Low complexity microwave device gas breakdown threshold transient high efficiency prediction method and system

Abstract

The application discloses a low-complexity microwave device gas breakdown threshold transient efficient prediction method and system, which comprises the following steps: adopting an arbitrary high-order derivative time difference format, converting a set of ordinary differential equations of electron concentration into a set of algebraic equations, and solving the electron concentration; comprehensively considering the set of electron concentration equations and the first derivative and the second derivative thereof, and designing a breakdown judgment condition; repeatedly solving the electron concentration by the electron concentration solving step, judging according to the breakdown judgment condition, and based on the judgment result, updating the incident field amplitude of the upper limit or the lower limit by using the dichotomy, and converting the power amplitude to obtain the port incident power at the breakdown time. The application effectively solves the problem of low calculation efficiency of large-scale calculation faced by the steady-state method and the traditional transient method in the process of predicting the microwave device gas breakdown threshold, and finally realizes the efficient prediction of the low-pressure gas breakdown threshold of the microwave device.

Description

Technical Field

[0001] The present invention relates to electromagnetic simulation technology for high-power microwave devices, and in particular to a method and system for efficiently predicting the transient gas breakdown threshold of low-complexity microwave devices. Background Art

[0002] With the rapid development of aerospace technology, satellite communications, space exploration, and other spaceborne missions are increasingly reliant on high-power microwave technology. High-power microwave devices play a critical role in the low-pressure onboard environment, but the gas breakdown problem they face poses a serious threat to their stable operation. Due to the low pressure of the onboard environment, the mean free path between gas molecules increases, and the probability of electron-gas collision ionization changes, making high-power microwave devices more susceptible to gas breakdown during operation. This breakdown not only leads to a sharp decline in microwave device performance, preventing them from properly performing tasks such as signal transmission and detection, but can also cause permanent damage to the device, leading to failure of the entire onboard microwave system and serious consequences for space missions. Therefore, accurately predicting the gas breakdown threshold of high-power microwave devices in low-pressure onboard environments is of paramount importance for ensuring the reliable operation of onboard microwave systems and improving the success rate of space missions. This has become a critical and pressing issue in the field of aerospace electronics technology.

[0003] At present, both the steady-state prediction method and the traditional transient method of the gas breakdown threshold of microwave devices have the problem of high computational complexity, and the prediction accuracy needs to be improved. The Chinese patent with the invention name "Efficient Prediction Method of Low-Pressure Discharge Threshold of Payload Microwave Devices" and patent number 202211439760.3 discloses an efficient prediction method of the low-pressure discharge threshold of payload microwave devices. It uses numerical methods to accurately obtain the electromagnetic field distribution inside the microwave device to correct the transport coefficients such as ionization rate and attachment rate, and combines the electron continuity equation to solve the breakdown threshold. Based on the regional decomposition technology, the area where the electric field changes drastically is intercepted to improve the computational efficiency. Although this patent has accelerated the calculation speed to a certain extent, there is inevitably the problem of solving the eigenvalue when facing complex problems, and there is still room for improvement in the efficiency of the algorithm. Reference Joshi MK, Nayek N, Tiwari T, et al. Multiphysics and Multipactor Analyses of TE022-Mode High-Power X-Band RF Window[J]. IEEE Microwave and Wireless Components Letters, 2020, 30(99): 272-275. A method for simulating the breakdown threshold of a transconducting X-band RF window for a high-power microwave tube using SPARK3D was proposed. This method uses a lower-order time integration algorithm, which results in a large time discretization error. Summary of the Invention

[0004] The purpose of the present invention is to provide a method and system for efficiently predicting the transient state of the gas breakdown threshold of low-complexity microwave devices. The method introduces an arbitrary high-order derivative time difference format to reduce the complexity of traditional transient calculations, and uses the time-domain spectral element method as a simulation calculation platform to improve calculation efficiency. Ultimately, the method can achieve efficient and accurate prediction of the transient state of the gas breakdown threshold of low-complexity microwave devices, which can reduce R&D costs while ensuring the accuracy of the results, and provide guidance for the design of high-power microwave devices in low-pressure spaceborne environments.

