A method for the collaborative optimization design of a gyro device coil magnet and electron gun

Abstract

The application discloses a kind of for gyro device coil magnet and electron gun collaborative optimization design method, belong to microwave millimeter wave technical field.The application first establishes the mapping relationship between multi-coil configuration parameter and three-dimensional magnetic field distribution;Then establish the potential distribution in the two-dimensional plane of electron gun, solve electron beam trajectory under given magnetic field distribution;Establish the mapping relationship between electron gun electrode structure parameter and electron beam performance parameter;Again establish the mapping relationship between electron gun performance parameter and electron gun electrode shape and solenoid configuration parameter;Finally, establish the fitness function of evaluating electron beam quality, introduce global optimization algorithm to realize the optimization design of electron gun performance.The application has high design freedom, high universality, can realize high-performance comprehensive design, and also has the advantages of fast calculation speed, high precision, good numerical calculation stability.

Description

Technical Field

[0001] This invention belongs to the field of microwave and millimeter-wave technology, and relates to the field of vacuum electronics technology. Specifically, it relates to a general gyroscopic device with a synergistic optimization design of coil magnet and electron gun. Background Technology

[0002] In the millimeter-wave band, cyclotron devices exhibit a significant high-power advantage. A focusing magnet provides a guiding magnetic field for electron motion, ensuring normal device operation. Specifically, the rising region of the magnetic field controls electron beam shaping, the uniform magnetic field ensures efficient synchronous energy exchange between electrons and electromagnetic waves, and the falling region is used for electron despinning and collection. The magnetron-controlled injection electron gun (hereinafter referred to as the electron gun) determines the quality of the electron beam source; generating high-quality electrons with a specific velocity ratio and low-velocity dispersion is a prerequisite for efficient beam-wave interaction energy exchange in cyclotron devices.

[0003] In gyropod design, the traditional approach involves designing a corresponding coil assembly based on the specific magnetic field distribution provided by the device. Alternatively, a matching device structure can be designed using a fixed magnetic field distribution and performance specifications. This approach, however, cannot alter the magnetic field distribution during optimization, making it difficult to achieve optimal design. Furthermore, as gyropods evolve towards higher frequencies and higher power, the constraints on electron gun design increase dramatically. To enhance the design freedom of gyropod electron guns and meet the high-performance design requirements under stringent constraints, a rapid and accurate collaborative optimization design method for gyropod electron guns and coil magnets is urgently needed. Summary of the Invention

[0004] This invention proposes a collaborative design method for the coil magnet and electron gun of a gyropod. It establishes a mapping relationship between electron gun performance and the electron gun electrode shape and the configuration parameters of the coil magnet solenoid. By introducing a global optimization algorithm, the optimal design of electron gun performance under strong constraints can be achieved. This method develops design modules for the gyropod coil magnet and electron gun. The coil magnet design module establishes a mapping relationship between the magnetic field distribution and the coil configuration parameters, while the electron gun design module establishes a mapping relationship between the electron gun performance parameters and the electron gun structural parameters under a given magnetic field distribution. This effectively ensures a unified data interface and the establishment of a collaborative optimization model.

[0005] The technical solution adopted in this invention is as follows:

[0006] A method for co-optimization design of coil magnets and electron guns in gyroscopic devices includes the following steps:

[0007] S1. Based on the theory of off-axis magnetic fields of solenoids, establish the mapping relationship between the configuration parameters of multi-coil circuits and the three-dimensional magnetic field distribution. Specifically:

[0008] The longitudinal magnetic field g(z) at any position z on the central axis of the solenoid coil (r=0) is expressed as:

[0009]

[0010] In the formula R in and R out Let be the innermost and outermost radii of the solenoid coil, respectively; t1 = z - z0 + L / 2 and t2 = z - z0 - L / 2 are intermediate variables; L and z0 are the length and axial center position of the solenoid, respectively; μ0 is the permeability of free space; and Js = I / d. r d z Let d be the current density, I be the conductor current, and d be the current density. r and d z These represent the radial width and axial width of the conductor, respectively. The current density Js is related to the radial coil turns N. R axial coil turns N z related.

[0011] The radial magnetic field b at the off-axis position (r≠0) is derived by power series expansion. r (r,z) and longitudinal magnetic field b z The (r,z) components are:

[0012]

[0013]

[0014] In the formula, r and z are the radial position and longitudinal position, respectively, and k is an integer not less than zero.

