Electromagnetic design analysis method, system, computer readable storage medium and electronic device for a pulsed coaxial coil system for an FRC device

Abstract

This invention provides an electromagnetic design and analysis method, system, computer-readable storage medium, and electronic device for a pulsed coaxial coil system in an FRC device, comprising: obtaining target physical requirement parameters of the coaxial coil system; establishing a parameter calculation model, the model including a set of simplified analytical formulas describing the mapping relationship between the target physical requirement parameters and key electrical parameters of the power supply; and, based on the parameter calculation model, calculating the electromagnetic design and analysis method for a pulsed coaxial coil system with a specific number of coils. N Perform a parameter space scan for the variables to generate a result that at least includes the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max With the number of coils N The parameter space scan plot changes; the key performance parameter thresholds of the solid-state switching device are obtained, and the parameter space scan plot is compared with the key performance parameter thresholds; based on the comparison analysis results, the number of coils that meet the performance parameter constraints of the solid-state switching device is determined. N This application significantly reduces the computational load, thereby improving the efficiency of system forward design and engineering analysis.

Description

Technical Field

[0001] This invention relates to the field of pulsed strong magnetic field and pulsed power supply technology, and more specifically, to an electromagnetic design and analysis method, system, computer-readable storage medium, and electronic device for a pulsed coaxial coil system for an FRC device. Background Technology

[0002] In FRC devices, a pulsed coaxial coil system powered by a pulsed power supply is typically used to generate a high-intensity pulsed magnetic field to achieve plasma formation, heating, and maintenance. In traditional pulsed coaxial coil system and power supply design, researchers usually employ a forward trial-and-error design logic. Designers first preset a set of coil geometry and power supply parameters based on experience, and then import them into complex finite element or circuit simulation software for detailed forward simulation calculations. If the simulation results do not meet the target requirements, or if the key electrical parameters of the power supply exceed the limits of the existing hardware, the parameters need to be readjusted and the simulation repeated.

[0003] The aforementioned traditional design methods have significant drawbacks: First, traditional methods require a detailed circuit and electromagnetic field simulation for each parameter adjustment. To meet the overall requirements of the electromagnetic system and determine the number of magnets and the power switch stacking scheme, several iterations lasting months are usually needed, and the overall design often takes several months.

[0004] Secondly, the sole pursuit of electromagnetic or energy storage performance leads to a disconnect between hardware and software design. Existing inductor or coil-aided design methods often focus only on the physical properties of the coil itself, neglecting the actual selection constraints of solid-state switching devices in pulse power supplies. This results in theoretically calculated optimal solutions often having to be scrapped and restarted in engineering implementation because it is difficult to find solid-state switching devices with matching voltage or current carrying capacity, or the device utilization rate is extremely low.

[0005] Therefore, there is an urgent need in this field for a rapid electromagnetic design and analysis method that can break free from the dependence on time-consuming simulations and deeply integrate theoretical calculations with the stress threshold of commercial switching devices. Summary of the Invention

[0006] This invention provides an electromagnetic design and analysis method, system, computer-readable storage medium, and electronic device for a pulse coaxial coil system of an FRC device. It aims to solve the problems in the prior art where the design of pulse coil systems relies heavily on detailed simulation, resulting in long iteration cycles and difficulty in efficiently implementing solutions due to detachment from actual hardware constraints. By significantly simplifying the computational load, it improves the efficiency of forward design and engineering analysis of the system.

