Methods for designing the optimal secondary electron emission coefficient rectangular slot array structure dimensions

Abstract

This invention discloses a method for designing the optimal secondary electron emission coefficient (SEEC) rectangular slot array structure size, comprising the following steps: S1, establishing the size and variation range characterizing the regular array rectangular slot structure; S2, calculating and obtaining the maximum SEEC and SEEC curve based on the size of the regular array rectangular slot structure; S3, calculating the surface impedance based on the operating frequency and the size of the regular array rectangular slot structure; S4, treating the size of the regular array rectangular slot structure as an individual in a population, calculating the fitness value of each particle, and obtaining the optimal combination of rectangular slot array structure sizes. This method can simultaneously reduce the SEEC and surface impedance, and can be used to reduce the SEEC of metal surfaces, providing support for suppressing micro-discharge in high-power microwave components in space.

Description

Technical Field

[0001] This invention relates to the field of space microwave unseen reliability, specifically to a method for designing the optimal dimensions of a rectangular slot array structure with the optimal secondary electron emission coefficient. Background Technology

[0002] Studies have shown that by influencing the secondary electron emission process and obtaining a low secondary electron emission coefficient through surface treatment of space microwave components, the micro-discharge threshold of microwave components can be improved without changing the structural design of the microwave components. Constructing trap structures on the inner surface of microwave components is the most direct way to modify the surface morphology to obtain a low secondary electron emission coefficient. Although constructing trap structures on the inner surface of microwave components can achieve a low secondary electron emission coefficient, the surface trap structures also increase the current path, inevitably increasing surface impedance and loss, thus affecting the electrical performance of the microwave components. For microwave components, to achieve the best micro-discharge suppression effect, it is necessary to simultaneously consider a low secondary electron emission coefficient and low loss. Therefore, it is essential to study the relationship between the size of regular array trap structures with low secondary electron emission coefficients and the resulting losses.

[0003] Currently published literature on constructing regular array trap structures on the inner surface of microwave components to reduce the secondary electron emission coefficient only considers minimizing the secondary electron emission coefficient and does not give much consideration to the loss caused by constructing trap structures on the component surface. Summary of the Invention

[0004] The purpose of this invention is to reduce the secondary electron emission coefficient of the rectangular groove array structure on the metal surface while taking into account the surface impedance problem caused by the structure, so that the secondary electron emission coefficient is reduced while the surface impedance is also minimized.

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method for designing the optimal dimensions of a rectangular slot array structure with the optimal secondary electron emission coefficient.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The method for designing the optimal dimensions of a rectangular slot array structure with the secondary electron emission coefficient includes the following specific steps:

[0008] S1. Establish the dimensions and variation range of the regular array rectangular groove structure;

[0009] S2. Calculate the secondary electron emission coefficient curve based on the dimensions of the regular array rectangular slot structure and obtain the corresponding maximum secondary electron emission coefficient;

[0010] S3. Calculate the surface impedance based on the operating frequency and the dimensions of the regular array rectangular slot structure;

[0011] The dimensions of the regular array rectangular slot structure are expressed as: (W, φ, A) s W is the width of a single rectangular groove, φ is the porosity and the range of φ is φ∈[φ1,φ2], A s The aspect ratio of each rectangular slot and A s The interval range is A s ∈[A s1 A s2 ];

[0012] S4. Treat the dimensions of the regular array of rectangular slot structures as individuals in a population, according to... Calculate the fitness value of each individual, where R s (W,φ,A s ) for individuals (W,φ,A) s ) surface impedance; δ SEY (W,φ,A s ) represents an individual (W, φ, A) s The corresponding secondary electron emission coefficient; A s The aspect ratio of each rectangular slot and A s The interval range is A s ∈[A s1 A s2 The range of φ is φ∈[φ1,φ2], SEY MAX For individual (W,φ1,A) s1 The maximum secondary electron emission coefficient of SEY; MIN For an individual (W, φ2, A) s2 The maximum secondary electron emission coefficient of SEY MAX and SEY MIN All are derived from the secondary electron emission coefficient curve; Rs MIN For individual (W,φ1,A) s1 Surface impedance; Rs MAX For an individual (W, φ2, A) s2 ) surface impedance;

[0013] S5. Store the current individual and fitness values ​​in the pbest array, obtain the best individual and store the best individual in the gbest array;

[0014] S6. Compare the individuals and fitness values ​​in the current pbest array and gbest array, obtain the fitness value of the best individual, and update the gbest array.

