A gyrotron output window design method

Abstract

The application discloses a gyrotron output window design method, and belongs to the technical field of microwave and millimeter wave. The application firstly establishes a thickness calculation formula of an ideal non-reflection layer window sheet of the output window and a theoretical calculation formula of a reflection coefficient S11 of the output window; then based on a mapping relationship between the thickness of each layer window sheet of the output window and the reflection coefficient S11 of the output window, a fitness function for evaluating the performance of the output window is established, and a global optimization algorithm is used to calculate the theoretical optimal thickness of each layer window sheet of the output window; then a simulation model is established to perform simulation verification or simulation optimization to obtain the output window with a bandwidth meeting the design requirements; finally, the energy absorbed by the output window is solved by the simulation model to serve as a heat source, a grid encryption method is used to perform thermal analysis on the output window, and post-processing is performed on the thermal analysis result until the output window with a power capacity meeting the design requirements is obtained. The application has high design freedom, fast calculation speed and high universality, and can realize high-performance comprehensive design.

Description

Technical Field

[0001] The present invention belongs to the field of microwave, millimeter wave and terahertz device technology simulation calculation, and specifically relates to a gyrotron traveling wave tube output window design method that meets different bandwidth and power capacity requirements. Background Art

[0002] Gyrotron traveling-wave tubes (TWTs) are important microwave, millimeter-wave, and terahertz (THz) sources. Due to their high power, wide bandwidth, and high gain, they hold broad application prospects in military and civilian fields, including high-resolution radar, high-power communications systems, and electronic warfare systems. Consequently, they have attracted considerable international attention.

[0003] As one of the core components of a traveling wave tube (TWT), the output window is responsible for isolating the internal vacuum of the TWT from the outside atmosphere, ensuring a high vacuum inside the tube and providing a channel for microwave transmission. The performance of the output window directly affects the overall performance of the TWT. On the one hand, if the high-power output window has poor transmission characteristics, microwaves will be reflected back to the high-frequency structure. When a high-power signal is transmitted, the reflected microwave energy will burn the interacting high-frequency structure. On the other hand, since the loss tangent of the output window material cannot be zero in reality, high-power microwaves will generate a large amount of dissipated power when passing through the output window, which can easily cause the output window to overheat and suffer excessive thermal stress, leading to damage. With the application of TWTs in military and civilian fields, there is a great demand for TWTs with different bandwidth and power capacity requirements. Therefore, how to quickly design an output window that meets different bandwidth and power capacity requirements and has excellent performance has become an important issue in the current development of TWTs.

[0004] Currently, the commonly used design method for gyrotron traveling wave tube output windows is based on different topological structures (beryllium oxide single-layer window, beryllium oxide double-layer window, sapphire double-layer window, quartz-sapphire-quartz triple-layer window, universal multi-layer dielectric window, and metamaterial window), using 3D electromagnetic simulation software such as HFSS and CST to perform large-scale multi-parameter modeling, simulation, and optimization. This method has the following problems: 1) Due to the different requirements for device bandwidth and power capacity, the requirements for the bandwidth and power capacity of the output window also vary. Therefore, it is impossible to automatically select topological structures that meet design requirements based on different bandwidths, power capacities, and processing difficulties, such as single-layer windows, multi-layer windows, and metamaterial windows made of different materials. 2) Manual settings for simulation software parameter scanning and optimization, manual review and processing of simulation results, and report writing are required. This has the disadvantages of long design cycles, time-consuming, and labor-intensive design, and cannot quickly design output windows with different topological structures that meet different bandwidth requirements.

[0005] Therefore, there is an urgent need to provide a gyrotron traveling wave tube output window design method that meets different bandwidth and power capacity requirements. Summary of the Invention

[0006] In view of the deficiencies of the prior art, the application provides a gyrotron output window design method, which can meet different bandwidth and power capacity requirements.

[0007] The technical scheme adopted by the application is as follows:

[0008] A gyrotron output window design method comprises the following steps:

[0009] S1. Based on the working mode, bandwidth and power capacity of the gyrotron, the working parameters and topological structure of the output window are set.

[0010] The working parameters include the working mode TE mn , the minimum working frequency f1, the maximum working frequency f2 and the output window radius R.

