Numerical simulation method for demagnetization behavior and beam dynamics coupling of permanent magnet focusing system

Abstract

The invention discloses a permanent magnet focusing system demagnetization behavior and beam dynamics coupling numerical simulation method, which comprises the following steps: S1, based on various parameters of a Ji les-Atherton hysteresis model, compiling a numerical equation of correlation between the various parameters and a permanent magnet magnetization behavior; s2, by taking electromagnetic field distribution described by a Maxwel l equation set as a medium, compiling a beam dynamic numerical equation under the influence of self-excitation demagnetization of the permanent magnet array based on an electron beam emission model; s3, electromagnetic field distribution is updated according to the electron beam motion trail, and the demagnetization behavior of the permanent magnet array in the cathode working state is updated in combination with input and output coupling terms of the three sets of numerical equations; and S4, establishing a numerical iteration process among all equations, and giving out a jumping condition of demagnetization behavior and beam dynamics coupling calculation by reasonably setting a parameter relative tolerance. According to the method, beam quality degradation caused by demagnetization in a high-power device can be accurately quantified, and a theoretical tool is provided for permanent magnet material type selection, focusing structure optimization and reliability verification.

Description

Technical Field

[0001] The present invention belongs to the technical field of vacuum electronic device design and numerical simulation, and in particular relates to a numerical simulation method for coupling demagnetization behavior and beam dynamics of a permanent magnet focusing system. Background Art

[0002] Permanent magnet focusing systems (PPMs) are widely used for beam control in vacuum electron devices due to their advantages, such as requiring no external power supply and having a compact structure. However, under high-power, long-pulse, or high-temperature conditions, permanent magnets (such as NdFeB) are prone to irreversible demagnetization, leading to magnetic field distortion, which in turn causes serious problems such as beam divergence and reduced transmission efficiency. Traditional design methods often assume a constant magnetic field in the permanent magnet or use a linear demagnetization model, ignoring hysteresis effects and the dynamic demagnetization-beam coupling mechanism. Specifically, the insufficient accuracy of the demagnetization model makes it impossible for the linear model to represent the nonlinear characteristics of the hysteresis loop (such as the pinning effect and reversible / irreversible magnetization components), resulting in inaccurate predictions of the magnetic field attenuation. The reverse demagnetization effect of the beam space charge field on the permanent magnet is not considered, resulting in a lack of dynamic coupling and an underestimated magnetic field attenuation under extreme conditions. The static magnetic field assumption forces the use of excessively large permanent magnet sizes or higher coercivity materials, leading to conservative designs and increased cost and volume.

[0003] In the existing technology, for example, patent CN116110760B, "A magnetic field optimization method for a permanent magnet focusing system," uses the equivalent magnetic charge method to calculate the static magnetic field distribution, but does not involve the dynamic demagnetization process. The beam-magnetic field unidirectional coupling model proposed in the literature "Research on Solenoidal Permanent Magnet for Guiding and Focusing Annular Electron Beams" [LI LK, CHENG JS, QIULIANG W. Research on Solenoidal Permanent Magnet for Guiding and Focusing Annular Electron Beams [J]. Ieee Transactions on Plasma Science, 2021, 49 (7): 2093-8.], although introducing the space charge effect, still assumes that the permanent magnet parameters are fixed. Such methods have difficulty accurately predicting the evolution of the magnetization state of the permanent magnet under high-temperature and strong-field conditions of the cathode, resulting in significant errors in device life and performance evaluation. Summary of the Invention

[0004] In order to solve the above technical problems, a technical solution adopted by the present invention is:

[0005] A method for numerically simulating the coupling between demagnetization behavior and beam dynamics of a permanent magnet focusing system comprises the following steps:

[0006] S1): Based on the parameters of the Jiles-Atherton hysteresis model, develop numerical equations that relate these parameters to the magnetization behavior of the permanent magnet.