[0005] The above-mentioned object of the present invention is achieved through the following technical solutions:

[0006] A method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device comprises the following steps:

[0007] Using arbitrary high-order derivative time difference format, the ordinary differential equations of electron concentration are transformed into algebraic equations to solve the electron concentration;

[0008] Comprehensively consider the electron concentration equations and their first-order and second-order derivatives to design the breakdown judgment conditions;

[0009] Repeat the electron concentration solving steps to solve the electron concentration, make a judgment according to the breakdown judgment condition, and based on the judgment result, use the dichotomy method to update the incident field amplitude of the upper or lower limit of the range, and convert the power amplitude to obtain the port incident power at the time of breakdown.

[0010] Furthermore, the use of an arbitrary high-order derivative time difference format to transform the ordinary differential equations of electron concentration into algebraic equations specifically includes:

[0011] Use Taylor series expansion to solve the electron continuity equation for the change of u at time t;

[0012] The designed GLL basis function is used to perform the Galerkin test on the unknown quantity of electron density in the electron continuity equation, and then the unknown quantity is expanded using the scalar basis function.

[0013] Based on Taylor series expansion equations and basis functions, arbitrary high-order derivative time difference format equations are obtained.

[0014] Furthermore, the electronic continuity equation is expanded using Taylor series to solve the change of u at time t:

[0015]

[0016] Where u (n) (t) is the nth derivative of the solution at time t, N is the highest order required, and Δt is the time change.

[0017] Furthermore, the GLL basis function is:

[0018]

[0019] Where j = 0, 1, ... N, L N (ξ) is the Nth order Legendre polynomial, L N ′(ξ) is its derivative, and the grid points {ξ j ,j=0,1...N} as GLL integration points, which are equations The (N+1) roots of the basis function satisfy φ j (ξ i )=δ ij characteristics.

[0020] Furthermore, the second-order, third-order, and fourth-order difference format equations of arbitrary high-order derivative time difference format equations are:

[0021]

[0022] Where A = [T] -1 (D[S]+(v i -v a)[T]), [T] and [S] are mass matrices, v i represents the ionization rate, v a represents the attachment rate, D represents the diffusion coefficient, n n is the electron concentration at the current moment.

[0023] Furthermore, the breakdown determination condition is:

[0024] if It is judged as breakdown, where n0 is the initial electron concentration, n n is the electron concentration at the current moment;

[0025] if It is judged as no breakdown;

[0026] When n n+1 、n n The order of magnitude difference is between 10, let the first derivative of electron concentration be: k n =n n+1 -n n , let the second derivative of electron concentration be: a n =k n -k n-1 , if a n =0 or the limit is close to 0, then determine n n+1 and n n The size relationship, if n n +1 >n n , then breakdown; otherwise, no breakdown.

[0027] A low-complexity microwave device gas breakdown threshold transient high-efficiency prediction system, comprising:

[0028] The electron concentration solving unit uses an arbitrary high-order derivative time difference format to transform the ordinary differential equations of electron concentration into algebraic equations to solve the electron concentration;

[0029] A breakdown determination unit determines whether the device has broken down based on the calculated electron concentration;

[0030] The prediction unit, based on the determination result, uses a binary method to update the incident field amplitude at the upper or lower limit of the range, and converts the power amplitude to obtain the port incident power at the time of breakdown.

[0031] A computer storage medium, characterized in that the computer storage medium stores an executable program, and the executable program is executed by a processor to implement the steps of the method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device.

[0032] Compared with the prior art, the present invention has the following significant advantages:

[0033] (1) The method mentioned in the present invention is a low-complexity and efficient method for predicting the gas breakdown threshold transient state of microwave devices. This numerical model introduces the arbitrary higher-order derivative (ADER) time difference format, combines the orthogonality of the basis functions of the time-domain spectral element method with the block diagonal characteristics of the mass matrix, avoids the inversion of large sparse matrices, and reduces the time complexity to O(N), significantly reducing the computation time and memory consumption. Compared with steady-state and traditional transient methods, it effectively shortens the computation time;

[0034] (2) The ADER time-difference format used in the method proposed in the present invention is based on Taylor series expansion and uses spatial derivatives to approximate time derivatives to achieve high-order accuracy. When dealing with complex microwave device gas breakdown threshold prediction problems, it can flexibly control the accuracy by adjusting the order, accurately simulate the changes in physical quantities, and has lower memory consumption. Compared with other difference formats, it is more suitable for large-scale simulation calculations;

[0035] (3) To improve the accuracy of breakdown threshold analysis for complex targets, the proposed method adopts a transient breakdown criterion for complex targets, comprehensively considering the electron concentration and its first-order and second-order derivatives. The method not only makes a judgment based on the relationship between the electron concentration and the multiple of the initial electron concentration, but also accurately determines the breakdown situation by analyzing the first-order and second-order derivatives of the electron concentration and the relationship between the electron concentration before and after the specific order of magnitude difference, thereby making the calculation result more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the physical structure of the T-microstrip model from different perspectives. Figure 1 (a) is a three-dimensional diagram of the T-microstrip structure. Figure 1 (b) in the figure is the front view of the T-microstrip.