[0011] The topological structure refers to the basic structure of the output window, including the number of layers of the output window and the materials of each layer; currently, the topological structure of the output window includes a beryllium oxide single-layer window, a beryllium oxide double-layer window, a sapphire double-layer window, a quartz-sapphire-quartz three-layer window, a general multi-layer dielectric window and a metamaterial window.

[0012] S2. Assuming that the output window has N window sheets, based on Snell's law, Fresnel's law and the circular waveguide field equation, the thickness of the ideal non-reflective window sheet of each layer is calculated:

[0013]

[0014] In the formula, t k is the thickness of the kth window sheet, ε rk is the dielectric constant of the kth window sheet, k=1, 2, …, N, λ is the waveguide wavelength, X mn is the eigenvalue of the Bessel function corresponding to the working mode TE mn , and p is an integer.

[0015] S3. Assuming that the sequence numbers of the interfaces from the input end to the output end of the output window are 1, 2, …, 2N in turn, the transmission matrix M i of the ith interface is expressed as:

[0016]

[0017] In the formula, i=1, 2, …, 2N, which represents the number of the output window interface; u i is the relative permeability of the ith interface; β mni and β mn(i+1) are the propagation constants on the ith and i+1th interfaces respectively; and z represents the axial coordinate.

[0018] Then, the transmission cascade matrix of the output window with N window sheets is:

[0019]

[0020] Where a 2N+1 =(M 11 M 22 -M 12 M 21 ) / M 22 、b 2N+1 =0 are the amplitudes of the total incident wave and the total reflected wave in the air respectively; a1=1, b1=-M 21 / M 22 are the amplitudes of the total incident wave and total reflected wave at the first interface respectively; M 2N 、M 2N-1 ...M2, M1 are the transmission matrices of the 2Nth, 2N-1...2nd, and 1st interfaces respectively; M 11 、M 12 、M 21 and M 22 They represent the elements in the 1st row and 1st column, the elements in the 1st row and 2nd column, the elements in the 2nd row and 1st column, and the elements in the 2nd row and 2nd column of the product matrix of the transmission matrices of the 2Nth, 2N-1…2nd, and 1st interfaces respectively.

[0021] Based on the field matching theory and the transmission cascade matrix, the reflection coefficient S of the output window is established. 11 Theoretical calculation formula:

[0022] S 11 =10lg|M 21 / M 22 | 2 =10lg|r| (4)

[0023] Where r is the power reflection coefficient, specifically:

[0024]

[0025] Where τ is the transmission coefficient, specifically:

[0026]

[0027] Where, ε i+1 , ε i are the relative dielectric constants at the i-th and i+1-th interfaces respectively.

[0028] S4. Based on the thickness of each layer of the output window t k and the reflection coefficient S of the output window 11 The mapping relationship between theoretical calculation formulas is established to establish a fitness function for evaluating the performance of the output window; the theoretical optimal thickness of each layer of the output window is calculated using a global optimization algorithm.

[0029] S5. Based on the output window's topological structure, output window radius, and theoretically optimal thickness of each window layer, a simulation model of the output window is established in the CST simulation software. The excitation mode and field amplitude are set according to the operating mode and power capacity of the gyrotron traveling wave tube. Electromagnetic simulation is performed on the simulation model to obtain the reflection coefficient S 11 Simulation value; if the bandwidth of the simulation model meets the design requirements, proceed to the next step. If not, the thickness of each layer of the output window is optimized based on the genetic algorithm in the CST simulation software until the bandwidth of the simulation model meets the design requirements.

[0030] S6. Based on the simulation model, the energy absorbed by the output window under normal working conditions is obtained. The energy absorbed by the output window is used as a heat source, and a thermal analysis is performed on the output window based on mesh encryption to obtain the thermal analysis results. The thermal analysis results are post-processed to obtain the actual temperature difference between the maximum temperature and the minimum temperature on the output window. If the actual temperature difference is smaller than the maximum critical temperature difference of the output window, the output window power capacity meets the design requirements. If the actual temperature difference is larger than the maximum critical temperature difference of the output window, a peripheral conductor material with a higher heat exchange coefficient is selected until the actual temperature difference is smaller than the maximum critical temperature difference of the output window, thereby meeting the output window power capacity design requirements and completing the output window design.