[0015] S7. Determine if the stopping condition is met. If the stopping condition is met, stop the search and output the dimensions of the rectangular slot array structure. Otherwise, if the condition is not met, jump to S4.

[0016] As a further preferred embodiment of the present invention, the secondary electron emission coefficient includes the following steps:

[0017] S21. Calculate the secondary electron emission coefficient of the smooth metal surface at different incident angles based on the initial electron incident parameters and the secondary electron emission coefficient of the smooth metal surface at the vertical incident angle, and obtain the secondary electron emission coefficient curve.

[0018] The initial electron incident parameters include the initial electron incident energy, the initial electron incident polar angle, the initial electron incident azimuth angle, and the atomic number of the metallic material;

[0019] S22. Based on the electron incident parameters when the second collision occurs, calculate the collision type of the incident electron after colliding with the metal, and calculate the emission energy, emission polar angle, and emission azimuth angle of the emitted electron after the collision.

[0020] The relevant parameters of the incident electrons include electron incident energy, electron incident polar angle, electron incident azimuth angle, and atomic number of the metallic material;

[0021] S23. Based on the dimensions of the regular array rectangular slot structure and the number of incident electrons, combined with the electron's exit polar angle, exit azimuth angle, and exit energy, calculate the collision position of the electron.

[0022] S24. Based on the collision position of the emitted electrons, determine whether the electrons escape. If electrons escape, count the number of escaped electrons. If no electrons escape, determine whether the electrons collide again. If they collide again, jump to S23 until there are no electrons inside the regular array rectangular slot structure, and update the number of escaped electrons.

[0023] S25, the calculation rules for the number of escaped electrons obtained through S23 and the number of incident electrons, and the secondary electron emission coefficient of the array rectangular slot structure;

[0024] S26. The total secondary electron emission coefficient of the metal regular array trap structure surface under different incident angles is obtained by calculating the secondary electron emission coefficient of the regular array rectangular groove structure and the secondary electron emission coefficient of the smooth metal surface under different incident angles.

[0025] As a further preferred embodiment of the present invention, the calculation of the secondary electron emission curves of the smooth metal surface at different incident angles includes:

[0026] S211. By combining the secondary electron emission coefficient of the smooth metal surface under the vertical incident angle, the undetermined parameters related to the material, the maximum intrinsic secondary electron emission coefficient under the vertical incident condition, and the energy of the incident electrons are calculated.

[0027] S212. The secondary electron emission coefficient of a smooth metal surface under different incident angles is calculated based on the elastic backscattering coefficient, the inelastic backscattering coefficient, and the intrinsic secondary electron emission coefficient.

[0028] As a further preferred embodiment of the present invention, the collision types include elastic backscattering, inelastic backscattering, and emission of intrinsic secondary electrons;

[0029] Determining the collision type includes the following steps:

[0030] 101. Generate a random number u1 within the interval (0,1);

[0031] 102. When u1 <P e (E' p ,θ' p When incident electrons collide with a metal, elastic backscattering occurs; where P e (E′ p , θ′ p () represents the elastic backscattering coefficient upon a second collision;

[0032] 103. Generate a random number u1 within the interval (0,1);

[0033] 104, u1 <P e (E' p ,θ' p )+P i (E' p ,θ' p If the incident electrons collide with the metal, inelastic backscattering occurs; where P i (E′ p , θ′ p () represents the inelastic backscattering coefficient upon a second collision;

[0034] 105. When u1 does not satisfy the above two conditions, the incident electron will emit intrinsic secondary electrons after colliding with the metal.

[0035] As a further preferred embodiment of the present invention, the collision locations of the electrons include electrons emitted from the bottom of the regularly arrayed rectangular slots on the metal surface and electrons emitted from the sidewalls of the regularly arrayed rectangular slots on the metal surface.

[0036] As a further preferred embodiment of the present invention, the collision position is calculated based on the electron emission position and the electron motion time.

[0037] As a further preferred embodiment of the present invention, obtaining the optimal individual includes:

[0038] Based on the individual's velocity and displacement in different spaces, the location of the individual with the best fitness is selected.

