A method for drawing micro-discharge sensitivity curve

Abstract

This invention discloses a method for plotting a microdischarge sensitivity curve. By quantifying the electron population variation trend under specified voltage conditions and utilizing the boundary continuity of sensitive regions within a calculated parameter region, this method employs a grid-based search method to rapidly locate the microdischarge thresholds surrounding a defined microdischarge threshold point. This method enables rapid plotting of the overall microdischarge sensitivity curve, significantly reducing the time required to plot the overall sensitivity curve. Compared to other methods, this method is applicable to all simulation methods that can generate electron population variation curves, as well as microdischarge scenarios with arbitrarily complex field distributions. This method significantly facilitates the design of "microdischarge-free" microwave devices for space microwave communication applications.

Description

Technical Field

[0001] The invention belongs to the technical field of special effect analysis of space microwave components, and particularly relates to a method for drawing a micro-discharge sensitivity curve. Background Art

[0002] The micro-discharge phenomenon can cause signal degradation and power attenuation in microwave systems, and even cause permanent damage to devices. Therefore, it has attracted widespread attention in the fields of high-power microwaves, high-energy accelerators, and space microwave communications. Ensuring that space microwave devices operate below their micro-discharge threshold is an effective way to avoid the risk of micro-discharge. In order to avoid the performance loss of microwave devices due to the application of excessive voltage margin, the micro-discharge threshold of microwave devices should be predicted as accurately as possible in engineering practice. The micro-discharge sensitivity curve is a curve with the microwave frequency and the device gap product fd as the horizontal axis and the microwave field voltage V rf The threshold parameter curve for microdischarge is plotted in the coordinate system with the vertical axis. The microdischarge sensitivity curve can be used to quickly determine the microdischarge threshold voltage conditions at different frequency spacing products, which is of great significance for the structural design and parameter selection of "microdischarge-free" microwave components.

[0003] Currently, microdischarge sensitivity curves are primarily drawn by sequentially scanning the microdischarge thresholds at different frequencies. This method still requires searching for the threshold voltage over a large range after changing the microwave frequency, resulting in a large computational load. However, the microdischarge sensitivity curve is often continuous within the solution range. Therefore, within the pre-gridded calculation region, the microdischarge threshold points must be "first in, last out" on the boundary grid of the sensitive region. The parameter conditions at these edge endpoints correspond to opposite trends in the electron number change. These quantitative conditions can be used to quickly determine subsequent microdischarge threshold points. Despite this, traditional sensitivity curve drawing methods often ignore the limitations of the sensitivity curve continuity on the threshold range.

[0004] Therefore, it is necessary to design a strategy method that can use the continuity of the sensitivity curve to quickly search for the micro-discharge threshold point within a specific range, so as to speed up the drawing of the overall micro-discharge sensitivity curve. In this way, the micro-discharge sensitivity curve of any microwave device and any SEY distribution can be quickly calculated in actual engineering applications, thereby facilitating the design of actual micro-discharge-free microwave devices. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the deficiencies in the above-mentioned prior art and provide a method for drawing a micro-discharge sensitivity curve. By gridding the parameter area and using known threshold data points to narrow the search range for subsequent thresholds, a large-scale search for micro-discharge threshold voltages of different frequencies when drawing the micro-discharge sensitivity curve is avoided. This can significantly reduce the calculation time of the entire sensitive area and solve the efficiency problem existing in the parameter design optimization of micro-discharge-free microwave devices.

[0006] The present invention adopts the following technical solutions:

[0007] A method for drawing a micro-discharge sensitivity curve comprises the following steps:

[0008] Calculate the effective secondary electron multiplication rate σ corresponding to the parameter conditions of each endpoint of the grid to be processed eff , and update the traversal identifier of the grid; based on the effective secondary electron multiplication rate of each endpoint, among the three grid edges to which the current threshold point does not belong, according to the effective secondary electron multiplication rate σ of the endpoints on both sides of the edge eff The relative size to 1 determines the grid edge where the next threshold point is located; based on the grid edge where the next threshold point is located, the two adjacent grids are determined as the next grids to be processed, and at the same time, the next threshold point is searched for using the binary search method within the parameter range of the two end points of the edge and the threshold results are recorded; according to the traversal identifier of the next grid to be processed, all thresholds are sorted and summarized and a curve is drawn.

