygonal cross-section skeleton.

[0112] In S21, the longitudinal surface current density Expressed as:

[0113]

[0114] the circumferential surface current density is expressed as:

[0115]

[0116] where I represents the wire current, and w is the longitudinal inter-turn spacing after one turn of the coil. Here the longitudinal surface current density and the circumferential surface current density are approximated from the CCT coil, which is consistent with the current density required by the conformal transformation, so as to generate the magnetic multipole field required in the interior. Due to the periodicity of the CCT winding, the circumferential surface current density is a constant, and the corresponding longitudinal magnetic field is uniform everywhere in the interior space of the skeleton.

[0117] In S22, the CCT coil path on the quasi-polygonal skeleton is expressed as:

[0118]

[0119] wherein, represents the real part of the mapping function, represents the imaginary part of the mapping function; ζ(z=(ρ0, θ)), i.e. ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the period number of the trigonometric function, |ζ ′ (z) is the derivative modulus of ζ(z), s represents the projection of the path on the cross section, X, Y and Z represent the Cartesian coordinates of the coil path, w is the longitudinal inter-turn spacing after one turn of the coil, ρ0 is the radius of the circular skeleton in the Z plane before mapping, used to control the specific shape of the quasi-polygonal skeleton in the ζ plane after mapping, and θ is the polar angle coordinate of the circular skeleton in the z plane before mapping. The CCT coil wound according to the above formula has the longitudinal surface current density proportional to wherein has no contribution to the internal magnetic field, and (∑ m A m cosmθ)|ζ ′ (z)| -1 is used to generate the magnetic multipole field, and the circumferential surface current density is a constant If a pure positive octupole magnetic field is generated in the quasi-square cross-section skeleton, the sine function required by the CCT winding only needs to take m=4. The longitudinal magnetic field generated by the circumferential current can be offset by a multi-layer coil, and the transverse magnetic field generated by the longitudinal current can be enhanced by a multi-layer coil.

[0120] The application further discloses a quasi-polygonal cross-section skeleton CCT coil magnet, wherein the CCT coil path of the coil magnet is:

[0121]

[0122] in, represents the real part of the mapping function, represents the imaginary part of the mapping function; ζ(z=(ρ0,θ)), namely ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of periods of the trigonometric function, |ζ ′ (z)| is the derivative modulus of ζ(z), s represents the projection of the path onto the cross section, X, Y, and Z represent the Cartesian coordinates of the coil path, w is the longitudinal turn spacing after one coil turn, ρ0 is the radius of the circular skeleton in the z plane before mapping, which controls the specific shape of the quasi-polygon after mapping, and θ is the polar coordinate of the circular skeleton before mapping. In some embodiments, even to generate a single positive multipole field, the superposition of multiple winding trigonometric functions may be required, which differs from conventional CCT coils with circular cross-section skeletons.

[0123] Example

[0124] Example 1

[0125] The quasi-square cross-section skeleton CCT coil magnet is manufactured in the following manner, including:

[0126] S1. Correlating the required magnetic multipole field within the quasi-polygonal cross-section skeleton with the continuous current density distribution on the quasi-polygonal cross-section skeleton to obtain an idealized continuous current distribution of the quasi-polygonal cross-section skeleton;

[0127] S2. Based on the idealized continuous current distribution, an inclined solenoid coil is used to approximate it, and a quasi-polygonal cross-section skeleton CCT coil magnet is obtained.

[0128] In S1, by establishing a precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton, the required magnetic multipole field in the complex quasi-polygonal cross-section skeleton is realized on the basis of the continuous current density distribution in the circular cross-section, which is associated with the continuous current density distribution on the quasi-polygonal skeleton.

[0129] The magnetic potential and current distribution of the circular cross-section skeleton are expressed as:

[0130]

[0131] Obtaining the precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton using conformal transformation includes the following sub-steps:

[0132] S111, using the complex variable z to represent the two-dimensional plane of the circular cross-section skeleton;

[0133] S112. Use conformal transformation to map the circle in the z plane to a quasi-polygon in the ζ plane.

[0134] The mapping relationship is set as:

[0135]

[0136] The quasi-square skeleton is idealized to generate a positive octupole magnetic field, and the vector potential within the skeleton in the ζ plane is expressed using the parameters of the z plane as follows:

[0137]

[0138] Correspondingly, the continuous current distribution on the quasi-square skeleton is:

[0139]

[0140] S2 includes the following sub-steps:

[0141] S21. Treat the differential current element as a vector and decompose it into longitudinal and transverse components;

[0142] By evenly distributing this line current over the tiny surface area where these current elements are located, the longitudinal surface current density and the circumferential surface current density are obtained;

[0143] S22, setting the CCT coil path on the quasi-polymorphic skeleton based on the idealized continuous current distribution;

[0144] S23 , winding the coil according to the CCT coil path to obtain a CCT coil magnet with a quasi-polygonal cross-section skeleton.

[0145] In S21, the longitudinal surface current density Expressed as:

[0146]

[0147] The annular surface current density Expressed as:

[0148]

[0149] In S22, the CCT coil path is obtained as:

[0150]

[0151] Among them, the radius of the circular skeleton in the z plane before mapping is ρ0 = 0.6, the longitudinal turn spacing w = 0.05, and the trigonometric function amplitude of the winding A4 = 0.80. The obtained CCT coil path is as follows Figure 7 According to the conformal transformation theory, the longitudinal surface current density is The contribution of A4cos4θ|ζ to the magnetic field inside the skeleton is 0; ′ (z)|-1 Item, generates a positive octupole magnetic field within the skeleton.