[0015] The magnetic field distribution of a multi-coil solenoid is characterized as a linear superposition of the magnetic field distributions of each individual coil, and its radial magnetic field B r (r,z) and longitudinal magnetic field B z The distribution of (r,z) can be represented as:

[0016]

[0017]

[0018] Where the subscript i represents the coil number. Equations (4) and (5) establish the magnetic field distribution B of the multi-coil system. r (r,z), B z (r,z) and the configuration parameters of each coil (R in ,R out N R N z The mapping relationship between (I, z0).

[0019] S2. Given the topology of the electron gun, establish the potential distribution in the two-dimensional plane of the electron gun; then solve the electron beam trajectory under the given magnetic field distribution; finally, establish the mapping relationship between the electron gun electrode structure parameters and the electron beam performance parameters.

[0020] Given the topology of the electron gun, the three-dimensional problem of solving the electric field is transformed into a two-dimensional problem by utilizing the axisymmetry of the electron gun. The potential distribution in the two-dimensional plane is obtained by numerically solving the Poisson equation (6):

[0021]

[0022] In equation (6), u(r,z) is the two-dimensional potential distribution, ρ is the space charge, and ε is the dielectric constant of space.

[0023] Furthermore, the process of solving for the electron beam trajectory given the potential distribution u(r,z) includes the following steps:

[0024] Magnetic field components B in the three directions of S21, x, y, and z x B y B z Simultaneously acting on the electron's directional motion, due to the magnetic force, in the time infinitesimal element dt, the electron velocity vector changes from v n Change to v n+1 ,Right now:

[0025] v n+1 =v n H (7)

[0026] H = H x H y H z (8)

[0027] In the formula:

[0028]

[0029]

[0030]

[0031] Among them, the magnetic field components B in the x, y, and z directions x B y B z The contribution to the electron's circular motion corresponds to the angular frequency ω in each direction. x ω y ω z ,Right now:

[0032]

[0033] Wherein, the electron charge e = 1.6 × 10 -19 C, electron rest mass m0 = 9.1 × 10 -31 kg, where γ is the relativistic factor.

[0034] S22. The change in electron momentum ΔP caused by the electric field E within the infinitesimal time dt. E for:

[0035] ΔP E =eE·dt (13)

[0036] S23. In a combined field where both electric and magnetic fields exist, the total change in momentum ΔP of an electron is:

[0037] ΔP=ΔP E +ΔP B =eE·dt+m0γv n H-m0γv n (14)

[0038] Where, ΔP B This represents the change in electron momentum caused by the magnetic field. Using the relationship P... n =m0γv n and ΔP=P n+1 -P n , where P n P n+1 Let the total momentum at time n and time n+1 be respectively, and we can finally obtain:

[0039] P n+1 =eE·dt+m0γv n H (15)

[0040] Equation (15) represents the momentum evolution law of electrons within a time element dt in a composite field where electric and magnetic fields coexist.

[0041] S23. Under relativistic effects, the relationship between the electron's velocity vector and momentum is:

[0042]

[0043] Among them, P n+1 For vector P n+1 The amplitude, and the displacement Δs within the electronic time element dt are:

[0044]

[0045] Numerical solutions to equations (15)-(17) yield the electron trajectory distribution, allowing for the evaluation of the electron gun's performance parameters: velocity ratio α and transverse velocity dispersion Δβ. t :

[0046]

[0047]

[0048] In the formula, j represents the electronic serial number, and N e v represents the total number of electrons. r and v z These are the radial and longitudinal velocity components of the electron, respectively. The mathematical meaning of the velocity ratio calculation is the mean of the velocity ratio (also the pitch ratio) of all electrons, while the mathematical meaning of the velocity discreteness is the ratio of the standard deviation to the mean of the transverse velocity of all electrons.

[0049] S3, combining the two mapping relationships in S1 and S2, establish the performance parameters (α, Δβ) of the magnetron injection electron gun. t ) and electron gun electrode shape and solenoid configuration parameters (R in ,R out N R The mapping relationship between Nz, I, z0) is established; the fitness function f(α, Δβ) for evaluating the quality of the electron beam is established. t The performance of the electron gun is optimized by introducing a global optimization algorithm.

[0050] Furthermore, the fitness function f(α,Δβ) t Construct it as follows:

[0051]

[0052] Where, α goal χ is the value of the target velocity ratio, and χ is the convergence weighting factor; the design reaches its optimum when the fitness function is minimized.

[0053] The present invention has the following advantages:

[0054] (1) High degree of design freedom, enabling high-performance integrated design. By adopting a collaborative optimization method, an adjustable magnetic field distribution is introduced into the electron gun design, which improves the degree of design freedom and meets the requirements of high-performance integrated design under strong constraints, especially under strong constraints such as high frequency, small size, limited power capacity, and size and processing accuracy constraints.