[0009] Specifically, the grids to be processed are:

[0010] According to the empirical results of the sensitive area of ​​the flat micro-discharge, the effective secondary electron multiplication rate σ eff The largest grid endpoint is used to find the parameter conditions for micro-discharge, and the initial threshold point is determined by bisection. The two grids adjacent to the edge where the initial threshold point is located are determined as the grids to be processed.

[0011] Furthermore, before finding the parameter conditions for micro-discharge, the threshold calculation area to be analyzed is first meshed, the mesh traversal identifier is initialized, and the frequency and voltage parameters of each mesh endpoint are determined. The specific steps are as follows:

[0012] According to the voltage upper limit V of the sensitive area max With the lower limit V min , upper frequency limit f max With the lower limit f min and its corresponding splitting numbers r and c, perform logarithmic uniform splitting to obtain the voltage array Λ and frequency array Γ;

[0013] According to the obtained voltage array Λ and frequency array Γ, the microwave voltage V corresponding to the matrix element is determined. rf and the frequency spacing product fd;

[0014] The grid is numbered two-dimensionally and denoted as G ij The lower left, upper left, lower right and upper right endpoints of each grid are represented by N ij 1 、N ij 2 、N ij 3 With Nij 4 ;

[0015] Denote the grid traversal identifier as C ij And initialize the grid identification array C ij The elements of are all set to 0, indicating a state to be calculated.

[0016] Furthermore, the i-th element Λ of the array Λ i and the jth element Γ of the array Γ j Specifically:

[0017]

[0018]

[0019] Specifically, the grid edge where the next threshold point is located is determined as follows:

[0020] If (σ eff (N ij 1 )-1)(σ eff (N ij 2 )-1)≤0, then the next threshold point is located at the left edge of the grid to be processed;

[0021] If (σ eff (N ij 2 )-1)(σ eff (N ij 4 )-1)≤0, then the next threshold point is located at the upper edge of the grid to be processed;

[0022] If (σ eff (N ij 4 )-1)(σ eff (N ij 3 )-1)≤0, then the next threshold point is located at the right edge of the grid to be processed;

[0023] If (σ eff (N ij 1 )-1)(σ eff (N ij 4 )-1)≤0, the next threshold point is located at the lower edge of the grid to be processed.

[0024] Furthermore, when the next threshold point is located at the left edge of the grid to be processed, the next grid to be processed is the grid to the left of the current grid;

[0025] When the next threshold point is located at the right edge of the grid to be processed, the next grid to be processed is the grid to the right of the current grid;

[0026] When the next threshold point is located at the upper edge of the grid to be processed, the next grid to be processed is the upper grid of the current grid;

[0027] When the next threshold point is located at the lower edge of the grid to be processed, the next grid to be processed is the lower grid of the current grid.

[0028] Specifically, the effective secondary electron multiplication rate σ eff The details are as follows:

[0029] The instantaneous SEY value corresponding to the collision kinetic energy is calculated by combining the SEY model, and the SEY phenomenological model is used to calculate the instantaneous SEY value; the K function distribution is calculated based on the instantaneous SEY value, and the simultaneous equations for solving the effective secondary electron multiplication rate are determined. Based on the simultaneous equations for the effective secondary electron multiplication rate, the micro-discharge effective secondary electron multiplication rate σ corresponding to each element in the parameter matrix S is calculated using a simultaneous iterative solution method. eff ; Effective secondary electron multiplication rate σ of microdischarge in statistical theory steady-state modeling eff ; The effective secondary electron multiplication rate σ is determined by the slope of the electron number time variation curve eff .

