A space charge limited current calculation method, device and storage medium

Abstract

The present invention discloses a method, device and storage medium for calculating space charge limited current, wherein the method comprises: S1, determining the structural model between the cathode metal plate and the anode dielectric plate; S2, using two current density values ​​as inputs of the Poisson trajectory process, calculating the amount of charge injected per unit time, and calculating the amount of charge in the process of calculating the electron trajectory and depositing it on the grid; S3, obtaining the potential distribution, and solving the electric field of each point by polynomial fitting through the extrapolation process according to the electric field definition; S4, using the secant method to obtain the updated current density, and obtaining the input current density of the next Poisson trajectory process according to the current density; S5, outputting the final current density distribution. The present invention provides a space charge limited current calculation scheme for a non-parallel plate structure, iteratively solves the electron motion trajectory in the process of calculating the electron trajectory, explores the motion law of particles under the influence of space charge, and can be widely used in the field of electronic devices.

Description

Technical Field

[0001] The present invention relates to the field of vacuum electronic devices, and in particular to a space charge limited current calculation method, device and storage medium. Background Art

[0002] Space charge limited current is a basic physical phenomenon in vacuum electronic devices. Under the action of heat or external electric field, the electrons on the cathode surface will gain energy. When the energy gained is greater than the work function of the cathode surface, electrons will escape across the potential barrier. Under the action of the space electric field force, the electrons move from the cathode to the anode, forming a space current. As electrons are continuously emitted from the cathode plate into the vacuum area, the space current gradually increases, and the electric field generated by the space current will balance the electric field generated by the potential difference between the two plates. In this process, the electric field on the cathode surface will gradually approach zero. When the electric field on the cathode surface is equal to zero, the electrons cannot obtain enough energy to cross the potential barrier, and no more electrons escape from the cathode surface. As a result, the space charge limits the output of the current, and the current eventually reaches stability and can no longer continue to increase. The current at this time is called space charge limited current.

[0003] The space charge limited current phenomenon is more obvious in thermionic energy converters, because the device is a vacuum diode device that directly converts thermal energy into electrical energy. Related applications generally reduce the influence of space charge effect by adding ions. For the one-dimensional case, the size of the space charge limited current can be solved by analytical methods, but for non-one-dimensional cases, it is more difficult to solve the multi-dimensional nonlinear Poisson equation. The existing numerical methods for calculating the space charge limited current have the following shortcomings: first, only the case of parallel plate structure is considered, and no calculation method is given for the case of non-parallel plate structure; second, it is impossible to explore the movement law of particles under the influence of space charge. Summary of the invention

[0004] In order to solve at least one of the technical problems existing in the prior art to a certain extent, the present invention aims to provide a method, device and storage medium for calculating space charge limited current applied to a non-parallel plate structure.

[0005] The technical solution adopted by the present invention is:

[0006] A space charge limited current calculation method comprises the following steps:

[0007] S1, determine the structural model between the cathode metal plate and the anode dielectric plate, and determine two initial current density values ​​J1 and J2;

[0008] S2, using the two current density values ​​J1 and J2 as inputs of the Poisson trajectory process, calculating the amount of charge injected per unit time, and calculating the amount of charge in the process of calculating the electron trajectory and depositing it on the grid, iterating until the charge distribution converges;

[0009] S3. After the Poisson trajectory process converges, the potential distribution V is obtained, and the electric field E at each point is solved by polynomial fitting through the extrapolation process according to the electric field definition;

[0010] S4. After the Poisson trajectory process converges, the updated current density J is obtained using the secant method. * , according to the current density J * Obtain the input current density of the next Poisson trajectory process, and repeat steps S2-S3 until the current density converges;

[0011] S5. Output the final current density distribution J.

[0012] Further, the determining of the structural model between the cathode metal plate and the anode dielectric plate includes:

[0013] Determine the length L of the plate and the width W of the emission area, extend the non-parallel cathode metal plate and anode dielectric plate in the opposite direction and intersect at point O, take point O as the origin, and the straight line where the surface of the anode dielectric plate is located as the x-axis to establish a two-dimensional Cartesian coordinate system. The angle between the two plates is recorded as θ, the distance from the midpoint of the cathode metal plate emission area to the origin of the coordinate is recorded as R, and the potential difference between the cathode metal plate and the anode dielectric plate is V g .