[0055] (2) High computational speed, high accuracy, and good numerical computation stability. Utilizing the axisymmetry of the electron gun and solenoid coil, the finite difference method is used to transform the solution of the electric field in three-dimensional space into the solution of the electric field in a two-dimensional plane. The potential is iteratively solved using mesh refinement and potential inheritance, achieving rapid convergence iteration of potential calculation under high-density mesh conditions. Unlike traditional methods that directly solve the Lorentz equation numerically to obtain the electron trajectory, this invention proposes an electron gun theory and design method based on numerical computation. This theory is directly derived in matrix form, fully utilizing the powerful matrix processing and computational capabilities of MATLAB. Simultaneously, the electron trajectory solution employs a simplified momentum and velocity vector infinitesimal evolution iteration method, significantly reducing sensitivity to time steps, greatly improving numerical stability, and reducing computation time.

[0056] (3) Versatility: The parameters of the magnetic field coil are arbitrary, the parameters of the electron gun structure are arbitrary, the operating frequency band is arbitrary, and the electron gun can be designed and optimized conveniently and quickly. Attached Figure Description

[0057] Figure 1 Flowchart of the electron gun optimization system calculation.

[0058] Figure 2 Schematic diagram of a solenoid coil

[0059] Figure 3 Schematic diagram of electron gun cathode structure.

[0060] Figure 4 Schematic diagram of the electron gun anode structure.

[0061] Figure 5 Plot showing the convergence results of the speed ratio.

[0062] Figure 6 The graph shows the convergence results of the velocity discrete convergence.

[0063] Figure 7 Comparison of two-dimensional trajectory results of electron injection.

[0064] Figure 8 Comparison of three-dimensional trajectory results of electron injection.

[0065] Figure 9 Comparison of electron energy distribution along the longitudinal direction. Detailed Implementation

[0066] Example 1:

[0067] The invention will now be described in detail with reference to a design example of the co-design of the electron gun and coil magnet in a Ka-band cyclotron device, along with accompanying drawings:

[0068] Appendix Figure 3The diagram shows the longitudinal cross-sectional profile of the electron gun cathode. This structure is composed of multiple smoothly connected curved segments, with smooth and continuous joints. The electron emitting surface of the cathode has a radius of curvature of R. r The angle θ between the tangent line passing through the center of the arc and the z-axis is used to characterize the tilt angle of the cathode emitting surface. The longitudinal coordinate of the midpoint of the arc is Z. c The radial coordinate is R c The arc length is D0, and the lengths of the straight lines connecting the two ends of the arc are D1 and D2, respectively. This cathode structure has a total of seven structural parameters.

[0069] Appendix Figure 4 The diagram shows the anode structure of the electron gun, which is controlled by seven structural parameters: R1, R2, L1, L2, L3, L4, and R... o , where R o This indicates the waveguide radius at the electron exit point; all other parameters are listed in the appendix. Figure 2 The identifier is placed in the middle.

[0070] Taking the design of an electron gun for a Ka-band cyclotron device with a center frequency of 35 GHz as an example, when the operating mode is TE... 01 When the mode is in operation, the corresponding high-frequency waveguide radius is 5.2 mm and the magnetic field strength is approximately 1.26 T.

[0071] Taking a magnet system consisting of four coils as an example, one of the coils is a reverse compensation coil used to adjust the magnetic compression ratio during actual testing. The inner diameter of the coil is fixed at 70 mm, the coil current I = 25 A, the anode voltage is given as 40 kV, the cathode current is 10 A, and the surface area of ​​the cathode electron emitting surface is 188 mm². 2 The speed ratio is designed to be 1.2. The optimized design parameters using the collaborative method of this invention are summarized in Tables 1 and 2.

[0072] Table 1. Structural parameters of the Ka-band electron gun

[0073]

[0074] Table 2 Structural parameters of Ka-band magnet coil

[0075]

[0076] Based on MATLAB, the potential distribution of each grid in the electron gun region is calculated using the finite difference method. After obtaining the space charge distribution, the potential distribution generated by the space charge distribution can be calculated.

[0077] Appendix Figure 5 and Figure 6 The results shown are the iterative results obtained by considering the space charge effect, which have fast convergence speed and high accuracy.

[0078] As attached Figure 7 and attached Figure 8 As shown, the electron beam trajectory is solved directly by iteratively using the infinitesimal evolution matrix based on velocity and displacement vectors, and the trajectory calculated by the program matches well with the trajectory calculated by CST simulation.