[0030] Furthermore, the micro-discharge effective secondary electron multiplication rate σ corresponding to each element in the parameter matrix S is calculated using the simultaneous iterative solution method. eff Specifically:

[0031] Assume that the number of first-generation electrons on the inner and outer diameters is equal and has a uniform emission phase distribution, substitute the steady-state equations to calculate the number of next-generation electrons and emission phase distribution on the inner and outer diameters respectively; then repeat the above iterative process until the total emission phase difference E between the two adjacent generations of electrons on the inner and outer diameters is equal to tot Not exceeding the error E thr , so that the electron emission phase reaches a steady state, and the effective secondary electron multiplication rate σ of the micro-discharge is obtained eff .

[0032] Furthermore, the effective secondary electron multiplication rate σ eff for:

[0033]

[0034] in, and is the number of electrons in two adjacent generations in the inner diameter after the micro-discharge develops to a steady state, and It is the number of electrons in two adjacent generations after the micro-discharge develops to a steady state.

[0035] Furthermore, the SEY phenomenological model is used to calculate the instantaneous SEY value σ(k) as follows:

[0036]

[0037] Where ω is the normalized incident kinetic energy parameter, σ m is the maximum SEY value; k 1-5 is the fitting parameter of the SEY distribution curve of the material.

[0038] Compared with the prior art, the present invention has at least the following beneficial effects:

[0039] A micro-discharge sensitivity curve drawing method, optimizing the threshold search process of the fast drawing method, and solving the effective secondary electron multiplication rate σ at the four endpoints of the current calculation grid eff In order to determine the next adjacent calculation grid and threshold point, the amount of calculation for solving the micro-discharge threshold point can be reduced while ensuring the accuracy of the results. Finally, the overall sensitivity curve can be drawn by integrating all threshold results, avoiding the huge amount of calculation generated by scanning the threshold over a large range of frequencies one by one.

[0040] Furthermore, meshing and initializing the mesh traversal identifier for the micro-discharge sensitive area can avoid repeated calculation of the effective secondary electron multiplication rate σ of the computational grid. eff , and speed up the operation.

[0041] Furthermore, the area required for drawing the sensitive curve is first gridded, the grid traversal identifier is initialized, and the frequency and voltage parameters of each grid endpoint are determined. Then, the micro-discharge steady-state statistical theory modeling is adopted, and the dependence of traditional statistical theory modeling on the electron trajectory expression is removed through the improved joint probability density function numerical modeling method.

[0042] Furthermore, the logarithmic transformation of the i-th voltage array Λ and the j-th frequency array Γ facilitates the linear interpolation calculation of subsequent results.

[0043] Furthermore, the position of the next grid to be processed is located around the current grid. The purpose of setting the grid edge where the next threshold point is located is to find the next grid to be processed adjacent to the current grid.

[0044] Furthermore, the microdischarge sensitivity threshold curve is a continuous curve. If the microdischarge sensitivity curve enters the current grid from a grid edge, it will exit from the grid edge of the current grid and enter the next grid to be processed. When the next threshold point is located at the left edge of the grid to be processed, the next grid to be processed is the grid to the left of the current grid; when the next threshold point is located at the right edge of the grid to be processed, the next grid to be processed is the grid to the right of the current grid; when the next threshold point is located at the top edge of the grid to be processed, the next grid to be processed is the grid above the current grid; and when the next threshold point is located at the bottom edge of the grid to be processed, the next grid to be processed is the grid below the current grid. This setting is intended to determine the next grid to be processed by the grid edge where the threshold point is located, thereby avoiding the calculation of other grids to be processed where no threshold point exists.