[0031] Furthermore, in step S4, the fitness function f(S11) is:

[0032] f(S11)=min[|S11-S11 goal |] x (7)

[0033] Among them, S11 goal is the target reflection coefficient value, χ is the convergence weighting factor; when the fitness function is minimized, the design reaches the optimal value.

[0034] Furthermore, in step S5, the field amplitude A is calculated based on the power capacity P0, and the calculation formula is as follows:

[0035]

[0036] Where ω is the angular frequency, μ is the magnetic permeability of the output window medium, β is the phase constant, and k c is the cutoff wave number, p′ 11 is the first root value of the Bessel function when n=1, and J1 is the Bessel function when n=1.

[0037] Furthermore, in step S6, the formula for calculating the energy absorbed by the output window is:

[0038]

[0039] Where ω is the angular frequency, Ew is the total electric field on the output window, ε0 is the relative dielectric constant of the output window, and ε" r is the imaginary part of the complex dielectric constant of the output window.

[0040] Further, the post-processing is performed by scanning the heat exchange coefficient of the peripheral conductor material from 1000 W / m^2 / ℃ to 3000 W / m^2 / ℃ in an arithmetic progression with 20 points in the bandwidth of the gyrotron, and performing heat conduction analysis on at least two frequency points in the bandwidth to obtain the maximum temperature and the minimum temperature on the output window and calculate the actual temperature difference.

[0041] Further, in step S6, the formula for calculating the maximum critical temperature difference ΔT of the output window is:

[0042]

[0043] where v is the Poisson's ratio, α is the thermal expansion coefficient, Y is the Young's modulus, δ f is the bending strength of the material.

[0044] The advantages of the present application are as follows:

[0045] The present application is based on Snell's law, Fresnel's law and the circular waveguide field equation to establish a thickness calculation formula of the ideal reflection-free window piece of the output window; based on the field matching theory and the transmission cascade matrix, a reflection coefficient S 11 theoretical calculation formula of the output window is established; based on the mapping relationship between the thickness of each window piece of the output window and the reflection coefficient S 11 of the output window, a fitness function for evaluating the performance of the output window is established, and the theoretical optimal thickness of each window piece of the output window is calculated by using a global optimization algorithm; then a simulation model is established for simulation verification or simulation optimization to obtain an output window with a bandwidth meeting the design requirements; finally, the energy absorbed by the output window obtained by solving the simulation model is used as a heat source, and the output window is analyzed by using the grid encryption method, and the heat analysis result is post-processed until the output window meeting the design requirements is obtained.

[0046] The present application obtains the theoretical optimal thickness of each window piece of the output window by theoretical calculation, fully utilizes the powerful matrix processing and operation capability of MATLAB, and can greatly reduce the design time. At the same time, the present application can improve the design freedom, meet the comprehensive design of strong constraints and high performance, and especially under the strong constraint conditions such as high frequency, small size, limited power capacity, size and machining precision constraints, the design of the output window can be completed conveniently and quickly. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 is the flow chart of the gyrotron output window design method of the present application.

[0048] Figure 2 Schematic diagram of the structure of the three-layer output window model of Example 1.

[0049] Figure 3 This is the fitness function convergence diagram of Example 1.

[0050] Figure 4 1 is a graph showing the theoretical reflection coefficient S11 result and a graph showing the simulated reflection coefficient S11 result of Example 1.

[0051] Figure 5 The maximum temperature and temperature difference on the output window under different heat exchange coefficients of the output window of Example 1.

[0052] Figure 6 Schematic diagram of the structure of the metamaterial output window model of Example 2.

[0053] Figure 7 This is a schematic diagram of the planar structure of the metamaterial output window of Example 2.

[0054] Figure 8 This is the fitness function convergence diagram of Example 2.

[0055] Figure 9 The graphs are the theoretical reflection coefficient S11 result and the simulation reflection coefficient S11 result of Example 2.

[0056] Figure 10 The maximum temperature and temperature difference on the output window under different heat exchange coefficients of the output window of Example 2.