[0079] Furthermore, attached Figure 9 The electron energy distribution was calculated as shown, and the calculated electron energy distribution of this invention agrees well with the CST simulation results.

[0080] Finally, based on the collaborative optimization model, the electron beam velocity ratio optimized by the method of this invention is 1.35, and the velocity dispersion is 1.8%. The electron beam velocity ratio calculated by CST simulation is 1.32, and the velocity dispersion is 1.5%. The comparison of the above results is shown in Table 3.

[0081] Table 3 Comparison of Ka-band Electron Gun Co-optimization Design Results

[0082]

[0083] Example 2:

[0084] This invention is illustrated through an example of the coordinated design of G-band magnetic field distribution and electron gun:

[0085] In the G-band electron gun, as described in S1, based on the off-axis magnetic field theory of solenoids, the longitudinal magnetic field g(z) is calculated sequentially. The magnetic field of the multi-coil solenoid is calculated by linear superposition of the magnetic field distributions of each single coil, establishing the relationship between the magnetic field and the configuration parameters (R) of each coil. in ,R out N R N z The mapping relationship between (I, z0). Taking a magnet system consisting of three coils as an example, one of the coils is a reverse compensation coil, used to adjust the magnetic compression ratio during actual testing. The coil current I = 62A, and the other parameters are used in the optimization design.

[0086] The magnetic field size in this design example is 8T. Based on the axisymmetry of the electron gun structure, a two-dimensional mesh is created. Considering the mesh division within the cross-section, the surface area of ​​the cathode electron emitting surface is 18.8 mm². 2 As described in S21, S22 and S23, the angular frequency of the electron's circular motion, the change in the electron's momentum, the change in the electron's total momentum, and the displacement Δs within the electron's time element are determined sequentially.

[0087] Based on the calculation of the electromagnetic field composite field, the electron trajectory is calculated, and the performance evaluation parameters of the electron gun are calculated using equations (18) and (19): velocity ratio and velocity drift. The mapping relationship between the electron gun electrode structure parameters and the electron beam performance parameters is established. The target velocity ratio for the G-band electron gun is 1.2, and the current of the cathode electron emitting surface is 3.5A.

[0088] In this invention, the calculation of the magnetic field distribution and the electron gun are combined into a complete calculation system, in which the magnet coil parameters and the electron gun structural parameters are optimized in a coordinated manner to meet the design objectives. The optimized structural parameters are shown in Tables 4 and 5.

[0089] Table 4 Structural parameters of G-band magnet coil

[0090]

[0091] Table 5. Structural parameters of the G-band electron gun

[0092]

[0093] Similarly, as described in S3, by integrating the mapping relationship between the two modules of magnetic field coil parameter optimization and electron trajectory solution, a global optimization algorithm for the performance parameters of the magnetically controlled injection electron gun is established. Based on MATLAB, the two-dimensional space is meshed, and the potential distribution of each mesh in the electron gun region is calculated using the finite difference method. After obtaining the space charge distribution, the potential distribution generated by the space charge distribution can be calculated. The electron beam trajectory is directly solved iteratively based on the infinitesimal evolution matrix of velocity and displacement vectors. The program-calculated trajectory matches well with the CST simulation trajectory, and its convergence speed is fast and its accuracy is high.

[0094] Finally, based on the collaborative optimization model, the electron beam velocity ratio optimized by the method of this invention is 1.30, and the velocity dispersion is 1.1%. The electron beam velocity ratio calculated by CST simulation is 1.29, and the velocity dispersion is 1.8%. The comparison of the above results is shown in Table 6.

[0095] Table 6 Comparison of G-band electron gun co-optimization design results

[0096]

[0097] By adjusting the position of the negative coil, the velocity ratio was corrected. An adjustable magnetic field distribution was introduced into the electron gun design, increasing the design freedom and meeting the requirements of highly constrained, high-performance integrated design, especially under conditions of high frequency, small size, limited power capacity, and constraints on size and manufacturing accuracy, without affecting the discrete velocity. The final optimization result is very close to the initial design objective.