[0045] Furthermore, the instantaneous SEY value corresponding to the collision kinetic energy is calculated in combination with the SEY model, and the SEY phenomenological model is used to calculate the instantaneous SEY value; the K function distribution is calculated based on the instantaneous SEY value, and the simultaneous equations for solving the effective secondary electron multiplication rate are determined. Based on the simultaneous equations for the effective secondary electron multiplication rate, the micro-discharge effective secondary electron multiplication rate σ corresponding to each element in the parameter matrix S is calculated using a simultaneous iterative solution method. eff ; Effective secondary electron multiplication rate σ of microdischarge in statistical theory steady-state modeling eff ; The effective secondary electron multiplication rate σ is determined by the slope of the electron number time variation curve eff The purpose of setting is to be able to visually express the effective secondary electron multiplication rate σ eff When the slope of the electron number time variation curve is greater than zero, the effective secondary electron multiplication rate σ eff Greater than 1; when the slope of the electron number time variation curve is less than zero, the effective secondary electron multiplication rate σ eff Less than 1; when the slope of the electron number time variation curve is equal to zero, the effective secondary electron multiplication rate σ eff Equal to 1.

[0046] Furthermore, the use of the simultaneous iterative solution method not only makes the calculation process more flexible, but also can accurately consider the effects of unilateral and bilateral collisions during the micro-discharge process.

[0047] Furthermore, the effective secondary electron multiplication rate σ of microdischarge eff The setting can quantitatively describe the changing trend and degree of the number of space electrons during the microdischarge process, and can be used to evaluate the degree of microdischarge and whether the microdischarge has reached a critical state.

[0048] Furthermore, the SEY phenomenological model is used to calculate the instantaneous SEY value σ(k). The SEY phenomenological model is a semi-empirical formula proposed by summarizing the laws of SEY curves of most materials, which facilitates the calculation of a large number of instantaneous SEYs in statistical theoretical modeling.

[0049] In summary, the present invention avoids redundant calculations of a large number of effective secondary electron multiplication rates at undetermined points, and provides great convenience for comparing microdischarge sensitivity curves of different materials or evaluating changes in microdischarge sensitivity curves under different conditions in engineering.

[0050] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Flow chart of the method of the present invention;

[0052] Figure 2 This is a schematic diagram of the micro-discharge sensitivity curve of a coaxial transmission line made of common copper materials obtained based on calculations in the present invention;

[0053] Figure 3 Schematic diagram of quickly finding the micro-discharge threshold point in the method of the present invention;

[0054] Figure 4 The slope of the electron number time variation curve is used to determine the effective secondary electron multiplication rate σ in the particle simulation method. eff . DETAILED DESCRIPTION

[0055] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0056] In the description of the present invention, it is to be understood that the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0057] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0058] It should be further understood that the term "and / or" as used in the present specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items. For example, A and / or B may represent: A alone, A and B simultaneously, or B alone. In addition, the character " / " herein generally indicates that the associated items are in an "or" relationship.

[0059] It should be understood that the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0060] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments disclosed herein. These figures are not drawn to scale; for clarity, some details are exaggerated and some details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0061] This invention provides a method for plotting a microdischarge sensitivity curve. This method uses microdischarge steady-state statistical theory to model the material's microdischarge threshold at the starting point based on the SEY parameter model. The method then optimizes the solution process to automatically find the microdischarge threshold point within the current computational grid area and store the data. This data is then used to plot the microdischarge sensitivity curve, significantly reducing the time required for microdischarge threshold calculation. Compared to existing methods, this method greatly facilitates comparing the microdischarge thresholds of different materials in engineering applications and evaluating the impact of different conditions on the microdischarge threshold.

[0062] See also Figure 1 The present invention provides a method for drawing a micro-discharge sensitivity curve, comprising the following steps:

[0063] S1. Grid the threshold calculation area to be analyzed, initialize the grid traversal identifier and determine the frequency and voltage parameters of each grid endpoint;

[0064] Mesh generation and parameter initialization are performed on the specified parameter area, specifically:

[0065] S101, according to the voltage upper limit V of the sensitive area max With the lower limit Vmin , upper frequency limit f max With the lower limit f min The voltage array Λ and the frequency array Γ are obtained by logarithmic uniform partitioning of the corresponding partitioning numbers r and c. The i-th element of the array Λ and the j-th element of the array Γ are specifically expressed as

[0066]

[0067]

[0068] S102, according to the partitioning setting of the voltage array Λ and the frequency array Γ, the microwave voltage V corresponding to the matrix element rf and the frequency spacing product fd are:

[0069]

[0070]

[0071] Where d is the device spacing value. In a coaxial transmission line, it is the difference between its outer diameter and inner diameter. In a parallel plate structure, it is the spacing between the upper and lower plates.