[0014] Furthermore, the electric field lines in the non-parallel plate structure are perpendicular to the equipotential lines. The cylindrical coordinates of the non-parallel plate structure model are expressed as:

[0015] x=r*cosθ, y=r*sinθ, z=z,

[0016] Among them, r is the distance from the calculation point to the origin of the coordinate system, θ is the angle between the cathode metal plate and the anode dielectric plate, z is the axial coordinate, the cylindrical coordinate is three-dimensional, z=z is the parametric equation for converting rectangular coordinates to cylindrical coordinates; x and y are the cross-sectional coordinates of the calculation point, the cylindrical coordinates are the same as the Cartesian coordinates z, except that the cross-sectional coordinates are converted to polar coordinates;

[0017] The transformation results in the following equation relationship:

[0018]

[0019] The charge density is zero outside the preset effective emission region:

[0020]

[0021] In the formula, θc Indicates the polar angle value corresponding to the cathode plate, J(r, θ c ) represents the coordinates (r, θ c ), R represents the distance from the middle point of the emission area of ​​the cathode metal plate to the origin of the coordinate system, and W represents the width of the emission area.

[0022] Furthermore, there is a vacuum between the cathode metal plate and the anode dielectric plate, and step S2 specifically includes:

[0023] In the Poisson trajectory process, the first iteration uses the finite difference method to solve the Laplace equation to obtain the vacuum potential distribution, and the vacuum electric field is obtained based on the vacuum potential distribution. Based on the vacuum electric field, the electron trajectory without considering the space charge effect is calculated by solving the Newtonian equation of motion;

[0024] In the process of calculating the electron trajectory, the particle grid method is used to calculate the charge through the particle motion trajectory and position weighting and deposit it on the grid to obtain the initial charge density distribution ρ old , use the initial charge density to solve Poisson's equation in the second iteration using the finite difference method to obtain an updated potential field, which will give an updated electric field. Use the updated electric field to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ * ;

[0025] In subsequent iterations, according to the charge density distribution ρ * Get the updated charge density distribution ρ new , repeat the Poisson trajectory process and the electron trajectory calculation process until the charge density distribution ρ converges.

[0026] Furthermore, the charge density distribution ρ is related to the potential difference V between the two plates. g The relationship between charge density and charge is:

[0027]

[0028] Where dV is the unit volume element, dQ is the charge per unit volume element, and the current flowing through the unit area element dS is I. The relationship between I and current density J is:

[0029] I=J*dS

[0030] Because the relationship between dQ and current is:

[0031] dQ=I*dt

[0032] In cylindrical coordinates, the equations for the unit area element dS and the unit volume element dV in cylindrical coordinates are as follows:

[0033] dS=dr*dz, dV=r*dθ*dr*dz,

[0034] Combining the above equations, we can get:

[0035]

[0036] Furthermore, the Poisson trajectory process and the process of calculating the electron trajectory are specifically as follows:

[0037] Using cylindrical coordinates to express the Poisson equation gives the following form:

[0038]

[0039] Where ε0 is the dielectric constant of vacuum;

[0040] Assuming that electrons are emitted uniformly in the z direction, we can obtain:

[0041]

[0042] Poisson's equation simplifies to:

[0043]

[0044] Assume that the polar angle corresponding to the surface boundary of the dielectric anode is 0, and the polar angle corresponding to the surface boundary of the metal cathode is θ c , the boundary conditions for solving Poisson's equation are as follows:

[0045] V(r,θ)=0 forθ=θ c ,

[0046] V(r,θ)=V g for θ=0,

[0047]

[0048] In order to facilitate numerical calculation using the finite difference method, the Poisson equation is transformed into a discrete difference equation form, which is as follows:

[0049]

