Quasi-polygonal cross section skeleton CCT coil magnet and manufacturing method thereof

Abstract

The invention discloses a method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton, which comprises the following steps of: associating a magnetic multi-pole field required in the quasi-polygonal cross-section skeleton with continuous current density distribution on the quasi-polygonal cross-section skeleton to obtain idealized continuous current distribution of the quasi-polygonal cross-section skeleton; based on idealized continuous current distribution, an inclined solenoid coil is adopted for approximation, and a quasi-polygonal cross section framework CCT coil magnet is obtained. According to the manufacturing method of the quasi-polygonal cross-section skeleton CCT coil magnet, a traditional CCT magnet is popularized from a circular skeleton to a quasi-polygonal skeleton, and any required magnetic multi-pole field is generated in the quasi-polygonal skeleton.

Description

Technical Field

[0001] The invention relates to a CCT coil magnet with a quasi-polygonal cross-section framework, 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 existing oblique solenoid coil magnets all have circular frames. However, the actual beam is not circular. The oblique solenoid coil magnets with circular frames do 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 force in the transmission process, and can generally be characterized by a quasi-polygon. For example, the initial beam from 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 orbit 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 frame, 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 magnetic multipole field required 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 quasi-polygonal cross-section skeleton CCT coil magnet is obtained.

[0010] In a preferred embodiment, 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 in the circular cross-section, the required magnetic multipole field in the complex quasi-polygonal cross-section skeleton is realized, which is linked to the continuous current density distribution on the quasi-polygonal skeleton.

[0011] In a preferred embodiment, a conformal transformation is used to obtain an accurate correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton.

[0012] In a preferred embodiment, 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:

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

[0014] A conformal transformation is used to map the circle in the z-plane to a quasi-polygon in the zeta-plane.

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

[0016]

[0017] 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-diagonal polygon, i.e., an ellipse. Multiplying the entire mapping relationship by a constant or a complex number is also within the scope of use of this patent.

[0018] In a preferred embodiment, the partial arc segments of the circle with a radius of ρ on the z plane before mapping are cut and removed, so that the curve on the ζ plane after mapping becomes closed and non-self-intersecting. According to the required magnetic multipole field in the quasi-polygonal skeleton, the idealized continuous current distributed on the quasi-polygonal skeleton is obtained through the conformal transformation theory.

[0019] In a preferred embodiment, the method of approximating the idealized continuous current distribution by using an inclined solenoid coil to obtain a quasi-polygonal cross-section skeleton CCT coil magnet comprises the following sub-steps:

[0020] Treat the differential current element as a vector and decompose it into longitudinal and transverse components;

[0021] By evenly distributing this line current over the tiny surface area where these current elements are located, the longitudinal surface current density and the annular 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 quasi-polygonal cross-section skeleton CCT coil magnet.

[0024] In a preferred embodiment, the longitudinal surface current density It is expressed as:

[0025]

[0026] The annular surface current density It is expressed as:

[0027]

[0028] Among them, I represents 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)), i.e. ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of cycles 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, Z represent the Cartesian coordinates of the path of the coil, w is the longitudinal turn spacing of the coil after 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-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, by selecting a trigonometric function with a period number of m for CCT winding, the generation of a positive 2m-pole magnetic field can be achieved.

[0032] The present invention also discloses a quasi-polygonal cross-section skeleton CCT coil magnet, wherein 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)), i.e. ζ(z) or ζ, represents the mapping relationship; A mis the amplitude of the winding trigonometric function, m represents the number of cycles 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, Z represent the Cartesian coordinates of the path of the coil, w is the longitudinal turn spacing after the coil is wound around once, 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 oblique multipolar fields 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 The quasi-polygonal figure after the 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 is shown;

[0040] Figure 3 The figure shows a curve obtained by mapping a circle in the z plane to the ζ plane at different radii through quasi-trilateral mapping 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;

[0041] Figure 4 The figure shows a curve obtained by mapping a circle in the z plane to the ζ plane at different radii through a quasi-square mapping 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;

[0042] Figure 5The figure shows a curve after the quasi-trilateral mapping of a circle in the z plane to the ζ plane at different radii and then clipping and domain constraint 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;

[0043] Figure 6 The diagram shows a curve after the circle in the z plane is mapped to the ζ plane at different radii and then clipped and domain constrained 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;

[0044] Figure 7 shows the CCT coil path diagram obtained in Example 1;

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

[0046] Fig. 9 The present invention shows a CCT magnet winding having an elliptical (i.e., bilateral) cross-section skeleton and generating a dipole magnetic field;