[0072] S103, number the grid in two dimensions and represent it as G ij The lower left, upper left, lower right and upper right endpoints of each grid are represented by N ij 1 、N ij 2 、N ij 3 With N ij 4 , and the frequency and voltage parameters corresponding to these endpoints are specifically

[0073]

[0074]

[0075]

[0076]

[0077] S104. Denote the grid traversal identifier as C ij And initialize the grid identification array C ij The elements of are all set to 0, indicating a state to be calculated.

[0078] S2, according to the empirical results of the sensitive area of ​​flat micro-discharge, the effective secondary electron multiplication rate (σ eff) The larger grid endpoint attempts to find the parameter conditions for micro-discharge, and determines the initial threshold point through bisection, and determines the two grids adjacent to the edge where it is located as the grids to be processed;

[0079] The initial threshold point is determined based on the empirical results of the parallel plate sensitive area, specifically:

[0080] S201, according to the previously calculated results of the parallel plate micro-discharge sensitive area, the effective secondary electron multiplication rate (σ eff ) to determine the initial point library Ω from the largest trial parameter point, and determine the effective secondary electron multiplication rate σ of each trial parameter point eff , if the parameter point satisfies σ eff ≥1, then the parameter point is included in the initial point library Ω;

[0081] S202, traverse the initial point library Ω (the frequency and voltage of the lth parameter point are represented by f l With V l ), using the dichotomy method in [V min , V l ] range to find the frequency f l The initial threshold point of

[0082] S203 , determining the left and right grids adjacent to the edge where the initial threshold point is located as grids to be processed.

[0083] S3. For the grid to be processed determined in step S2 or step S6, calculate the effective secondary electron multiplication rate σ corresponding to the parameter conditions of each endpoint of the grid eff , and update the traversal identifier of the grid;

[0084] S4, based on the effective secondary electron multiplication rate of each endpoint obtained in step S3, among the three grid edges to which the current threshold point does not belong, according to the effective secondary electron multiplication rate σ of the endpoints on both sides of the edge eff The relative size to 1 determines the grid edge where the next threshold point is located;

[0085] According to the effective secondary electron multiplication rate σ at each end point of the grid eff Searching for the grid edge where the next threshold point is located can be divided into the following four cases:

[0086] (1) If (σ eff (N ij 1 )-1)(σ eff (N ij 2 )-1)≤0, then the next threshold point is located at the left edge of the grid to be processed;

[0087] (2) If (σ eff (Nij 2 )-1)(σ eff (N ij 4 )-1)≤0, then the next threshold point is located at the upper edge of the grid to be processed;

[0088] (3) If (σ eff (N ij 4 )-1)(σ eff (N ij 3 )-1)≤0, then the next threshold point is located at the right edge of the grid to be processed;

[0089] (4) If (σ eff (N ij 1 )-1)(σ eff (N ij 4 )-1)≤0, then the next threshold point is located at the lower edge of the grid to be processed;

[0090] The next grid to be processed is determined according to different situations in step S3, which is specifically:

[0091] (1) When the next threshold point is located at the left edge of the grid to be processed, the next grid to be processed is the grid to the left of the current grid;

[0092] (2) When the next threshold point is located at the right edge of the grid to be processed, the next grid to be processed is the grid to the right of the current grid;

[0093] (3) When the next threshold point is located at the upper edge of the grid to be processed, the next grid to be processed is the upper grid of the current grid;

[0094] (4) When the next threshold point is located at the lower edge of the grid to be processed, the next grid to be processed is the lower grid of the current grid.