[0039] The fitness value calculated for an individual is compared with the fitness of its selected optimal position;

[0040] If the calculated fitness value is small, then the position corresponding to its fitness value is saved as the current best position.

[0041] Otherwise, its best position remains unchanged.

[0042] As a further preferred embodiment of the present invention, the stopping condition includes a preset computational precision or a preset number of iterations.

[0043] As a further preferred embodiment of the present invention, the calculation of surface impedance based on the operating frequency and the dimensions of the regular array rectangular slot structure includes:

[0044] The surface impedance includes Rs MIN and Rs MAX Based on the size combination (W, φ1, A) s1 () and (W,φ2,A) s2 ) was calculated.

[0045] The advantages of this invention are that it can not only reduce the secondary electron emission coefficient of the regular array rectangular groove structure on the metal surface, but also take into account the surface impedance problem caused by the array structure. This results in the secondary electron emission coefficient being reduced while the surface impedance is also minimized, thereby increasing the micro-discharge threshold of microwave components while minimizing the increase in loss.

[0046] Advantages: This invention also includes the following

[0047] 1. This invention obtains the optimal size of the regular array rectangular slot structure on the metal surface by comprehensively optimizing the secondary electron emission coefficient and surface impedance of the regular array rectangular slot structure on the metal surface, which meets the design requirements of the secondary electron emission coefficient. This not only effectively reduces the secondary electron emission coefficient, but also takes into account the surface impedance problem caused by the array structure, so as to reduce the loss as much as possible while improving the micro-discharge threshold of microwave components.

[0048] 2. The method for determining the dimensions of a regular array of rectangular grooves on a metal surface proposed in this invention can be applied to metal materials commonly used in spacecraft microwave components.

[0049] 3. The results of this invention can be used to study the reduction of the secondary electron emission coefficient of metal surfaces, providing support for the suppression of micro-discharge in high-power microwave components in space. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the surface of a regular array of rectangular groove structures;

[0051] Figure 2This is a schematic diagram of the design process of the present invention;

[0052] Figure 3 These are experimental test data of the secondary electron emission coefficient of the smooth surface Al material used in the embodiments of the present invention;

[0053] Figure 4 This is an optimization result of an embodiment of the present invention. Detailed Implementation

[0054] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0055] Example 1

[0056] This invention proposes a method for determining the dimensions of a regular array of rectangular slot structures on a metal surface with low secondary electron emission coefficients. The method includes calculating the secondary electron emission coefficients of rectangular slot array structures of different sizes (including three parameters: width of a single rectangular slot, aspect ratio of a single rectangular slot, and porosity of the rectangular slot array structure), as well as the corresponding surface impedance, thereby constructing a fitness function. By using a particle swarm optimization algorithm and the constructed fitness function, the individual fitness values ​​of rectangular slot array structures of different sizes are obtained. The dimensions of the rectangular slot array structure corresponding to the optimal fitness value are then identified, and this combination of dimensions represents the design result.

[0057] Combination Figure 2 The method for designing the optimal dimensions of a rectangular slot array structure with the secondary electron emission coefficient includes the following specific steps:

[0058] S1. Establish the dimensions and variation range of the regular array rectangular slot structure.

[0059] Based on the type of metal material and the specific implementation process, dimensions characterizing the regular array rectangular groove structure are established, where the dimensions characterizing the regular array rectangular groove structure are denoted as (W, φ, A). s );

[0060] W is the width of a single rectangular groove, φ is the porosity, and A s The aspect ratio of each rectangular slot and A s The interval range is A s ∈[A s1 A s2 The value range of φ is φ∈[φ1,φ2]. See the specific structure below. Figure 1 .

[0061] S2. Calculate the secondary electron emission coefficient curve based on the dimensions of the regular array rectangular slot structure and obtain the corresponding maximum secondary electron emission coefficient.

[0062] The secondary electron emission coefficient includes the following steps:

[0063] S21. Calculate the secondary electron emission coefficient δ of the smooth metal surface at different incident angles based on the initial electron incident parameters and the secondary electron emission coefficient of the smooth metal surface at the perpendicular incident angle. flat And obtain the secondary electron emission coefficient curve.

[0064] The initial electron incident parameters include the initial electron incident energy E. p Initial electron incident polar angle θ p Initial electron incident azimuth angle φ p And the atomic number Z of metallic materials.