[0047] Fig.10 The CCT magnet winding having a quasi-square (i.e., quadrilateral) cross-section skeleton and generating a quadrupole magnetic field according to the present invention is shown;

[0048] Fig.11 The figure shows a CCT magnet winding having a quasi-triangular (ie, triangular) cross-section skeleton and generating a six-pole magnetic field according to the present invention. DETAILED DESCRIPTION

[0049] The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

[0050] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0051] The present invention provides a method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton, such as Figure 1 As shown, the following steps are included:

[0052] S1. The magnetic multipole field required in the quasi-polygonal cross-section skeleton is linked to 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;

[0053] S2. Based on the idealized continuous current distribution, the 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 related to 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] Set up 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 is 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 of 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] Get the magnetic potential and current distribution of the 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 framework, 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] The correspondence of traditional two-dimensional structures is usually converted into a problem of solving a plane potential function under specific boundary conditions, which is generally performed using the separation of variables method or integral solution formula. However, the structural difference between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton is large, and the boundary geometry is highly complex, so the traditional method cannot achieve the corresponding relationship acquisition. How to obtain the accurate corresponding relationship between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton is the difficulty of the present invention.

[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 remain in equivalent 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 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 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] The existing conformal transformation does not have a known mapping that can directly map a circle to a quasi-polygon. Through a lot of research, in the present invention, by constructing the following mapping relationship, a finite field around the origin of the z plane is mapped to the global field in the z plane to generate 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 complex number is also within the scope of use 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 previous 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-difference polygon (i.e., ellipse) obtained by mapping the circle are shown in sequence.

[0079] For example, the mapping relationship from the circle in the z plane to the quasi-triangular shape 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 itself and have some knotted parts. For example, in the mapping of the quasi-trilateral, the more it shrinks inward, the more it looks like 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 cut and removed, so that the mapped curve becomes closed and does not intersect 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 invention, those skilled in the art can perform tailoring and domain establishment on their own according to the actually obtained mapped curve, which is not particularly limited here.

[0087] For example, in the quasi-triangulated mapping, clipping and domain constraints on the curves in ζ are expressed as:

[0088]

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

[0090] For another example, in the quasi-square mapping, the clipping and domain constraints on the curves in ζ are expressed as:

[0091]

[0092] The curve after clipping and domain constraint is as follows Figure 6 shown.

[0093] According to the present invention, when mapping, the cross-sectional radius ρ0 of the circular cross-sectional skeleton should not be too large, otherwise the quasi-polygonal skeleton obtained by mapping will no longer satisfy the properties of a convex polygon, and the cross-sectional radius ρ0 of the circular cross-sectional skeleton should not be too small, otherwise the corresponding quasi-triangular skeleton will approach a circle and the polygonal shape will not be obvious. Those skilled in the art can reasonably select the cross-sectional radius ρ0 of the circular cross-sectional skeleton according to actual needs.

[0094] According to the present invention, based on the continuous current density distribution of the circular cross section, the idealized continuous current distribution of the quasi-polygonal cross section skeleton can be obtained by applying the precise correspondence between the quasi-polygonal cross section skeleton and the circular cross section skeleton.

[0095] According to a preferred embodiment of the present invention, a quasi-square skeleton is selected as a quasi-polygonal cross-section skeleton, and more preferably, the following mapping is performed:

[0096]

[0097] The circular skeleton of the z plane can be transformed into a quasi-square skeleton of the ζ plane after mapping:

[0098]

[0099] Where ζ0 represents the quasi-square skeleton on the mapped plane, and i represents a unit imaginary number.

[0100] For example, if the magnetic field in the quasi-square frame is required to be a positive octupole magnetic field, the vector potential in the frame in the ζ plane is expressed using the parameters of 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, where ρ and θ 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, which modulates the original longitudinal spiral climbing path by introducing periodic trigonometric functions, thereby creating a unique spiral winding trajectory. However, according to the specific winding path of the CCT coil, how to average it to the corresponding surface current density distribution is another difficulty of the present invention.

[0107] S2 includes the following sub-steps:

[0108] S21. Consider 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 annular surface current density are obtained;

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

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

[0112] In S21, the longitudinal surface current density It is expressed as:

[0113]

[0114] The annular surface current density It is expressed as:

[0115]

[0116] Where I represents the conductor current, and w is the longitudinal turn spacing after the coil is wound once. The longitudinal surface current density and the annular surface current density are approximated by the CCT coil, which is consistent with the current density required by the conformal transformation in order to generate the magnetic multipole field we need inside. Due to the periodicity of the CCT winding, the annular surface current density is a constant, and its corresponding longitudinal magnetic field is uniform everywhere in the internal space of the skeleton.