[0095] S5. Based on the grid edge where the next threshold point determined in step S4 is located, determine another grid adjacent to it as the next grid to be processed, and use a binary search method to search for the next threshold point within the parameter range of the two end points of the edge and record the threshold result;

[0096] The effective secondary electron multiplication rate σ corresponding to the parameter conditions at each end point of the grid is determined by the electron number curve obtained by statistical theoretical steady-state modeling or particle simulation method. eff , specifically:

[0097] (1) Combined with the SEY model, the instantaneous SEY value corresponding to the collision kinetic energy is calculated. The instantaneous SEY value is calculated using the SEY phenomenological model as follows:

[0098]

[0099] Where ω is the normalized incident kinetic energy parameter (the kinetic energy E corresponding to the maximum SEY m Normalized), σ m is the maximum SEY value; k 1-5 is the fitting parameter of the SEY distribution curve of the material.

[0100] (2) Calculate the K function distribution based on the instantaneous SEY value and determine the simultaneous equations for solving the effective secondary electron multiplication rate, specifically:

[0101]

[0102]

[0103] in, is the number of inner diameter electrons of the l-1 generation, is the function of probability density function and SEY, is the phase distribution function of the inner diameter electron emission of the l-1 generation. The superscripts l and l-1 represent the corresponding parameters of the l- and l-1-generation electrons. The subscripts i and o are used to distinguish the parameters of the inner and outer conductors of the coaxial transmission line.

[0104] (3) Based on the above simultaneous equations, the simultaneous iterative solution method is used to calculate the micro-discharge effective secondary electron multiplication rate σ corresponding to each element in the parameter matrix S. eff The specific steps are:

[0105] Assume that the number of first-generation electrons on the inner and outer diameters is equal and has a uniform emission phase distribution, substitute the steady-state equations to calculate the number of next-generation electrons and emission phase distribution on the inner and outer diameters respectively; then repeat the above iterative process until the total emission phase difference E between the two adjacent generations of electrons on the inner and outer diameters is equal to tot Not exceeding the error E thr , so that the electron emission phase reaches a steady state, and the effective secondary electron multiplication rate σ of the micro-discharge is obtained eff .

[0106] (4) Effective secondary electron multiplication rate σ of microdischarge in statistical theory steady-state modeling eff for:

[0107]

[0108] in, and is the number of electrons in two adjacent generations in the inner diameter after the micro-discharge develops to a steady state, and It is the number of electrons in two adjacent generations after the micro-discharge develops to a steady state.

[0109] (5) In the particle simulation method, the slope of the electron number time variation curve is used to determine the effective secondary electron multiplication rate σ eff .

[0110] See also Figure 4 In the particle simulation method, the CST simulation software is first run to derive a curve showing the change of the number of electrons over time. Then, a fitting straight line is plotted after the back end of the curve stabilizes. The slope of the curve is used to determine the effective secondary electron multiplication rate.

[0111] S6. Based on the next grid to be processed determined in step S5, determine whether to end the loop according to whether the search of its traversal identifier exceeds the overall parameter range; summarize all thresholds and draw a curve.

[0112] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0113] Example

[0114] The inner and outer diameters of the coaxial transmission line are calculated using copper material, and the secondary electron emission model is the Vaughan model;

[0115] The rapid drawing method of the micro-discharge sensitivity curve proposed in the present invention has a shorter calculation time than the traditional method, automatically solves the adjacent micro-discharge threshold points, avoids the calculation of the effective secondary electron multiplication rate of a large number of points to be solved, and greatly reduces the calculation time of drawing the micro-discharge sensitivity curve.

[0116] See also Figure 2 , which is the sensitivity curve calculated in this example, with the product fd of microwave frequency and device gap (the gap of coaxial transmission line is the difference between its outer diameter and inner diameter) as the horizontal axis, and the microwave field equivalent voltage V rf The black curve in the figure is the micro-discharge sensitivity curve obtained by the traditional drawing method, and the dotted line is the micro-discharge sensitivity curve obtained by the fast drawing method.

