Saddle-type nonlinear gradient coil, design method thereof and magnetic shielding compensation system

Abstract

The invention relates to the technical field of magnetic shielding compensation, and discloses a saddle-type nonlinear gradient coil, a design method thereof and a magnetic shielding compensation system.The coil is used for compensating a nonlinear residual magnetic field in a magnetic shielding device with a single-end opening, and the coil comprises multiple pairs of coil units arranged in the axial direction of the magnetic shielding device; wherein all the coil units share the same coil radius and arc field angle, and the axial length and the axial center position of each pair of coil units are different; the number of the coil units, the arc field angle and the axial length and the axial center position of each pair of coil units are optimized and determined, so that a resultant magnetic field generated after the saddle-type nonlinear gradient coil is electrified is matched with a target nonlinear residual magnetic field of a preset target area in the magnetic shielding device; through the design of a plurality of pairs of coil units sharing coil radiuses and arc field angles, differentiated axial lengths and axial center positions, a resultant magnetic field generated after parameter optimization can be accurately matched with a nonlinear residual magnetic field in the single-end open magnetic shielding device.

Description

Technical Field

[0001] This invention relates to the field of magnetic shielding compensation technology, specifically to a saddle-shaped nonlinear gradient coil and its design method, and a magnetic shielding compensation system. Background Technology

[0002] In fields such as ultra-weak magnetic signal measurement, biomagnetic detection, quantum magnetic sensing, and precision experimental environment control, obtaining a stable and uniform near-zero magnetic field environment is a crucial prerequisite for ensuring measurement accuracy and equipment performance. Therefore, passive magnetic shielding devices (such as magnetic shielding cylinders) made of high-permeability materials are typically used to shield against interference from external environmental magnetic fields. However, due to practical application requirements, such as equipment entry / exit points, cable channels, and observation windows, these structures are often designed with single-end openings and necessary holes. These structural factors severely compromise the integrity of the shielding cylinder, allowing external magnetic fields to intrude through the openings and holes. This induces complex magnetic flux distortion and leakage magnetic effects within and at the boundaries of the high-permeability shielding layer, resulting in a complex spatial nonlinear distribution of the residual magnetic field in the working area inside the shielding cylinder, rather than a uniform or simple linear gradient field. To counteract the residual magnetic field and spatial gradient magnetic field inside the shielding cavity, existing technologies typically employ active magnetic field compensation structures such as Helmholtz coils (generating a uniform field), saddle coils (generating an axial or radial linear gradient field), and Maxwell coils (generating a linear gradient field). Among them, saddle-shaped coils are widely used in magnetic shielding environments due to their advantages such as simple structure, ease of manufacturing, and ability to form axial gradient fields.

[0003] However, traditional saddle-shaped coil designs are mostly based on the assumption of a uniform or linear approximate magnetic field, failing to fully consider the reflected magnetic field caused by the thickness of the magnetic shielding layer, the end cap structure and openings, the mirror effect, and the nonlinear magnetic permeability characteristics of high-permeability materials. This leads to compensation deviations under the linear magnetization assumption, resulting in limited compensation efficiency. Furthermore, for the problem of nonlinear spatial magnetic field compensation within a magnetically shielded environment, some studies have attempted to use inverse design methods, such as the target field method, to obtain the current distribution and reconstruct the target magnetic field. However, such methods are computationally complex, difficult to optimize, and prone to instability or even unreachability when considering multi-layer magnetic shielding, holes, and the nonlinearity of magnetic materials.

[0004] Therefore, there is still an urgent need for a saddle coil design scheme that can combine the actual physical characteristics of magnetic shielding devices, accurately model the mirror effect, and be applicable to multi-turn wiring structures, so as to achieve accurate compensation of the nonlinear residual magnetic field inside the device and thus improve the stability of the shielding environment. Summary of the Invention

[0005] This invention provides a saddle-shaped nonlinear gradient coil and its design method, as well as a magnetic shielding compensation system, to solve the problem that the existing technology lacks effective compensation for nonlinear residual magnetic fields, making it difficult for the designed coil to effectively match and suppress the complex nonlinear residual magnetic field in a single-ended open magnetic shielding device, thus resulting in limited compensation accuracy and effect.

[0006] In a first aspect, the present invention provides a saddle-shaped nonlinear gradient coil for compensating for a nonlinear residual magnetic field within a magnetic shielding device having a single-ended opening. The coil includes: Multiple pairs of coil units are arranged along the axial direction of the magnetic shielding device; wherein, all coil units share the same coil radius and arc angle, but the axial length and axial center position of each pair of coil units are not the same; The number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position are optimized and determined so that the synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after energization matches the target nonlinear residual magnetic field of the preset target area in the magnetic shielding device.

[0007] This invention uses a coil unit design with multiple pairs of shared coil radii and arc angles, differentiated axial lengths and axial center positions. After parameter optimization, the resulting synthetic magnetic field can accurately match the nonlinear residual magnetic field in a single-ended open magnetic shielding device, thereby effectively offsetting the residual magnetic field disturbance after shielding. This improves the compensation accuracy and effect while solving the problem that traditional coils are difficult to adapt to nonlinear magnetic fields.

[0008] In one alternative implementation, the number of coil units is determined based on the spatial complexity of the target nonlinear residual magnetic field.

[0009] The number of coil units in this invention can be precisely adapted to the nonlinear magnetic field compensation requirements based on the spatial complexity of the target nonlinear residual magnetic field. This ensures the compensation effect in complex magnetic field scenarios while avoiding problems such as material waste, increased processing difficulty, and cumbersome assembly caused by an excessive number of units in simple magnetic field scenarios, thus achieving an optimal balance between coil structure and manufacturing cost.

[0010] In one optional implementation, the target nonlinear residual magnetic field is a radial gradient magnetic field that varies nonlinearly along the axis of the magnetic shielding device. The distribution of the radial gradient magnetic field is determined by a preset method, which includes at least a measurement method and a simulation method.

[0011] This invention defines the target nonlinear residual magnetic field as a radial gradient magnetic field that changes nonlinearly along the axis of the magnetic shielding device. This field can precisely match the magnetic field distortion characteristics of a single-ended open magnetic shield, thereby accurately locking the compensation target and specifically improving the magnetic field compensation effect.

[0012] In one alternative implementation, the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field is achieved by minimizing the difference in magnetic field strength between the two within a preset target region.

