Low-complexity microwave device gas breakdown threshold transient efficient prediction method and system

Abstract

The invention discloses a transient efficient prediction method and system for a gas breakdown threshold of a low-complexity microwave device, and the method comprises the steps: converting an ordinary differential equation set of electron concentration into an algebraic equation set through employing an arbitrary higher derivative time difference format, and solving the electron concentration; an electron concentration equation set, a first derivative and a second derivative are comprehensively considered, and breakdown judgment conditions are designed; and the electron concentration solving step is repeated to solve the electron concentration, judgment is carried out according to breakdown judgment conditions, the incident field amplitude of the upper limit or the lower limit of the range is updated by adopting a dichotomy method based on a judgment result, and the power amplitude is converted to obtain the port incident power during breakdown. The method effectively solves the problem of low large-scale calculation efficiency in the process of predicting the gas breakdown threshold of the microwave device in a steady-state method and a traditional transient method, and finally realizes efficient prediction of the low-pressure gas breakdown threshold of the microwave device.

Description

Technical Field

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

[0002] With the rapid development of space technology, satellite communication, space exploration and other spaceborne missions are increasingly dependent on high-power microwave technology. In the low-pressure spaceborne environment, high-power microwave devices play a crucial role. However, the gas breakdown problem they face seriously threatens the stable operation of the system. Due to the low-pressure characteristics of the spaceborne environment, the average free path between gas molecules increases, and the probability of electron-impact ionization with gas molecules changes, making it easier for high-power microwave devices to experience gas breakdown during operation. Such breakdown not only causes a sharp decline in the performance of microwave devices, making it impossible to complete tasks such as signal transmission, detection and sensing normally, but also may cause permanent damage to the devices, thereby triggering the failure of the entire spaceborne microwave system and bringing serious consequences to space missions. Therefore, accurately predicting the gas breakdown threshold of high-power microwave devices in the low-pressure spaceborne environment is of great practical significance for ensuring the reliable operation of spaceborne microwave systems and improving the success rate of space missions, and this has also become an important issue that urgently needs to be overcome in the current 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 for Low-Pressure Discharge Threshold of Payload Microwave Devices" and patent number 202211439760.3 discloses an efficient prediction method for 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 calculation efficiency. Although this patent has accelerated the calculation speed to a certain extent, there is inevitably the problem of solving eigenvalues ​​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 the transconducting X-band RF window for high-power microwave tubes using SPARK3D was proposed. This method will produce a large time discretization error due to the use of a lower-order time integration algorithm. 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 a low-complexity microwave device, introduce an arbitrary high-order derivative time difference format, reduce the complexity of traditional transient calculations, and use the time domain spectral element method as a simulation calculation platform to improve calculation efficiency, ultimately achieving efficient and accurate prediction of the transient state of the gas breakdown threshold of a low-complexity microwave device, which can reduce research and development costs while ensuring the accuracy of the results, and provide guidance for the design of high-power microwave devices in a low-pressure satellite environment.

[0005] The above 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 derivatives and second-order derivatives to design the breakdown judgment conditions;

[0009] Repeat the above steps for solving the electron concentration, make a judgment according to the breakdown determination condition. Based on the determination result, the incident field amplitude of the upper or lower limit of the range is updated by the bisection method, and the port incident power at breakdown is obtained by converting the power amplitude.

[0010] Further, the conversion of the ordinary differential equation group of electron concentration into an algebraic equation group by using any high-order derivative time difference format specifically includes:

[0011] Expand the change of the solution u at time t in the electron continuity equation by Taylor series;

[0012] Use the designed GLL basis function to perform a Galerkin test on the unknown electron density in the electron continuity equation, and then expand the unknown using a scalar basis function;

[0013] Based on the Taylor series expansion equation and the basis function, obtain the high-order derivative time difference format equation.

