Method for designing optimal cylindrical hole array structure size of secondary electron emission coefficient

Abstract

The application discloses a method for designing optimal secondary electron emission coefficient cylindrical hole array structure size, comprising the following steps: S1, establishing size range of regular array cylindrical hole trap structure; S2, regarding the size of the regular array cylindrical hole trap structure as an individual in a population, performing binary coding on all individuals to form a binary coded bit string, and numbering each individual one by one; S3, calculating a secondary electron emission coefficient curve according to the size of the regular array cylindrical hole trap structure and obtaining the corresponding maximum secondary electron emission coefficient; S4, calculating surface impedance based on the working frequency and the size of the regular array cylindrical hole trap structure; the method can simultaneously reduce the secondary electron emission coefficient and the surface impedance, can be used for reducing the secondary electron emission coefficient of a metal surface, and provides support for inhibiting micro-discharge of a space high-power microwave component.

Description

Technical Field

[0001] This invention relates to the field of space microwave unseen reliability, and specifically to a method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size. 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 regularly arrayed cylindrical hole trap structure on the metal surface while taking into account the surface impedance problem caused by the construction of the trap 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 size of a cylindrical aperture array structure with 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 secondary electron emission coefficient cylindrical aperture array structure dimensions includes the following steps:

[0008] S1. Establish the size range of the regular array cylindrical hole trap structure, and denote the iteration number N as 1;

[0009] S2. Treat the size of the regular array of cylindrical hole trap structure as an individual in the population, encode all individuals into binary code bit strings, and number each individual one by one.

[0010] The binary encoded bit string consists of a binary code for porosity of length L1 and a binary code for the aspect ratio of a regular array of cylindrical hole trap structures of length L2.

[0011] S3. Calculate the secondary electron emission coefficient curve based on the dimensions of the regular array cylindrical hole trap structure and obtain the corresponding maximum secondary electron emission coefficient.

[0012] S4. Calculate the surface impedance based on the operating frequency and the dimensions of the regular array of cylindrical hole trap structures;

[0013] The dimensions of the regular array of cylindrical hole trap structure are expressed as: (2a, φ, A) s ), where a is the radius of each cylindrical hole, φ is the porosity and the range of φ is φ∈[φ1,φ2], A s The aspect ratio of each cylindrical hole and A s The interval range is A s ∈[A s1 A s2 ];

[0014] S5, according to Calculate the fitness value of each individual.

[0015] Among them, R s (2a,φ,A s ) for individual (2a,φ,A) s ) surface impedance; δ SEY (2a,φ,A s ) represents an individual (2a,φ,A) s The corresponding secondary electron emission coefficient; As is the aspect ratio of each cylindrical hole and the range of As is As∈[A s1 A s2 The range of φ is φ∈[φ1,φ2], SEY MAX For individual (2a,φ1,A) s1 The maximum secondary electron emission coefficient of SEY; MIN For individual (2a,φ2,A) s2 The maximum secondary electron emission coefficient of SEY; and SEY MAX and SEY MIN All are derived from the secondary electron emission coefficient curve; Rs MIN For individual (2a,φ1,A) s1 Surface impedance; Rs MAX For individual (2a,φ2,A) s2 ) surface impedance;

[0016] S6. Determine if the stopping condition has been met. If the stopping condition has been met, the individual is the optimal individual and jump to S8; otherwise, use the roulette wheel strategy to select an individual from the population for genetic operations to form a new generation of population, increment the iteration count by 1, and jump to S3.

[0017] The stopping conditions include preset computational precision or number of iterations, specifically:

[0018] Determine whether an individual's fitness value is the set minimum fitness value;

[0019] If an individual's fitness value is the set minimum fitness value, then that individual is the optimal individual;

[0020] S8. Decode the binary encoded bit string of the individual to obtain the structural dimension parameters corresponding to the individual. The structural dimension parameters corresponding to the individual include the diameter of the cylindrical hole, the aspect ratio, and the porosity.

[0021] S9. If the fitness value of an individual is not the set minimum fitness value, then determine whether the number of iterations is the maximum number of iterations.

[0022] S10. If the number of iterations is the maximum number of iterations, then the individual is the optimal individual, and the process jumps to S8.

[0023] S11. If the number of iterations is not the maximum number of iterations, then use the roulette wheel strategy to select individuals from the population for genetic operations to form a new generation of population. Record the number of iterations N as N+1 and jump to S3.