[0013] This invention uses minimizing the difference in magnetic field strength as the core criterion for matching degree, transforming the matching from a vague functional description into a quantifiable indicator. This ensures that the synthesized magnetic field can accurately counteract the nonlinear residual magnetic field of the target, making the magnetic field of the target region approach the ideal state, thereby achieving quantitative and controllable compensation accuracy.

[0014] In a second aspect, the present invention provides a design method for a saddle-shaped nonlinear gradient coil, applicable to a saddle-shaped nonlinear gradient coil as described in the first aspect above or any corresponding embodiment thereof, the method comprising: Determine the saddle-shaped nonlinear gradient coil to be designed, and the target nonlinear residual magnetic field in the preset target area within the magnetic shielding device; The number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil are optimized to obtain the optimal saddle-shaped nonlinear gradient coil, so that the synthetic magnetic field generated by the optimal saddle-shaped nonlinear gradient coil after energization matches the target nonlinear residual magnetic field to be compensated in the magnetic shielding device.

[0015] The design method of the saddle-shaped nonlinear gradient coil of the present invention can achieve targeted optimization by clearly defining the number of coil units, the arc angle, the axial length of each pair of coil units and the axial center position as the core optimization objects. This enables the synthesized magnetic field to accurately match the target nonlinear residual magnetic field, avoids the compensation deviation caused by blind adjustment of parameters in traditional design, and greatly improves the accuracy of magnetic field cancellation in the target area.

[0016] In one alternative implementation, determining the saddle-shaped nonlinear gradient coil to be designed includes: Obtain the structural parameters of the magnetic shielding device; Based on the structural parameters, the initial structure of the saddle-shaped nonlinear gradient coil is designed, and the saddle-shaped nonlinear gradient coil to be designed is determined based on the initial structure. The structural parameters include at least the inner and outer radii, axial length, opening size and material permeability. The initial structure includes the number of coil units, the arc angle, the axial length of each pair of coil units and the axial center position.

[0017] This invention uses the core structural parameters of the magnetic shielding device as the design basis to ensure the precise matching between the initial coil structure and the magnetic shielding device, thereby guaranteeing the engineering feasibility of the coil from the source and greatly reducing the design risk and trial and error cost of the coil.

[0018] In one optional implementation, the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil are optimized to obtain the optimal saddle-shaped nonlinear gradient coil, including: Determine the combined magnetic field generated by the saddle-shaped nonlinear gradient coil after it is energized; Using a pre-defined optimization algorithm, the number of coil units, the arc angle, the axial length and axial center position of each pair of coil units of the saddle-shaped nonlinear gradient coil are used as optimization variables, and the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field is used as the optimization objective. Iterative optimization is performed to obtain the optimized saddle-shaped nonlinear gradient coil. The pre-defined optimization algorithm includes at least one of the escape algorithm and the particle swarm optimization algorithm.

[0019] This invention covers the key influencing factors of the magnetic field distribution of saddle-shaped coils by using the number of coil units, arc angle, axial length, and center position as core optimization variables. Furthermore, through multi-variable collaborative iteration, it can achieve full-dimensional adaptation of the magnetic field distribution, avoid local compensation deviations caused by single parameter optimization, and ensure that the synthesized magnetic field and the target nonlinear residual magnetic field are completely matched in terms of spatial distribution and gradient change trend, thus significantly improving the compensation accuracy.

[0020] In one alternative implementation, determining the resultant magnetic field generated by the saddle-shaped nonlinear gradient coil after energization includes: Based on the Biot-Savart law, the magnetic field expression of the saddle-shaped nonlinear gradient coil placed in the magnetic shielding device in cylindrical coordinates is derived; wherein, a mirror coil is introduced into the magnetic field expression to characterize the reflection effect of the end cap of the magnetic shielding device, and the mirror order is set to 0 and 1. The synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after energization is determined based on the magnetic field expression.

[0021] This invention takes into account that the end cap of the end-opening magnetic shielding device will produce a reflection / scattering effect on the magnetic field of the coil. By introducing a mirror coil to characterize this reflection effect, and specifying that the mirror order is 0 and 1, the main influence of the end cap on the magnetic field can be accurately covered, avoiding calculation errors caused by missing boundary conditions, and making the calculation result of the synthesized magnetic field closer to the real magnetic field distribution of the coil in the actual magnetic shielding environment.

[0022] In one alternative implementation, after obtaining the optimal saddle-shaped nonlinear gradient coil, the design method for the saddle-shaped nonlinear gradient coil further includes: The optimal saddle-shaped nonlinear gradient coil is simulated and verified, and it is determined whether the verification results meet the preset coil design requirements. If the verification results do not meet the preset coil design requirements, return to the steps of optimizing the number of coil units, arc angle, axial length and axial center position of each pair of coil units for the saddle-shaped nonlinear gradient coil until the verification results meet the preset coil design requirements.

[0023] This invention uses a simulation verification process to simulate the actual working scenario of the optimal coil in a magnetic shielding device before physical processing. This allows for the verification of key indicators such as the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field, and the compatibility of coil installation. This avoids deviations between theory and practice and aims to ensure the reliability of coil performance from the design stage.

[0024] Thirdly, the present invention provides a magnetic shielding compensation system, the system comprising: A single-ended open magnetic shielding device, and a saddle-shaped nonlinear gradient coil as described in the first aspect above or any corresponding embodiment thereof; wherein the saddle-shaped nonlinear gradient coil is mounted on the inner wall of the magnetic shielding device for actively generating a compensation magnetic field to suppress the nonlinear residual magnetic field within the magnetic shielding device.

[0025] The magnetic shielding compensation system of this invention adopts a composite scheme of passive shielding and active compensation. The single-end open magnetic shielding device serves as the foundation, and firstly, a high permeability material is used to achieve passive attenuation of the external magnetic field. The saddle-shaped nonlinear gradient coil serves as the core of active compensation, and specifically generates a compensation magnetic field that matches the target nonlinear residual magnetic field to accurately offset the axial nonlinear radial gradient magnetic field remaining after shielding. Compared with traditional simple passive shielding or generalized active compensation design, this collaborative design can reduce the magnetic field interference in the target area to a lower level, which greatly meets the stringent requirements of scenarios such as extremely weak magnetic field measurement and quantum experiments. Attached Figure Description

[0026] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0027] Figure 1 This is a structural block diagram of a saddle-shaped nonlinear gradient coil according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the design method of a saddle-shaped nonlinear gradient coil according to an embodiment of the present invention; Figure 3 This is a flowchart illustrating another design method for a saddle-shaped nonlinear gradient coil according to an embodiment of the present invention; Figure 4 This is a mirror image; Figure 5 This is a schematic diagram of the coil optimization process; Figure 6 This is a schematic diagram of the nonlinear gradient magnetic field generated along the Z-axis by the optimized coil; Figure 7 This is a structural block diagram of a magnetic shielding compensation system according to an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] In practical applications, the design principles of traditional coils are based on the assumptions of free space or an infinitely long ideal shielding tube, aiming to generate a uniform or strictly linear gradient magnetic field. They fail to adequately consider and model several key physical characteristics of real magnetic shielding devices: 1. Limited size and opening effect: The single-end opening structure and limited length of the magnetic shielding cylinder make the end cap act like a "magnetic mirror", causing significant reflection and mirroring effects on the magnetic field generated by the coil, thus destroying the ideal distribution of the magnetic field.