[0014] Further, the change of the solution u at time t in the electron continuity equation expanded by Taylor series is:

[0015]

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

[0017] Further, the GLL basis function is:

[0018]

[0019] where j = 0, 1, … N, L N (ξ) is the Nth Legendre polynomial, L N ′(ξ) is its derivative, and the grid points {ξ j , j = 0, 1... N} within ξ ∈ [-1, 1] are used as GLL integration points, which are the (N + 1) roots of the equation , and this basis function satisfies φ j (ξ i ) = δ ij .

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

[0021]

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

[0023] Furthermore, the breakdown determination condition is:

[0024] If is determined to be breakdown, where n 0 is the initial electron concentration and n n is the electron concentration at the current moment;

[0025] If then it is determined not to break down;

[0026] When the order of magnitude difference between n n+1 and n n is between 10, let the first derivative of the electron concentration be: k n = n n+1 - n n , and let the second derivative of the electron concentration be: a n = k n - k n-1 . If a n = 0 or extremely close to 0, then determine the magnitude relationship between n n+1 and n n . If n n +1 > n n , then it breaks down; otherwise, it does not break down.

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

[0028] An electron concentration solving unit, which uses an arbitrary high-order derivative time difference format to convert the ordinary differential equation system of the electron concentration into an algebraic equation system and solve the electron concentration;

[0029] A breakdown determination unit, which determines whether the device breaks down based on the solved electron concentration;

[0030] A prediction unit, based on the determination result, updates the upper or lower limit of the incident field amplitude using the bisection method and converts the power amplitude to obtain the incident power at the port when breakdown occurs.

[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 transient high-efficiency prediction method for the gas breakdown threshold of the low-complexity microwave device.

[0032] Compared with the prior art, the significant advantages of the present invention are as follows:

[0033] (1) The method mentioned in the present invention is a transient high-efficiency prediction method for the gas breakdown threshold of low-complexity microwave devices. This numerical model introduces an Arbitrary high-order Derivative Explicit Runge-Kutta (ADER) time-differencing scheme, combines the orthogonality of the basis functions of the spectral element method in the time domain and the block-diagonal property of the mass matrix, avoids the inversion of large sparse matrices, and has a time complexity as low as O(N), greatly reducing the calculation time and memory consumption. Compared with the steady-state and traditional transient methods, it effectively shortens the calculation time;

[0034] (2) The ADER time-differencing scheme adopted by the method proposed in the present invention is based on the Taylor series expansion and uses the spatial derivative to approximate the time derivative to achieve high-order accuracy. When dealing with the prediction problem of the gas breakdown threshold of complex microwave devices, it can flexibly control the accuracy by adjusting the order, accurately simulate the change of physical quantities, and consume less memory. Compared with other differencing schemes, it is more suitable for large-scale simulation calculations;

[0035] (3) To improve the accuracy of the breakdown threshold analysis of complex targets, the method proposed in the present invention adopts a transient breakdown criterion for complex targets, comprehensively considering the electron concentration and its first and second derivatives. It not only judges based on the multiple relationship between the electron concentration and the initial electron concentration, but also accurately determines the breakdown situation by analyzing the first and second derivatives of the electron concentration and the magnitude relationship of the electron concentrations at the previous and current moments under a specific order-of-magnitude difference, thereby making the calculation results more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0037] Figure 2 is a comparison diagram of the breakdown power threshold varying with pressure at a frequency of 200 MHz by different methods.

[0038] Figure 3 is a comparison diagram of the calculation time.

[0039] Figure 4 is a flow chart of the breakdown criterion determined by the present invention.

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

[0041] Figure 6 is a comparison diagram of the calculation time complexity. DETAILED DESCRIPTION OF THE INVENTION

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

[0043] Using an arbitrary high-order derivative time-difference format, transform the ordinary differential equation set of electron concentration into an algebraic equation set, and solve the electron concentration;

[0044] Comprehensively considering the electron concentration equation set and its first-order derivative and second-order derivative, design the breakdown determination condition;

[0045] Repeat the above-mentioned electron concentration solving step to solve the electron concentration, make a determination according to the breakdown determination condition, and based on the determination result, use the bisection method to update the incident field amplitude of the upper limit or lower limit of the range, and convert the power amplitude to obtain the port incident power at breakdown.