[0024] As a further preferred embodiment of the present invention, the calculation of the secondary electron emission coefficient includes the following steps:

[0025] S31. 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.

[0026] 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;

[0027] S32. 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.

[0028] 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.

[0029] S33. Based on the size of the regular array cylindrical hole trap 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.

[0030] S34. 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 S33 until there are no electrons inside the regular array cylindrical hole trap structure, and update the number of escaped electrons.

[0031] S35, the calculation rules for the number of escaped electrons and the number of incident electrons obtained through S33, and the secondary electron emission coefficient of the array cylindrical hole trap structure;

[0032] S36. The total secondary electron emission coefficient of the surface of the regular array trap structure of metal is obtained by calculating the secondary electron emission coefficient of the regular array cylindrical hole trap structure and the secondary electron emission coefficient of the smooth metal surface under different incident angles.

[0033] As a further preferred embodiment of the present invention, the calculation of the secondary electron emission curves of the smooth metal surface under different incident angles includes:

[0034] S311. 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.

[0035] S312. 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.

[0036] As a further preferred embodiment of the present invention, the collision types include elastic backscattering, inelastic backscattering, and emission of intrinsic secondary electrons;

[0037] Determining the collision type includes the following steps:

[0038] 101. Generate a random number u1 within the interval (0,1);

[0039] 102. When u1 <P e (E' p ,θ' p Upon a second collision, the incident electrons undergo elastic backscattering after colliding with the metal.

[0040] Among them, P e (E' p ,θ' p () represents the elastic backscattering coefficient upon a second collision;

[0041] 103. Generate a random number u1 within the interval (0,1);

[0042] 104, u1 <P e (E' p ,θ' p )+P i (E' p ,θ' p If the incident electrons collide with the metal, inelastic backscattering will occur.

[0043] Among them, P i (E' p ,θ' p () represents the inelastic backscattering coefficient upon a second collision;

[0044] 105. When u1 does not satisfy the above two conditions, the incident electron will emit intrinsic secondary electrons after colliding with the metal.

[0045] 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 cylindrical hole trap on the metal surface and electrons emitted from the sidewall of the regularly arrayed cylindrical hole trap on the metal surface.

[0046] 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.

[0047] 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 of cylindrical hole traps includes:

[0048] The surface impedance includes Rs MIN and Rs MAX According to the size combination (2a, φ1, A) s1 ) and (2a,φ2,A s2 ) was calculated.

[0049] As a further preferred embodiment of the present invention, the step of determining whether the fitness value of an individual is the minimum fitness includes:

[0050] S61. Determine if the iteration count N is greater than 1;

[0051] S62. If the number of iterations is equal to 1, then based on the different binary code bit strings of individuals in the population, select the binary code bit string of the individual with the smallest fitness.

[0052] S62. Compare the fitness value calculated for an individual with the fitness of the binary encoded bit string of the best individual selected.

[0053] S63. The individual with the smaller fitness value is the best individual in the current population, and the binary encoding bit string of the best individual is saved.

[0054] S64. Determine if the fitness value of the current best individual is the set minimum value; if the fitness value of the current best individual is the set minimum value, then skip to S8.

[0055] S65. If the fitness value of the best individual is not the set minimum value, then skip to S9.

[0056] S66. If the number of iterations is greater than 1, then select the individual with the smallest fitness value from the fitness values ​​of each individual in the calculated new population as the optimal individual.

[0057] S67. Compare the fitness value of the current best individual with the fitness value of the best individual in the previous generation population. The individual with the smaller fitness value is the best individual in the current population, and save the binary encoding bit string of the best individual; skip to S64.

[0058] As a further preferred embodiment of the present invention, the step of selecting individuals from the population for genetic operations includes:

[0059] S111. Calculate the selection probability and cumulative probability of each individual in the population. i ;

[0060] S112. Take a random number r in the interval (0,1). When PP i-1 ≤r<PP i When the i-th individual is selected as the father individual, one individual is randomly selected from the remaining individuals as the mother individual, and a position posCut is randomly selected in the binary encoded bit string as the crossover point, and another position posMut is selected as the mutation point.