[0030] 2. Physical properties of the shielding layer: The limited thickness of the shielding layer and the nonlinear magnetic permeability of the high permeability material make the boundary conditions of the magnetic field at the interface of the shielding layer complex, which directly affects the spatial shape of the internal magnetic field.

[0031] 3. Complex interference sources: The interference magnetic field introduced by openings and holes is inherently highly nonlinear, and its spatial distribution pattern is fundamentally different from that of a linear gradient field.

[0032] Therefore, traditional uniform field coils and linear gradient coils designed based on uniform or linear assumptions are difficult to effectively match and suppress the complex nonlinear residual magnetic field caused by the above factors, resulting in limited compensation accuracy and effectiveness. Furthermore, for the compensation problem of nonlinear magnetic fields, recent studies have attempted to use inverse design methods, such as the target field method (this method first sets the desired magnetic field distribution in the target region, i.e., the nonlinear magnetic field to be compensated, and then inversely calculates the required current density distribution by solving the electromagnetic inverse problem). Although theoretically any field type can be designed, this method has significant drawbacks when applied to this field: the calculation process is extremely complex, the optimization variables are highly dimensional, and the solution is difficult; especially when multi-layer shielding, complex perforated structures, and material nonlinearity need to be considered simultaneously, the solution to the inverse problem is often unstable or even unsolvable, making the designed coil structure physically difficult to realize or manufacture. In summary, the existing technology mainly suffers from the following problems: 1. Inherent defects of passive shielding: Practical single-end open, perforated magnetic shielding cylinders have a complex spatial nonlinear distribution of residual magnetic field inside, which is an inherent defect that passive shielding cannot overcome.

[0033] 2. Limitations of traditional active compensation methods: Traditional compensation coils (such as standard saddle coils) designed based on uniform or linear gradient fields do not integrate key physical constraints such as shielding cylinder openings, end caps, and finite thicknesses in their design models. Therefore, the magnetic field generated cannot effectively match the aforementioned nonlinear residual magnetic field, resulting in poor compensation performance.

[0034] 3. Difficulty in implementing existing alternatives (reverse design): Although it can handle nonlinear fields, reverse design methods, represented by the target field method, are computationally complex, have unstable solutions, poor engineering practicality, and are difficult to reliably use for designing practically manufacturable multi-turn coil structures.

[0035] Therefore, there is an urgent need in this field for a new coil design idea and method that should be able to: (1) address the compensation requirements of nonlinear magnetic fields in a positive manner; (2) accurately incorporate the physical model of the actual shielding structure, such as single-end opening and finite thickness, into the forward design; and (3) derive a multi-turn coil scheme with clear structural parameters that is easy to implement in engineering, thereby achieving accurate and stable compensation for the complex nonlinear residual magnetic field inside the magnetic shielding cylinder.

[0036] Based on this, this embodiment provides a saddle-shaped nonlinear gradient coil to compensate for the nonlinear residual magnetic field inside the magnetic shielding barrel caused by structural factors such as single-end opening and moving holes, thereby solving the problem that conventional uniform coils and linear gradient coils are difficult to suppress such coils.

[0037] This embodiment provides a saddle-shaped nonlinear gradient coil. Figure 1This is a structural block diagram of a saddle-shaped nonlinear gradient coil according to an embodiment of the present invention. The coil is used to compensate for the nonlinear residual magnetic field within a magnetic shielding device having a single-ended opening. Figure 1 As shown, the coil includes multiple pairs of coil units arranged along the axial direction of the magnetic shielding device; wherein all coil units share the same coil radius R and arc angle φ, and the axial length of each pair of coil units is 2. l i and axial center position x i They are not the same; the number of coil units i , arc angle φ, axial length of each pair of coil units 2 l i and axial center position x i After optimization, it was determined that the synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after energization matches the target nonlinear residual magnetic field in the preset target area within the magnetic shielding device.

[0038] It should be noted that in this embodiment, all coil units share the same coil radius R (distance from the coil center to the inner wall) and arc angle φ (circumferential angle parameter, reflecting the arc distribution characteristics of the saddle-shaped winding), simplifying the coil manufacturing process. The axial arrangement of multiple pairs of coil units facilitates installation on the inner wall of the magnetic shielding device, eliminating the need for complex assembly processes and balancing practicality and economy. Furthermore, the number of coil units... i 2 axial lengths of each pair of coil units l i and axial center position x i It can be flexibly optimized and adjusted according to the distribution characteristics of the target nonlinear residual magnetic field, such as spatial complexity and gradient change rate, without reconstructing the overall coil structure, and can be adapted to single-ended magnetic shielding devices of different sizes and opening designs. Moreover, the synthesized magnetic field is precisely matched with the target nonlinear residual magnetic field, which can significantly reduce the magnetic field deviation in the preset target area within the magnetic shielding device, improve the uniformity and time stability of the magnetic field in the area, and provide a near-zero magnetic and highly stable magnetic field environment for extremely weak magnetic field measurement and precision instrument operation.

[0039] It should be noted that the coil in this embodiment is a multi-turn saddle-shaped gradient coil structure. The figure shows a three-dimensional spatial view and an axial cross-sectional view of the coil. As can be seen from the figure, the coil consists of 3 pairs of saddle-shaped coils (i.e., coil units, the number of coil units is...). i The configuration can be adapted to actual needs (the diagram only illustrates 3 pairs of saddle-shaped coils). All coil pairs share the same arc angle φ and coil radius R, but the axial length of each coil pair is 2. l i and axial center position x iThey are all different. By optimizing the distribution parameters φ of each coil pair, l i and x i This can achieve the non-uniform radial gradient magnetic field required for the target.