[0007] The following parameters are defined: Ms: saturation magnetization; α: interdomain coupling factor; a: shape parameter; k: hysteresis loss coefficient; c: magnetization reversibility coefficient;

[0008] The JA hysteresis model describes the nonlinear evolution of the permanent magnet magnetization M with the magnetic field H through the following differential equation: e =H ext +αM, where H e is the effective magnetic field, H ext is the external magnetic field;

[0009] S2): Using the electromagnetic field distribution described by Maxwell's equations as a medium, the numerical equations of the beam dynamics under the influence of self-excited demagnetization of the permanent magnet array are written based on the electron beam emission model;

[0010] The specific steps include:

[0011] S21): Calculate the demagnetization behavior through the dynamic correction magnetization intensity M of the JA hysteresis model, where M = M × e (x, y, z), specifically

[0012]

[0013] Where, J ext is the external current density, M is calculated by the JA dynamic hysteresis model in step 1;

[0014] S22): Calculate the transverse magnetic field gradient of the periodic focusing magnetic field of the permanent magnet array

[0015]

[0016] Where λ is the period length of the permanent magnet array, B0 is the peak magnetic field intensity;

[0017] S23): Calculate the B0 attenuation caused by demagnetization

[0018]

[0019] Where, δ De (t) is the dynamic nonlinear demagnetization rate, which is output by the JA hysteresis model;

[0020] S24): Calculate the single-particle Lorentz force in the initial phase space

[0021]

[0022] Where, γ=sqrt(1+|P| 2 / m e 2 c 2 ) is the relativistic factor, E=E 加速场 +E 空间电荷 ;

[0023] S25): Using the quasi-static approximation, the space charge field is obtained by solving the Poisson equation

[0024]

[0025] Where the charge density ρ is calculated by particle simulation method;

[0026] S26): Combining the demagnetization effect of the permanent magnet focusing field and the space charge force, the transverse beam envelope evolution equation and the radial envelope equation are obtained.

[0027]

[0028] The third term in the equation is the space charge divergence force, and the fourth term is the emittance constraint term;

[0029] S27): Calculate the effect of permanent magnet array demagnetization on beam dynamics using a self-consistent field iterative algorithm;

[0030] S28): Finite element method is used to discretize Maxwell equations to ensure discretization and stability control, and Boris algorithm is used to push particles.

[0031] The grid size must meet the following requirements:

[0032] The time step must satisfy:

[0033] S29): Dynamically adjust the radial grid size Δz according to the beam envelope curvature:

[0034]

[0035] S3): Update the electromagnetic field distribution according to the electron beam trajectory, and update the demagnetization behavior of the permanent magnet array in the cathode working state by combining the input and output coupling terms of the three sets of numerical equations;

[0036] In step 3, a dynamic coupling iterative algorithm is introduced to describe the mutual influence between the demagnetization behavior of the permanent magnet array and the beam dynamics behavior, which specifically includes the following steps:

[0037] S31): Loading non-demagnetizing magnetic field B 0 , initialize the beam distribution f(x,y,p,0);

[0038] S32): Realize synchronous advancement of field and beam;

[0039] S4): Establish a numerical iterative process between the equations and give the exit conditions for the coupled calculation of demagnetization behavior and beam dynamics by reasonably setting the relative tolerance of the parameters.

[0040] Furthermore, the step 1 is specifically divided into the following steps:

[0041] S11): Calculate the magnetization intensity Man under the condition of no hysteresis by the Langevin function description formula:

[0042]

[0043] S12): Calculate the irreversible magnetization M irr

[0044]

[0045] Where δ is the direction factor, δ = sign (dH / dt);

[0046] S13): Calculate the total magnetization intensity M

[0047] M=(1-c)M irr +cM an

[0048] S13): The magnetization intensity M irr The evolution formula uses the Euler method or Runge-Kutta method to discretize the differential equation, iteratively update Mirr and M

[0049]

[0050] When the local magnetic field H local =H ext +H demag When the coercivity is lower than Hc, the irreversible demagnetization calculation is triggered.

[0051] Furthermore, the charge density ρ in step 25 is specifically expressed as

[0052]

[0053] Where I is the electron injection current, v z ≈βc is the longitudinal velocity of the electron.