[0057] Explanation of the accompanying figures: 1. Input end, 2. Output end, 3. Metal waveguide, 4. Vacuum layer, 5. Three-layer dielectric window, 6. Metamaterial window. DETAILED DESCRIPTION

[0058] The present invention is further elaborated below in conjunction with two design examples and accompanying drawings; it is necessary to point out here that this example is only used to further illustrate the present invention and cannot be understood as a limitation on the protection of the present invention. Technical personnel familiar with this field can make some non-essential improvements and adjustments based on the above content of the present invention.

[0059] Example 1:

[0060] The following is a Ku-band TE with a working center frequency of 17 GHz. 11 The output window of the gyrotron traveling wave tube (TWT) is designed quickly for the mode, requiring an average power of 100kW and a relative bandwidth of no less than 5%. The design steps are as follows:

[0061] S1. It is known that the operating frequency band of the gyrotron traveling wave tube is Ku band, the center frequency is 17 GHz, and the operating mode is TE 11mode, relative bandwidth is not less than 5%, average power is 100kW; the selected topology is as follows Figure 2 The quartz-sapphire-quartz three-layer output window structure shown has a metal waveguide on the outside of the output window; the minimum operating frequency of the output window is set to f1 = 16 GHz, the maximum operating frequency is set to f2 = 18 GHz, the number of operating modes is m = 1, n = 1, and the output window radius is R = 16 mm.

[0062] S2. The output window has three layers of windows. Based on Snell's law, Fresnel's law, and the circular waveguide field equation, the thickness of each layer of the ideal non-reflective output window is calculated according to formula (1): 1.92 mm, 1.28 mm, and 1.92 mm, respectively.

[0063] S3. Assume that the interfaces from the input to the output of the output window are numbered 1, 2…6, and the transmission matrix M of the i-th interface is i The expression is:

[0064]

[0065] Where i = 1, 2, ..., 6, represents the number of the output window interface; u i is the relative magnetic permeability of the i-th interface; β mni , β mn(i+1) are the propagation constants at the i-th and i+1-th interfaces respectively; z represents the axial coordinate.

[0066] Then the transmission cascade matrix of the output window with 3 layers of windows is:

[0067]

[0068] Where a7=(M 11 M 22 -M 12 M 21 ) / M 22 , b7=0 are the amplitudes of the total incident wave and the total reflected wave in the air respectively; a1=1, b1=-M 21 / M 22 are the amplitudes of the total incident wave and total reflected wave of the first interface respectively; M6, M5…M2, M1 are the transmission matrices of the sixth, fifth…second, and first interfaces respectively; M 11 、M 12 、M 21 and M 22 They represent the elements in the 1st row and 1st column, the elements in the 1st row and 2nd column, the elements in the 2nd row and 1st column, and the elements in the 2nd row and 2nd column of the product matrix of the transmission matrices of the 6th, 5th…2nd, and 1st interfaces respectively.

[0069] Based on the field matching theory and the transmission cascade matrix, the reflection coefficient S of the output window is established.11 Theoretical calculation formula:

[0070] S 11 =10lg|M 21 / M 22 | 2 =10lg|r|

[0071]

[0072] Where r is the power reflection coefficient, τ is the transmission coefficient, and ε i+1 , ε i are the relative dielectric constants at the i-th and i+1-th interfaces respectively.

[0073] S4. The thickness t of each layer of the output window obtained in step S2 k The reflection coefficient S of the output window established in step S3 11 The mapping relationship between theoretical calculation formulas is used to establish the fitness function f(S11) for evaluating the output window performance:

[0074] f(S11)=min[|S11-S11 goal |] x

[0075] Among them, S11 goal is the value of the target reflection coefficient, χ is the convergence weighting factor; Figure 3 It is the convergence graph of the fitness function, which has fast convergence speed and high accuracy. When the fitness function is minimized, the design reaches the optimal value.

[0076] Using MATLAB based on the global optimization algorithm, the theoretical optimal thickness of each layer of the output window is calculated to be 2.18mm, 0.59mm, and 2.18mm respectively.

[0077] S5. Based on the output window's topological structure, output window radius, and theoretically optimal thickness of each window layer, a simulation model of the output window is established in the CST simulation software.