[0061] S113. Take a random number r1 in the interval (0,1). If r1≤Pc, where Pc is the crossover probability, take the first posCut bits of the binary code bit string of the father individual and the last (L1+L2-posCut) bits of the binary code bit string of the mother individual, combine them to form a new individual, and save the binary code bit string of the new individual; if r1>Pc, do not perform this operation.

[0062] S114. Take a random number r2 in the interval (0,1). If r2≤Pm, where Pm is the mutation probability, then invert the position posMut in the binary code bit string of the selected i-th individual to form a new individual and save the binary code bit string of that individual; if r2>Pm, then do not perform this operation.

[0063] The advantages of this invention are that it can not only reduce the secondary electron emission coefficient of the regular array of cylindrical hole trap structure on the metal surface, but also take into account the surface impedance problem caused by the construction of the trap 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.

[0064] Advantages: This invention also includes the following

[0065] 1. This invention obtains the optimal size of the regular array cylindrical hole trap structure on the metal surface by comprehensively optimizing the secondary electron emission coefficient and surface impedance of the trap structure. This not only effectively reduces the secondary electron emission coefficient, but also takes into account the surface impedance problem caused by the trap structure, thereby improving the micro-discharge threshold of microwave components while minimizing losses.

[0066] 2. The method for determining the structural dimensions of a regular array of cylindrical holes on a metal surface proposed in this invention can be applied to metal materials commonly used in spacecraft microwave components.

[0067] 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

[0068] Figure 1 This is a schematic diagram of the surface of a regularly arrayed cylindrical hole trap structure;

[0069] Figure 2 This is a schematic diagram of the design process of the present invention;

[0070] Figure 3 These are experimental test data on the secondary electron emission coefficient of the smooth surface Ag material used in the embodiments of this invention;

[0071] Figure 4 This is an optimization result of an embodiment of the present invention. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0073] Example 1

[0074] This invention proposes a method for determining the dimensions of a regularly arrayed cylindrical hole trap structure with a low secondary electron emission coefficient on a metal surface. The method includes calculating the secondary electron emission coefficient (including three parameters: diameter, aspect ratio, and porosity) of regularly arrayed cylindrical hole trap structures of different sizes, as well as the corresponding surface impedance, thereby constructing a fitness function. Using a genetic algorithm and the constructed fitness function, the individual fitness values ​​of regularly arrayed cylindrical hole trap structures of different sizes are obtained. The optimal dimensions for these structures are then identified, and this combination of dimensions represents the design result.

[0075] Combination Figure 2 The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size includes the following specific steps:

[0076] S1. Establish the size range of the regular array cylindrical hole trap structure, and denote the iteration number N as 1.

[0077] Based on the type of metal material and the specific implementation process, the dimensions characterizing the regular array cylindrical hole trap structure are established, where the dimensions characterizing the regular array cylindrical hole trap structure are denoted as (2a,φ,As).

[0078] 2a is the diameter of each cylindrical hole, φ is the porosity, and A s The aspect ratio of each cylindrical hole 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 .

[0079] S2. Treat the size of the regular array of cylindrical hole trap structures as individuals in a population, encode all individuals into binary bits to form a binary bit string, and number each individual sequentially. i (i = 1, 2, 3, ... NP).

[0080] Combining different regular array cylindrical hole trap structure sizes (2a, φ, A) s Consider each individual in the population as an example. Within the given range of parameters for the regular array of cylindrical hole trap structures, randomly initialize each individual in the population. The initial population size NP is 50, the maximum number of generations NG is 1000, the crossover probability Pc is 0.9, and the mutation probability Pm is 0.04.

[0081] The binary encoded bit string consists of a binary code for porosity of length L1 and a binary code for the aspect ratio of a regular array of cylindrical hole trap structures of length L2.

[0082] according to The binary code length L1 of the porosity is calculated, where eps1 is the porosity precision. A random number is selected from the interval (0,1), and rounded off. This process is repeated L1 times to obtain the binary code bit string of length L1 for the porosity.

[0083] according to The length L2 of the aspect ratio binary code is calculated. Here, eps2 is the precision of the aspect ratio. A random number is selected in the interval (0,1), and the obtained random number is rounded. L2 times are calculated continuously, and the number obtained each time is recorded, thus obtaining a binary code bit string with an aspect ratio of length L2.

[0084] The obtained binary encoded bit string of length L1 and binary encoded bit string of length L2 are combined to form a binary encoded bit string of total length L1+L2.