[0037] Figure 2 This is a comparison chart of the breakdown power threshold changes with pressure for different methods at a frequency of 200MHz.

[0038] Figure 3 This is a calculation time comparison chart.

[0039] Figure 4 It is a flow chart of the present invention for determining the breakdown criterion.

[0040] Figure 5 is the relationship between electron density and the number of iteration steps, Figure 5 (a) and (c) are the non-breakdown states. Figure 5 (b) and (d) are breakdown states.

[0041] Figure 6 This is a comparison chart of computational time complexity. DETAILED DESCRIPTION

[0042] This embodiment provides a low-complexity microwave device gas breakdown threshold transient efficient prediction method, including:

[0043] Using arbitrary high-order derivative time difference format, the ordinary differential equations of electron concentration are transformed into algebraic equations to solve the electron concentration;

[0044] Comprehensively consider the electron concentration equations and their first-order and second-order derivatives to design the breakdown judgment conditions;

[0045] Repeat the electron concentration solving steps to solve the electron concentration, make a judgment according to the breakdown judgment condition, and based on the judgment result, use the dichotomy method to update the incident field amplitude of the upper or lower limit of the range, and convert the power amplitude to obtain the port incident power at the time of breakdown.

[0046] The method of using an arbitrary high-order derivative time difference format to transform the ordinary differential equations of electron concentration into algebraic equations specifically includes:

[0047] Use Taylor series expansion to solve the electron continuity equation for the change of u at time t;

[0048] The designed GLL basis function is used to perform the Galerkin test on the unknown quantity of electron density in the electron continuity equation, and then the unknown quantity is expanded using the scalar basis function.

[0049] The electron continuity equation can be expressed as:

[0050]

[0051] Where n represents the electron density, v i represents the ionization rate, v a represents the adhesion rate, D represents the diffusion coefficient, D=10 6 / p, p is the pressure of the filling gas.

[0052] Based on the Taylor series expansion equation, the time difference format equation for arbitrary high-order derivatives is obtained.

[0053] The ADER format is based on the Taylor series expansion, which uses spatial derivatives to approximate time derivatives, thereby achieving high-order accuracy in time integration. To express the ADER format, we first need to use the Taylor series expansion to solve for the change of u at time t:

[0054]

[0055] Where u (n) (t) is the nth derivative of the solution at time t, where N is the highest order required;

[0056] The GLL basis function is used to perform the Galerkin test on the unknown electron density in the electron continuity equation, and then the unknown is expanded using the scalar basis function. In the 1-D standard reference unit ξ∈[-1,1], we define the Nth-order GLL (Gauss-Lobatto-Legendre) basis function as:

[0057]

[0058] Where j = 0, 1, ... N, L N (ξ) is the Nth order Legendre polynomial, L N ′(ξ) is its derivative. j ,j=0,1...N} as GLL integration points, which are equations The (N+1) roots of Equation (3) satisfy φ j (ξ i )=δ ij characteristics.

[0059] Substituting (2) into (1), we can obtain the first-order form of the arbitrary high-order derivative time-domain spectral element method (ADER-SETD), which is as follows:

[0060]

[0061] Where V is the volume fraction within the unit, ψ i , ψ j are the test basis and the expansion basis respectively, i and j are the subscripts of the test basis and the expansion basis respectively, J is the Jacobian matrix, n n+1 is the electron concentration at the next moment, n n is the electron concentration at the current moment;

[0062] Further solving equation (4) yields:

[0063] n n+1 =n n +Δt[T] -1 (D[S]+(v i -v a )[T])n n (5)

[0064] in:

[0065] [T]=∫ V ψ i ψ j |J|dV

[0066]

[0067] Analysis of [T] matrix calculation:

[0068]

[0069] Wherein the reference coordinate system (ξ,η,ζ)∈[-1,1]×[-1,1]×[-1,1], N ξ 、N η 、 are the interpolation orders of the basis functions along the three directions of ξ, η, and ζ in the reference domain (here N ξ =N η =N ζ = 2). r, s, t are the numbers of the GLL integration points of the unit cube (a total of 27 points), represents a direction in (ξ,η,ζ), To test the basis function, is the expanded basis function, w r 、w s 、w t is the weight value of the GLL point.