[0054] Furthermore, the specific steps of step 27 are as follows:

[0055] S271): Calculate the initial magnetic field B based on the parameters of the non-demagnetized permanent magnet 0 , and solve the electron trajectory by particle tracking, and calculate the spatial charge density ρn , calculate the space charge field E n and the space magnetic field H n ;

[0056] S272): Call JA hysteresis model to update M n With B n+1 , if max|B n+1 -B n ∣<ε B And the beam envelope change rate Δσ x，y / σ x，y <ε σ , the iteration is terminated; otherwise, return to step 2 and solve again.

[0057] Furthermore, based on step 2, considering that the strong electric field and thermal effect on the cathode surface lead to the aggravation of local demagnetization, it is necessary to introduce the temperature-dependent JA hysteresis parameter correction formula

[0058]

[0059] Where T is the cathode surface temperature, calculated by the heat conduction model; κ is the saturation magnetization temperature coefficient, T c is the characteristic temperature of hysteresis loss.

[0060] Furthermore, the step 32 specifically includes

[0061] S321): Solve the beam phase space evolution through particle tracking and output the charge density ρ n and current density J n ;

[0062] S322): Solve the Poisson equation to update the space charge field E space n , calculate its equivalent demagnetizing field on the permanent magnet:

[0063]

[0064] S323): The total external magnetic field H ext n =H inital n +H space n Input JA hysteresis model and update magnetization M n+1 ;

[0065] S324): Solve Maxwell's equations to obtain the new magnetic field Bn+1, and map it to the beam solver grid;

[0066] S325): Convergence judgment is performed. If

[0067]

[0068] Then the iteration is terminated; otherwise, let n←n+1 and return to step 321.

[0069] Furthermore, in step 3, for the dynamic coupling iterative algorithm, in order to avoid numerical divergence, a relaxation factor ω (0.5<ω<1) is introduced into the magnetic field update:

[0070] B n+1 =ωB new +(1-ω)B n

[0071] At the same time, the iteration step size Δt is dynamically adjusted according to the residual change rate:

[0072]

[0073] The singular points in the space charge field are smoothed to ensure the stability of the magnetic field solution.

[0074] Beneficial effects of the present invention:

[0075] 1. This invention quantitatively links the JA hysteresis model with the demagnetization behavior of a permanent magnet focusing system for the first time, resolving the inability of traditional linear models to describe irreversible demagnetization and hysteresis losses. Combined with measured parameters of the permanent magnet array, this method accurately simulates the magnetization state evolution of the permanent magnet under dynamic operating conditions, providing high-fidelity magnetic field input for subsequent coupled beam dynamics. Compared to the traditional static magnetic field assumption, this method can quantitatively predict the following effects:

[0076] (1) Beam envelope oscillation caused by demagnetization: The magnetic field gradient decay causes insufficient focusing force, resulting in periodic expansion of the beam radius;

[0077] (2) Space charge accelerated demagnetization: The reverse magnetic field generated by the high current beam intensifies the irreversible demagnetization of the permanent magnet;

[0078] (3) Emittance growth: The synergistic effect of demagnetization and space charge force leads to an increase in the spatial volume of the beam phase.

[0079] 2. Compared with the traditional unidirectional field-beam coupling method, this scheme can achieve high-fidelity dynamic feedback by accurately capturing the accelerating effect of the space charge field on demagnetization, avoiding the optimistic calculation of the magnetic field; and simultaneously optimizing the permanent magnet material parameters (M s ,k, etc.), focusing period (λ) and beam parameters (I, ε n ) can realize multi-parameter collaborative optimization, thereby improving device reliability; at the same time, by simulating the time-varying curve of the demagnetization rate, it can warn of the critical point of irreversible demagnetization of the permanent magnet and guide the formulation of maintenance strategies.