[0085] S3. Calculate the secondary electron emission coefficient curve based on the dimensions of the regular array cylindrical hole trap structure and obtain the corresponding maximum secondary electron emission coefficient.

[0086] The secondary electron emission coefficient includes the following steps:

[0087] S31. 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.

[0088] 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.

[0089] 311. 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 , where P e (Ep ,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.

[0090] Calculate the elastic backscattering coefficient P e (E p ,θ p ),

[0091] The elastic backscattering coefficient

[0092] in,

[0093]

[0094] Calculate the inelastic backscattering coefficient P i (E p ,θ p ),

[0095] The inelastic backscattering coefficient

[0096] Calculate the intrinsic second electron emission coefficient δ(E) p ,θ p ),

[0097] The intrinsic secondary electron emission coefficient

[0098]

[0099] 312. 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 311 with the maximum intrinsic secondary electron emission coefficient δ under perpendicular incidence conditions, the maximum intrinsic secondary electron emission coefficient is determined. m and the corresponding energy E of the incident electron m0 , through δ flat (E p ,θ p ) = P e (E p ,θp )+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 .

[0100] S32. 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 ;

[0101] 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.

[0102] Generate a uniformly distributed random number u1 within the interval (0,1), and perform classification calculations based on the magnitude of u1:

[0103] 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 .

[0104] 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).

[0105] Otherwise, the incident electron will emit intrinsic secondary electrons after colliding with the metal, which will then be obtained through the integral equation.

[0106] 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);

[0107] in,

[0108]

[0109]

[0110]

[0111] The energy E of the emitted electron e =E se ,

[0112] 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), the azimuth angle of the exit. u4 and u5 are both random numbers uniformly distributed within the interval (0,1).

[0113] S33. The dimensions of the regularly arrayed cylindrical hole trap 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.

[0114] The collision locations of the electrons include electrons emitted from the bottom of the regularly arrayed cylindrical hole trap on the metal surface and electrons emitted from the sidewalls of the regularly arrayed cylindrical hole trap on the metal surface.

[0115] Given the number of incident electrons Num, and based on the dimensions of the trap structure (cylindrical aperture diameter 2a, cylindrical aperture height H = 2a × As).

[0116] For an electron emitted from the bottom surface, its velocity components in the x, y, and z directions are:

[0117]

[0118] For an electron exiting from the side wall, its velocity components in the x, y, and z directions are:

[0119]

[0120] Where, m e For electronic quality.

[0121] According to the electron emission position (x) e y e , z e ) and electron motion time t tr The collision position (x) of the electron can be calculated using the formula. b y b , z b )

[0122] x b =x e +v eix ·t tr

[0123] y b =y e +v eiy ·t tr

[0124] z b =z e +v eiz ·t tr (9)

[0125] in,

[0126]

[0127] S34. Based on the collision position of the emitted electrons, determine whether an electron escapes. If an electron escapes, count the number of escaped electrons. If no electron escapes, determine whether the electron collides again. If it collides again, proceed to S33. Repeat the above steps until there are no more electrons in the regular array cylindrical hole trap structure, and update the number of escaped electrons N.out ;

[0128] S35, via δ hole =N out / Num, the secondary electron emission coefficient δ of the regular array cylindrical hole trap structure is calculated. hole ;

[0129] S36. The secondary electron emission coefficient based on the regular array cylindrical hole trap structure and the secondary electron emission coefficient of the 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 metal regular array trap structure was calculated. Total .

[0130] Using a size combination (0.5×10) -6 Calculate its secondary electron emission coefficient curve using (0.05, 0.1) and obtain the corresponding maximum secondary electron emission coefficient SEY on the curve. MAX The value is 1.456878722; using a size combination (0.5×10). -6 Calculate its secondary electron emission coefficient curve using 0.5,4), and obtain the maximum secondary electron emission coefficient SEY corresponding to the curve. MIN The value is 0.845579444; using a size combination (0.5×10 -6 ,φ,A s Calculate the secondary electron emission coefficient curve and obtain the corresponding maximum secondary electron emission coefficient δ. SEY (2a,φ,A s ).

[0131] S4. Calculate the surface impedance based on the operating frequency f and the dimensions of the regular array of cylindrical hole trap structures.