[0070] According to the properties of the basis function in formula (3): φ j (ξ i )=δ ij , if (m,n,p)≠(m′,n′,p′), then the integration point (r,s,t) is either (m,n,p) or (m′,n′,p′), Φ i , Φ j One of them must be zero, otherwise the integral is 0. Therefore, the above formula is non-zero only when r=m=m′, s=n=n′, t=p=p′. After the above analysis, the [T] matrix can be expressed as follows:

[0071]

[0072] Matrix form:

[0073]

[0074] Therefore, the mass matrix [T] is non-diagonal, but if the unknowns formed by each node are sorted, the mass matrix can be a block diagonal matrix. In this way, we can use the block diagonal matrix inversion method to find the inverse of the mass matrix in advance, making the equation explicit and reducing the amount of calculation.

[0075] Then formula (5) is simplified to

[0076] n n+1 =n n +ΔtAn n (9)

[0077] Where A = [T] -1 (D[S]+(v i -v a )[T]).

[0078] Substituting the ADER difference format of formula (2) into (9) we can obtain the second-order, third-order, and fourth-order ADER formulas:

[0079] ADER-Second Order:

[0080] ADER-3rd order:

[0081] ADER-Fourth Order:

[0082] The initial incident field strength can be expressed as:

[0083]

[0084] Where E a , E b Indicates setting the minimum and maximum values ​​of the initial incident electric field intensity;

[0085] Ionization rate v i and adhesion rate v a It can be expressed as:

[0086]

[0087] Where a represents the effective electric field E eff The ratio of pressure p;

[0088] The breakdown criterion in step 5 is:

[0089] (1) If (where n0 is the initial electron concentration), it is determined to be a breakdown;

[0090] (2) If It is judged as no breakdown;

[0091] (3) When n n+1 、n n When the order of magnitude difference is between (1) and (2), let the first derivative of electron concentration be: k n =n n+1 -n n , let the second derivative of electron concentration be: a n =k n -k n-1 , if a n =0 (or the limit is close to 0), in determining n n+1 and n n The size relationship, if nn+1 >n n , then breakdown; otherwise, no breakdown, where n n+1 is the electron concentration at the next moment, n n is the electron concentration at the current moment.

[0092] The amplitude of the incident power at the port is:

[0093]

[0094] Where S represents the tangential cross section of the waveguide excitation port, Z is the mode impedance, and E r (t,x,y,z) is the tangential electric field, is the tangential electric field, A0 is the amplitude of the time component, and a(ω) is the normalized excitation signal.

[0095] This embodiment also provides a low-complexity microwave device gas breakdown threshold transient efficient prediction system, including:

[0096] The electron concentration solving unit uses an arbitrary high-order derivative time difference format to transform the ordinary differential equations of electron concentration into algebraic equations to solve the electron concentration;

[0097] A breakdown determination unit determines whether the device has broken down based on the calculated electron concentration;

[0098] The prediction unit, based on the determination result, uses a binary method to update the incident field amplitude at the upper or lower limit of the range, and converts the power amplitude to obtain the port incident power at the time of breakdown.

[0099] This embodiment further provides a computer storage medium, characterized in that the computer storage medium stores an executable program, and the executable program is executed by a processor to implement the steps of the method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device.

[0100] In order to reduce the complexity of traditional transient calculations, the present invention introduces an arbitrary high-order derivative time difference format and adopts the time-domain spectral element method as the simulation calculation platform to improve the calculation efficiency, and ultimately achieves efficient and accurate prediction of the gas breakdown threshold transient of low-complexity microwave devices. It can reduce R&D costs while ensuring the accuracy of the results, and provide guidance for the design of high-power microwave devices in low-pressure spaceborne environments.

[0101] Example 2

[0102] Based on Example 1, the present invention proposes a method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device. Figure 1 Taking the ridge waveguide structure shown in FIG. 1 as an example, the specific steps of the present invention are further described in detail.