[0050] The equation is simplified computationally to obtain the expression for updating V(i, j). For the first iteration of the Poisson trajectory process, the finite difference method is used to solve the Laplace equation:

[0051]

[0052] The vacuum potential distribution is obtained, and the electric field at each point is solved according to the electric field definition. These vacuum electric fields are used to calculate the electron trajectory by solving Newton's equations of motion. Assume that the electric fields along the x and y directions are Ex and E y , then Newton's equation of motion is as follows:

[0053]

[0054] Assume that the electric fields along the r direction and the θ direction are E r and E θ , then the electric field transformation relationship between the Cartesian coordinate system and the cylindrical coordinate system is as follows:

[0055]

[0056] Taking the partial derivatives of x and y with respect to r and θ respectively, we get:

[0057]

[0058] In the process of solving the electron trajectory by the first Poisson trajectory iteration in the vacuum electric field, the initial charge density distribution ρ is obtained by depositing the particle charge weighted calculation onto the grid through the particle-grid method. old , and then the initial charge density is used to solve the Poisson equation in the next Poisson trajectory iteration to obtain an updated potential field; the updated potential field will give an updated electric field, and then the updated electric field is used to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ * ; Repeat the Poisson trajectory iteration until convergence, and obtain the updated charge density ρ before each iteration new :

[0059] ρ new =0.9*ρ old +0.1*ρ *

[0060] Furthermore, after the Poisson trajectory process converges, the potential distribution V is obtained, and the electric field E at each point is solved by polynomial fitting through an extrapolation process according to the electric field definition, including:

[0061] E(θ)=Aθ 2 +Bθ+C

[0062] In the formula, A, B, and C are all unknown coefficients, so the three electric field values ​​closest to the cathode are needed to determine the values ​​of A, B, and C. The extrapolation process obtains the potential values ​​at the three nearest grid points from the cathode surface, where the electric field value is defined as the electric field value between two adjacent nodes:

[0063]

[0064] E(θ c -Δθ)=A(θ c -Δθ) 2 +B(θc -Δθ)+C,

[0065]

[0066] By fitting the function, the electric field value is calculated for each grid point of the cathode, and the cathode boundary electric field distributions E1 and E2 are obtained.

[0067] Furthermore, in step S4, for the electron emission model of the infinite electron emission source, it is assumed that the metal plate cathode can provide a sufficiently high current density so as to push the electric field intensity to zero in all electron emission regions, that is:

[0068]

[0069] Use the secant method to get the updated current density J * :

[0070]

[0071] Repeat the iteration until the current density J converges, and obtain the updated charge density before each iteration:

[0072] J new =0.9*J old +0.1*J *

[0073] J * is the predicted current density value. Through the iterative formula, the current density is predicted for each grid point of the cathode to obtain the cathode current density distribution. The whole process is repeated until the current density converges to output the current density J.

[0074] Another technical solution adopted by the present invention is:

[0075] A space charge limited current calculation method and device, comprising:

[0076] at least one processor;

[0077] at least one memory for storing at least one program;

[0078] When the at least one program is executed by the at least one processor, the at least one processor implements the above method.

[0079] Another technical solution adopted by the present invention is:

[0080] A computer-readable storage medium stores a program executable by a processor, wherein the program executable by the processor is used to execute the method described above when executed by the processor.

[0081] The beneficial effects of the present invention are as follows: the present invention provides a space charge limited current calculation scheme for a non-parallel plate structure, iteratively solves the electron motion trajectory in the process of calculating the electron trajectory, and explores the motion law of particles under the influence of space charge. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the embodiments of the present invention or the drawings of related technical solutions in the prior art are introduced below. It should be understood that the drawings introduced below are only for the convenience of clearly describing some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0083] Figure 1 is a schematic diagram of electron emission using a non-parallel plate structure according to an embodiment of the present invention;

[0084] Figure 2 is a calculation flow chart of a space charge limited current calculation method according to an embodiment of the present invention;

[0085] Figure 3 is a schematic diagram of the convergence process of cathode electric field and current density distribution during the application iteration process of an embodiment of the present invention;

