Marx generator inductance acquisition method

Abstract

The application discloses a Marx generator inductance acquisition method, comprising the following steps: outputting single-stage area inductance according to the length and radius of the single-stage area in the single FMG discharge main circuit of the Marx generator; the single-stage area inductance comprises switch section inductance, high-voltage plate section inductance, capacitor section inductance and output section inductance; outputting backflow area inductance according to the distance between backflow plates, the width of the backflow area and the length of the backflow area in the single FMG discharge main circuit of the Marx generator; outputting output area inductance according to the length and radius of the output area in the single FMG discharge main circuit of the Marx generator; and outputting the total inductance of the Marx generator according to the single-stage area inductance, the backflow area inductance and the output area inductance and the number of the single-stage area, the backflow area and the output area in the single FMG discharge main circuit of the Marx generator. The method can more accurately acquire the Marx generator loop inductance.

Description

Technical Field

[0001] This invention relates to the field of Marx generator inductance acquisition technology, and particularly to a method for acquiring Marx generator inductance. Background Technology

[0002] The Marx generator, a classic high-voltage pulse generator, offers numerous advantages over LTD (Linear Transformer Driver), Tesla transformers, and Van der Graff generators, including higher output voltage, higher energy density, simpler structure, and easier operation and maintenance. Since its invention by Erwin Otto Marx in 1923, it has been widely used in high-energy physics experimental research (electron and ion beam generation and acceleration, plasma compression, strong radiation environment simulation, etc.) and pulsed power technology applications (industry, medicine, environment, agriculture, etc.). Furthermore, in applications requiring GW-level power or MV-level voltage output, the internal switching of the Marx generator still primarily utilizes gas gaps. In recent years, the development of high-voltage Marx generators, as the primary primary energy storage solution, has shown new trends such as parallel operation of multiple units, rapid discharge, and controllable build-up processes.

[0003] Loop inductance is one of the most important parameters of a Marx generator. It, along with capacitance, determines the generator's characteristic discharge time, and the rate of discharge directly affects its internal insulation. To control the overall performance of the generator, its loop inductance must be estimated accurately.

[0004] Therefore, based on existing technologies, how to accurately obtain the loop inductance of the Marx generator has become a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of the above problems, the present invention proposes a method for obtaining the inductance of a Marx generator that at least solves some of the above technical problems. This method can accurately obtain the circuit inductance of a Marx generator.

[0006] This invention provides a method for obtaining the inductance of a Marx generator, comprising:

[0007] Based on the length and radius of the single-stage zone in the main FMG discharge circuit of the Marx generator, the single-stage zone inductance is output; the single-stage zone inductance includes: switching section inductance, high-voltage board section inductance, capacitor section inductance, and output section inductance.

[0008] Based on the distance between return plates, the width of the return zone, and the length of the return zone in the single FMG discharge main circuit of the Marx generator, the output return zone inductance is calculated.

[0009] The output inductance is determined based on the length and radius of the output region in the single FMG discharge main circuit of the Marx generator.

[0010] The total inductance of the Marx generator is output based on the single-stage inductance, return-current inductance, and output-current inductance, as well as the number of single-stage, return-current, and output-current areas in a single FMG discharge main circuit of the Marx generator.

[0011] Furthermore, the inductance of the switching electrode and the switching lead in the switching segment inductance is calculated using the following formula:

[0012]

[0013] In the above formula, l represents the length of a single-level region; r represents the radius of a single-level region.

[0014] Furthermore, the return current region inductance is calculated using the following formula:

[0015]

[0016] In the above formula, d represents the distance between reflow plates; w represents the width of the reflow zone; and l represents the length of the reflow zone.

[0017] Furthermore, the output region inductance is calculated using the following formula:

[0018]

[0019] In the above formula, d represents the radius of the output area; l represents the length of the output area.

[0020] The beneficial effects of the above-described technical solutions provided in the embodiments of the present invention include at least the following:

[0021] This invention provides a method for obtaining the inductance of a Marx generator, comprising: outputting the inductance of a single-stage region based on the length and radius of a single-stage region in the main discharge circuit of a single FMG of the Marx generator; the single-stage region inductance includes: switching section inductance, high-voltage board section inductance, capacitor section inductance, and output section inductance; outputting the return current region inductance based on the distance between return current boards, the width of the return current region, and the length of the return current region in the main discharge circuit of a single FMG of the Marx generator; outputting the output region inductance based on the length and radius of the output region in the main discharge circuit of a single FMG of the Marx generator; and outputting the total inductance of the Marx generator based on the single-stage region inductance, the return current region inductance, the output region inductance, and the number of single-stage regions, the return current region, and the output region in the main discharge circuit of a single FMG of the Marx generator. This method can obtain the circuit inductance of the Marx generator relatively accurately.