[0040] It should be noted that the meanings of coil radius, arc angle, axial length and axial center position in this embodiment can be adapted to the knowledge known in the art. For example, the coil radius is the coil cylinder radius in the cylindrical coordinate system. In addition, the relevant content of magnetic shielding device and preset target area in this embodiment can be adapted to the actual needs. For example, the magnetic shielding device is a magnetic shielding barrel.

[0041] In this embodiment, the design of multiple pairs of coil units with shared coil radius and arc angle, differentiated axial length and axial center position, after parameter optimization, generates a synthetic magnetic field that can accurately match the nonlinear residual magnetic field in the single-ended open magnetic shielding device. This effectively counteracts the residual magnetic field disturbance after shielding, improves the compensation accuracy and effect, and solves the problem that traditional coils are difficult to adapt to nonlinear magnetic fields.

[0042] In this embodiment, the number of coil units is determined based on the spatial complexity of the target nonlinear residual magnetic field. It should be noted that the number of coil units (also called the number of coil turns) in this embodiment is set as needed. That is, when the spatial complexity of the magnetic field is high (e.g., abrupt gradient changes in multiple regions), the number of coil units is increased to cover the complex magnetic field distribution through the superposition of multiple unit magnetic fields; when the spatial complexity is low (e.g., a gentle gradient), the number of coil units is reduced to avoid redundancy, achieving precise compensation for complexity-adaptive turns. This solves the problem that traditional coils with a fixed number of units cannot accommodate magnetic fields of varying complexity. Furthermore, considering that the spatial complexity of the internal nonlinear residual magnetic field of a single-ended magnetic shielding device varies depending on its size, opening size, and material permeability, this embodiment uses a design where the number of coil units adjusts according to the spatial complexity of the magnetic field. This eliminates the need to reconstruct the overall coil structure; only the number of units needs to be adjusted to adapt to single-ended magnetic shielding devices of different specifications, significantly improving the coil's adaptability and reusability. Specifically, the number of coil units can be precisely adapted to the nonlinear magnetic field compensation requirements based on the spatial complexity of the target nonlinear residual magnetic field. This ensures the compensation effect in complex magnetic field scenarios while avoiding problems such as material waste, increased processing difficulty, and cumbersome assembly caused by an excessive number of units in simple magnetic field scenarios, thus achieving the optimal balance between coil structure and manufacturing cost.

[0043] In this embodiment, the target nonlinear residual magnetic field is a radial gradient magnetic field that varies nonlinearly along the axis of the magnetic shielding device. The distribution of the radial gradient magnetic field is determined by a preset method, which includes at least a measurement method and a simulation method.

[0044] It should be noted that the specific content of the measurement and simulation methods in this embodiment can be adaptively set according to actual needs. For example, the measurement method (such as actual measurement with a fluxgate magnetometer) can obtain the actual distribution of the magnetic field inside the magnetic shielding device, truly reflecting the magnetic field deviation caused by processing errors and environmental interference; the simulation method (such as finite element simulation) can cover all measurement points in the target area, making up for the limitation of the limited measurement points in actual measurement, and can predict the magnetic field distribution of the unprocessed device in advance. The two methods in this embodiment are complementary, providing a comprehensive and accurate basis for coil parameter optimization and avoiding compensation failure caused by inaccurate magnetic field distribution data. Specifically, it is clear that the target nonlinear residual magnetic field is a radial gradient magnetic field that changes nonlinearly along the axis of the magnetic shielding device, which can accurately match the magnetic field distortion characteristics of a single-ended open magnetic shield, thereby accurately locking the compensation object and improving the magnetic field compensation effect in a targeted manner.

[0045] In this embodiment, the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field is achieved by minimizing the difference in magnetic field strength between the two within a preset target region.

[0046] It should be noted that, in this embodiment, by minimizing the difference in magnetic field strength at each point within the preset target area, the problems of over-compensation or under-compensation in certain areas can be avoided. That is, whether in regions with abrupt changes in axial gradient or regions with gentle gradients, targeted cancellation can be achieved, significantly reducing magnetic field fluctuations at each measurement point within the target area. This provides a reliable environment for scenarios with extremely high requirements for magnetic field uniformity, such as extremely weak magnetic field measurements and quantum experiments. Furthermore, the coil designed based on minimizing differences has a stronger adaptability of its synthesized magnetic field to the target nonlinear residual magnetic field. Even if the magnetic shielding device experiences slight magnetic field drift due to environmental changes or long-term use, the parameters can be quickly adjusted through quantified difference indicators to maintain the compensation effect and avoid compensation failure due to ambiguity in matching degree. Specifically, by using the minimization of magnetic field strength difference as the core evaluation criterion for matching degree, the matching is transformed from an ambiguous functional description into a quantifiable indicator, ensuring that the synthesized magnetic field can accurately cancel the target nonlinear residual magnetic field, making the magnetic field in the target area approach an ideal state, thereby achieving quantifiable and controllable compensation accuracy.

[0047] In this embodiment, a design method embodiment for a saddle-shaped nonlinear gradient coil is provided based on the aforementioned saddle-shaped nonlinear gradient coil. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than that shown here.

[0048] This embodiment provides a design method for a saddle-shaped nonlinear gradient coil. Figure 2 This is a flowchart illustrating the design method of a saddle-shaped nonlinear gradient coil according to an embodiment of the present invention, as shown below. Figure 2 As shown, the process includes the following steps: Step S201: Determine the saddle-shaped nonlinear gradient coil to be designed, and the target nonlinear residual magnetic field in the preset target area within the magnetic shielding device.

[0049] It should be noted that the relevant content of the saddle-shaped nonlinear gradient coil, magnetic shielding device and preset target area in this embodiment can be found in the previous text and will not be repeated here.

[0050] Step S202: Optimize the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil to obtain the optimal saddle-shaped nonlinear gradient coil, so that the synthetic magnetic field generated by the optimal saddle-shaped nonlinear gradient coil after energization matches the target nonlinear residual magnetic field to be compensated in the magnetic shielding device.

[0051] It should be noted that the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position directly determine the magnetic field distribution pattern of the saddle-shaped coil. This embodiment specifically optimizes these parameters, which allows the synthesized magnetic field to accurately match the target nonlinear residual magnetic field, avoiding the compensation deviation caused by blindly adjusting parameters in traditional designs, and greatly improving the accuracy of magnetic field cancellation in the target area.

[0052] The design method of the saddle-shaped nonlinear gradient coil in this invention can achieve targeted optimization by clearly defining the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position as the core optimization objects. This enables the synthesized magnetic field to accurately match the target nonlinear residual magnetic field, avoiding the compensation deviation caused by blind parameter adjustment in traditional design, and greatly improving the accuracy of magnetic field cancellation in the target area.