[0065] 211. Combining the secondary electron emission coefficient of a smooth metallic surface at a perpendicular incident angle, through δ flat (E p ,θ p ) = P e (E p ,θ p )+P i (E p ,θ p )+δ(E p ,θ p The undetermined material-related parameter s and the maximum intrinsic secondary electron emission coefficient δ under perpendicular incidence conditions were calculated. m and the corresponding energy E of the incident electron m0 Among them, P e (E p ,θ p P is the elastic backscattering coefficient. i (E p ,θ p ) represents the inelastic backscattering coefficient; δ(E) p ,θ p ) represents the intrinsic second electron emission coefficient, δ flat is the secondary electron emission coefficient of a smooth metallic surface.

[0066] Calculate the elastic backscattering coefficient P e (E p ,θ p ),

[0067] The elastic backscattering coefficient

[0068] in,

[0069]

[0070] Calculate the inelastic backscattering coefficient P i (E p ,θ p ),

[0071] The inelastic backscattering coefficient

[0072] Calculate the intrinsic second electron emission coefficient δ(E) p ,θ p ),

[0073] The intrinsic secondary electron emission coefficient

[0074]

[0075] 212. Based on the elastic backscattering coefficient P e (E p ,θ p Inelastic backscattering coefficient P i (E p ,θ p ), intrinsic secondary electron emission coefficient δ(E) p ,θ p Combining the undetermined material-related parameters s obtained in section 211 with the maximum intrinsic secondary electron emission coefficient δ under perpendicular incidence conditions, m and the corresponding energy E of the incident electron m0 , through δ flat (E p ,θ p ) = P e (E p ,θ p )+P i (E p ,θ p )+δ(E p ,θ p The secondary electron emission coefficient δ of the smooth metallic surface under different incident angles was calculated. flat .

[0076] S22. Based on the electron incident parameters at the time of the second collision, calculate the emission energy E of the electrons after the collision, according to the collision type after the incident electrons collide with the metal. e , emission polar angle θ e , emission azimuth angle φ e ;

[0077] The electron incident parameters at the time of the second collision include the electron incident energy E' p Electron incident polar angle θ' p Electron incident azimuth angle φ' p The atomic number of metallic materials is Z' = Z.

[0078] Generate a uniformly distributed random number u1 within the interval (0,1), and perform classification calculations based on the magnitude of u1:

[0079] If the random variable satisfies u1 <P e (E' p ,θ' p If the incident electron collides with the metal, elastic backscattering occurs. In this case, the number of emitted electrons is 1, and the energy of the emitted electron is E. e =E' p Polar angle of emission θ e =θ' p azimuth angle φ e =π+φ' p .

[0080] If the random variable satisfies u1 <P e (E' p ,θ' p )+P i (E' p ,θ' p If the incident electron collides with the metal, inelastic backscattering occurs. In this case, the number of emitted electrons is 1, and the energy of the emitted electron is determined by the formula E. e =E' p ·(π·0.9 1.5 ) -1 / 1.5 (arccos(1-(1-cos(π·0.9 1.5 ))·u2)) 1 / 1.5 Calculate the polar angle θ. e =θ' p azimuth angle φ e =π+φ' p , where u2 is a random number uniformly distributed in the interval (0,1).

[0081] Otherwise, the incident electron will emit intrinsic secondary electrons after colliding with the metal, which will then be obtained through the integral equation.

[0082] Different electron incident energies E' were obtained p and electron incident angle θ' p The number of intrinsic secondary electrons n, where u3 is a random number uniformly distributed in the interval (0,1);

[0083] in,

[0084]

[0085]

[0086]

[0087] The energy E of the emitted electron e=E se ,

[0088] For the first intrinsic second electron, we have E re =E re,1 =E' p Starting from the second intrinsic secondary electron and continuing until the nth intrinsic secondary electron, the formula E is used sequentially. re,i =E re,i-1 -E se,i-1 Perform calculations, where E re,i E is the value when the i-th intrinsic secondary electron is emitted. re E se,i-1 The energy of the (i-1)th intrinsic secondary electron, and the emission polar angle θ e =arcsin(u4), azimuth angle of exit φ e =2π·u5, where u4 and u5 are both random numbers uniformly distributed within the interval (0,1).

[0089] S23. Based on the dimensions of the regular array rectangular slot structure and the number of incident electrons Num, combined with the electron exit polar angle θ e azimuth angle φ e and the emitted energy E e Calculate the collision locations of electrons.