[0080] 3. The numerical simulation method of coupling demagnetization behavior with beam dynamics in the present invention provides a key theoretical tool for the long-life design of vacuum electronic devices, and is particularly suitable for scenarios such as high-power traveling wave tubes and electron guns that have strict requirements on magnetic field stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0082] Figure 1 This is a schematic diagram of the numerical simulation process of the coupling between demagnetization behavior and beam dynamics of the present invention;

[0083] Figure 2 This is a schematic diagram of the model of Example 1 of the present invention;

[0084] Figure 3 is a grid schematic diagram of Example 1 of the present invention;

[0085] Figure 4 It is a schematic diagram of important simulation parameters of the present invention;

[0086] Figure 5 is a reference legend of the simulation parameters of the present invention;

[0087] Figure 6 The difference between the calculation results of electromagnetic field and beam dynamics between the traditional numerical algorithm and the improved algorithm of this embodiment;

[0088] Figure 7 It is the calculation result of magnetization and magnetic field by traditional algorithm;

[0089] Figure 8 is the calculation result of magnetization and magnetic field by the improved algorithm of this embodiment;

[0090] Figure 9 Beam dynamics calculation results of traditional algorithms;

[0091] Figure 10 This is the beam dynamics calculation result of the improved algorithm of this embodiment. DETAILED DESCRIPTION

[0092] The preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more precise definition of the protection scope of the present invention. Specific embodiment 1:

[0094] like Figures 1 to 10 As shown, a numerical simulation method for coupling demagnetization behavior and beam dynamics of a permanent magnet focusing system includes the following steps:

[0095] Step 1: Explain the physical meaning of the parameters of the Jiles-Atherton hysteresis model and write numerical equations related to the parameters and the magnetization behavior of the permanent magnet;

[0096] Step 2: Using the electromagnetic field distribution described by Maxwell's equations as a medium, a numerical equation for the beam dynamics under the influence of self-excited demagnetization of the permanent magnet array is written based on the electron beam emission model;

[0097] Step 3: Update the electromagnetic field distribution according to the electron beam motion trajectory, and update the demagnetization behavior of the permanent magnet array in the cathode working state by combining the input and output coupling terms of the three sets of numerical equations;

[0098] Step 4: Establish a numerical iteration process between the equations and give the exit condition of the demagnetization behavior-beam dynamics coupling calculation by reasonably setting the relative tolerance of the parameters.

[0099] As a key theoretical model in the coupled calculation, in step 1, the numerical equations included in the Jiles-Atherton hysteresis constitutive model are first established based on five basic parameters:

[0100] The Jiles-Atherton hysteresis model describes the hysteresis behavior of permanent magnets using the following five parameters, each of which is directly related to the magnetic domain dynamics and energy dissipation mechanism:

[0101] Five parameters of Jiles-Atherton hysteresis constitutive model

[0102]

[0103] Based on the above parameters, the JA hysteresis model describes the nonlinear evolution of the permanent magnet magnetization M with the magnetic field H through the following differential equation. First, the effective magnetic field H e By the external magnetic field H ext and the interdomain demagnetization field determine:

[0104] H e =H ext +αM (1)

[0105] Where αM represents the demagnetization effect caused by the coupling between magnetic domains, which directly affects the magnetization direction and intensity. Assuming no hysteresis, the magnetization intensity M an Described by the Langevin function:

[0106]

[0107] Or simplified to:

[0108]

[0109] This function reflects the ideal lossless magnetization process and is the central reference line of the hysteresis loop. irr The evolution of is dominated by the pinning effect, satisfying:

[0110]

[0111] Where δ is the direction factor (δ = sign (dH / dt)), which ensures the closure of the hysteresis loop; the denominator δk-α (M an -M irr ) reflects the dynamic balance between the pinning effect and the demagnetization field. The total magnetization intensity M is the weighted sum of the irreversible component and the reversible component:

[0112] M=(1-c)M irr +cM an (4)

[0113] The reversibility coefficient c controls the proportion of reversible behavior during the magnetization process and directly affects the recovery characteristics of the magnetization state after demagnetization. For equation (4), the Euler method or Runge-Kutta method is used to discretize the differential equation and iteratively update M irr The discretized numerical form of the M,JA hysteresis model is expressed as:

[0114]

[0115] When the local magnetic field H local =H ext +H demag Lower than the coercive force H c , the irreversible demagnetization calculation is triggered.