[0053] This embodiment provides a design method for a saddle-shaped nonlinear gradient coil. Figure 3 This is a flowchart illustrating another design method for a saddle-shaped nonlinear gradient coil according to an embodiment of the present invention, as shown below. Figure 3 As shown, the process includes the following steps: Step S301: Determine the saddle-shaped nonlinear gradient coil to be designed, and the target nonlinear residual magnetic field in the preset target area within the magnetic shielding device.

[0054] In this embodiment, the step S301 above, which determines the saddle-shaped nonlinear gradient coil to be designed, includes: Step a1: Obtain the structural parameters of the magnetic shielding device.

[0055] In this embodiment, the specific methods for obtaining the structural parameters can be found in relevant art, such as directly reading them from the design and processing drawings or technical manuals of the magnetic shielding device, including the inner diameter, outer diameter, axial height, radial width of the opening, and related geometric parameters such as the inner and outer radii and total axial length of the magnetic shielding device; if no drawings are available, the maximum radial dimension and axial extension dimension of the opening can be measured using calipers or a laser rangefinder, and the inner wall radius and effective axial length of the magnetic shielding device can be re-measured simultaneously to ensure that the parameters match the actual installation space.

[0056] Step a2: Based on the structural parameters, design the initial structure of the saddle-shaped nonlinear gradient coil, and determine the saddle-shaped nonlinear gradient coil to be designed based on the initial structure; wherein, the structural parameters include at least the inner and outer radii, axial length, opening size and material permeability, and the initial structure includes the number of coil units, the arc angle, the axial length of each pair of coil units and the axial center position.

[0057] It should be noted that the initial structure in this embodiment clearly defines the basic values ​​of core parameters such as the number of coil units and the arc angle, avoiding a blind start to the optimization process without a benchmark. A reasonable initial structure can significantly shorten the parameter iteration optimization cycle, reduce invalid calculations, and improve overall design efficiency. In addition, designing the initial coil based on the actual structural parameters of the magnetic shielding device can avoid rework in later designs due to structural mismatches, such as coils that are too large to install. At the same time, the parameter range of the initial structure can be reasonably limited based on the parameters of the shielding device, avoiding optimization variables from deviating from actual processing capabilities and reducing R&D trial and error costs. Furthermore, since the material permeability and opening size of the magnetic shielding device directly affect the internal residual magnetic field distribution, the initial design, combined with these parameters, allows the magnetic field coverage and distribution trend of the initial coil to initially match the generation environment of the target residual magnetic field, laying the foundation for subsequent optimization to accurately match and compensate for the magnetic field.

[0058] It should be noted that the target nonlinear residual magnetic field in the preset target area within the magnetic shielding device in this embodiment is the radial gradient magnetic field that remains in the preset target area after the single-ended open magnetic shielding device is passively shielded. Its distribution can be determined through both actual measurement (i.e., measurement method) and simulation (i.e., simulation method). Specifically, the actual measurement method involves directly collecting magnetic field data within the preset target area of ​​the finished single-ended open magnetic shielding device using professional magnetic measurement equipment, and fitting the complete distribution of the nonlinear residual magnetic field. This includes: a high-precision point measurement method (in the preset target area, such as the core area of ​​the measurement cavity, measurement points are arranged at equal axial intervals and radially layered, with an axial measurement point spacing ≤ 50mm and at least 3 radial layers, such as the center, middle diameter, and near-wall, with a total of ≥ 20 measurement points covering key locations of nonlinear magnetic field abrupt changes; then, a superconducting quantum interference magnetometer and fluxgate magnetometer are used to simultaneously collect the radial magnetic field strength, axial magnetic field gradient, and magnetic field direction of each measurement point; finally, through interpolation fitting, such as cubic spline fitting, a magnetic field distribution cloud map and axial nonlinear gradient curve of the target area are generated, ultimately determining the mathematical model of the target nonlinear residual magnetic field). Methods include: (1) Type and distribution pattern; (2) Scanning mapping method (using a magnetic scanning probe and a precision displacement stage to build an automated scanning system with a displacement stage positioning accuracy ≤0.1mm; then performing continuous surface scanning along the axial and radial directions of the magnetic shielding device, collecting magnetic field data on the scanning path in real time; finally stitching the continuous scanning data into a global magnetic field distribution matrix, extracting the axial nonlinear variation characteristics of the radial gradient magnetic field, and determining the peak, abrupt change, and uniform distribution range of the residual magnetic field); and (3) Long-term monitoring method (fixing magnetometers at key measuring points in the target area, continuously monitoring for ≥24 hours, recording the changes in magnetic field with time and environment, such as temperature and external magnetic field disturbances; then removing environmental interference noise, extracting the inherent nonlinear residual magnetic field of the magnetic shielding device, ensuring that the determined target magnetic field is the residual magnetic field of the device itself, rather than the environmental disturbance magnetic field).The simulation method is based on the structural and material parameters of the magnetic shielding device. A three-dimensional model is built using specialized simulation software, and numerical simulation is performed to obtain the nonlinear residual magnetic field of the preset target area. This method is suitable for scenarios where the device is unprocessed and coils need to be designed in advance. It includes: finite element simulation (using the inner and outer radii, axial length, single-end opening size, material permeability, and external magnetic field strength of the magnetic shielding device as input parameters, in COMSOL / ANSYS). A three-dimensional magnetic shielding simulation model is built using finite element software such as Maxwell; then the magnetic reflection boundary of the single-ended opening and the magnetic saturation characteristics of the magnetic shielding material are simulated, and a preset target area is defined as the simulation calculation domain; finally, the magnetic field control equation is solved, and the axial distribution data of the radial gradient magnetic field and the nonlinear gradient change curve in the target area are output, directly obtaining the distribution law and numerical model of the target nonlinear residual magnetic field) and analytical simulation method (adapted to rapid initial calculation and auxiliary optimization, such as deriving the magnetic field analytical formula of the single-ended opening magnetic shielding device based on magnetic shielding theory and the mirror method, introducing the reflection effect of the opening end cap (such as the mirror order 0 and 1, consistent with the calculation logic of the coil magnetic field; then substituting the structural parameters of the magnetic shielding device and the material permeability into the analytical formula, and calculating through MATLAB / Python programming to quickly obtain the approximate distribution of the nonlinear residual magnetic field in the target area; it can be used for rapid magnetic field prediction in the initial design of the coil, and the accuracy can be corrected by combining the experimental method or the finite element method later); this is only an example.