[0086] Figure 4 It is a schematic diagram of electron trajectories and equipotential lines during the application process of an embodiment of the present invention. DETAILED DESCRIPTION

[0087] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limitations of the present invention. For the step numbers in the following embodiments, they are only provided for the convenience of explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0088] In the description of the present invention, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., and orientations or positional relationships indicated are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0089] In the description of the present invention, "several" means one or more, "more" means more than two, "greater than", "less than", "exceed" etc. are understood as not including the number itself, and "above", "below", "within" etc. are understood as including the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0090] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0091] like Figure 1 Schematic diagram of electron emission of the non-parallel plate structure shown in the figure, given the plate length L and the emission area width W, the non-parallel cathode metal plate and anode dielectric plate are extended in the opposite direction and intersect at point O, point O is taken as the origin, the straight line where the surface of the anode dielectric plate is located is taken as the x-axis, and a two-dimensional Cartesian coordinate system is established. The angle between the two plates is recorded as θ, the distance from the midpoint of the emission area of ​​the cathode metal plate to the origin of the coordinate is recorded as R, there is a vacuum between the cathode metal plate and the anode dielectric plate, and the potential difference between the two plates is V g .

[0092] like Figure 2 The calculation flow chart shown includes three layers of loops: the outer loop updates the current density distribution, the middle loop updates the charge density distribution, and the inner loop updates the potential distribution; and three layers of iterations: inner iteration (finite difference method), middle iteration (Poisson trajectory process) and outer iteration (secant method).

[0093] like Figure 3 The convergence process of cathode electric field and current density distribution during the iteration process is shown. Finally, the cathode electric field is pushed to zero and the cathode current density converges.

[0094] like Figure 4 The electron trajectories (black and gray areas in the vertical direction) and equipotential lines (black solid and dashed lines in the horizontal direction) in the process shown are: the gray area and solid line (black area and dashed line) are calculated with (without) space charge effect. The electron trajectories considering the space charge effect in the figure are broadened, especially at the edge of the effective emission area of ​​the flat plate, where the emission of electrons is more divergent, and they do not follow the trajectory of the vacuum electric field lines, and the equipotential curves considering the space charge effect deviate greatly from the vacuum situation, especially in the area of ​​the cathode near the center of the effective emission area.

[0095] Embodiment 1

[0096] When other conditions remain unchanged and the radius R corresponding to the center of the effective emission area changes, the space charge limited current calculation method applied to the non-parallel plate structure includes the following steps:

[0097] Step 1: Initial parameter setting

[0098] The non-parallel plate structure model is expressed using cylindrical coordinates (r, θ, and z):

[0099] x=r*cosθ, y=r*sinθ, z=z,

[0100] Where r is the distance from the calculation point to the origin of the coordinate system, and θ is the angle between the cathode metal plate and the anode dielectric plate. Based on the relationship of the parameter equation given above, we can transform it into the following equation relationship:

[0101]

[0102] The charge density is zero outside a given effective emission region:

[0103]

[0104] In the formula, r, θ c , J(r, θ c ), R and W represent the polar coordinate radius value corresponding to each point on the cathode plate, the polar angle value corresponding to the cathode plate, and the coordinate (r, θ c ), the distance from the middle point of the cathode metal plate emission area to the coordinate origin, and the width of the emission area.

[0105] Step 2: Calculate the injected charge

[0106] Given two smaller current density values ​​J1 and J2 as inputs to the Poisson trajectory process (intermediate iteration), the amount of charge injected per unit time, the distribution of charge density ρ, the cathode emission current density J, and the potential difference V between the two plates are calculated. g As with the traditional particle-point grid method (PIC), the relationship between charge density and charge is calculated by weighting the particle trajectory and position:

[0107]

[0108] Where dV is the unit volume element, dQ is the charge per unit volume element, and the current flowing through the unit area element dS is I. The relationship between I and current density J is:

[0109] I=J*dS,

[0110] And because the relationship between dQ and current is:

[0111] dQ=I*dt,

[0112] In cylindrical coordinates, the equations for the unit area element dS and the unit volume element dV in cylindrical coordinates are as follows:

[0113] dS=dr*dz, dV=r*dθ*dr*dz,

[0114] Combining the above equations, we can get:

[0115]

[0116] Step 3: Internal iteration (finite difference method)

[0117] First, use the cylindrical coordinate form to express the Poisson equation, giving the following form:

[0118]

[0119] Assuming that electrons are emitted uniformly in the z direction, we can obtain:

[0120]

[0121] So the Poisson equation simplifies to:

[0122]

[0123] Assume that the polar angle corresponding to the surface boundary of the dielectric anode is 0, and the polar angle corresponding to the surface boundary of the metal cathode is θ c , the boundary conditions for solving Poisson's equation are as follows:

[0124] V(r,θ)=0 for θ=θ c ,

[0125] V(r,θ)=V g for θ=0,

[0126]

[0127] In order to facilitate numerical calculation using the finite difference method (internal iteration), the Poisson equation is converted into a discrete difference equation form, which is as follows:

[0128]

[0129] The above equation is computationally simplified to obtain the expression for updating V(i, j).

[0130] Step 4: Intermediate iteration (Poisson trajectory process)

[0131] For the first iteration of the Poisson trajectory process, the finite difference method is used to solve the Laplace equation:

[0132]

[0133] Thus, the vacuum potential distribution is obtained. The electric field at each point is solved according to the electric field definition. These vacuum electric fields are used to calculate the electron trajectory by solving Newton's equations of motion. Assume that the electric fields along the x and y directions are E x and E y , then Newton's equation of motion is as follows:

[0134]

[0135] Assume that the electric fields along the r direction and the θ direction are E r and E θ , then the electric field transformation relationship between the Cartesian coordinate system and the cylindrical coordinate system is as follows:

[0136]

[0137] Taking the partial derivatives of x and y with respect to r and θ respectively, we get:

[0138]

[0139] In the process of solving the electron trajectory in the vacuum electric field for the first Poisson trajectory iteration, we deposit the particle charge weighted calculation onto the grid through the particle point grid method (PIC) to obtain the initial charge density distribution ρ old , which is a function of r and θ. This initial charge density is then used to iterate the Poisson trajectory to solve the Poisson equation to obtain an updated potential field. This updated potential field will give an updated electric field, which is then used to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ * Repeat the Poisson trajectory iteration until convergence, and obtain the updated charge density ρ before each iteration new :

[0140] ρ new =0.9*ρ old +0.1*ρ * .

[0141] Step 5: Perform polynomial fitting to solve the electric field E at each point

[0142] After the Poisson trajectory process converges, the potential distribution V is obtained after considering the space charge effect under the corresponding input current density. Then, according to the definition of the electric field, the electric field E at each point is solved by polynomial fitting through the extrapolation process:

[0143] E(θ)=Aθ 2 +Bθ+C,

[0144] Wherein, A, B, and C are all unknown coefficients. Therefore, three electric field values closest to the cathode are required to determine the values of A, B, and C. This extrapolation process obtains the potential values at the three closest grid points from the cathode surface, where the electric field value is defined as the electric field value in the middle of two adjacent nodes:

[0145]

[0146] E(θ c -Δθ) = A(θ c -Δθ) 2 +B(θ c -Δθ)+C,

[0147]

[0148] By using the above fitting function, the electric field value is calculated for each grid point of the cathode, and the electric field distributions E1 and E2 at the cathode boundary can be obtained;

[0149] Step Six: External Iteration (Secant Method)

[0150] For the electron emission model of an infinite electron emission source, it is assumed that the metal plate cathode can provide a high enough current density to push the electric field strength to zero in all electron emission regions (R - W / 2 < r < R + W / 2), that is:

[0151]

[0152] Use the secant method (external iteration) to obtain the updated current density J * :

[0153]

[0154] Repeat the external iteration until the current density J converges. Before each iteration, obtain the updated charge density:

[0155] J new = 0.9*J old + 0.1*J * .

[0156] J * is the predicted current density value. By using the above iteration formula, the current density is predicted for each grid point of the cathode to obtain the cathode current density distribution. Repeat the whole process until the current density converges and output the current density J.