[0007] To achieve the above objectives, the present invention provides an electromagnetic design and analysis method for a pulsed coaxial coil system for an FRC device. The pulsed coaxial coil system includes multiple coaxially arranged coils, each coil being powered by an independent pulse capacitor power supply. The method includes: Obtain the target physical requirements parameters of the coaxial coil system; the target physical requirements parameters include at least the total axial length. l Coil radius r Target internal magnetic field B and the rise time of the magnetic field t rise ; A parameter calculation model is established, which includes a set of simplified analytical formulas describing the mapping relationship between the target physical requirement parameters and the key electrical parameters of the power supply, including the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max The simplified analytical formula set is based on the number of coils. N As core variables; Based on the parameter calculation model, with the number of coils N Perform a parameter space scan for the variables to generate a result that at least includes the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max With the number of coils N A spatial scan of the changing parameters; The key performance parameter thresholds of solid-state switching devices are obtained, and the parameter space scan map is compared and analyzed with the key performance parameter thresholds. Based on the comparative analysis results, the number of coils that meet the performance parameter constraints of the solid-state switching device was determined. N .

[0008] In one embodiment, the simplified analytical formula set specifically includes:

[0009] in, μ 0 The permeability of free space, S The cross-sectional area of ​​the coil is... K This is the Nagaoka coefficient.

[0010] In one embodiment, the number of coils that meet the performance parameter constraints of the solid-state switching device is determined based on the comparative analysis results. NSpecifically, it includes: Obtain the maximum allowable voltage of the solid-state switching device. U swith Maximum current I swith and maximum current change rate di / dt| swith As the threshold for the aforementioned key performance parameters; Assuming the number of switches connected in series is n and the number of switches connected in parallel is m, the solution involves calculating the voltage equalization / current equalization coefficients. The following set of inequalities determines the number of coils that satisfy the hardware constraints. N Feasible domain:

[0011] Taking into account the cost of switching devices, the final number of coils N and the corresponding series-parallel stacking scheme of switches are determined in the feasible region; Where α1, α2, and α3 are the pressure equalization / flow equalization coefficients in the above three inequalities, respectively.

[0012] In one embodiment, the step of performing a parameter space scan using the number of coils N as a variable to generate a parameter space scan map specifically includes: Discretize the maximum voltage using a data processing program. U max Maximum current I max and maximum current change rate di / dt| max The independent variable includes the target's internal magnetic field. B The number of coils N and the rise time of the magnetic field t rise ; Numerical calculations are performed by substituting the simplified analytical formula set into the multidimensional grid nodes composed of the independent variables. Based on the calculation results, contour maps are drawn as the parameter space scan map, and the key performance parameter thresholds of the solid-state switching device are drawn as constraint lines. The intersection points of the constraint lines and the contour map are read to determine the number of coils that simultaneously satisfy the threshold constraints of each performance parameter. N The range or minimum value of .

[0013] In one embodiment, the drawing of contour maps based on the calculation results as the parameter space scan map includes at least one of the following forms: With the target's internal magnetic field B and the number of coils N Use the coordinate axes as variables to plot and display the maximum current.I max Or the maximum current change rate di / dt| max Contour map of numerical distribution; With the target's internal magnetic field B and the rise time of the magnetic field t rise Use the coordinate axes as variables to plot and display the maximum voltage. U max Contour map of numerical distribution.

[0014] In one embodiment, the number of coils required to satisfy the performance parameter constraints of the solid-state switching device is determined. N Subsequently, the method further includes: Based on the determined number of coils N And using the simplified analytical formula set, the key electrical parameters and actual capacitance value of the pulse capacitor power supply can be calculated in reverse. C ; The series-parallel stacking scheme of the pulse capacitor power supply is determined based on the key electrical parameters. Combined with the actual capacitance value C The complete electromagnetic design scheme of the output pulse coaxial coil system is derived from the series-parallel stacking scheme of the aforementioned switches.

[0015] In one embodiment, the method further includes: When the number of coils that meet the performance parameter constraints of the solid-state switching device cannot be found in the parameter space scan diagram. N At that time, the total axial length in the target physical requirement parameters is iteratively adjusted. l The radius of the coil r Or the rise time of the magnetic field t rise ; The steps of establishing the parameter calculation model and parameter space scanning are repeated using the adjusted target physical requirement parameters until a feasible number of coils is found. N .