[0103] See also Figure 1 The schematic diagram of the T-microstrip structure is shown in the figure. The geometric dimensions of the model are as follows: 12mm×2mm×20mm, with a thickness of h=2mm and a relative dielectric constant of ε r A waveguide with a width of W = 2 mm is printed on a grounded dielectric substrate. Figure 1 The specific steps of the transient efficient prediction method for the gas breakdown threshold of a low-complexity microwave device with a T-microstrip structure are as follows:

[0104] The first step is to Figure 1 The geometric model of the T-microstrip structure shown is first modeled using Ansys software, and then meshed using a curved hexahedron to obtain the node coordinate information and unit information of the structure. For the boundary conditions of the microstrip structure, the four surfaces except the transmission direction port are set as ideal metals, and the transmission direction port adopts a first-order absorption boundary. In addition, the position of the excitation source is set. The excitation source is a sinusoidal plane wave polarized along the direction. The model uses a sine wave with a center frequency of f = 200 MHz as the excitation source, and calculates the electric field distribution inside the device based on the applied excitation source.

[0105] In the second step, the electron continuity equation that determines the breakdown threshold and power capacity of microwave devices is substituted into the arbitrary higher-order derivative (ADER) time-difference format. The GLL basis function is then used to perform a Galerkin test on the electron density unknown in the electron continuity equation. The unknown is then expanded using a scalar basis function. The resulting system of equations is shown below:

[0106]

[0107] The matrix equation is then simplified to formula (4), which is shown below:

[0108] n n+1 =n n +ΔtAn n (15)

[0109] in:

[0110] [T]=∫ V ψ i ψ j |J|dV

[0111]

[0112] A=[T] -1 (D[S]+(v i -v a )[T])

[0113] Therefore, the problem of predicting the microwave breakdown threshold can be transformed into a problem of solving the electron concentration.

[0114] The third step is to set the working pressure and initial incident field strength. The effective electric field strength is calculated based on the incident wave frequency, the collision rate in the transport coefficient, and the normalized electric field distribution. The current ionization rate and attachment rate are calculated using the effective electric field strength. The [T] and [S] matrices are then filled to obtain the A matrix. The calculation formulas for the initial incident field strength, collision rate, effective electric field strength, ionization rate, and attachment rate are as follows:

[0115]

[0116] v c =5×10 9 p(17)

[0117]

[0118] v i =5.14×10 11 pexp(-73a -0.44 )(19)

[0119] v a =7.6×10 -4 pa 2 (a+218) 2 (20)

[0120] The fourth step is to calculate and fill the corresponding matrix according to the ADER-4th order time domain spectral element method format to find the electron concentration that changes with time:

[0121]

[0122] Step 5: Based on the electron concentration obtained in step 4, Figure 4 The breakdown criteria flow chart is used to determine if it is a breakdown. Figure 5 (a); If it is determined that there is no breakdown, such as Figure 5 (b); when n n+1 、n n The order of magnitude difference is between 10, if n n+1 >n n , then breakdown, such as Figure 5 (c); Otherwise, it will not penetrate. Figure 5 (d).

[0123] When the device does not break down, the minimum value E in the electric field strength range is updated. a ; When the device breaks down, update the maximum value E in the electric field strength range b .

[0124] Step 6: When the breakdown threshold interval meets the set range (|E a -Eb |≤1), the loop is stopped, the incident field strength at this time is output, and the power amplitude is converted according to Poynting's theorem to obtain the port incident power at the time of breakdown.

[0125] The seventh step is to calculate the time complexity of the steady-state method and the transient method, which are O(N 3 ) and O(N), such as Figure 6 shown.

[0126] According to the method of the present invention, Figure 1 The T-microstrip model shown in the figure is simulated, and the breakdown power threshold of different methods is compared with the pressure at a frequency of 200MHz. Figure 2 As shown in the figure, the results are consistent with those of the steady-state method and the commercial software SPARK3D. In the absence of a dielectric, the transmission line can be simplified as a two-wire transmission line in a uniform medium (such as air), in which case the electromagnetic wave propagation is relatively simple. However, the presence of a dielectric, especially the unfilled upper air region, complicates the electromagnetic characteristics of the microstrip line. In the dielectric region, the phase velocity of the TEM wave is different from that in the air region, which results in a phase mismatch at the interface between the dielectric and the air. Therefore, the microstrip line cannot support the ideal TEM wave mode, but instead exhibits a quasi-TEM mode, in which the propagation speeds of the electric and magnetic fields are different, which in turn affects the impedance, signal transmission speed, and loss characteristics of the microstrip line. Figure 3 The figure shows a comparison of the calculation time of the method proposed in the present invention and that of steady-state analysis. It can be seen from the figure that the calculation time of the method proposed in the present invention is greatly reduced.