[0022] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0025] Figure 1 This is a flowchart of a Marx generator inductance acquisition method provided in an embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of the first two rows of the Marx generator mechanism provided in an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the current flow path during discharge of the Marx generator provided in an embodiment of the present invention;

[0028] Figure 4 A schematic diagram of the main circuit equivalent to a transmission line model provided in the embodiments of the present invention;

[0029] Figure 5 A schematic diagram of a single FMG discharge main circuit of a Marx generator provided in an embodiment of the present invention. Detailed Implementation

[0030] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0031] This invention provides a method for obtaining the inductance of a Marx generator, referring to... Figure 1 As shown, it includes:

[0032] Based on the length and radius of the single-stage zone in the main FMG discharge circuit of the Marx generator, the output single-stage zone inductance is determined; the single-stage zone inductance includes: the switching section inductance, the high-voltage board section inductance, the capacitor section inductance, and the output section inductance.

[0033] The output return zone inductance is determined based on the distance between return plates, the width of the return zone, and the length of the return zone in a single FMG discharge main circuit of the Marx generator.

[0034] The output inductance is determined based on the length and radius of the output region in the main FMG discharge circuit of a single Marx generator.

[0035] The total inductance of the output Marx generator is determined by the inductance of the single-stage region, the return current region, and the output region, as well as the number of single-stage regions, the return current region, and the output region in a single FMG discharge main circuit of the Marx generator.

[0036] The Marx generator inductance acquisition method provided in this embodiment proposes an estimation method applicable to the specific structure of each part of the Marx generator, which can obtain the Marx generator loop inductance relatively accurately.

[0037] The following is a detailed explanation of the method for obtaining the inductance of the Marx generator:

[0038] The inductance of the Marx generator circuit is influenced not only by the selected capacitor and gas switch structure, but also by the main current flow path during generator discharge. Capacitor inductance is relatively easy to measure, usually provided by the manufacturer, and the spark gap inductance of the gas switch can also be estimated relatively accurately. The remaining challenge lies in estimating the inductance of the generator's main circuit connections. Impedance analysis and component analysis can be used in this case.

[0039] The wave impedance method treats the generator's main circuit wiring as a series connection of multiple wave impedances of various types, and calculates the generator's inductance by measuring the parameters of each wave impedance. The inductance parameters of the wave impedance implicitly include the self-inductance and mutual inductance of the wiring, eliminating the need to separately consider the influence between the wirings.

[0040] Specifically, taking the Marx generator in the American PBFA-II as an example, it uses iron-cased square capacitors, with both the internal and inter-bank main currents flowing in an S-shape to reduce inductance. (Refer to...) Figure 2 The diagram shows the first two rows of the Marx generator mechanism. The numbers on the capacitors indicate the order in which the current flows through them during generator discharge. The arrows indicate the direction of the current in the generator, with "·" indicating current outflow and "X" indicating current inflow.

[0041] Reference Figure 3The diagram shows the current flow path during the discharge of a Marx generator, excluding the current within the capacitor. The vertical dashed lines represent the metal connection plates within the row, and the horizontal dashed lines represent the metal connection plates between rows. The horizontal solid lines with numerical designations represent the gas switches and their connections to the capacitors. By equating lines with identical structures, equal current magnitudes, opposite flow directions, and close proximity to each other as a pair of transmission lines, the main circuit can be further described as follows: Figure 4 Several transmission line models are used to reasonably equate these transmission line types and sizes: the horizontal gas switch electrode leads and the vertical connecting conductors are equated to parallel cylindrical wires. The wave impedance and electrical length between wires or between wires and flat plates are calculated, and the inductance of the connecting conductors can be obtained. Finally, the capacitor inductance and the inductance of the gas spark channel (gas switch spark gap inductance) are added to obtain the inductance of the entire generator.

[0042] Furthermore, the component rule decomposes the entire generator into components such as switches, capacitors, and electrode connections, and calculates the inductance of the entire generator by calculating the self-inductance of each component and the mutual inductance between them. Taking the Northwest Nuclear Technology Research Institute's Flash-II generator as an example, its core structure is similar to that of the PBFA-II generator. The following are calculated separately: (1) the self-inductance of the switch electrodes, the conductors connecting within and between rows; (2) the mutual inductance between connecting conductors, between rows, and between connecting conductors and the generator return plate; (3) the inductance of the switch spark gap and the capacitor. The inductance of the entire generator is obtained by adding the above three together. When calculating the mutual inductance, it should be considered that the mutual inductance between currents in the same direction is positive, and the mutual inductance between currents in opposite directions is negative.