[0016] A rapid electromagnetic design and analysis system for pulsed coaxial coil systems in FRC devices, comprising: The parameter acquisition module acquires the target physical requirement parameters of the coaxial coil system; the target physical requirement parameters include at least the total axial length of the coaxial coil system. l Coil radius r Target internal magnetic field B and the rise time of the magnetic field t rise ; The model building module establishes a parameter calculation model based on the data acquired by the parameter acquisition module. This model includes a set of simplified analytical formulas describing the mapping relationship between the target physical requirement parameters and key electrical parameters of the power supply. The key electrical parameters of the power supply include the maximum current of the power supply. I max Maximum voltage U max and maximum current change rate di / dt| max The simplified analytical formula set is based on the number of coils. N As core variables; The spatial scanning module is used to calculate the model based on the parameters of the model construction module, using the number of coils. N Perform a parameter space scan for the variables to generate a result that at least includes the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max A parameter space scan diagram showing how the number of coils N varies; The comparison constraint module is used to obtain the key performance parameter thresholds of solid-state switching devices, and compares and analyzes the key performance parameter thresholds as constraint boundaries with the parameter space scan map generated by the space scan module. The scheme determination module is used to determine the number of coils that satisfy the performance parameter constraints of the solid-state switching device based on the comparative analysis results of the comparative constraint module. N .

[0017] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0018] An electronic device, comprising: Memory, used to store computer programs; A processor for executing a computer program stored in the memory to implement the steps of the method.

[0019] The present invention has the following beneficial effects: 1. Simplification: This invention breaks away from the lengthy process of pre-setting + finite element simulation in traditional design, deriving and employing a simplified set of engineering approximation formulas. Verified in actual projects, the relative error between the calculation results using the simplified analytical formulas of this invention and the normal simulation results is controlled within 10%, achieving computational dimensionality reduction while ensuring acceptable engineering errors.

[0020] 2. Low Cost: This invention does not limit the optimization objective to the purely physical extreme values ​​of the coil itself, but rather crosses boundaries by using the limiting stress parameters of existing commercial solid-state switching devices, such as maximum withstand voltage, maximum current carrying capacity, and di / dt withstand capability, as mandatory inequality constraints. This ensures that the calculated number of coils and circuit topology can match existing commercial devices, effectively improving the utilization efficiency of existing devices and reducing the overall cost.

[0021] 3. High efficiency: Designing the number of magnets and the stacking scheme of power switches using traditional methods usually requires several detailed simulation iterations and takes about 6 months; however, using the rapid electromagnetic design and analysis method of this invention, designers can quickly and accurately determine the number of magnets and the stacking scheme of power switches within a week, thus improving design efficiency. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating a rapid electromagnetic design and analysis method for a pulse coaxial coil system in an FRC device according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of a rapid electromagnetic design and analysis system for a pulse coaxial coil system of an FRC device according to an embodiment of the present invention; Figure 3 This is a contour plot showing the variation of the required coil current with the required magnetic field and the number of coil turns in an embodiment of the present invention. Figure 4 This is a contour plot showing the variation of capacitor or coil voltage with required magnetic field and rise time according to an embodiment of the present invention. Figure 5 This is a contour plot showing the rate of change of coil current as a function of the required magnetic field and the number of coil turns, according to an embodiment of the present invention.