[0116] Secondly, in step 2, the magnetic field distribution of the permanent magnet focusing system is determined by Maxwell's static magnetic field equation and the material constitutive relationship. The demagnetization behavior is dynamically corrected by the JA hysteresis model to obtain the magnetization intensity M (M = M × e (x, y, z)). The specific equation is as follows:

[0117]

[0118] Where, J ext is the external current density (the electron beam current contribution can be ignored, and only the spontaneous demagnetization of the permanent magnet is considered). M is calculated by the JA dynamic hysteresis model in step 1, reflecting the demagnetization effect. The periodic focusing magnetic field of the permanent magnet array is distributed along the beam propagation direction (z-axis), and the transverse magnetic field gradient is:

[0119]

[0120] Where λ is the period length of the permanent magnet array and B0 is the peak magnetic field strength. The attenuation of B0 caused by demagnetization can be described as:

[0121]

[0122] Where, δ De (t) is the dynamic nonlinear demagnetization rate, which is output by the JA hysteresis model. Considering the electron beam emitted by the hot cathode, the initial phase space distribution obeys the Gaussian distribution. The dynamic equation includes the single-particle Lorentz force equation and the space charge field calculation. The single-particle Lorentz force equation is described as:

[0123]

[0124] Where, γ=sqrt(1+|P| 2 / m e 2 c 2 ) is the relativistic factor, E=E 加速场 +E 空间电荷 Using the quasi-static approximation, the space charge field is obtained by solving the Poisson equation:

[0125]

[0126] The charge density ρ is calculated by the particle simulation (Particle In Cell, PIC) method and can be expressed as:

[0127]

[0128] Where I is the electron injection current, v z ≈βc is the electron longitudinal velocity. Combining the demagnetization effect of the permanent magnetic focusing field and the space charge force, the transverse beam envelope evolution equation can be described as the decrease in equivalent focusing intensity caused by the attenuation of the magnetic field gradient:

[0129]

[0130] As well as the expansion of the radial envelope, the envelope equation σ x,y (z) Satisfy:

[0131]

[0132] The third term in the equation is the space charge divergence force, and the fourth term is the emittance constraint term. The self-consistent field iteration algorithm is used to calculate the effect of permanent magnet array demagnetization on beam dynamics. First, the initial magnetic field B is calculated based on the parameters of the non-demagnetized permanent magnets. 0 , and solve the electron trajectory by particle tracking, and calculate the spatial charge density ρ n , calculate the space charge field E n and the space magnetic field H n, then call JA hysteresis model to update M n With B n+1 , if max|B n+1 -B n ∣<ε B And the beam envelope change rate Δσ x，y / σ x，y <ε σ , the iteration is terminated; otherwise, return to step 2 and solve again.

[0133] In terms of discretization and stability control, the finite element method is used to discretize the Maxwell equations, and the grid size must meet the following requirements:

[0134]

[0135] When using the Boris algorithm to push particles, the time step must meet the following requirements:

[0136]

[0137] Secondly, the radial grid size Δz is dynamically adjusted according to the beam envelope curvature:

[0138]

[0139] Based on step 2, considering that the strong electric field and thermal effect on the cathode surface lead to aggravated local demagnetization, it is necessary to introduce temperature-dependent JA hysteresis parameter correction:

[0140]

[0141] Where T is the cathode surface temperature, calculated by the heat conduction model; κ is the saturation magnetization temperature coefficient, T c is the characteristic temperature of hysteresis loss. A dynamic coupling iterative algorithm is introduced to describe the mutual influence between the demagnetization behavior of the permanent magnet array and the beam dynamics behavior. First, the non-demagnetization magnetic field B is loaded. 0 , initialize the beam distribution f(x,y,p,0), and then achieve field-beam synchronization through five specific sub-steps. In sub-step 321, solve the beam phase space evolution through particle tracking and output the charge density ρ n and current density J n In sub-step 322, solve the Poisson equation to update the space charge field E space n , calculate its equivalent demagnetizing field on the permanent magnet:

[0142]

[0143] In sub-step 323, the total external magnetic field H ext n =H inital n+H space n Input JA hysteresis model and update magnetization M n+1 ; In step 324, solve Maxwell's equations to obtain the new magnetic field B n+1 , mapped to the beam solver grid; in step 325, perform convergence judgment, if

[0144]

[0145] Then the iteration is terminated; otherwise, let n←n+1 and return to step 321. For the dynamic coupling iterative algorithm, in order to avoid numerical divergence, a relaxation factor ω (0.5<ω<1) is introduced into the magnetic field update, and:

[0146] B n+1 =ωB new +(1-ω)B n (20)

[0147] At the same time, the iteration step size Δt is dynamically adjusted according to the residual change rate:

[0148]

[0149] The singular points in the space charge field are smoothed to ensure the stability of the magnetic field solution.