[0043] Specifically, in terms of similarities, both estimation methods primarily focus on inductance estimation for loop connections, considering both mutual and self-inductance. For switch gap inductance and capacitor inductance, they are simply summed. Both estimation methods require appropriate equivalence, the appropriateness of which depends on the actual engineering application; inappropriate equivalence will lead to significant calculation errors. In terms of differences, the wave impedance method treats the entire connecting conductor as a transmission line, making the calculation process simple. The difficulty lies in determining the effective calculated dimensions of each connecting conductor and the distances between them during equivalence. The component method calculates the self-inductance of each unit and the overall mutual inductance, especially mutual inductance, which is influenced by many factors, making the calculation process more complex. The difficulty lies in the irregular shape of the actual connecting conductors or their non-compliance with the calculation formula conditions. Therefore, how to perform equivalence to make it conform to the calculation conditions of the formula becomes crucial for calculation accuracy.

[0044] Regarding its applicability, the wave impedance method treats planar conductors as equivalent transmission lines, viewing energy transmission as being confined within these lines. This assumption only applies when there are large, closely spaced current-carrying conductors in the circuit. Therefore, this calculation method is suitable for generators using metal-cased capacitors because the relative area of ​​current flow is relatively large, resulting in smaller calculation errors. For generators composed of plastic-cased capacitors, to reduce circuit inductance, the core structure is very compact, with the capacitor and gas switch tightly connected as a single unit, resulting in few large connecting conductors. Using the wave impedance method in these cases would introduce significant errors. The component method is more suitable, as it calculates the self-inductance and mutual inductance of each component separately. As long as the applicable conditions of the calculation formula are met, the self-inductance and mutual inductance values ​​of each part can be calculated.

[0045] Reference Figure 5 As shown, this is the main discharge circuit of a single FMG in a Marx generator, comprising 7 single-stage zones, 2 return zones, and 1 output zone. The return zones are in parallel, while the others are in series. The inductance of the FMG main circuit is estimated using a segmented method, meaning the three zones are calculated separately, with each zone calculated in segments. First, the inductance of each single-stage zone is calculated. The single-stage zone structure is divided into four parts: the switching section, the high-voltage board section, the capacitor section, and the output section. Based on the inductance calculation formulas for a flat transmission line with edge effects, a cylindrical conductor, and a single-channel gas gap, the inductance of each single-stage zone is calculated as shown in Table 1.

[0046] Table 1. Estimated inductance of each part of a single FMG discharge main circuit.

[0047]

[0048] From the table, we know that the inductance of the entire single-stage region is 98nH, of which the switching section is approximately 46nH and the capacitor and connecting plate section is approximately 52nH. Next, we calculate the inductance of the return current region. The single-sided return current region is a long rectangular shape, which can be calculated using the formula for the inductance of a flat transmission line. The width of the return current region W = 220mm, the length of the return current region l = 1330mm, and the distance between the return current plates d = 115mm, so its inductance is calculated to be 576nH. Since the two return current regions are connected in parallel, the estimated inductance of the entire return current region is 288nH. Finally, we calculate the inductance of the output region, using the formula for the inductance of an isolated cylindrical conductor. The output region is a cylindrical water resistor filled with electrolyte, with a length l = 260mm and a radius r = 36mm. Using the formula for the inductance of an isolated cylindrical conductor, its inductance is approximately 87nH. In summary, the total inductance of the generator is estimated to be 1061nH, which is the sum of the inductances of the seven single-stage regions, the two return regions, and the output region. Actual test results show that the estimated value is always slightly larger than the actual value. Using the estimated value in the simulation allows for a certain margin in the design.

[0049] Specifically, when the generator to be simulated uses a plastic-cased capacitor, the component method is used to estimate its inductance. Through the appropriate loop connection equivalent method and appropriate inductance calculation formula provided by the Marx generator inductance acquisition method in this embodiment, the estimation method is universally applicable to the inductance estimation of this type of generator.

[0050] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for obtaining the inductance of a Marx generator, characterized in that, include: Based on the length and radius of the single-stage region in the main FMG discharge circuit of the Marx generator, the output single-stage region inductance is determined. The single-stage inductor includes: switching section inductor, high-voltage board section inductor, capacitor section inductor, and output section inductor; Based on the distance between return plates, the width of the return zone, and the length of the return zone in the single FMG discharge main circuit of the Marx generator, the output return zone inductance is calculated. The output inductance is determined based on the length and radius of the output region in the single FMG discharge main circuit of the Marx generator. Based on the inductance of the single-stage region, the return current region, and the output region, as well as the number of single-stage regions, return current regions, and output regions in a single FMG discharge main circuit of the Marx generator, the total inductance of the Marx generator is output; the specific calculation method is as follows: in, Indicates the length of a single-level region; Indicates the radius of a single-level region; Indicates the distance between recirculation plates; Indicates the width of the recirculation zone; Indicates the length of the recirculation zone; Indicates the length of the output area; Indicates the radius of the output region.

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