[0023] Among them, 100 is the parameter acquisition module; 200 is the model construction module; 300 is the spatial scanning module; 400 is the comparison constraint module; and 500 is the scheme determination module. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0025] like Figure 1As shown, this embodiment provides a rapid electromagnetic design and analysis method for a pulsed coaxial coil system in an FRC device. In the FRC device, the pulsed coaxial coil system consists of multiple coils arranged coaxially in space. To achieve flexible control of the magnetic field, each coil is independently powered by a set of pulsed capacitor power supplies, which include energy storage capacitors, charging modules, and solid-state discharge switches. The method of this embodiment is executed by a computer, server, or similar data processing equipment, and the specific steps are as follows: S1: Obtain target physical requirement parameters: Based on the physical experimental requirements or engineering design outline of the FRC device, obtain the reference parameters of the coaxial coil system, including: the total axial length of the coaxial coil system. l The radius of the coil r Target internal central magnetic field strength B And the required time to reach the peak magnetic field, i.e., the magnetic field rise time. t rise The radius of the coil r It can be determined based on the size of the vacuum chamber of the device.

[0026] S2: Establish a system based on the number of coils N Simplified parameter calculation model for core variables: Traditional methods require dividing the coil inductance and current distribution into infinitesimal elements and calculating a massive mutual inductance matrix. This embodiment abandons this time-consuming approach and directly derives a set of engineering analytical formulas tailored to the characteristics of pulsed strong magnetic field systems. Due to the total axial length... l With parameters fixed, this embodiment will specify the number of coils. N As the core independent variable, the simplified analytical formula set containing the mapping relationship is as follows: Maximum current formula:

[0027] Equivalent inductance formula:

[0028] Maximum voltage formula:

[0029] Formula for maximum current change rate:

[0030] in, μ 0 Let be the free permeability, and be a known constant. S Let be the cross-sectional area of ​​the coil. K The introduced Nagaoka coefficient is used to provide an engineering approximation correction for the end effects of finite-length solenoids. Experiments show that, after adopting the simplified formula above, the relative error with the full-scale electromagnetic field simulation results remains within 10%.

[0031] It should be noted that, as shown in the above formula, in the total axial length l Coil radius r and the target's internal magnetic field B Under fixed conditions, the maximum voltage required by the power supply U max Essentially related to the number of coils N Irrelevant, but maximum current I max and maximum current change rate di / dt| max All are related to the number of coils N It is inversely proportional. This mathematical law provides a theoretical basis for subsequently adjusting N to avoid hardware overload.

[0032] S3: Perform a parameter space scan: Use programming languages ​​such as Python to write data processing programs. First, define the target's internal magnetic field in the code. B Number of coils N and magnetic field rise time t rise The independent variable is set, and its reasonable discrete step size is set for discretization.

[0033] Subsequently, on the multidimensional grid nodes composed of these discrete independent variables, the program automatically substitutes the simplified analytical formula set in S2 to calculate the corresponding values ​​for each grid node in batches. U max , I max and di / dt| max The specific value.

[0034] Finally, the plotting function is called to plot the maximum current with B and N as the coordinate axes. I max Contour plot and maximum current change rate di / dt| max contour maps, and with B and t rise Maximum voltage of coordinate axis variables U max Contour map.

[0035] S4: Perform hard constraint comparison by combining the parameter thresholds of solid-state switching devices: This is a crucial step in implementing the solution in this embodiment. It involves obtaining the factory performance limits of commercially available solid-state switching devices, such as thyristors and IGBTs, i.e., the maximum allowable turn-off voltage. U switch Maximum on-state current Iswitch and maximum allowable rate of change of current di / dt| switch .

[0036] These physical limits are used as rigid constraint lines and superimposed on the contour plot generated by S3. By observing the intersection points of the constraint lines and the scan relationship curve through the graphical interface, the number of coils that meet the safety stress requirements can be intuitively determined. N The range of values ​​for is given. In the specific numerical solution process, it is assumed that the number of switches connected in series in the power module is n, and the number connected in parallel is m. To account for the actual voltage / current imbalance problem in the circuit, a current / voltage sharing safety factor is introduced. The following set of inequalities will be solved:

[0037] Taking into account the cost of switching devices, the final number of coils N and the corresponding series-parallel stacking scheme of switches are determined in the feasible region; Where α1, α2, and α3 are the pressure equalization / flow equalization coefficients in the above three inequalities, respectively.