[0127] This invention addresses the high computational complexity and low efficiency of existing transient methods. The time-domain spectral element method uses a hexahedral discrete grid to effectively describe the device geometry. It uses an orthogonal basis function test expansion to generate a block-diagonal mass matrix. This method excels in addressing large-scale microwave device gas breakdown problems, complex boundary conditions, and long-duration simulations. It significantly reduces matrix inversion time and memory consumption, and numerically predicts the gas breakdown threshold of microwave devices. Its high-order polynomial basis functions and sparse matrix structure optimize memory usage and make it more suitable for parallel computing and adaptive meshing.

[0128] The present invention effectively solves the problem of low large-scale computing efficiency faced by traditional transient methods in predicting the gas breakdown threshold of microwave devices, and ultimately achieves efficient prediction of the low-pressure gas breakdown threshold of microwave devices.

[0129] Obviously, those skilled in the art may make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if such changes and modifications of the embodiments of the present invention fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A low-complexity microwave device gas breakdown threshold transient efficient prediction method, characterized by: Including steps: Using arbitrary high-order derivative time difference format, the ordinary differential equations of electron concentration are transformed into algebraic equations to solve the electron concentration; Comprehensively consider the electron concentration equations and their first-order and second-order derivatives to design the breakdown judgment conditions; Repeat the electron concentration solving step to solve the electron concentration, make a judgment according to the breakdown judgment condition, and based on the judgment result, use the dichotomy method to update the incident field amplitude at the upper or lower limit of the range, and convert the power amplitude to obtain the port incident power at the time of breakdown; The method of using an arbitrary high-order derivative time difference format to transform the ordinary differential equations of electron concentration into algebraic equations specifically includes: Use Taylor series expansion to solve the electron continuity equation for the change of u at time t; The designed GLL basis function is used to perform the Galerkin test on the unknown quantity of electron density in the electron continuity equation, and then the unknown quantity is expanded using the scalar basis function. Based on the Taylor series expansion equation, the time difference format equation of arbitrary high-order derivatives is obtained; The GLL basis functions are: Where j = 0, 1, ... N, L N (ξ) is the Nth order Legendre polynomial, L N ′(ξ) is its derivative, and the grid points {ξ j ,j=0,1...N} as GLL integration points, which are equations The (N+1) roots of the basis function satisfy φ j (ξ i )=δ ij characteristics.

2. The method for efficiently predicting the gas breakdown threshold transient state of a low-complexity microwave device according to claim 1 is characterized in that: The electronic continuity equation is expanded using Taylor series to solve the change of u at time t: Where u (n) (t) is the nth derivative of the solution at time t, N is the highest order required, and Δt is the time change.

3. The method for efficiently predicting the gas breakdown threshold transient state of a low-complexity microwave device according to claim 1, characterized in that: The second-order, third-order, and fourth-order difference format equations of arbitrary high-order derivative time difference format equations are: Where A = [T] -1 (D[S]+(v i -v a )[T]), [T] and [S] are mass matrices, v i represents the ionization rate, v a represents the attachment rate, D represents the diffusion coefficient, n n is the electron concentration at the current moment.

4. The method for efficiently predicting the gas breakdown threshold transient state of a low-complexity microwave device according to claim 1, characterized in that: The breakdown determination conditions are: if It is judged as breakdown, where n0 is the initial electron concentration, n n is the electron concentration at the current moment; if It is judged as no breakdown; When n n+1 、n n The order of magnitude difference is between 10, let the first derivative of electron concentration be: k n =n n+1 -n n , let the second derivative of electron concentration be: a n =k n -k n-1 , if a n =0 or the limit is close to 0, then determine n n+1 and n n The size relationship, if n n+1 >n n , then breakdown; otherwise, no breakdown.

5. A low-complexity microwave device gas breakdown threshold transient high-efficiency prediction system implementing the method according to any one of claims 1 to 4, characterized in that: include: The electron concentration solving unit uses an arbitrary high-order derivative time difference format to transform the ordinary differential equations of electron concentration into algebraic equations to solve the electron concentration; A breakdown determination unit determines whether the device has broken down based on the calculated electron concentration; The prediction unit, based on the determination result, uses a binary method to update the incident field amplitude at the upper or lower limit of the range, and converts the power amplitude to obtain the port incident power at the time of breakdown.

6. A computer storage medium, characterized in that The computer storage medium stores an executable program, and the executable program is executed by a processor to implement the steps of the method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device according to any one of claims 1 to 4.

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