[0157] Example Two

[0158] With other conditions unchanged, for the case where the potential difference V between the two plates g changes, the method for calculating the space charge limited current applied to a non - parallel plate structure includes the following steps:

[0159] Step 1: Initial parameter setting

[0160] The non-parallel plate structure model is expressed using cylindrical coordinates (r, θ, and z):

[0161] x=r*cosθ, y=r*sinθ, z=z,

[0162] Where r is the distance from the calculation point to the origin of the coordinate system, and θ is the angle between the cathode metal plate and the anode dielectric plate. Based on the relationship of the parameter equation given above, we can transform it into the following equation relationship:

[0163]

[0164] The charge density is zero outside a given effective emission region:

[0165]

[0166] In the formula, r, θ c , J(r, θ c ), R and W represent the polar coordinate radius value corresponding to each point on the cathode plate, the polar angle value corresponding to the cathode plate, and the coordinate (r, θ c ), the distance from the middle point of the cathode metal plate emission area to the coordinate origin, and the width of the emission area.

[0167] Step 2: Calculate the injected charge

[0168] Given two smaller current density values ​​J1 and J2 as inputs to the Poisson trajectory process (intermediate iteration), the amount of charge injected per unit time, the distribution of charge density ρ, the cathode emission current density J, and the potential difference V between the two plates are calculated. g As with the traditional particle-point grid method (PIC), the relationship between charge density and charge is calculated by weighting the particle trajectory and position:

[0169]

[0170] Where dV is the unit volume element, dQ is the charge per unit volume element, and the current flowing through the unit area element dS is I. The relationship between I and current density J is:

[0171] I=J*dS,

[0172] And because the relationship between dQ and current is:

[0173] dQ=I*dt,

[0174] In cylindrical coordinates, the equations for the unit area element dS and the unit volume element dV in cylindrical coordinates are as follows:

[0175] dS=dr*dz, dV=r*dθ*dr*dz,

[0176] Combining the above equations, we can get:

[0177]

[0178] Step 3: Internal iteration (finite difference method)

[0179] First, use the cylindrical coordinate form to express the Poisson equation, giving the following form:

[0180]

[0181] Assuming that electrons are emitted uniformly in the z direction, we can obtain:

[0182]

[0183] So the Poisson equation simplifies to:

[0184]

[0185] Assume that the polar angle corresponding to the surface boundary of the dielectric anode is 0, and the polar angle corresponding to the surface boundary of the metal cathode is θ c , the boundary conditions for solving Poisson's equation are as follows:

[0186] V(r,θ)=0 for θ=θ c ,

[0187] V(r,θ)=V g for θ=0,

[0188]

[0189] In order to facilitate numerical calculation using the finite difference method (internal iteration), the Poisson equation is converted into a discrete difference equation form, which is as follows:

[0190]

[0191] The above equation is computationally simplified to obtain the expression for updating V(i, j).

[0192] Step 4: Intermediate iteration (Poisson trajectory process)

[0193] For the first iteration of the Poisson trajectory process, the finite difference method is used to solve the Laplace equation:

[0194]

[0195] Thus, the vacuum potential distribution is obtained. The electric field at each point is solved according to the electric field definition. These vacuum electric fields are used to calculate the electron trajectory by solving Newton's equations of motion. Assume that the electric fields along the x and y directions are E x and E y , then Newton's equation of motion is as follows:

[0196]

[0197] Assume that the electric fields along the r direction and the θ direction are E r and E θ , then the electric field transformation relationship between the Cartesian coordinate system and the cylindrical coordinate system is as follows:

[0198]

[0199] Taking the partial derivatives of x and y with respect to r and θ respectively, we get:

[0200]

[0201] In the process of solving the electron trajectory in the vacuum electric field for the first Poisson trajectory iteration, we deposit the particle charge weighted calculation onto the grid through the particle point grid method (PIC) to obtain the initial charge density distribution ρ old , which is a function of r and θ. This initial charge density is then used to iterate the Poisson trajectory to solve the Poisson equation to obtain an updated potential field. This updated potential field will give an updated electric field, which is then used to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ * Repeat the Poisson trajectory iteration until convergence, and obtain the updated charge density ρ before each iteration new :

[0202] ρ new =0.9*ρ old +0.1*ρ * .