[0038] Using this system of inequalities, the algorithm can quickly traverse and filter out reasonable options that ensure the safe operation of the system. (N, n, m) Parameter combination scheme.

[0039] Preferably, the values ​​of α1, α2, and α3 are in the range of 0.8-0.9.

[0040] S5: Determine the number of coils and the final output scheme: Taking into account both the procurement cost of the switching devices and the installation complexity of the system, an optimal number of coils is selected from the valid parameter combinations. N And the corresponding series and parallel connection schemes for switches.

[0041] Based on this, according to the selected N Substitute the values ​​back into the formula to deduce the actual required power supply capacitor value. C The final output is a complete electromagnetic design scheme for a pulsed coaxial coil system, including the mechanical layout. N Stacking schemes for quantity and electrical topology.

[0042] As a protection mechanism, if the program finds that under the current physical input, all parameter space scan results cannot meet the threshold of existing switching devices, it indicates that the original physical specifications exceed the limits of real-world engineering. In this case, the system will prompt the designer to fine-tune the input parameters in step S1, such as appropriately increasing the rise time. t rise Or adjust the total length l Then, the scan iterations of S2-S5 are quickly re-executed until a usable solution is found.

[0043] In a medium-sized FRC device construction project, the target parameters were set as follows: a specific magnetic field distribution was required, and the overall system requirements were strict.

[0044] Using traditional methods, the design team needs to pre-define the coil structure, draw a 3D model, and import it into finite element software such as Ansys. Each mesh generation and transient field solution takes several hours. After obtaining the current waveform, it was found that it exceeded the selected IGBT's... d|dt The limits were reached. Therefore, the process was repeated, adjusting the number of coil turns and spacing, and performing co-simulation again. This trial-and-error cycle often required dozens of iterations, taking approximately six months to finalize the number of coils and the power supply topology.

[0045] In the rapid electromagnetic design method of this invention, engineers only need to input the target physical parameters into the program. The computer can generate a parameter space scan map within seconds by analyzing the set of formulas and performing a grid scan. By substituting the pre-selected IGBT specifications (such as 4500V / 3000A) as constraints into the set of inequalities, the program can accurately calculate the optimal number of coils within a week or even a few days. N=12 It also directly provided corresponding suggestions for series and parallel power switch topologies, which greatly accelerated the research and development process.

[0046] Figure 2 A schematic diagram of a rapid electromagnetic design and analysis system for a pulsed coaxial coil system used in an FRC device is shown, including: The parameter acquisition module 100 acquires the target physical requirement parameters of the coaxial coil system; the target physical requirement parameters include at least the total axial length of the coaxial coil system. l Coil radius r Target internal magnetic field B and the rise time of the magnetic field t rise ; The model building module 200 establishes a parameter calculation model based on the data acquired by the parameter acquisition module 100. The parameter calculation model includes a set of simplified analytical formulas describing the mapping relationship between the target physical requirement parameters and key electrical parameters of the power supply. The key electrical parameters of the power supply include the maximum current of the power supply. I max Maximum voltage U max and maximum current change rate di / dt| max The simplified analytical formula set is based on the number of coils. N As core variables; The spatial scanning module 300 is used to calculate the model based on the parameters of the model construction module 200, using the number of coils. NPerform a parameter space scan for the variables to generate a result that at least includes the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max A parameter space scan diagram showing how the number of coils N varies; The comparison constraint module 400 is used to obtain the key performance parameter thresholds of the solid-state switching device, and compares and analyzes the key performance parameter thresholds as constraint boundaries with the parameter space scan map generated by the space scan module 300. The scheme determination module 500 is used to determine the number of coils that meet the performance parameter constraints of the solid-state switching device based on the comparison analysis results of the comparison constraint module 400. N .

[0047] Based on the same inventive concept, this embodiment provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, it can implement the rapid electromagnetic design and analysis method described in any step of Embodiment 1 above.