[0090] The collision locations of the electrons include electrons emitted from the bottom of the regularly arrayed rectangular slots on the metal surface and electrons emitted from the sidewalls of the regularly arrayed rectangular slots on the metal surface.

[0091] Given the number of incident electrons Num, and the dimensions of the rectangular slot structure (width W of a single rectangular slot, height H = W × A of a single rectangular slot). s ).

[0092] For an electron emitted from the bottom surface, its velocity components in the x and y directions are:

[0093]

[0094] Electron motion time t tr for:

[0095]

[0096] For an electron exiting from the side wall, its velocity components in the x and y directions are:

[0097]

[0098]

[0099] Electron motion time ttr for:

[0100]

[0101] Where, m e For electronic quality.

[0102] According to the electron emission position (x) e y e ) and electron motion time t tr The collision position (x) of the electron can be calculated using the formula. b y b ),

[0103]

[0104] S24. Based on the collision position of the emitted electrons, determine whether any electrons escape. If any electrons escape, count the number of escaped electrons. If no electrons escape, determine whether any electrons collide again. If any electrons collide again, proceed to S23. Repeat the above steps until there are no more electrons within the regular array rectangular slot structure, and update the number of escaped electrons N. out ;

[0105] S25, via δ hole =N out / Num, the secondary electron emission coefficient δ of the regular array rectangular slot structure is calculated. hole ;

[0106] S26. The secondary electron emission coefficient based on a regular array rectangular groove structure and the secondary electron emission coefficient of a smooth metal surface under different incident angles, through δ Total =(1-φ)δ flat +φδ hole The total secondary electron emission coefficient δ on the surface of the regular metallic array structure was calculated. Total .

[0107] Using a size combination (0.6×10) -6 Calculate its secondary electron emission coefficient curve using (0.01, 0.1) and obtain the corresponding maximum secondary electron emission coefficient SEY on the curve. MAX The value is 3.17666958; using a size combination (0.6 × 10 -6 Calculate its secondary electron emission coefficient curve (0.45, 3.3) and obtain the maximum secondary electron emission coefficient SEY corresponding to the curve. MIN The value is 2.52947117643184; using a size combination (0.6×10 -6 ,φ,A s Calculate the secondary electron emission coefficient curve and obtain the corresponding maximum secondary electron emission coefficient δ.SEY (W,φ,A s ).

[0108] S3. Calculate the surface impedance based on the operating frequency f and the dimensions of the regular array rectangular slot structure.

[0109] The surface impedance includes Rs MIN and Rs MAX The size combinations (W, φ1, A) are used respectively. s1 () and (W,φ2,A) s2 The result is obtained by calculating using the following formula:

[0110]

[0111] Where ω is the angular frequency, ω = 2πf, f is a given frequency, 40 GHz; μ is the free permeability, 4π × 10⁻⁶. -7 ;R q Roughness is determined by surface structure. And Rs is calculated corresponding to φ1. MIN φ is taken as φ2, and Rs is calculated accordingly. MAX H is the depth of a regular array of rectangular grooves on the metal surface, δ skin For skin depth and σ is the electrical conductivity of the metal, 3.816 × 10⁻⁶. 7 .

[0112] Using a size combination (0.6×10) -6 Calculate the surface impedance Rs (0.01, 0.1) MIN The value is 0.0643411476522203; using a size combination (0.6×10 -6 ,0.45,3.3) Calculate the surface impedance Rs MAX It is 0.123679409176167.

[0113] S4. Treat the size of the regular array rectangular slot structure as an individual in the population.

[0114] Combining different regular array rectangular slot structure dimensions (W, φ, A) s Consider X as the position of each particle in the population. i The change in each parameter in the size combination is denoted as V. i Within a given range of parameters for a regular array of rectangular slot structures, randomly initialize the position X of each particle in the population. i =(x i,1 ,x i,2 ,…,x i,d ) and velocity V i =(v i,1 ,vi,2 ,…,v i,d The initial population is set with 40 particles N, 3 independent variables d, 2 learning factors c1 and c2, 0.5 inertia weight w, and 500 maximum iterations M.