[0150] Step 4 is based on the reasonable connection between Step 1, Step 2 and Step 3. Through the iterative exchange of input and output between the above numerical equations, the specific demagnetization behavior-beam dynamics coupling calculation is realized. The details can be seen in Figure 1 .

[0151] This embodiment is achieved by Figure 2 The physical model and finite element mesh shown are Figure 2 The Halbach magnetic focusing example of the JA hysteresis model parameters and beam dynamics parameters shown is as follows Figure 1 The technical route shown was numerically calculated, and the results of the demagnetization behavior-beam dynamics coupling numerical simulation were compared with the results obtained by traditional linear demagnetization beam dynamics calculation. The comparison results are shown in the figure. Figures 5-10 As shown in the figure, it is observed that under the method proposed in this paper, the radial magnetization array undergoes obvious nonlinear demagnetization, which causes the magnetic field at the center to attenuate by about 6%. At the same time, the magnetic flux density distribution is more uneven than the traditional calculation results, which leads to a significant increase in the beam radius. The contraction-expansion beam under the traditional method is transformed into an expansion-contraction beam under the existing method.

[0152] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's description and drawings, or directly or indirectly applied to other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A numerical simulation method for coupling demagnetization behavior and beam dynamics of a permanent magnet focusing system, characterized by: The following steps are involved: S1): Based on the parameters of the Jiles-Atherton hysteresis model, develop numerical equations that relate these parameters to the magnetization behavior of the permanent magnet. The following parameters are defined: Ms: saturation magnetization; α: interdomain coupling factor; a: shape parameter; k: hysteresis loss coefficient; c: magnetization reversibility coefficient; The JA hysteresis model describes the nonlinear evolution of the permanent magnet magnetization M with the magnetic field H through the following differential equation: e =H ext +αM, where H e is the effective magnetic field, H ext is the external magnetic field; S2): Using the electromagnetic field distribution described by Maxwell's equations as a medium, the numerical equations of the beam dynamics under the influence of self-excited demagnetization of the permanent magnet array are written based on the electron beam emission model; The specific steps include: S21): Calculate the demagnetization behavior through the dynamic correction magnetization intensity M of the JA hysteresis model, where M = M × e (x, y, z), specifically Where, J ext is the external current density, M is calculated by the JA dynamic hysteresis model in step 1; S22): Calculate the transverse magnetic field gradient of the periodic focusing magnetic field of the permanent magnet array Where λ is the period length of the permanent magnet array, B0 is the peak magnetic field intensity; S23): Calculate the B0 attenuation caused by demagnetization B0(t)=B0(inital)·(1-δ De (t)), Where, δ De (t) is the dynamic nonlinear demagnetization rate, which is output by the JA hysteresis model; S24): Calculate the single-particle Lorentz force in the initial phase space Where, γ=sqrt(1+|P| 2 / m e 2 c 2 ) is the relativistic factor, E=E 加速场 +E 空间电荷 ; S25): Using the quasi-static approximation, the space charge field is obtained by solving the Poisson equation Where the charge density ρ is calculated by particle simulation method; S26): Combining the demagnetization effect of the permanent magnet focusing field and the space charge force, the transverse beam envelope evolution equation and the radial envelope equation are obtained. The third term in the equation is the space charge divergence force, and the fourth term is the emittance constraint term; S27): Calculate the effect of permanent magnet array demagnetization on beam dynamics using a self-consistent field iterative algorithm; S28): Finite element method is used to discretize Maxwell equations to ensure discretization and stability control, and Boris algorithm is used to push particles. The grid size must meet the following requirements: The time step must satisfy: S29): Dynamically adjust the radial grid size Δz according to the beam envelope curvature: S3): Update the electromagnetic field distribution according to the electron beam trajectory, and update the demagnetization behavior of the permanent magnet array in the cathode working state by combining the input and output coupling terms of the three sets of numerical equations; In step 3, a dynamic coupling iterative algorithm is introduced to describe the mutual influence between the demagnetization behavior of the permanent magnet array and the beam dynamics behavior, which specifically includes the following steps: S31): Loading non-demagnetizing magnetic field B 0 , initialize the beam distribution f(x,y,p,0); S32): Realize synchronous advancement of field and beam; S4): Establish a numerical iterative process between the equations and give the exit conditions for the coupled calculation of demagnetization behavior and beam dynamics by reasonably setting the relative tolerance of the parameters.