[0048] Based on the same inventive concept, this embodiment provides an electronic device, including a memory and a processor. The memory is used to store a computer program; the processor is used to execute the computer program stored in the memory, thereby implementing all the steps of the rapid electromagnetic design and analysis method described in Embodiment 1.

[0049] In one embodiment, the length of the coaxial coil system l Coil radius r Internal magnetic field B Number of coils N and magnetic field rise time t rise The required current in the coil, i.e., the maximum current in the coil, can be calculated using the formula. Given the length of the coaxial coil system... l and coil radius r The value of the required coil current and the relationship between the required magnetic field and the number of coil turns are as follows: Figure 3 As shown.

[0050] Using the long solenoid model, when N is sufficiently large and the coils are relatively close together, this system is a hollow solenoid. The formula for calculating the total inductance of the entire solenoid is:

[0051] in, μ 0 It is the vacuum permeability. S It is the cross-sectional area S=πr 2, K It is the Nagaoka coefficient, used to correct the edge effect of solenoids of finite length, especially for slender solenoids. K The value is close to 1. Since all coils are coaxial and carry the same current, the total energy of the system can be expressed by the total inductance, or by... N The equivalent inductance of a single coil is represented.

[0052]

[0053] Therefore, the equivalent inductance of a single coil is:

[0054] As can be seen from the above formula, once the length and radius of the coil system are determined, the equivalent inductance of each coil is only related to the number of coils. The more coils there are, the greater the equivalent inductance of a single coil.

[0055] Calculate the required capacitance of the power supply and the maximum voltage required by the capacitor: Magnetic field rise time Equal to 1 / 4 of the cycle of the LRC circuit:

[0056] Known rise time And with inductor L, the required capacitance value is:

[0057] Since the circuit resistance is extremely small and negligible, the LRC circuit can be approximated as an LC circuit. The LC circuit has the following equation:

[0058] The maximum voltage can be deduced as follows:

[0059] Will Substituting into the above formula, we get:

[0060] Then ， and generation Substituting the above equation, we get:

[0061] As can be seen from the above formulas: once the length and radius of the coaxial coil system are determined, the maximum voltage across the capacitor is directly proportional to the required magnetic field and the cross-sectional area of ​​the coil array, and inversely proportional to the rise time of the magnetic field. For example, given the length of the coaxial coil system... Coil radius and Nagaoka coefficient KThe value of the capacitor or coil voltage and its relationship with the required magnetic field and rise time are as follows: Figure 4 As shown.

[0062] Next, calculate the maximum rate of change of current: LC The current waveform of the circuit is as follows:

[0063] Differentiate with respect to current:

[0064] The maximum rate of change of current at time zero is:

[0065] Will generation Substituting the above equation, we get:

[0066] It can be seen that the maximum current change rate is directly proportional to the maximum current and inversely proportional to the rise time.

[0067] Further generation Substituting the above equation, we get:

[0068] As can be seen from the above formula: when the length of the coaxial coil system l and coil radius Given a specific condition, the maximum rate of change of current in a circuit is affected by the required magnetic field, the number of coils, and the rise time. For example, given the length of a coaxial coil system... Coil radius The relationship between rise time, rate of change of coil current, required magnetic field, and number of coil turns is as follows: Figure 5 As shown.

[0069] By using the parameter space scan analysis of the following four formulas, combined with the key parameters of existing mature solid-state switching devices, the number of coils, the equivalent inductance of the coils, and the performance parameters related to capacitors and switches in the pulse power supply can be quickly determined.

[0070]

[0071] Finally, circuit analysis and simulation were performed based on the above parameters.

[0072] The present invention has the following beneficial effects: 1. Simplification: This invention breaks away from the lengthy process of pre-defined parameters plus finite element simulation in traditional design, deriving and employing a simplified set of engineering approximation formulas. Verified in actual projects, the relative error between the calculation results using the simplified analytical formulas of this invention and the normal simulation results is controlled within 10%. This represents a reduction in computational dimensionality while ensuring acceptable engineering errors.