[0132] The surface impedance includes Rs MIN and Rs MAX The size combinations (2a, φ1, A) are used respectively. s1 ) and (2a,φ2,A s2 The result is obtained by calculating using the following formula:

[0133]

[0134] Where ω is the angular frequency, ω = 2πf, f is a given frequency, 50 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. MINφ is taken as φ2, and Rs is calculated accordingly. MAX H is the depth of a regular array of cylindrical holes on the metal surface, δ skin For skin depth and σ is the electrical conductivity of the metal, 6.173 × 10⁻⁶. 7 .

[0135] Using a size combination (0.5×10) -6 Calculate the surface impedance Rs (0.05, 0.1) MIN The value is 0.056620859; using a size combination (0.5×10 -6 ,0.5,4) Calculate the surface impedance Rs MAX It is 0.110987984.

[0136] S5. Treat the size of the regular array of cylindrical hole trap structures as an individual in the population.

[0137] according to Calculate the fitness value (fitness) for each individual, where R... s (2a,φ,A s ) for individual (2a,φ,A) s ) surface impedance; δ SEY (2a,φ,A s ) represents an individual (2a,φ,A) s The corresponding secondary electron emission coefficient; A s The aspect ratio of each cylindrical hole 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 (2a,φ1,A) s1 The maximum secondary electron emission coefficient of SEY; MIN For individual (2a,φ2,A) s2 The maximum secondary electron emission coefficient of SEY; and SEY MAX and SEY MIN All are derived from the secondary electron emission coefficient curve; Rs MIN For individual (2a,φ1,A) s1 Surface impedance; Rs MAX For individual (2a,φ2,A) s2 Surface impedance.

[0138] S6. Determine whether the fitness value of an individual is the set minimum fitness value.

[0139] The determination of whether an individual's fitness value is minimum fitness includes:

[0140] S61. Determine if the iteration count N is greater than 1;

[0141] S62. If the number of iterations is equal to 1, then based on the different binary code bit strings of individuals in the population, select the binary code bit string of the individual with the smallest fitness.

[0142] S62. Compare the fitness value calculated for an individual with the fitness of the binary encoded bit string of the best individual selected.

[0143] S63. The individual with the smallest fitness value is the best individual in the current population, and the binary encoding bit string of the best individual is saved.

[0144] S64. Determine if the fitness value of the current best individual is the set minimum value; if the fitness value of the current best individual is the set minimum value, then skip to S8.

[0145] S65. If the fitness value of the best individual is not the set minimum value, then skip to S9.

[0146] S66. If the number of iterations is greater than 1, then select the individual with the smallest fitness value from the fitness values ​​of each individual in the calculated new population as the optimal individual.

[0147] S67. Compare the fitness value of the current best individual with the fitness value of the best individual in the previous generation population. The individual with the smaller fitness value is the best individual in the current population, and save the binary encoding bit string of the best individual; skip to S64.

[0148] S7. If an individual's fitness value is the set minimum fitness value, then that individual is the optimal individual.

[0149] S8. Decode the binary encoded bit string of the individual to obtain the structural dimension parameters corresponding to the individual. The structural dimension parameters corresponding to the individual include the diameter 2a of the cylindrical hole and the aspect ratio A. s , porosity φ.

[0150] according to

[0151]

[0152] Decode the selected individuals; where b i c is the value in the binary encoded bit string corresponding to porosity. i It represents the value in the binary encoded bit string corresponding to the aspect ratio.

[0153] Output the dimensions of the cylindrical hole array structure: cylindrical hole diameter 2a, aspect ratio A. s , porosity φ.

[0154] S9. Determine if the stopping condition has been met. If the stopping condition has been met, then the individual is the optimal individual and jump to S8; otherwise, use the roulette wheel strategy to select individuals from the population for genetic operations to form a new generation of population. Record the number of iterations N as N+1 and jump to S3.

[0155] The stopping conditions include preset computational precision or number of iterations.

[0156] In the specific implementation of S9, the steps include: if the fitness value of an individual is not the set minimum fitness value, then determine whether the number of iterations is the maximum number of iterations; if the number of iterations is the maximum number of iterations, then the individual is the optimal individual and jump to S8; if the number of iterations is not the maximum number of iterations, then use the roulette wheel strategy to select individuals from the population for genetic operations to form a new generation of population, record the number of iterations N as N+1, and jump to S3.