[0115] according to Calculate the fitness value for each particle, where R s (W,φ,A s ) for individuals (W,φ,A) s ) surface impedance; δ SEY (W,φ,A s ) represents an individual (W, φ, A) s The corresponding secondary electron emission coefficient; A s The aspect ratio of each rectangular slot and A s The interval range is A s ∈[A s1 A s2 The range of φ is φ∈[φ1,φ2], SEY MAX For individual (W,φ1,A) s1 The maximum secondary electron emission coefficient of SEY; MIN For an individual (W, φ2, A) s2 The maximum secondary electron emission coefficient of SEY MAX and SEY MIN All are derived from the secondary electron emission coefficient curve; Rs MIN For individual (W,φ1,A) s1 Surface impedance; Rs MAX For an individual (W, φ2, A) s2 Surface impedance.

[0116] S5. Store the current position and fitness value of each individual in the pbest array, obtain the best individual and store the best individual in gbest.

[0117] according to Update the velocity and displacement of the individual in different spaces.

[0118] Among them, v i,j Let x be the velocity of the i-th individual in the j-dimensional space. i,j Let r1 and r2 be the position of the i-th individual in the j-dimensional space, where r1 and r2 are both random numbers between (0,1), t is the number of steps for updating the individual, and p i,j p represents the position of the i-th individual in the j-dimensional space. g,j This represents the position of the individual with the best fitness value in the population in the j-dimensional space.

[0119] The system selects the location of the individual with the best fitness in the spatial space; it compares the fitness value of the individual with the fitness of the selected best location; if the calculated fitness value is smaller, the location corresponding to the fitness value is saved as the current best location; otherwise, the best location it has experienced remains unchanged.

[0120] S6. Compare the individuals and fitness values ​​in the current pbest array and gbest array, obtain the fitness value of the best individual, and update the gbest array.

[0121] S7. Determine if the stopping condition is met. If the stopping condition is met, stop the search and output the dimensions of the rectangular slot array structure, including the width W of a single rectangular slot and the aspect ratio A of a single rectangular slot. s If the porosity φ is not satisfied, proceed to S4.

[0122] The stopping conditions include preset computational precision or number of iterations;

[0123] The output of this calculation example, calculated using this method, is: W = 0.6 × 10⁻⁶. -6 The aspect ratio of the rectangular groove is A. s The porosity φ of the rectangular slot array structure is 0.442168182, with a value of 0.35323439. At this point, the surface impedance is 0.0681456495494889, and the maximum SEY is 3.07167765 (e.g., ...). Figure 4 (As shown).