[0078] According to the working mode of the gyrotron traveling wave tube, the excitation mode is set to TE 11 The field amplitude A is set to 427.5 V / m according to the power capacity of the gyrotron traveling wave tube and formula (8). The simulation model is subjected to electromagnetic simulation to obtain the simulation transmission coefficient S11; Figure 4 The results of the theoretical reflection coefficient S11 and the simulated reflection coefficient S11 are shown. It can be seen that the trends of the theoretical calculation and simulation calculation results are well consistent. The frequency range of the output window simulation is 16 GHz to 18 GHz, the center frequency is 17 GHz, the bandwidth is 2 GHz, and the relative bandwidth is about 11.8%>5%, which meets the relative bandwidth design target.

[0079] S6. Based on the simulation model and formula (9), the energy absorbed by the output window in normal working state is 113.86W. The energy absorbed by the output window is used as the heat source to perform thermal analysis on the output window. The thermal analysis results are post-processed to obtain the following Figure 5 The maximum and minimum temperatures on the output window shown, that is, the actual temperature difference, is about 203°C. According to formula (10), the maximum critical temperature difference of the output window is calculated to be ΔT ≈ 300°C. Therefore, the actual temperature difference is less than the maximum critical temperature difference of the output window, so the output window can achieve a power capacity of 100kW, completing the output window design.

[0080] Example 2:

[0081] The following is a W-band TE with a working center frequency of 92.5GHz. 01 The output window of the gyrotron traveling wave tube (TWT) is designed quickly for the mode, requiring an average power of 20kW and a relative bandwidth of no less than 30%. The design steps are as follows:

[0082] S1. It is known that the operating frequency band of the gyrotron traveling wave tube is W band, the center frequency is 92.5GHz, and the operating mode is TE 01 Mode, relative bandwidth is not less than 30%, average power is 20kW. The topology selected is as follows Figure 6 The metamaterial output window structure shown in FIG. has a metal waveguide on the outside of the output window. The metamaterial output window includes a dielectric layer in the middle and metamaterial layers on both sides thereof, which can be regarded as a three-layer window output window structure of metamaterial layer-dielectric layer-metamaterial layer. Figure 7 As shown, the metamaterial layer is actually composed of a periodic arrangement of square units, with the initial value of the side length w of each square unit set to 0.59 mm and the initial value of the gap g set to 0.30743 mm; however, in the theoretical calculation process (i.e., steps S2 to S4), it is equivalent to a uniform dielectric layer in calculating its thickness.

[0083] The minimum operating frequency of the output window is set to f1 = 75 GHz, the maximum operating frequency is set to f2 = 110 GHz, the number of operating modes is set to m = 0, n = 1, and the output window waveguide is set to R = 16 mm.

[0084] S2. The output window has three layers of windows. Based on Snell's law, Fresnel's law, and the circular waveguide field equation, the thickness of each layer of the ideal non-reflective output window is calculated according to formula (1): 1.92 mm, 1.28 mm, and 1.92 mm, respectively.

[0085] S3. Assume that the interfaces from the input to the output of the output window are numbered 1, 2…6, and the transmission matrix M of the i-th interface is i The expression is:

[0086]

[0087] where i = 1, 2, …, 6, represents the number of the output window interface; u i is the relative permeability of the i-th interface; β mni , β mn(i+1) are the propagation constants on the i-th and i+1-th interfaces, respectively; z represents the axial coordinate.

[0088] The transmission cascade matrix of the output window with 3-layer window sheets is:

[0089]

[0090] where a7= (M 11 M 22 -M 12 M 21 ) / M 22 , b7= 0 are the amplitude of the total incident wave and the total reflected wave in the air, respectively; a1= 1, b1= -M 21 / M 22 are the amplitude of the total incident wave and the total reflected wave on the 1st interface, respectively; M6, M5…M2, M1 are the transmission matrices of the 6th, 5th…2nd, 1st interfaces, respectively; M 11 , M 12 , M 21 and M 22 represent the elements of the 1st row and 1st column, the 1st row and 2nd column, the 2nd row and 1st column, and the 2nd row and 2nd column of the 1st row and 1st column, respectively.

[0091] Based on the field matching theory and the transmission cascade matrix, the reflection coefficient S 11 of the output window is established:

[0092] S 11 = 10lg|M 21 / M 22 | 2 = 10lg|r|

[0093]

[0094] where r is the power reflection coefficient, τ is the transmission coefficient, ε i+1 , ε i are the relative permittivities on the i-th and i+1-th interfaces, respectively.