[0046] The specific process of using an arbitrary high-order derivative time-difference format to transform the ordinary differential equation set of electron concentration into an algebraic equation set includes:

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

[0048] Use the designed GLL basis function to perform Galerkin test on the unknown electron density in the electron continuity equation, and then expand the unknown using a scalar basis function;

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

[0050]

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

[0052] Based on the Taylor series expansion equation, obtain the arbitrary high-order derivative time-difference format equation.

[0053] The ADER format is based on Taylor series expansion and uses spatial derivatives to approximate time derivatives, so as to achieve high-order accuracy in time integration. To express the ADER format, first, it is necessary to use Taylor series expansion to solve the change of u at time t:

[0054]

[0055] In the formula, u (n) (t) is the nth-order derivative of the solution at time t, and N is the required highest order;

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

[0057]

[0058] where j = 0, 1, … N, L N (ξ) is the Nth-order Legendre polynomial, and L N ′(ξ) is its derivative. The grid points {ξ j , j = 0, 1... N} within ξ ∈ [-1, 1] are used as GLL integration points, which are the (N + 1) roots of the equation . The basis functions in Equation (3) satisfy the property φ j (ξ i ) = δ ij .

[0059] Substituting Equation (2) into Equation (1), the first-order form of the arbitrary high-order derivative time-domain spectral element method (ADER-SETD) can be obtained, and the equation is as follows:

[0060]

[0061] where V is the volume integration region within the element, 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, and n n is the electron concentration at the current moment;

[0062] Further solving Equation (4) gives:

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

[0064] where:

[0065] [T] = ∫ V ψ i ψ j |J|dV

[0066]

[0067] Analysis of the [T] matrix calculation:

[0068]

[0069] In the formula, the reference coordinate system (ξ, η, ζ) ∈ [-1, 1] × [-1, 1] × [-1, 1], N ξ 、N η 、 are respectively the interpolation orders of the basis functions along the three directions of ξ, η, ζ in the reference domain (here is the case where 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 certain direction in (ξ, η, ζ), is the test basis function, is the expansion basis function, w r 、w s 、w t are the weight values of the GLL points.

[0070] From the property of the basis function in formula (3): φ j (ξ i ) = δ ij , if (m, n, p) ≠ (m′, n′, p′), then no matter whether the integration point (r, s, t) takes (m, n, p) or (m′, n′, p′), Φ i 、Φ j must be zero for one of them, and then the integral is 0. So only when r = m = m′, s = n = n′, t = p = p′, the above formula is non - zero. After the above analysis, the [T] matrix can be expressed in the following form:

[0071]

[0072] Matrix form:

[0073]

[0074] Therefore, the formed mass matrix [T] is a non - diagonal matrix. However, 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 method of inverting the block - diagonal matrix to calculate the inverse of the mass matrix in advance, making the equation an explicit equation and reducing the computational amount;

[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] Substitute the ADER difference scheme of Equation (2) into (9) to obtain the second-order, third-order, and fourth-order ADER equations:

[0079] ADER - second order:

[0080] ADER - third order:

[0081] ADER - fourth order:

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

[0083]

[0084] where \(E a , E b represent the minimum and maximum values of the set initial incident electric field strength;

[0085] The ionization rate \(v i and the attachment rate \(v a can be expressed as:

[0086]

[0087] where \(a\) represents the ratio of the effective electric field \(E eff to the pressure \(p\);

[0088] The breakdown criterion described in Step Five is:

[0089] (1) If (where \(n 0 is the initial electron concentration), it is determined to be breakdown;

[0090] (2) If then it is determined not to be breakdown;

[0091] (3) When the order of magnitude difference between \(n n+1 and \(n n is between (1) and (2), let the first derivative of the electron concentration be: \(k n = n n+1 - n n , and let the second derivative of the electron concentration be: \(a n = k n - k n-1 . If \(a n = 0\) (or extremely close to 0), when determining \(n n+1 and \(n nThe size relationship, if n n+1 > n n , then breakdown occurs; otherwise, it does not break down, where n n+1 is the electron concentration at the next moment, and n n is the electron concentration at the current moment.