[0098] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. A method for the collaborative optimization design of coil magnets and electron guns in gyroscopic devices, characterized in that, Includes the following steps: S1. Based on the theory of off-axis magnetic field of solenoids, establish the mapping relationship between the configuration parameters of multi-coil and the three-dimensional magnetic field distribution; specifically: The longitudinal magnetic field g(z) at any position z on the central axis of the solenoid coil where r = 0 is expressed as: In the formula R in and R out Let be the innermost and outermost radii of the solenoid coil, respectively; t1 = z - z0 + L / 2 and t2 = z - z0 - L / 2 are intermediate variables; L and z0 are the length and axial center position of the solenoid, respectively; μ0 is the permeability of free space; and Js = I / d. r d z Let d be the current density, I be the conductor current, and d be the current density. r and d z These represent the radial width and axial width of the conductor, respectively; where the current density Js is related to the radial coil turns N. R axial coil turns N z related; The radial magnetic field b at the off-axis position r≠0 is derived by power series expansion. r (r,z) and longitudinal magnetic field b z The (r,z) components are: In the formula, r and z are the radial position and longitudinal position, respectively, and k is an integer not less than zero; The magnetic field distribution of a multi-coil solenoid is characterized as a linear superposition of the magnetic field distributions of each individual coil, and its radial magnetic field B r (r,z) and longitudinal magnetic field B z The distribution of (r,z) can be represented as: Where the subscript i represents the coil number; Equations (4) and (5) establish the magnetic field distribution B of the multi-coil system. r (r,z), B z The mapping relationship between (r,z) and the configuration parameters of each coil; S2. Given the topology of the electron gun, establish the potential distribution in the two-dimensional plane of the electron gun; then, solve for the electron beam trajectory under a given magnetic field distribution; finally, establish the mapping relationship between the electron gun electrode structure parameters and the electron beam performance parameters. Given the topology of the electron gun, the three-dimensional problem of solving the electric field is transformed into a two-dimensional problem by utilizing the axisymmetry of the electron gun. The potential distribution in the two-dimensional plane is obtained by numerically solving the Poisson equation (6): In equation (6), u(r,z) is the two-dimensional potential distribution, ρ is the space charge, and ε is the dielectric constant of space. S3. Combining the two mapping relationships in S1 and S2, establish the mapping relationship between the performance parameters of the magnetron-controlled injection electron gun and the electron gun electrode shape and solenoid configuration parameters; establish the fitness function f(α, Δβ) for evaluating the electron beam quality. t The performance of the electron gun is optimized by introducing a global optimization algorithm.

2. The method for collaborative optimization design of coil magnet and electron gun in a gyroscopic device as described in claim 1, characterized in that, Step 2, the process of solving for the electron beam trajectory under a given potential distribution u(r,z) includes the following steps: Magnetic field components B in the three directions of S21, x, y, and z x B y B z Simultaneously acting on the electron's directional motion, due to the magnetic force, in the time infinitesimal element dt, the electron velocity vector changes from v n Change to v n+1 ,Right now: v n+1 =v n H (7) H=H x H y H z (8) In the formula: Among them, the magnetic field components B in the x, y, and z directions x B y B z The contribution to the electron's circular motion corresponds to the angular frequency ω in each direction. x ω y ω z ,Right now: Wherein, the electron charge e = 1.6 × 10 -19 C, electron rest mass m0 = 9.1 × 10 -31 kg, where γ is the relativistic factor; S22. The change in electron momentum ΔP caused by the electric field E within the infinitesimal time dt. E for: ΔP E = eE·dt (13) S23. In a combined field where both electric and magnetic fields exist, the total change in momentum ΔP of an electron is: ΔP=ΔP E +ΔP B =eE·dt+m0γv n H-m0γv n (14) Where, ΔP B The change in electron momentum caused by the magnetic field; using the relationship P n =m0γv n and ΔP=P n+1 -P n , where P n P n+1 Let the total momentum at time n and time n+1 be respectively, and we can finally obtain: P n+1 =eE·dt+m0γv n H (15) Equation (15) is the momentum evolution law of electrons in a time infinitesimal element dt in a composite field where electric and magnetic fields coexist. S23. Under relativistic effects, the relationship between the electron's velocity vector and momentum is: Among them, P n+1 For vector P n+1 The amplitude, and the displacement Δs within the electronic time element dt are: Numerical solutions to equations (15)-(17) are used to obtain the trajectory distribution of electrons, and then the performance parameters of the electron gun are evaluated: velocity ratio α and transverse velocity dispersion Δβ. t : In the formula, j represents the electronic serial number, and N e v represents the total number of electrons. r and v z These are the radial and longitudinal velocity components of the electron, respectively.

3. The method for collaborative optimization design of coil magnet and electron gun in a gyroscopic device as described in claim 2, characterized in that, The fitness function f(α,Δβ) t Construct it as follows: Where, α goal χ is the value of the target velocity ratio, and χ is the convergence weighting factor; the design reaches its optimum when the fitness function is minimized.

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