[0095] S4. Based on the thickness t k of each layer of the window sheets of the output window obtained in step S2 and the reflection coefficient S 11The mapping relationship between theoretical calculation formulas is used to establish the fitness function f(S11) for evaluating the output window performance:

[0096] f(S11)=min[|S11-S11 goal |] x

[0097] Among them, S11 goal is the value of the target reflection coefficient, χ is the convergence weighting factor; Figure 8 It is the convergence graph of the fitness function, which has fast convergence speed and high accuracy. When the fitness function is minimized, the design reaches the optimal value.

[0098] The theoretical optimal thicknesses of each layer of the output window were calculated using MATLAB based on the global optimization algorithm, which are 1.2736 mm, 0.54856 mm, and 1.2736 mm, respectively.

[0099] S5. Build a simulation model of the output window in CST simulation software based on the output window's topology, output window radius, and theoretically optimal thickness of each window layer.

[0100] According to the working mode of the gyrotron traveling wave tube, the excitation mode is set to TE 01 The field amplitude A is set to 218.5 V / m according to the power capacity of the gyrotron traveling wave tube and formula (8). The simulation model is subjected to electromagnetic simulation to obtain the simulation transmission coefficient S11; Figure 9 The results of the theoretical reflection coefficient S11 and the simulated reflection coefficient S11 are shown. It can be seen that the theoretical calculation results and the CST simulation calculation results are in good agreement. The frequency range of the output window simulation is 75 GHz to 110 GHz, the center frequency is 92.5 GHz, the bandwidth is 35 GHz, and the relative bandwidth is about 37.8%>30%, which meets the relative bandwidth design target.

[0101] S6. Based on the simulation model and formula (9), the energy absorbed by the output window under normal working conditions is 14.87W. The energy absorbed by the output window is used as a heat source to perform thermal analysis on the output window. The thermal analysis results are post-processed to obtain the following Figure 10 The maximum and minimum temperatures on the output window shown, that is, the actual temperature difference, is 6.5°C. According to formula (10), the maximum critical temperature difference of the output window is calculated to be ΔT≈150°C. Therefore, the actual temperature difference is less than the maximum critical temperature difference of the output window, so the output window can achieve a power capacity of 20kW, completing the output window design.