[0117] Figure 2 Color temperature is used to represent the degree of microdischarge, and the color temperature varies with the effective secondary electron multiplication rate σeff increases with the increase of ; eff The area where σ > 1 is the sensitive area of ​​micro-discharge, and the fast drawing method is used to obtain σ eff =1 micro-discharge sensitivity curve. Figure 2 The transition between microdischarge regions is smooth; the color temperature is higher at the center of the sensitive region, indicating more intense microdischarges under these conditions. Compared to the commonly used material Cu in the figure, the microdischarge sensitivity curve obtained by the rapid rendering method matches well with experimental results, demonstrating the high numerical accuracy of this example calculation. Compared with traditional sensitivity curve rendering methods, the rapid rendering method significantly improves calculation speed, reducing the calculation time to one-sixtieth of the original time.

[0118] See also Figure 3 , determine the initial point library Ω based on the previously calculated parallel plate micro-discharge sensitive area results, then traverse the initial point library Ω and use the dichotomy method to find the initial threshold point, and determine the two grids adjacent to the edge where the initial threshold point is located as the grid to be processed. Then, based on the effective secondary electron multiplication rate at the four endpoints of the grid, determine the grid edge where the threshold point is located and the next grid to be processed, and use the dichotomy method to calculate the precise threshold point. Finally, repeat the previous step on the next grid to be processed, which is Figure 3 The present invention can avoid the calculation of effective secondary electron multiplication rates of a large number of points to be calculated, automatically solve the adjacent micro-discharge threshold points, and greatly reduce the calculation time for drawing the micro-discharge sensitivity curve.

[0119] In summary, the present invention provides a method for drawing a microdischarge sensitivity curve. This method utilizes the continuity of the sensitivity curve to rapidly search for microdischarge threshold points within a specific range, accelerating the drawing of the overall microdischarge sensitivity curve. This allows for rapid calculation of the microdischarge sensitivity curve for any microwave device and any SEY distribution in practical engineering applications, thereby facilitating the design of practical microdischarge-free microwave devices. The method also ensures the accuracy of the calculation results while significantly reducing computation time, allowing for rapid generation of a microdischarge sensitivity curve.