[0152] The CCT coils were verified using the Biot-Savart law, one of the fundamental laws of magnetostatics. The Biot-Savart law describes the magnetic field generated by a current element at any point in space and was derived experimentally and theoretically by French physicists Jean-Baptiste Biot and Felix Savart.

[0153] During the verification process, the parameter range is θ∈[-200π,200π], which is divided into 2 22 Segment current element, analyzed 2 22 The magnetic field generated by the segment current element on the Z=0 plane of the CCT is as follows: Figure 8 shown.

[0154] exist Figure 8 (a) shows the transverse magnetic field strength generated by the longitudinal current of the CCT coil. It can be seen that it conforms to the characteristics of the octupole magnetic field; Figure 8 (b) shows the relative deviation of the magnetic field from the ideal octupole magnetic field, and the relative error is within 0.001; Figure 8 (c) shows the longitudinal magnetic field generated by the circular current of the CCT coil. It can be seen that the longitudinal magnetic field is relatively uniform, and its relative deviation is within 0.05.

[0155] Example 2

[0156] The same method as in Example 1 was used to prepare the elliptical frame-dipolar magnetic field, the quasi-square frame-quadrupole magnetic field, and the quasi-triangular frame-hexapole magnetic field. The CCT winding results obtained were as follows: Figure 9 、 Figure 10 、 Figure 11 , it can be seen that the skeleton shape and magnetic field configuration of this method can be selected arbitrarily.

[0157] In the description of the present invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear" and the like, indicating positions or locations, are based on the operating state of the present invention and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0158] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention in specific contexts.

[0159] The present invention has been described above with reference to preferred embodiments, but these embodiments are merely exemplary and serve only as illustrations. On this basis, various replacements and improvements can be made to the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton, characterized in that: The following steps are involved: The desired magnetic multipole field in the quasi-polygonal cross-section skeleton is linked to the continuous current density distribution on the quasi-polygonal cross-section skeleton to obtain the idealized continuous current distribution of the quasi-polygonal cross-section skeleton; Based on the idealized continuous current distribution, the inclined solenoid coil is used to approximate it and the quasi-polygonal cross-section skeleton CCT coil magnet is obtained. By establishing a precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton, the required magnetic multipole field in the complex quasi-polygonal cross-section skeleton is realized on the basis of the continuous current density distribution on the circular cross-section, which is linked to the continuous current density distribution on the quasi-polygonal skeleton. The precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton is obtained by using conformal transformation. The method of obtaining the precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton by using conformal transformation includes the following sub-steps: The complex variable z is used to represent the two-dimensional plane of the circular cross-section skeleton; A conformal transformation is used to map the circle in the z plane to a quasi-polygon in the ζ plane. By constructing the following mapping relationship, the finite domain around the origin of the z plane is mapped to the full domain in the ζ plane to generate a quasi-polygonal skeleton. The mapping relationship is expressed as: Where z represents the plane before mapping, ζ represents the plane after mapping, c controls the shape of the mapping and is used to adjust the dimension, and n represents the number of sides of the quasi-polygon after transformation.

2. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 1, characterized in that: The arc segments of the circle with a radius of ρ on the z plane before mapping are trimmed and removed, so that the corresponding curve on the ζ plane after mapping becomes closed and non-self-intersecting, ensuring a one-to-one correspondence between the values ​​before and after mapping.

3. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 1, characterized in that: The method of obtaining a CCT coil magnet with a quasi-polygonal cross-section skeleton based on an idealized continuous current distribution and approximating it with an inclined solenoid coil includes the following sub-steps: Treat the differential current element as a vector and decompose it into longitudinal and transverse components; By evenly distributing this line current over the tiny surface area where these current elements are located, the longitudinal surface current density and the circumferential surface current density are obtained; Based on the idealized continuous current distribution, the CCT coil path on the quasi-polymorphic skeleton is set; Winding is performed according to the CCT coil path to obtain a CCT coil magnet with a quasi-polygonal cross-section skeleton.

4. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 3, characterized in that: The longitudinal surface current density Expressed as: The annular surface current density Expressed as: Where I represents the conductor current, w is the longitudinal turn spacing after the coil is wound one circle, Z represents the height value of the coil's path coordinates, and s represents the projection of the path on the cross section.

5. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 1, characterized in that: The CCT coil path on the quasi-polygonal skeleton is expressed as: in, represents the real part of the mapping function, represents the imaginary part of the mapping function; ζ(z=(ρ0,θ)), namely ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of periods of the trigonometric function, |ζ ′ (z)| is the derivative modulus of ζ(z), s represents the projection of the path on the cross section, and X, Y, and Z represent the Cartesian coordinates of the coil path.

6. A quasi-polygonal cross-section skeleton CCT coil magnet, manufactured according to the method for manufacturing a quasi-polygonal cross-section skeleton CCT coil magnet according to claim 1, characterized in that: The CCT coil path of this coil magnet is: in, represents the real part of the mapping function, represents the imaginary part of the mapping function; ζ(z=(ρ0,θ)), namely ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of periods of the trigonometric function, |ζ ′ (z)| is the derivative modulus of ζ(z), s represents the projection of the path on the cross section, X, Y, and z represent the Cartesian coordinates of the coil path, w is the longitudinal turn spacing after the coil is wound one circle, ρ0 is the radius of the circular skeleton in the z plane before mapping, which is used to control the specific shape of the quasi-polygon after mapping, and θ is the polar coordinate of the circular skeleton in the z plane before mapping.

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