Claims

1. A method for designing a gyrotron traveling wave tube output window, characterized in that: The following steps are involved: S1. Set the output window operating parameters and topology based on the gyrotron TWT's operating mode, bandwidth, and power capacity. Among them, the working parameters include the working mode TE of the output window mn , minimum operating frequency f1, maximum operating frequency f2, output window radius R; The topology refers to the basic structure of the output window, including the number of layers of the output window and the materials of each layer; S2. Assume that the output window has N layers of windows. Calculate the thickness of each ideal non-reflective window layer according to formula (1): Where, t k is the thickness of the kth window, ε rk is the dielectric constant of the kth window, k=1,2,…,N, λ is the waveguide wavelength, X mn Working mode TE mn The corresponding characteristic root of the Bessel function, p is an integer; S3. Assume that the interfaces from the input to the output of the output window are numbered 1, 2…2N, and the transmission matrix M of the i-th interface is i The expression is: Where i = 1, 2, ..., 2N, represents the number of the output window interface; u i is the relative magnetic permeability of the i-th interface; β mni , β mn(i+1) are the propagation constants at the i-th and i+1-th interfaces, respectively; z represents the axial coordinate; j represents the imaginary unit; Then the transmission cascade matrix of the output window with N layers of windows is: Where a 2N+1 =(M 11 M 22 -M 12 M 21 ) / M 22 、b 2N+1 =0 are the amplitudes of the total incident wave and the total reflected wave in the air respectively; a1=1, b1=-M 21 / M 22 are the amplitudes of the total incident wave and total reflected wave at the first interface respectively; M 2N 、M 2N-1 ...M2, M1 are the transmission matrices of the 2Nth, 2N-1...2nd, and 1st interfaces respectively; M 11 、M 12 、M 21 and M 22 represent the element in the 1st row and 1st column, the element in the 1st row and 2nd column, the element in the 2nd row and 1st column, and the element in the 2nd row and 2nd column of the product matrix of the transmission matrices of the 2Nth, 2N-1…2nd, and 1st interfaces respectively; Establish the reflection coefficient S of the output window 11 Theoretical calculation formula: S 11 =10lg|M 21 / M 22 | 2 =10lg|r| (4) Where r is the power reflection coefficient, specifically: Where τ is the transmission coefficient, specifically: Where, ε i+1 , ε i are the relative dielectric constants at the i-th and i+1-th interfaces respectively; S4. Based on the thickness of each layer of the output window t k and the reflection coefficient S of the output window 11 The mapping relationship between theoretical calculation formulas is used to establish a fitness function for evaluating the performance of the output window; the theoretical optimal thickness of each layer of the output window is calculated using a global optimization algorithm; S5. Based on the output window's topological structure, output window radius, and theoretically optimal thickness of each window layer, a simulation model of the output window is established in the CST simulation software. The excitation mode and field amplitude are set according to the operating mode and power capacity of the gyrotron traveling wave tube. Electromagnetic simulation is performed on the simulation model to obtain the reflection coefficient S i1 Simulation value; if the bandwidth of the simulation model meets the design requirements, proceed to the next step; if not, optimize the thickness of each layer of the output window based on the genetic algorithm in the CST simulation software until the bandwidth of the simulation model meets the design requirements; S6. Based on the simulation model, the energy absorbed by the output window under normal working conditions is obtained. The energy absorbed by the output window is used as a heat source, and a thermal analysis is performed on the output window based on mesh encryption to obtain the thermal analysis results. The thermal analysis results are post-processed to obtain the actual temperature difference between the maximum temperature and the minimum temperature on the output window. If the actual temperature difference is smaller than the maximum critical temperature difference of the output window, the power capacity of the output window meets the design requirements. If the actual temperature difference is larger than the maximum critical temperature difference of the output window, a peripheral conductor material with a higher heat exchange coefficient is selected until the actual temperature difference is smaller than the maximum critical temperature difference of the output window, so as to meet the design requirements of the output window power capacity and complete the output window design.

2. The method for designing a gyrotron traveling wave tube output window according to claim 1, wherein: In step S4, the fitness function f(S11) is: f(S11)=min[|S11-S11 goal |] x (7) Among them, S11 goal is the target reflection coefficient value, χ is the convergence weighting factor; when the fitness function is minimized, the design reaches the optimal value.

3. The method for designing a gyrotron traveling wave tube output window according to claim 1, wherein: In step S5, the field amplitude A is calculated based on the power capacity P0, and the calculation formula is as follows: Where ω is the angular frequency, μ is the magnetic permeability of the output window medium, β is the phase constant, and k c is the cutoff wave number, p′ 11 is the first root value of the Bessel function when n=1, J1 is the Bessel function when n=1, and a represents the waveguide radius.

4. The method for designing a gyrotron traveling wave tube output window according to claim 1, wherein: In step S6, the energy absorbed by the output window is calculated as follows: Where ω is the angular frequency, E w is the total electric field on the output window, ε0 is the relative dielectric constant of the output window, ε″ r is the imaginary part of the complex dielectric constant of the output window.

5. The method for designing a gyrotron traveling wave tube output window according to claim 1, wherein: In step S6, the post-processing method is: based on the energy absorbed by the output window, within the bandwidth of the gyrotron traveling wave tube, the heat exchange coefficient of the peripheral conductor material is scanned at 20 points in the range of 1000W / m^2 / ℃ to 3000W / m^2 / ℃, and heat conduction analysis is performed on at least two frequency points within the bandwidth to obtain the maximum temperature and minimum temperature on the output window and calculate the actual temperature difference.

6. The method for designing a gyrotron traveling wave tube output window according to claim 5, wherein: In step S6, the calculation formula of the maximum critical temperature difference ΔT of the output window is: Where v is Poisson's ratio, α is the thermal expansion coefficient, Y is Young's modulus, δ f is the flexural strength of the material.

7. The method for designing a gyrotron traveling wave tube output window according to claim 1, wherein: The topological structures of the output window include: beryllium oxide single-layer window, beryllium oxide double-layer window, sapphire double-layer window, quartz-sapphire-quartz triple-layer window, universal multi-layer dielectric window and metamaterial window.

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