[0073] 2. Low Cost: This invention does not limit the optimization objective to the purely physical extreme values ​​of the coil itself, but rather crosses boundaries by using the limiting stress parameters of existing commercial solid-state switching devices, such as maximum withstand voltage, maximum current carrying capacity, and di / dt withstand capability, as mandatory inequality constraints. This ensures that the calculated number of coils and circuit topology can match existing commercial devices, effectively improving the utilization efficiency of existing devices and reducing the overall cost.

[0074] 3. High efficiency: Designing the number of magnets and the stacking scheme of power switches using traditional methods usually requires several detailed simulation iterations and takes about 6 months; however, using the rapid electromagnetic design and analysis method of this invention, designers can quickly and accurately determine the number of magnets and the stacking scheme of power switches within a week, thus improving design efficiency.

[0075] In the description of this application, it should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. For ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0076] It should be noted that, in this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. It should also be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Furthermore, features described with reference to certain examples may be combined in other examples.

[0077] The embodiments described above are merely further illustrations of the present invention and are not intended to limit the present invention in any other way. The present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding modifications and changes based on the present invention, but all such modifications and changes should fall within the protection scope of the present invention.

Claims

1. An electromagnetic design and analysis method for a pulsed coaxial coil system for an FRC device, the pulsed coaxial coil system comprising multiple coaxially arranged coils, each coil being powered by an independent pulse capacitor power supply, characterized in that, The method includes: S1, Obtain the target physical requirements parameters of the coaxial coil system; the target physical requirements parameters include at least the total axial length. l Coil radius r Target internal magnetic field B and the rise time of the magnetic field trise ; S2, Establish a parameter calculation model. This model includes a set of simplified analytical formulas describing the mapping relationship between the target physical requirement parameters and the key electrical parameters of the power supply. The key electrical parameters of the power supply include the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max The simplified analytical formula set is based on the number of coils. N As core variables; S3, based on the parameter calculation model, with the number of coils N Perform a parameter space scan for the variables to generate a result that at least includes the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max With the number of coils N A spatial scan of the changing parameters; S4, obtain the key performance parameter thresholds of the solid-state switching device, and compare and analyze the parameter space scan map with the key performance parameter thresholds; S5. Based on the comparative analysis results, determine the number of coils that meet the performance parameter constraints of the solid-state switching device. N .

2. The electromagnetic design and analysis method for a pulse coaxial coil system for an FRC device according to claim 1, characterized in that, The simplified analytical formula set is specifically as follows: in, μ 0 The permeability of free space, S The cross-sectional area of ​​the coil is... K This is the Nagaoka coefficient.

3. The electromagnetic design and analysis method for a pulse coaxial coil system for an FRC device according to claim 1, characterized in that, Based on the comparative analysis results, the number of coils that meet the performance parameter constraints of the solid-state switching device is determined. N Specifically, it includes: Obtain the maximum allowable voltage of the solid-state switching device. U swith Maximum current I swith and maximum current change rate di / dt | swith As the threshold for the aforementioned key performance parameters; Assuming the number of switches connected in series is n and the number of switches connected in parallel is m, the feasible region for the number of coils N that satisfies the hardware constraints is determined by solving the following set of inequalities, which include voltage / current sharing coefficients: Taking into account the cost of the switching devices, the final number of coils is determined within the feasible region. N And the corresponding series and parallel stacking schemes for switches; Where α1, α2, and α3 are the pressure equalization / flow equalization coefficients in the above three inequalities, respectively.