[0059] Step S302: Optimize the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil to obtain the optimal saddle-shaped nonlinear gradient coil, so that the synthetic magnetic field generated by the optimal saddle-shaped nonlinear gradient coil after energization matches the target nonlinear residual magnetic field to be compensated in the magnetic shielding device.

[0060] Specifically, step S302 above optimizes the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil to obtain the optimal saddle-shaped nonlinear gradient coil, including: Step S3021: Determine the combined magnetic field generated by the saddle-shaped nonlinear gradient coil after it is energized.

[0061] Specifically, step S3021 includes: Step b1: Based on the Biot-Savart law, derive the magnetic field expression of the saddle-shaped nonlinear gradient coil placed inside the magnetic shielding device in cylindrical coordinates; wherein, a mirror coil is introduced into the magnetic field expression to characterize the reflection effect of the end cap of the magnetic shielding device, and the mirror order is set to 0 and 1.

[0062] In this embodiment, the end cap of the single-ended magnetic shielding device reflects / scatters the coil's magnetic field, which is a key factor causing magnetic field distortion (traditional calculations often ignore this effect, leading to a large deviation between the synthesized magnetic field and the actual field). This embodiment introduces a mirror coil to characterize this reflection effect, explicitly defining the mirror order as 0 (original coil) and 1 (first-order reflection mirror). This accurately covers the main influence of the end cap on the magnetic field (first-order reflection is the core contributor to end cap reflection; higher-order reflections have negligible influence), avoiding calculation errors caused by missing boundary conditions and making the calculated synthesized magnetic field more closely approximate the actual magnetic field distribution of the coil in a real magnetic shielding environment. Furthermore, the saddle-shaped coil's windings are distributed along a cylindrical surface, naturally adapting to the spatial modeling logic of cylindrical coordinates. That is, in this embodiment, the magnetic field expression is derived based on cylindrical coordinates, allowing direct integration using the geometric parameters of the saddle-shaped coil (coil radius, arc angle, axial length), eliminating the need for complex coordinate transformations and significantly simplifying the integration process of the Biot-Savart law. Compared to Cartesian coordinates, the magnetic field expression in cylindrical coordinates can more intuitively relate coil structural parameters to magnetic field components (radial magnetic field and axial magnetic field), providing clear mathematical support for subsequent parameter optimization.

[0063] It should be noted that the Biot-Savart law is an analytical formula for deriving the expression of the magnetic field, and its specific content can be found in relevant well-known content in this field for adaptive understanding.

[0064] Step b2: Determine the synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after energization based on the magnetic field expression.

[0065] In this embodiment of the invention, considering that the end cap of the end-opening magnetic shielding device will produce a reflection / scattering effect on the magnetic field of the coil, by introducing a mirror coil to characterize the reflection effect and specifying that the mirror order is 0 and 1, the main influence of the end cap on the magnetic field can be accurately covered, avoiding calculation errors caused by missing boundary conditions, and making the calculation result of the synthesized magnetic field closer to the real magnetic field distribution of the coil in the actual magnetic shielding environment.

[0066] Step S3022: Using a preset optimization algorithm, with the number of coil units, arc angle, axial length and axial center position of each pair of coil units as optimization variables, and the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field as the optimization objective, iterative optimization is performed to obtain the optimized saddle-shaped nonlinear gradient coil; wherein, the preset optimization algorithm includes at least one of the escape algorithm and particle swarm optimization algorithm.

[0067] It should be noted that the particle swarm optimization algorithm has fast convergence speed and strong robustness, and can quickly approach the optimal parameter range, making it suitable for initial optimization. The escape algorithm has the ability to escape local optima, which can avoid the optimization getting stuck in the blind zone due to parameter coupling and ensure the acquisition of the global optimal solution. In this embodiment, two algorithms can be selected or used in combination, which not only solves the blindness of traditional manual adjustment and experience design, but also balances the optimization accuracy and iteration efficiency, and can significantly improve the optimization efficiency compared with traditional optimization methods.

[0068] In this embodiment of the invention, the key influencing factors of the magnetic field distribution of the saddle-shaped coil are covered by using the number of coil units, the arc angle, the axial length, and the center position as core optimization variables. Furthermore, through multi-variable collaborative iteration, the magnetic field distribution can be fully adapted in all dimensions, avoiding local compensation deviations caused by single parameter optimization. This ensures that the synthesized magnetic field and the target nonlinear residual magnetic field are completely matched in terms of spatial distribution and gradient change trend, thus significantly improving the compensation accuracy.

[0069] It should be noted that in practical applications, there are differences between theoretical derivations (such as simplification of magnetic field expressions and assumptions in optimization algorithms) and actual working conditions, which can easily lead to the optimized coil theoretically meeting the requirements but failing in practice. Therefore, after obtaining the optimal saddle-shaped nonlinear gradient coil, the design method of the saddle-shaped nonlinear gradient coil in this embodiment also includes: Step c1: Perform simulation verification on the optimal saddle-shaped nonlinear gradient coil and determine whether the verification results meet the preset coil design requirements.

[0070] In this embodiment, the specific requirements for the preset coil design can be adaptively adjusted according to actual needs, such as the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field, and the compatibility of coil installation.

[0071] Step c2: If the verification result does not meet the preset coil design requirements, return to the step of optimizing the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil until the verification result meets the preset coil design requirements.

[0072] In this embodiment of the invention, if the simulation finds that the local magnetic field difference in the target area exceeds the standard, the axial length / center position of the corresponding coil unit can be adjusted by focusing on the area. If the complex magnetic field is not fully covered due to insufficient number of coil units, the number of units can be increased iteratively and the parameters can be re-optimized to specifically correct the details that were not covered in the single optimization. This helps to overcome the limitations of single optimization and greatly improve the design accuracy.

[0073] In this embodiment of the invention, the simulation verification process can simulate the actual working scenario of the optimal coil in the magnetic shielding device before physical processing, thereby verifying key indicators such as the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field, and the coil installation adaptability, avoiding deviations between theory and practice, and aiming to ensure the reliability of coil performance from the design stage.