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

[0093]

[0094] In the formula, 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, A 0 is the amplitude of the time part, and a(ω) is the normalized excitation signal.

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

[0096] An electron concentration solving unit, which uses an arbitrary high-order derivative time difference format to convert the ordinary differential equation group of electron concentration into an algebraic equation group to solve the electron concentration;

[0097] A breakdown determination unit, which determines whether the device breaks down based on the solved electron concentration;

[0098] A prediction unit, based on the determination result, updates the upper or lower limit of the incident field amplitude using the bisection method and converts the power amplitude to obtain the incident power at the port when breakdown occurs.

[0099] This embodiment also provides a computer storage medium, which is 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 low-complexity microwave device gas breakdown threshold transient high-efficiency prediction method.

[0100] In order to reduce the complexity of traditional transient calculations, the present invention introduces an arbitrary high-order derivative time difference format, uses the spectral element method in the time domain as a simulation calculation platform to improve the calculation efficiency, and finally realizes the low-complexity microwave device gas breakdown threshold transient high-efficiency and accurate prediction, which can reduce the R & D cost under the condition of ensuring the result accuracy and provide guidance for the design of high-power microwave devices in a low-pressure spaceborne environment.

[0101] Embodiment 2

[0102] Based on Embodiment 1, the present invention proposes a low-complexity microwave device gas breakdown threshold transient high-efficiency prediction method. The following further describes the specific steps of the present invention in detail with reference to the accompanying drawings, taking Figure 1 the shown ridge waveguide structure as an example.

[0103] See Figure 1 the schematic diagram of the T - microstrip structure shown. The geometric dimensions of the model are as follows: 12mm×2mm×20mm. On a grounded dielectric substrate with a thickness of h = 2mm and a relative dielectric constant of ε r , a waveguide with a width of W = 2mm is printed. According to the analysis of the present invention Figure 1 a method for efficiently predicting the transient gas breakdown threshold of a low - complexity microwave device with the T - microstrip structure shown, the specific operation steps are as follows:

[0104] Step 1, according to Figure 1 the geometric model of the T - microstrip structure shown, first use Ansys software for modeling, perform mesh division on it using hexahedrons, obtain the node coordinate information and element information of the structure. For the boundary conditions of the microstrip structure, the four faces except the port in the transmission direction are set as ideal metals, and the port in the transmission direction adopts a first - order absorbing boundary. In addition, set the position of the excitation source. The excitation source is a sinusoidal plane wave polarized along the direction. The model uses a sinusoidal wave with a center frequency f = 200MHz as the excitation source, and calculate the internal electric - field distribution of the device according to the applied excitation source.

[0105] Step 2, for the electron continuity equation that determines the breakdown threshold and power capacity of the microwave device, substitute the arbitrary high - order derivative (ADER) time - difference format, then use the GLL basis function to perform Galerkin testing on the unknown electron density in the electron continuity equation, and then expand the unknown using scalar basis functions. The system of equations is as follows:

[0106]

[0107] After that, simplify the matrix equation to Equation (4), and the equation is as follows:

[0108] n n+1 =n n +ΔtAn n (15)

[0109] Where:

[0110] [T]=∫ V ψ i ψ j |J|dV

[0111]

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

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

[0114] In the third step, set the working pressure and the initial incident field strength. Calculate the effective electric field strength based on the incident wave frequency, the collision rate in the transport coefficient, and the normalized electric field distribution. Calculate the current ionization rate and attachment rate through the effective electric field strength, fill the [T] and [S] matrices, and 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] In the fourth step, according to the ADER-4th order time-domain spectral element method format, calculate and fill the corresponding matrices to obtain the electron concentration varying with time:

[0121]

[0122] In the fifth step, based on the electron concentration obtained in the fourth step, make a determination according to the breakdown criterion flow chart as shown in Figure 4 . If it is determined to be breakdown, as shown in Figure 5 (a); if it is determined not to be breakdown, as shown in Figure 5 (b); when the order of magnitude difference between n n+1 and n n is between 10, if n n+1 > n n , then it is breakdown, as shown in Figure 5 (c); otherwise it is not breakdown as shown in Figure 5 (d).