[0203] Step 5: Perform polynomial fitting to solve the electric field E at each point

[0204] After the Poisson trajectory process converges, the potential distribution V is obtained after considering the space charge effect under the corresponding input current density. Then, according to the definition of the electric field, the electric field E at each point is solved by polynomial fitting through the extrapolation process:

[0205] E(θ)=Aθ 2 +Bθ+C,

[0206] In the formula, A, B, and C are all unknown coefficients. Therefore, three electric field values closest to the cathode are required to determine the values of A, B, and C. The extrapolation process obtains the potential values at the three closest grid points from the cathode surface, where the electric field value is defined as the electric field value in the middle of two adjacent nodes:

[0207]

[0208] E(θ c -Δθ) = A(θ c -Δθ) 2 + B(θ c -Δθ) + C,

[0209]

[0210] By using the above fitting function, the electric field value is calculated for each grid point of the cathode, and the electric field distributions E1 and E2 at the cathode boundary can be obtained;

[0211] Step Six. External Iteration (Secant Method)

[0212] For the electron emission model of an infinite electron emission source, it is assumed that the metal plate cathode can provide a high enough current density to push the electric field strength to zero in all electron emission regions (R - W / 2 < r < R + W / 2), that is:

[0213]

[0214] The updated current density J is obtained using the secant method (external iteration) * :

[0215]

[0216] Repeat the external iteration until the current density J converges. Before each iteration, the updated charge density is obtained:

[0217] J new = 0.9 * J old + 0.1 * J * .

[0218] J * is the predicted current density value. By using the above iteration formula, the current density is predicted for each grid point of the cathode to obtain the cathode current density distribution. Repeat the whole process until the current density converges and output the current density J.

[0219] Example Three

[0220] With other conditions unchanged and the width W of the effective emission region varying, the method for calculating the space charge limited current applied to a non-parallel plate structure includes the following steps:

[0221] Step 1: Initial parameter setting

[0222] The non-parallel plate structure model is expressed using cylindrical coordinates (r, θ, and z):

[0223] x=r*cosθ, y=r*sinθ, z=z,

[0224] Where r is the distance from the calculation point to the origin of the coordinate system, and θ is the angle between the cathode metal plate and the anode dielectric plate. Based on the relationship of the parameter equation given above, we can transform it into the following equation relationship:

[0225]

[0226] The charge density is zero outside a given effective emission region:

[0227]

[0228] In the formula, r, θ c , J(r, θ c ), R and W represent the polar coordinate radius value corresponding to each point on the cathode plate, the polar angle value corresponding to the cathode plate, and the coordinate (r, θ c ), the distance from the middle point of the cathode metal plate emission area to the coordinate origin, and the width of the emission area.

[0229] Step 2: Calculate the injected charge

[0230] Given two smaller current density values ​​J1 and J2 as inputs to the Poisson trajectory process (intermediate iteration), the amount of charge injected per unit time, the distribution of charge density ρ, the cathode emission current density J, and the potential difference V between the two plates are calculated. g As with the traditional particle-point grid method (PIC), the relationship between charge density and charge is calculated by weighting the particle trajectory and position:

[0231]

[0232] Where dV is the unit volume element, dQ is the charge per unit volume element, and the current flowing through the unit area element dS is I. The relationship between I and current density J is:

[0233] I=J*dS,

[0234] And because the relationship between dQ and current is:

[0235] dQ=I*dt,

[0236] In cylindrical coordinates, the equations for the unit area element dS and the unit volume element dV in cylindrical coordinates are as follows:

[0237] dS=dr*dz, dV=r*dθ*dr*dz,

[0238] Combining the above equations, we can get:

[0239]

[0240] Step 3: Internal iteration (finite difference method)