[0120] The above content is only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for drawing a micro-discharge sensitivity curve, characterized in that: The following steps are involved: Traverse the initial point library Ω and use the bisection method to find the initial threshold point. The two grids adjacent to the edge of the initial threshold point are determined as the grids to be processed. The effective secondary electron multiplication rate corresponding to the parameter conditions of each endpoint of the grid to be processed is calculated. σ eff , and update the traversal identifier of the grid, the effective secondary electron multiplication rate σ eff The details are as follows: The instantaneous SEY value corresponding to the collision kinetic energy is calculated by combining the SEY model and the SEY phenomenological model; the K function distribution is calculated based on the instantaneous SEY value, and the simultaneous equations for solving the effective secondary electron multiplication rate are determined. Based on the simultaneous equations for the effective secondary electron multiplication rate, the parameter matrix is ​​calculated using the simultaneous iterative solution method. S Micro-discharge effective secondary electron multiplication rate corresponding to each element σ eff ; Effective secondary electron multiplication rate of microdischarge in statistical theory steady-state modeling σ eff ; The effective secondary electron multiplication rate is determined by the slope of the electron number time variation curve σ eff ; Based on the effective secondary electron multiplication rate of each endpoint, among the three grid edges to which the initial threshold point does not belong, the effective secondary electron multiplication rate of the endpoints on both sides of the edge is calculated. σ eff The relative size of 1 determines the grid edge where the next threshold point is located; the grid edge where the next threshold point is located is determined as follows: If it satisfies ( σ eff ( N ij 1 )-1)( σ eff ( N ij 2 )-1)≤0, then the next threshold point is located at the left edge of the grid to be processed; If it satisfies ( σ eff ( N ij 2 )-1)( σ eff ( N ij 4 )-1)≤0, then the next threshold point is located at the upper edge of the grid to be processed; If it satisfies ( σ eff ( N ij 4 )-1)( σ eff ( N ij 3 )-1)≤0, then the next threshold point is located at the right edge of the grid to be processed; If it satisfies ( σ eff ( N ij 1 )-1)( σ eff ( N ij 4 )-1)≤0, then the next threshold point is located at the lower edge of the grid to be processed; Based on the grid edge where the next threshold point is located, the two grids adjacent to the edge where the next threshold point is located are determined as the grids to be processed. At the same time, the next threshold point is searched for using the binary search method within the parameter range of the two end points of the edge and the threshold result is recorded. Finally, the previous step is repeated on the next grid to be processed. When the next threshold point is located at the left edge of the grid to be processed, the next grid to be processed is the grid to the left of the current grid; When the next threshold point is located at the right edge of the grid to be processed, the next grid to be processed is the grid to the right of the current grid; When the next threshold point is located at the upper edge of the grid to be processed, the next grid to be processed is the upper grid of the current grid; When the next threshold point is located at the lower edge of the grid to be processed, the next grid to be processed is the grid below the current grid; Based on the next grid to be processed, whether to end the loop is determined based on whether the search for its traversal identifier exceeds the overall parameter range, and all thresholds are summarized and a curve is drawn; The grids to be processed are: According to the empirical results of the sensitive area of ​​the flat micro-discharge, the effective secondary electron multiplication rate σ eff The largest grid endpoint searches for the parameter conditions for microdischarge, and uses a bisection method to determine the initial threshold point. The two grids adjacent to the edge where the initial threshold point is located are determined as the grids to be processed. Before searching for the parameter conditions for microdischarge, the threshold calculation area to be analyzed is first meshed, the grid traversal identifier is initialized, and the frequency and voltage parameters of each grid endpoint are determined. The specific steps are as follows: According to the voltage upper limit of the sensitive area V max With lower limit V min , frequency cap f max With lower limit f min and its corresponding decomposition number r and c， Perform logarithmic uniform partitioning to obtain the voltage array Λ and the frequency array Γ; According to the obtained voltage array Λ and frequency array Γ, the microwave voltage corresponding to the matrix element is determined. V rf Frequency-spacing product fd ; The grid is numbered two-dimensionally and represented as G ij , the lower left, upper left, lower right and upper right endpoints of each grid are represented as N ij 1 、 N ij 2 、 N ij 3 and N ij 4 ; Denote the grid traversal identifier as C ij And initialize the grid identification array C ij The elements of are all set to 0, indicating a state to be calculated; The first i Elements and the first j Elements Specifically: 。 2. The micro-discharge sensitivity curve drawing method according to claim 1, characterized in that: Calculate the parameter matrix using the simultaneous iterative solution method S Micro-discharge effective secondary electron multiplication rate corresponding to each element σ eff Specifically: Let the number of first-generation electrons on the inner and outer diameters be equal and have a uniform emission phase distribution, substitute the steady-state equations to calculate the number of next-generation electrons and emission phase distribution on the inner and outer diameters respectively; then repeat the above iterative process until the sum of the emission phase differences between the two adjacent generations of electrons on the inner and outer diameters is equal to E tot No more than the error E thr , so that the electron emission phase reaches a steady state and the effective secondary electron multiplication rate of micro-discharge is obtained σ eff .

3. The method for drawing a micro-discharge sensitivity curve according to claim 2, wherein: Effective secondary electron multiplication rate σ eff for: in, and is the number of electrons in two adjacent generations in the inner diameter after the micro-discharge develops to a steady state, and It is the number of electrons in two adjacent generations after the micro-discharge develops to a steady state.

4. The method for drawing a micro-discharge sensitivity curve according to claim 2, wherein: Calculation of instantaneous SEY value using SEY phenomenological model as follows: in, is the normalized incident kinetic energy parameter, σ m is the maximum SEY value; k 1-5 is the fitting parameter of the SEY distribution curve of the material.

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