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

[0124] In the sixth step, when the breakdown threshold interval meets the set range (|Ea -E b Stop the loop when |≤1), output the incident field strength at this time, and perform power amplitude conversion according to Poynting's theorem to obtain the incident power at the port at breakdown.

[0125] Step 7, calculate the time complexities of the steady-state method and the transient method, which are O(N 3 ), respectively, and O(N), as Figure 6 shown.

[0126] According to the method described in the present invention, Figure 1 the T microstrip model shown in the figure is simulated. The comparison of the breakdown power thresholds of different methods with the change of pressure at a frequency of 200 MHz is as Figure 2 shown. Compared with the steady-state method and the commercial software SPARK3D, the results are in good agreement. In the absence of a dielectric, the transmission line can be simplified to a two-wire transmission line in a homogeneous medium (such as air), and the propagation of electromagnetic waves is relatively simple at this time. 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 the inability to match the phase at the interface between the dielectric and the air. Therefore, the microstrip line cannot support the ideal TEM wave mode, but presents a quasi-TEM mode, in which there is a difference in the propagation speeds of the electric field and the magnetic field, which in turn affects the impedance, signal transmission speed, and loss and other characteristics of the microstrip line. Figure 3 This is the comparison of the calculation time between the method proposed in the present invention and the 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] Aiming at the problems of high calculation complexity and low efficiency of the existing transient method, the time-domain spectral element method uses hexahedral elements to discretize the grid, which can well describe the geometric shape of the device. The basis functions with orthogonal properties are used for testing and expansion, and the generated mass matrix has a block diagonal property. It performs better especially when dealing with large-scale problems of gas breakdown in microwave devices, complex boundary conditions, and long-time simulations, greatly reducing the time of matrix inversion operation and reducing the memory consumption, and predicting the gas breakdown threshold of microwave devices through numerical methods. Its high-order polynomial basis functions and sparse matrix structure make the memory usage more optimized, and it is more suitable for parallel computing and adaptive grid division.

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

[0129] Obviously, those skilled in the art can 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 these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. A method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device, characterized in that: Includes 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 derivatives and second-order derivatives to design the breakdown judgment conditions; 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 binary 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.

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 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 variation of u in time t for the continuity equation of electrons; 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 for arbitrary high-order derivatives is obtained.

3. The method for efficiently predicting the gas breakdown threshold transient state of a low-complexity microwave device according to claim 2 is characterized in that: The electronic continuity equation is expanded using Taylor series to solve the change of u at time t: In the formula, 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.

4. The method for efficiently predicting the gas breakdown threshold transient state of a low-complexity microwave device according to claim 3 is characterized in that: 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, they are equations The (N+1) roots of the basis function satisfy φ j (ξ i )=δ ij characteristics.

5. A method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device according to claim 4, 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 both 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.

6. The method for efficiently predicting the transient gas breakdown threshold of a low-complexity microwave device according to claim 1 is characterized in that: The breakdown determination condition is: 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 When the electron concentration is between 10 and 10, the first derivative of the electron concentration is: k n =n n+1 -n n , let the second-order 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 If n n+1 >n n , then breakdown; otherwise, no breakdown.

7. A low-complexity microwave device gas breakdown threshold transient efficient prediction system implementing any of the methods described in claims 1-6, 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 solved electron concentration; The prediction unit, based on the determination result, uses a binary method to update the incident field amplitude of the upper or lower limit of the range, and converts the power amplitude to obtain the port incident power at the time of breakdown.

8. 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 as described in any one of claims 1 to 6.

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