[0074] In practical applications, saddle-shaped coils are often used to compensate for the magnetic field inside magnetically shielded barrels. However, the shielding layer made of high-permeability materials can cause magnetic field distortion, and leakage magnetic effects such as openings in the magnetically shielded barrel can lead to a nonlinear distribution of the internal magnetic field, reducing the compensation capability of existing compensation coils. Currently, in the field of electromagnetic coil design, there are generally two main technical paths. One is the reverse design method, such as the target field method. This method differs significantly from the traditional forward design. It first solves the inverse problem of electromagnetism based on the desired magnetic field distribution characteristics of the target region, and then calculates the current density distribution required to generate the magnetic field. The continuous current density is then discretized to finally determine the specific geometric structure of the coil winding. This method can be viewed as the reverse process of electromagnetism, and it has significant advantages in designing complex coils with arbitrary field distributions. This application focuses on the existing problems and proposes a new scheme based on the mirror method, an improved multi-turn saddle-shaped nonlinear gradient coil, and an escape algorithm optimization. This scheme uses a more classic and fundamental forward design method. In contrast to reverse engineering, forward engineering first predetermines the physical parameters of the coil (such as the saddle-shaped coil in this embodiment), including its geometry, dimensions, and winding method. Then, based on fundamental principles of electromagnetism such as the Biot-Savart Law, a mathematical and physical model of the coil structure is established. The magnetic field distribution generated by this specific structure in space (especially within the target area) is calculated and analyzed in a forward manner. The actual magnetic field distribution within the magnetic shielding device is taken as the final design target for the coil's magnetic field. By adjusting the preset geometric parameters and repeating the forward calculations, the design is continuously optimized until the generated magnetic field meets the predetermined requirements.

[0075] In this embodiment, considering the influence of the magnetic shielding cylinder, the general expression for the magnetic field generated by the coil can be written as:

[0076] in, This represents the continuous surface current density of the coil at the target field point. The magnetic field generated at that location; , , These represent the radial distance, azimuth, and altitude of the target field point in cylindrical coordinates, respectively; other relevant parameters are defined as follows:

[0077] In the above formulas, The permeability of free space, and These are the first and second type modified Bessel functions, respectively. and These are the first derivatives of the corresponding functions. The relative permeability of the magnetic shielding cylinder material. Where is the coil radius, and These are the inner and outer radii of the magnetic shielding cylinder, respectively. Coil current density Fourier transform. , , , , , and This is an intermediate variable with no practical meaning; subscript Indicates the order, parameter This represents the integration parameter.

[0078] Furthermore, the end cap of the magnetic shielding cylinder affects the magnetic field generated by the coil, acting similarly to a "magnetic mirror." For example... Figure 4 As shown, the reflection effect of the end cap can be modeled by introducing image coils located symmetrically. It should be noted that in the figure, the Z-axis represents the axis of the coil (corresponding to the axis of the magnetic shielding device), and ⊙ indicates that the current is perpendicular to the paper and outwards. This indicates that the current is perpendicular to the paper and pointing inwards, and that within each layer, the current directions on the left and right sides are symmetrical and opposite (e.g., layer p=0: from top to bottom, the left side is...). And ⊙, the right side is ⊙ and ⊙ This is the core current layout for the saddle-shaped coil to generate a radial gradient magnetic field. The multi-layered reverse current units along the Z-axis are a concrete manifestation of "multiple pairs of coil units distributed along the axial direction." That is, by superimposing the currents in different layers, a radial gradient magnetic field that varies non-linearly along the axial direction can be synthesized, which precisely matches the non-linear residual magnetic field in the single-ended open magnetic shielding device, achieving accurate compensation. Therefore, the mirrored coil in the figure and the original coil (p=0) jointly contribute to the magnetic field of the target region.

[0079] Furthermore, considering the mirror effect in this embodiment, the current density of the saddle-shaped coil inside the magnetic shielding cylinder... It can be derived from a series of Heaviside step functions and Dirac The function is represented as follows:

[0080] further, The total number of coil pairs, for Regarding the number of turns of the coil, For current, and The first For the half-angle and half-length of the coil, p is the mirror order (p=0 represents the original coil). This is half the length of the magnetic shielding cylinder.

[0081] Performing a Fourier transform on the above current density, we obtain:

[0082]

[0083] Furthermore, since the magnetic shielding cylinder targeted in this embodiment has a single-end open structure, its end cap effect only needs to consider the superposition of the magnetic fields of the original coil (p=0) and its first-order mirror coil (p=1). Substituting equation (4) into equation (1) and summing only for p=0 and p=1, we can obtain the expression for the magnetic field of the radial gradient saddle-shaped coil inside the single-end open magnetic shielding cylinder:

[0084] Furthermore, inside the magnetic shielding cylinder, the magnetic field components in the Cartesian coordinate system... and Components in cylindrical coordinate system and The result of the conversion is:

[0085] Furthermore, the compensation coil designed in this embodiment is composed of multi-turn wires. Therefore, the total magnetic field at any point inside the magnetic shielding cylinder... The components can be obtained by superimposing the magnetic fields generated by each turn of the coil. Its mathematical expression is:

[0086] in, This represents the total number of turns of the coil. and The first The radial and angular components of the magnetic field generated by the coil at the target point. Specifically, in this embodiment, the magnetic field generated by the designed saddle-shaped coil structure can be accurately calculated in the forward direction using equations (5) to (7).

[0087] In this embodiment, optimization of the designed coil is also included, using an escape algorithm to iteratively find the optimal coil parameters that satisfy the target magnetic field. Figure 5This is a schematic diagram of the coil optimization process. As shown in the diagram, the process includes: starting, setting the crowd size and number of iterations (30 is sufficient for a normal scale), setting the target area and extracting the target magnetic field (the target area depends on the area needed inside the magnetic shielding barrel), setting the coil and magnetic shielding barrel size parameters, setting the coil turns optimization range, setting the coil turns (increasing the coil turns one by one), setting the escape algorithm optimization parameters, simultaneously setting parameter limits, the escape algorithm optimization calculation to obtain the optimal coil parameters, completing the optimization within the number of turns in the line graph, determining the optimal number of coil turns to obtain the optimal coil winding, and ending.

[0088] In this embodiment, the optimal coil parameters that satisfy the target magnetic field can be obtained through the above coil optimization process. Simulation calculations can then be performed to obtain a corresponding magnetic field cloud map, which visually demonstrates the shielding effect of the magnetic shielding structure. Figure 6 This is a schematic diagram of the nonlinear gradient magnetic field generated along the Z-axis by the optimized coil. As shown in the figure, the multiple colored planes in the device represent different spatial sections of the target area (such as multiple XY planes along the Z-axis), used to show the magnetic field distribution characteristics in three-dimensional space. The magnetic field cloud map in the lower left corner of the figure is a schematic diagram of the quantitative distribution of the interference magnetic field in the XZ plane. The coordinate system is centered at the origin (0 in the figure) and shows the magnetic field in the X (horizontal) and Z (vertical) directions. The unit of the color scale is "nT (nanotesla)", and the color ranges from blue (-4nT) to red (4nT), corresponding to the positive and negative signs and magnitude of the magnetic field strength. The distribution characteristics are: the left side is dominated by negative magnetic field (blue) and the right side is dominated by positive magnetic field (red), which reflects the non-uniformity of the interference magnetic field in this plane.