2. The method for numerically simulating the coupling between demagnetization behavior and beam dynamics of a permanent magnet focusing system according to claim 1, characterized in that: The step 1 is specifically divided into the following steps S11): Calculate the magnetization intensity Man under the condition of no hysteresis by the Langevin function description formula: or S12): Calculate the irreversible magnetization M irr Where δ is the direction factor, δ = sign (dH / dt); S13): Calculate the total magnetization intensity M M=(1-c)M irr +cM an S13): The magnetization intensity M irr The evolution formula uses the Euler method or Runge-Kutta method to discretize the differential equation, iteratively update Mirr and M When the local magnetic field H local =H ext +H demag When the coercivity is lower than Hc, the irreversible demagnetization calculation is triggered.

3. The method for numerically simulating the coupling between demagnetization behavior and beam dynamics of a permanent magnet focusing system according to claim 1, characterized in that: The charge density ρ in step 25 is specifically expressed as Where I is the electron injection current, v z ≈βc is the longitudinal velocity of the electron.

4. The method for numerically simulating the coupling between demagnetization behavior and beam dynamics of a permanent magnet focusing system according to claim 1, characterized in that: The specific steps of step 27 are as follows: S271): Calculate the initial magnetic field B based on the parameters of the non-demagnetized permanent magnet 0 , and solve the electron trajectory by particle tracking, and calculate the spatial charge density ρ n , calculate the space charge field E n and the space magnetic field H n ; S272): Call JA hysteresis model to update M n With B n+1 , if max|B n+1 -B n ∣<ε B And the beam envelope change rate Δσ x，y / σ x，y <ε σ , the iteration is terminated; otherwise, return to step 2 and solve again.

5. The method for numerically simulating the coupling between demagnetization behavior and beam dynamics of a permanent magnet focusing system according to claim 1, characterized in that: Based on step 2, considering that the strong electric field and thermal effect on the cathode surface lead to the aggravation of local demagnetization, it is necessary to introduce the temperature-dependent JA hysteresis parameter correction formula Where T is the cathode surface temperature, calculated by the heat conduction model; κ is the saturation magnetization temperature coefficient, T c is the characteristic temperature of hysteresis loss.

6. The method for numerically simulating the coupling between demagnetization behavior and beam dynamics of a permanent magnet focusing system according to claim 1, characterized in that: The step 32 specifically includes S321): Solve the beam phase space evolution through particle tracking and output the charge density ρ n and current density J n ; S322): Solve the Poisson equation to update the space charge field E space n , calculate its equivalent demagnetizing field on the permanent magnet: S323): The total external magnetic field H ext n =H inital n +H space n Input JA hysteresis model and update magnetization M n+1 ; S324): Solve Maxwell's equations to obtain the new magnetic field Bn+1, and map it to the beam solver grid; S325): Convergence judgment is performed. If Then the iteration is terminated; otherwise, let n←n+1 and return to step 321.

7. The method for numerically simulating the coupling between demagnetization behavior and beam dynamics of a permanent magnet focusing system according to claim 6, characterized in that: In step 3, for the dynamic coupling iterative algorithm, in order to avoid numerical divergence, a relaxation factor ω (0.5<ω<1) is introduced for the magnetic field update: B n+1 =ωB new +(1-ω)B n At the same time, the iteration step size Δt is dynamically adjusted according to the residual change rate: The singular points in the space charge field are smoothed to ensure the stability of the magnetic field solution.

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