4. The electromagnetic design and analysis method for a pulse coaxial coil system for an FRC device according to claim 1, characterized in that, The number of coils N Perform a parameter space scan for the variables to generate a parameter space scan graph, specifically including: Discretize the maximum voltage using a data processing program. U max Maximum current I max and maximum current change rate di / dt| max The independent variable includes the target's internal magnetic field. B The number of coils N and the rise time of the magnetic field t rise ; Numerical calculations are performed by substituting the simplified analytical formula set into the multidimensional grid nodes composed of the independent variables. Based on the calculation results, contour maps are drawn as the parameter space scan map, and the key performance parameter thresholds of the solid-state switching device are drawn as constraint lines. The intersection points of the constraint lines and the contour map are read to determine the number of coils that simultaneously satisfy the threshold constraints of each performance parameter. N The range or minimum value of .

5. The electromagnetic design and analysis method for a pulse coaxial coil system for an FRC device according to claim 4, characterized in that, The contour map drawn based on the calculation results as the parameter space scan map includes at least one of the following forms: With the target's internal magnetic field B and the number of coils N Use the coordinate axes as variables to plot and display the maximum current. I max Or the maximum current change rate di / dt| max Contour map of numerical distribution; With the target's internal magnetic field B and the rise time of the magnetic field t rise Use the coordinate axes as variables to plot and display the maximum voltage. U max Contour map of numerical distribution.

6. The electromagnetic design and analysis method for a pulse coaxial coil system for an FRC device according to claim 1, characterized in that, The number of coils required to satisfy the performance parameter constraints of the solid-state switching device is determined. N Subsequently, the method further includes: Based on the determined number of coils N And using the simplified analytical formula set, the key electrical parameters and actual capacitance value of the pulse capacitor power supply can be calculated in reverse. C ; The series-parallel stacking scheme of the pulse capacitor power supply is determined based on the key electrical parameters. Combined with the actual capacitance value C The complete electromagnetic design scheme of the output pulse coaxial coil system is derived from the series-parallel stacking scheme of the aforementioned switches.

7. The electromagnetic design and analysis method for a pulse coaxial coil system for an FRC device according to claim 1, characterized in that, The method further includes: When the number of coils that meet the performance parameter constraints of the solid-state switching device cannot be found in the parameter space scan diagram. N At that time, the total axial length in the target physical requirement parameters is iteratively adjusted. l The radius of the coil r Or the rise time of the magnetic field t rise ; The steps of establishing the parameter calculation model and parameter space scanning are repeated using the adjusted target physical requirement parameters until a feasible number of coils is found. N .

8. A rapid electromagnetic design and analysis system for a pulse coaxial coil system in an FRC device, characterized in that, include: The parameter acquisition module acquires the target physical requirement parameters of the coaxial coil system, wherein the target physical requirement parameters include at least the total axial length of the coaxial coil system. l Coil radius r Target internal magnetic field B and the rise time of the magnetic field t rise ; The model building module establishes a parameter calculation model based on the data acquired by the parameter acquisition module. This model includes a set of simplified analytical formulas describing the mapping relationship between the target physical requirement parameters and key electrical parameters of the power supply. The key electrical parameters of the power supply include the maximum current of the power supply. I max Maximum voltage U max and maximum current change rate di / dt | max The simplified analytical formula set is based on the number of coils. N As core variables; The spatial scanning module calculates the model based on the parameters of the model construction module, using the number of coils. N Perform a parameter space scan for the variables to generate a result that at least includes the maximum current. I max Maximum voltage U max and maximum current change rate di / dt| max A parameter space scan diagram showing how the number of coils N varies; The comparison constraint module obtains the key performance parameter thresholds of the solid-state switching device, and compares and analyzes the key performance parameter thresholds as constraint boundaries with the parameter space scan map generated by the space scan module. The scheme determination module, based on the comparative analysis results of the comparison constraint module, determines the number of coils that satisfy the performance parameter constraints of the solid-state switching device. N .

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

10. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing a computer program stored in the memory to implement the steps of the method according to any one of claims 1 to 7.

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