[0157] 111. According to Calculate the selection probability of each individual in the population, based on Calculate the cumulative probability. Where, fitness(LL) i ) represents the fitness value of the i-th individual;

[0158] 112. Take a random number r in the interval (0,1). When PP i-1 ≤r<PP i When the time comes, select the i-th individual as the father. Randomly select one individual from the remaining individuals as the mother. Then, in the binary encoded bit string of length L1+L2, randomly select a position posCut as the intersection point;

[0159] 113. Take a random number r1 in the interval (0,1). If r1≤Pc, take the first posCut bits of the binary code bit string of the father individual and the last (L1+L2-posCut) bits of the binary code bit string of the mother individual, combine them to form a new individual, and save the binary code bit string of the new individual. If r1>Pc, do not perform this operation.

[0160] 114. Take a random number r2 in the interval (0,1). If r2≤Pm, then randomly select a position posMut in the binary encoded bit string of L1+L2 as the mutation point; invert the position posMut in the binary encoded bit string of the selected i-th individual, that is, change the number at this position from 0 to 1, or from 1 to 0, thereby forming a new individual, and save the binary encoded bit string of this individual; if r2>Pm, then do not perform this operation.

[0161] The calculation result of this example, based on this method, is: the diameter 2a of the cylindrical hole is 0.5 × 10⁻⁶. -6With an aspect ratio As of 0.527305166 and a porosity φ of 0.5, the surface impedance is 0.066923031, and the maximum SEY is 1.277364874 (e.g., Figure 4 (As shown).

[0162] 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 secondary electron emission coefficient cylindrical aperture array structure dimensions, characterized in that, Includes the following steps: S1. Establish the size range of the regular array cylindrical hole trap structure, and denote the iteration number N as 1; S2. Treat the size of the regular array of cylindrical hole trap structure as an individual in the population, encode all individuals into binary code bit strings, and number each individual one by one. The binary encoded bit string consists of a binary code for porosity of length L1 and a binary code for the aspect ratio of a regular array of cylindrical hole trap structures of length L2. S3. Calculate the secondary electron emission coefficient curve based on the dimensions of the regular array cylindrical hole trap structure and obtain the corresponding maximum secondary electron emission coefficient. S4. Calculate the surface impedance based on the operating frequency and the dimensions of the regular array of cylindrical hole trap structures; The dimensions of the regular array of cylindrical hole trap structure are expressed as: (2a, φ, A) s ), where a is the radius of each cylindrical hole, φ is the porosity and the range of φ is φ∈[φ1,φ2], A s The aspect ratio of each cylindrical hole and A s The interval range is A s ∈[A s1 A s2 ]; S5, according to Calculate the fitness value of each individual. Among them, R s (2a,φ,A s ) for individual (2a,φ,A) s ) surface impedance; δ SEY (2a,φ,A s ) represents an individual (2a,φ,A) s The corresponding secondary electron emission coefficient; As is the aspect ratio of each cylindrical hole and the range of As is As∈[A s1 A s2 The range of φ is φ∈[φ1,φ2], SEY MAX For individual (2a,φ1,A) s1 The maximum secondary electron emission coefficient of SEY; MIN For individual (2a,φ2,A) s2 The minimum secondary electron emission coefficient of SEY; and SEY MAX and SEY MIN All are derived from the secondary electron emission coefficient curve; Rs MIN For individual (2a,φ1,A) s1 Surface impedance; Rs MAX For individual (2a,φ2,A) s2 ) surface impedance; S6. Determine if the stopping condition has been met. If the stopping condition has been met, the individual is the optimal individual and jump to S8; otherwise, use the roulette wheel strategy to select an individual from the population for genetic operations to form a new generation of population, increment the iteration count by 1, and jump to S3. The stopping conditions include preset computational precision or number of iterations, specifically: Determine whether an individual's fitness value is the set minimum fitness value; If an individual's fitness value is the set minimum fitness value, then that individual is the optimal individual; S8. Decode the binary encoded bit string of the individual to obtain the structural dimension parameters corresponding to the individual. The structural dimension parameters corresponding to the individual include the diameter of the cylindrical hole, the aspect ratio, and the porosity. S9. If the fitness value of an individual is not the set minimum fitness value, then determine whether the number of iterations is the maximum number of iterations. S10. If the number of iterations is the maximum number of iterations, then the individual is the optimal individual, and the process jumps to S8. S11. If the number of iterations is not the maximum number of iterations, then use the roulette wheel strategy to select individuals from the population for genetic operations to form a new generation of population. Record the number of iterations N as N+1 and jump to S3.

2. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 1, characterized in that, The calculation of the secondary electron emission coefficient includes the following steps: S31. 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; S32. 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. S33. Based on the size of the regular array cylindrical hole trap 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. S34. 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 S33 until there are no electrons inside the regular array cylindrical hole trap structure, and update the number of escaped electrons. S35, the calculation rules for the number of escaped electrons and the number of incident electrons obtained through S33, and the secondary electron emission coefficient of the array cylindrical hole trap structure; S36. The total secondary electron emission coefficient of the surface of the regular array trap structure of metal is obtained by calculating the secondary electron emission coefficient of the regular array cylindrical hole trap structure and the secondary electron emission coefficient of the smooth metal surface under different incident angles.

3. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 2, characterized in that, The calculation of the secondary electron emission curves of a smooth metallic surface at different incident angles includes: S311. 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. S312. 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.

4. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 3, 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 u1 within the interval (0,1); 102. When u1 <P e (E' p ,θ' p Upon a second collision, the incident electrons undergo elastic backscattering after colliding with the metal. Among them, P e (E' p ,θ' p () represents the elastic backscattering coefficient upon a second collision; 103. Generate a random number u1 within the interval (0,1); 104, u1 <P e (E' p ,θ' p )+P i (E' p ,θ' p If the incident electrons collide with the metal, inelastic backscattering will occur. Among them, P i (E' p ,θ' p () represents 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.

5. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 2, characterized in that, The collision locations of the electrons include electrons emitted from the bottom of the regularly arrayed cylindrical hole trap on the metal surface and electrons emitted from the sidewalls of the regularly arrayed cylindrical hole trap on the metal surface.

6. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 5, characterized in that, The collision location is calculated based on the electron emission location and the electron motion time.

7. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 1, characterized in that, The surface impedance calculation based on the operating frequency and the dimensions of the regularly arrayed cylindrical hole trap structure includes: The surface impedance includes Rs MIN and Rs MAX According to the size combination (2a, φ1, A) s1 ) and (2a,φ2,A s2 ) was calculated.

8. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 1, characterized in that, The determination of whether an individual's fitness value is minimum fitness includes: S61. Determine if the iteration count N is greater than 1; S62. If the number of iterations is equal to 1, then based on the different binary code bit strings of individuals in the population, select the binary code bit string of the individual with the smallest fitness. S62. Compare the fitness value calculated for an individual with the fitness of the binary encoded bit string of the best individual selected. S63. The individual with the smallest fitness value is the best individual in the current population, and the binary encoding bit string of the best individual is saved. S64. Determine if the fitness value of the current best individual is the set minimum value; if the fitness value of the current best individual is the set minimum value, then skip to S8. S65. If the fitness value of the best individual is not the set minimum value, then skip to S9. S66. If the number of iterations is greater than 1, then select the individual with the smallest fitness value from the fitness values ​​of each individual in the calculated new population as the optimal individual. S67. Compare the fitness value of the current best individual with the fitness value of the best individual in the previous generation population. The individual with the smaller fitness value is the best individual in the current population, and save the binary encoding bit string of the best individual; skip to S64.

9. The method for designing the optimal secondary electron emission coefficient cylindrical aperture array structure size according to claim 1, characterized in that, The selection of individuals from the population for genetic operations includes: S111. Calculate the selection probability and cumulative probability of each individual in the population. i ; S112. Take a random number r in the interval (0,1). When PP i-1 ≤r<PP i When the i-th individual is selected as the father individual, one individual is randomly selected from the remaining individuals as the mother individual, and a position posCut is randomly selected in the binary encoded bit string as the crossover point, and another position posMut is selected as the mutation point. S113. Take a random number r1 in the interval (0,1). If r1≤Pc, where Pc is the crossover probability, take the first posCut bits of the binary code bit string of the father individual and the last (L1+L2-posCut) bits of the binary code bit string of the mother individual, combine them to form a new individual, and save the binary code bit string of the new individual; if r1>Pc, do not perform this operation. S114. Take a random number r2 in the interval (0,1). If r2≤Pm, where Pm is the mutation probability, then invert the position posMut in the binary code bit string of the selected i-th individual to form a new individual and save the binary code bit string of that individual; if r2>Pm, then do not perform this operation.

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