[0089] This embodiment also provides a magnetic shielding compensation system. Figure 7 This is a structural block diagram of a magnetic shielding compensation system according to an embodiment of the present invention. As shown in the figure, the system includes: a single-ended open magnetic shielding device 701 and a saddle-shaped nonlinear gradient coil 702; wherein, the saddle-shaped nonlinear gradient coil 702 is installed on the inner wall of the magnetic shielding device 701 and is used to actively generate a compensation magnetic field to suppress the nonlinear residual magnetic field within the magnetic shielding device. Note that the compensation magnetic field in this embodiment is the synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after being energized, which matches the target nonlinear residual magnetic field of a preset target area within the magnetic shielding device. It should be noted that this system is used to implement the above embodiments and preferred embodiments, and details already described will not be repeated.

[0090] The magnetic shielding compensation system of this invention employs a composite scheme of passive shielding and active compensation. A single-ended open magnetic shielding device serves as the foundation, first using high-permeability materials to passively attenuate the external magnetic field. A saddle-shaped nonlinear gradient coil acts as the core of active compensation, specifically generating a compensation magnetic field that matches the target nonlinear residual magnetic field. This precisely counteracts the axial nonlinear radial gradient magnetic field remaining after shielding. Compared to traditional purely passive shielding or generalized active compensation designs, this collaborative design can reduce magnetic field interference in the target area to a much lower level, greatly satisfying the stringent requirements of scenarios such as extremely weak magnetic field measurement and quantum experiments.

[0091] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and all such modifications and variations fall within the scope defined by the appended claims.

Claims

1. A saddle-shaped nonlinear gradient coil, said coil being used to compensate for a nonlinear residual magnetic field within a magnetic shielding device having a single-ended opening, characterized in that, The coil includes: Multiple pairs of coil units are arranged along the axial direction of the magnetic shielding device; wherein, all coil units share the same coil radius and arc angle, but the axial length and axial center position of each pair of coil units are not the same; The number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position are optimized and determined so that the synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after being energized matches the target nonlinear residual magnetic field of the preset target area within the magnetic shielding device.

2. The saddle-shaped nonlinear gradient coil according to claim 1, characterized in that, The number of coil units is determined based on the spatial complexity of the target nonlinear residual magnetic field.

3. The saddle-shaped nonlinear gradient coil according to claim 1 or 2, characterized in that, The target nonlinear residual magnetic field is a radial gradient magnetic field that varies nonlinearly along the axis of the magnetic shielding device. The distribution of the radial gradient magnetic field is determined by a preset method, which includes at least a measurement method and a simulation method.

4. The saddle-shaped nonlinear gradient coil according to claim 1, characterized in that, The matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field is achieved by minimizing the difference in magnetic field strength between the two within a preset target region.

5. A design method for a saddle-shaped nonlinear gradient coil, applied to the saddle-shaped nonlinear gradient coil according to any one of claims 1 to 4, characterized in that, The method includes: Determine the saddle-shaped nonlinear gradient coil to be designed, and the target nonlinear residual magnetic field in the preset target area within the magnetic shielding device; The number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil are optimized to obtain the optimal saddle-shaped nonlinear gradient coil, so that the synthetic magnetic field generated by the optimal saddle-shaped nonlinear gradient coil after being energized matches the target nonlinear residual magnetic field to be compensated in the magnetic shielding device.

6. The design method of the saddle-shaped nonlinear gradient coil according to claim 5, characterized in that, The process of determining the saddle-shaped nonlinear gradient coil to be designed includes: Obtain the structural parameters of the magnetic shielding device; Based on the structural parameters, an initial structure for a saddle-shaped nonlinear gradient coil is designed, and the saddle-shaped nonlinear gradient coil to be designed is determined based on the initial structure. The structural parameters include at least the inner and outer radii, axial length, opening size, and material permeability. The initial structure includes the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position.

7. The design method of the saddle-shaped nonlinear gradient coil according to claim 5, characterized in that, The optimization of the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil to obtain the optimal saddle-shaped nonlinear gradient coil includes: Determine the combined magnetic field generated by the saddle-shaped nonlinear gradient coil after it is energized; Using a preset optimization algorithm, with the number of coil units, arc angle, axial length and axial center position of each pair of coil units as optimization variables, and the matching degree between the synthesized magnetic field and the target nonlinear residual magnetic field as the optimization objective, iterative optimization is performed to obtain the optimized saddle-shaped nonlinear gradient coil; wherein, the preset optimization algorithm includes at least one of the escape algorithm and particle swarm optimization algorithm.

8. The design method of the saddle-shaped nonlinear gradient coil according to claim 7, characterized in that, Determining the synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after energization includes: Based on the Biot-Savart law, the magnetic field expression of the saddle-shaped nonlinear gradient coil placed inside the magnetic shielding device in cylindrical coordinates is derived; wherein, the magnetic field expression introduces a mirror coil to characterize the reflection effect of the end cap of the magnetic shielding device, and the mirror order is set to 0 and 1; The synthetic magnetic field generated by the saddle-shaped nonlinear gradient coil after energization is determined based on the magnetic field expression.

9. The design method of the saddle-shaped nonlinear gradient coil according to claim 5, characterized in that, After obtaining the optimal saddle-shaped nonlinear gradient coil, the method further includes: The optimal saddle-shaped nonlinear gradient coil is simulated and verified, and it is determined whether the verification results meet the preset coil design requirements. If the verification result does not meet the preset coil design requirements, the process returns to the step of optimizing the number of coil units, the arc angle, the axial length of each pair of coil units, and the axial center position of the saddle-shaped nonlinear gradient coil until the verification result meets the preset coil design requirements.

10. A magnetic shielding compensation system, characterized in that, The system includes: A single-ended open magnetic shielding device, and a saddle-shaped nonlinear gradient coil as described in any one of claims 1 to 4; wherein the saddle-shaped nonlinear gradient coil is installed on the inner wall of the magnetic shielding device for actively generating a compensation magnetic field to suppress the nonlinear residual magnetic field within the magnetic shielding device.

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