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

[0118]

[0119] in, 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 number of cycles 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, Z represent the Cartesian coordinates of the coil path, w is the longitudinal turn spacing of the coil after one circle, ρ0 is the radius of the circular skeleton of the Z plane before mapping, which is used to control the specific shape of the ζ plane quasi-polygon after mapping, and θ is the polar angle coordinate of the circular skeleton of the Z plane before mapping. The longitudinal surface current density of the CCT coil wound with the above formula is approximated Proportional to in Zero contribution to the internal magnetic field, (∑ m A m cosmθ)|ζ ′ (z)| -1 Used to generate magnetic multipole field, and the toroidal surface current density is a constant If a pure octupole magnetic field is generated inside the quasi-square cross-section frame, the sine function required for CCT winding only needs to be m = 4. The longitudinal magnetic field generated by the toroidal current can be offset by multiple layers of coils, while the transverse magnetic field generated by the longitudinal current can be enhanced by multiple layers of coils.

[0120] The present invention also 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)), i.e. ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of cycles 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, Z represent the Cartesian coordinates of the path of the coil, w is the longitudinal turn spacing of the coil after 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 some embodiments, even in order to generate a single positive multipole field, the superposition of multiple winding trigonometric functions may be required, which is different from the conventional circular cross-section skeleton CCT coil.

[0123] Example

[0124] Example 1

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

[0126] S1. The magnetic multipole field required in the quasi-polygonal cross-section skeleton is linked to 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, the 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 linked to 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] The accurate correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton is obtained by using conformal transformation, including the following sub-steps:

[0132] S111, using 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 set to idealize and generate a positive octupole magnetic field. The vector potential in the skeleton in the ζ plane is expressed as follows using the parameters in the z plane:

[0137]

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

[0139]

[0140] S2 includes the following sub-steps:

[0141] S21. Consider 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 annular surface current density are obtained;

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

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

[0145] In S21, the longitudinal surface current density It is expressed as:

[0146]

[0147] The annular surface current density It is 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 selected as 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 The contribution of A4cos4θ|ζ to the magnetic field inside the skeleton is 0; ′ (z)|-1 Item, a positive octupole magnetic field is generated inside the skeleton.

[0152] The Biot-Savart law is used to verify the above CCT coil. The Biot-Savart law is one of the basic laws of magnetostatics, which describes the law of the magnetic field generated by a current element at any point in space. It was derived by French physicists Jean-Baptiste Biot and Felix Savart through experiments and theoretical deductions.

[0153] During the verification process, the parameter range is θ∈[-200π,200π], which is evenly 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 intensity 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 toroidal 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: Fig. 9 , Fig.10 , Fig.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", "rear", etc. indicate positions or positional relationships based on the working state of the present invention, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", and "fourth" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0158] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0159] The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims

1. A method for manufacturing a quasi-polygonal cross-section skeleton CCT coil magnet, characterized in that: The following steps are involved: The magnetic multipole field required 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 a quasi-polygonal cross-section skeleton CCT coil magnet is obtained.

2. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 1, characterized in that: 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 linked to the continuous current density distribution on the quasi-polygonal skeleton.

3. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 2, characterized in that: The precise correspondence between the quasi-polygonal cross-section skeleton and the circular cross-section skeleton is obtained using conformal transformation.

4. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 3, characterized in that: 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 zeta-plane.

5. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 4, characterized in that: By constructing the following mapping relationship, the finite domain around the origin of the z plane is mapped to the global domain in the ζ plane to generate a quasi-polygonal skeleton. The mapping relationship is expressed as: Among them, 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.

6. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 4, characterized in that: The partial 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.

7. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 1, characterized in that: The method is based on the idealized continuous current distribution and approximated by using an inclined solenoid coil to obtain a quasi-polygonal cross-section skeleton CCT coil magnet, including 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 annular 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 quasi-polygonal cross-section skeleton CCT coil magnet.

8. The method for manufacturing a CCT coil magnet with a quasi-polygonal cross-section skeleton according to claim 7, characterized in that: The longitudinal surface current density It is expressed as: The annular surface current density It is expressed as: Among them, 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 path coordinate of the coil, and s represents the projection of the path on the cross section.

9. 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-polymorphic 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)), i.e. ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of cycles 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 path of the coil.

10. A quasi-polygonal cross-section skeleton CCT coil magnet, 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)), i.e. ζ(z) or ζ, represents the mapping relationship; A m is the amplitude of the winding trigonometric function, m represents the number of cycles 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, Z represent the Cartesian coordinates of the path of the coil, w is the longitudinal turn spacing of the coil after one turn, ρ o 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 in the z plane before mapping.

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