[0124] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any way, and all technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A method for designing the optimal dimensions of a rectangular slot array structure with the secondary electron emission coefficient, characterized in that, Includes the following steps: S1. Establish the dimensions and variation range of the regular array rectangular groove structure; S2. Calculate the secondary electron emission coefficient curve based on the dimensions of the regular array rectangular slot structure and obtain the corresponding maximum secondary electron emission coefficient; S3. Calculate the surface impedance based on the operating frequency and the dimensions of the regular array rectangular slot structure; The dimensions of the regular array rectangular slot structure are expressed as follows: W is the width of a single rectangular slot. Porosity and The range of the interval is [ 1, 2], A s The aspect ratio of each rectangular slot and A s The interval range is A s [A s1 A s2 ]; S4. Treat the dimensions of the regular array of rectangular slot structures as individuals in a population, according to... Calculate the fitness value of each individual. in, For individuals Surface impedance; Represents an individual The corresponding secondary electron emission coefficient; A s The aspect ratio of each rectangular slot and A s The interval range is A s [A s1 A s2 ], The range of values ​​is [ , ], For individuals (W, A s1 The maximum secondary electron emission coefficient; For individuals (W, A s2 The maximum secondary electron emission coefficient, and and All are derived from the secondary electron emission coefficient curve; For individuals (W, A s1 ) surface impedance; For individuals (W, A s2 ) surface impedance; S5. Store the current individual and fitness values ​​in the pbest array, obtain the best individual and store the best individual in the gbest array; S6. Compare the individuals and fitness values ​​in the current pbest array and gbest array, obtain the fitness value of the best individual, and update the gbest array. S7. Determine if the stopping condition is met. If the stopping condition is met, stop the search and output the dimensions of the rectangular slot array structure. Otherwise, if the condition is not met, jump to S4. The calculation of the secondary electron emission coefficient includes the following steps: S21. Calculate the secondary electron emission coefficient of the smooth metal surface at different incident angles based on the initial electron incident parameters and the secondary electron emission coefficient of the smooth metal surface at the vertical incident angle, and obtain the secondary electron emission coefficient curve. The initial electron incident parameters include the initial electron incident energy, the initial electron incident polar angle, the initial electron incident azimuth angle, and the atomic number of the metallic material; S22. Based on the electron incident parameters when the second collision occurs, calculate the electron's emission energy, emission polar angle, and emission azimuth angle after the collision, according to the collision type after the incident electron collides with the metal. The electron incident parameters when a second collision occurs include electron incident energy, electron incident polar angle, electron incident azimuth angle, and atomic number of the metallic material. S23. Based on the dimensions of the regular array rectangular slot structure and the number of incident electrons, combined with the electron's exit polar angle, exit azimuth angle, and exit energy, calculate the collision position of the electron. S24. Based on the collision position of the emitted electrons, determine whether the electrons escape. If electrons escape, count the number of escaped electrons. If no electrons escape, determine whether the electrons collide again. If they collide again, jump to S23 until there are no electrons inside the regular array rectangular slot structure, and update the number of escaped electrons. S25, the calculation rules for the number of escaped electrons obtained through S23 and the number of incident electrons, and the secondary electron emission coefficient of the array rectangular slot structure; S26. The total secondary electron emission coefficient of the metal regular array structure surface is obtained by calculating the secondary electron emission coefficient of the regular array rectangular groove structure and the secondary electron emission coefficient of the smooth metal surface under different incident angles. The calculation of the secondary electron emission curves of a smooth metallic surface at different incident angles includes: S211. By combining the secondary electron emission coefficient of the smooth metal surface under the vertical incident angle, the undetermined parameters related to the material, the maximum intrinsic secondary electron emission coefficient under the vertical incident condition, and the energy of the incident electrons are calculated. S212. The secondary electron emission coefficient of a smooth metal surface under different incident angles is calculated based on the elastic backscattering coefficient, the inelastic backscattering coefficient, and the intrinsic secondary electron emission coefficient.

2. The method for designing the optimal secondary electron emission coefficient rectangular slot array structure dimensions according to claim 1, characterized in that, The collision types include elastic backscattering, inelastic backscattering, and emission of intrinsic secondary electrons; Determining the collision type includes the following steps:

101. Generate a random number within the interval (0,1). ; 102. When At that time, the incident electrons undergo elastic backscattering after colliding with the metal; in, This is the elastic backscattering coefficient upon a second collision; 103. Generate random numbers within the interval (0,1). ; 104. Then, the incident electrons undergo inelastic backscattering after colliding with the metal. in, This is the inelastic backscattering coefficient upon a second collision; 105. When u1 does not satisfy the above two conditions, the incident electron will emit intrinsic secondary electrons after colliding with the metal.

3. The method for designing the optimal secondary electron emission coefficient rectangular slot array structure dimensions according to claim 1, characterized in that, The collision locations of the electrons include electrons emitted from the bottom of the regularly arrayed rectangular slots on the metal surface and electrons emitted from the sidewalls of the regularly arrayed rectangular slots on the metal surface.

4. The method for designing the optimal secondary electron emission coefficient rectangular slot array structure dimensions according to claim 3, characterized in that, The collision location is calculated based on the electron emission location and the electron motion time.

5. The method for designing the optimal secondary electron emission coefficient rectangular slot array structure dimensions according to claim 1, characterized in that, The process of obtaining the optimal individual includes: Based on the individual's velocity and displacement in different spaces, the location of the individual with the best fitness is selected. The fitness value calculated for an individual is compared with the fitness of its selected optimal position; If the calculated fitness value is small, then the position corresponding to its fitness value is saved as the current best position. Otherwise, its best position remains unchanged.

6. The method for designing the optimal secondary electron emission coefficient rectangular slot array structure dimensions according to claim 1, characterized in that, The stopping conditions include preset computational precision or number of iterations.

7. The method for designing the optimal secondary electron emission coefficient rectangular slot array structure dimensions according to claim 1, characterized in that, The calculation of surface impedance based on the operating frequency and the dimensions of the regular array rectangular slot structure includes: The surface impedance includes and According to the size combination (W, A s1 ) and (W, A s2 ) was calculated.

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