[0241] First, use the cylindrical coordinate form to express the Poisson equation, giving the following form:

[0242]

[0243] Assuming that electrons are emitted uniformly in the z direction, we can obtain:

[0244]

[0245] So the Poisson equation simplifies to:

[0246]

[0247] Assume that the polar angle corresponding to the surface boundary of the dielectric anode is 0, and the polar angle corresponding to the surface boundary of the metal cathode is θ c , the boundary conditions for solving Poisson's equation are as follows:

[0248] V(r,θ)=0 for θ=θ c ,

[0249] V(r,θ)=V g for θ=0,

[0250]

[0251] In order to facilitate numerical calculation using the finite difference method (internal iteration), the Poisson equation is converted into a discrete difference equation form, which is as follows:

[0252]

[0253] The above equation is computationally simplified to obtain the expression for updating V(i, j).

[0254] Step 4: Intermediate iteration (Poisson trajectory process)

[0255] For the first iteration of the Poisson trajectory process, the finite difference method is used to solve the Laplace equation:

[0256]

[0257] Thus, the vacuum potential distribution is obtained. The electric field at each point is solved according to the electric field definition. These vacuum electric fields are used to calculate the electron trajectory by solving Newton's equations of motion. Assume that the electric fields along the x and y directions are E x and E y , then Newton's equation of motion is as follows:

[0258]

[0259] Assume that the electric fields along the r direction and the θ direction are E r and E θ , then the electric field transformation relationship between the Cartesian coordinate system and the cylindrical coordinate system is as follows:

[0260]

[0261] Taking the partial derivatives of x and y with respect to r and θ respectively, we get:

[0262]

[0263] In the process of solving the electron trajectory in the vacuum electric field for the first Poisson trajectory iteration, we deposit the particle charge weighted calculation onto the grid through the particle point grid method (PIC) to obtain the initial charge density distribution ρ old , which is a function of r and θ. This initial charge density is then used to iterate the Poisson trajectory to solve the Poisson equation to obtain an updated potential field. This updated potential field will give an updated electric field, which is then used to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ * Repeat the Poisson trajectory iteration until convergence, and obtain the updated charge density ρ before each iteration new :

[0264] ρ new =0.9*ρ old +0.1*ρ * .

[0265] Step 5: Perform polynomial fitting to solve the electric field E at each point

[0266] After the Poisson trajectory process converges, the potential distribution V is obtained after considering the space charge effect under the corresponding input current density. Then, according to the definition of the electric field, the electric field E at each point is solved by polynomial fitting through the extrapolation process:

[0267] E(θ)=Aθ 2 +Bθ+C,

[0268] Wherein, A, B, and C are all unknown coefficients. Therefore, three electric field values closest to the cathode are required to determine the values of A, B, and C. The extrapolation process obtains the potential values at the three closest grid points from the cathode surface, where the electric field value is defined as the electric field value in the middle of two adjacent nodes:

[0269]

[0270] E(θ c -Δθ) = A(θ c -Δθ) 2 + B(θ c -Δθ) + C,

[0271]

[0272] By using the above fitting function, the electric field value is calculated for each grid point of the cathode, and the electric field distributions E1 and E2 at the cathode boundary can be obtained;

[0273] Step Six: External Iteration (Secant Method)

[0274] For the electron emission model of an infinite electron emission source, it is assumed that the metal plate cathode can provide a high enough current density to push the electric field strength to zero in all electron emission regions (R - W / 2 < r < R + W / 2), that is:

[0275]

[0276] Use the secant method (external iteration) to obtain the updated current density J * :

[0277]

[0278] Repeat the external iteration until the current density J converges. Before each iteration, obtain the updated charge density:

[0279] J new = 0.9 * J old + 0.1 * J * .

[0280] J * is the predicted current density value. By using the above iteration formula, the current density is predicted for each grid point of the cathode to obtain the cathode current density distribution. Repeat the whole process until the current density converges and output the current density J.

[0281] Example Four

[0282] With other conditions unchanged, for the case where the included angle θ between the two plates changes, the method for calculating the space charge limited current applied to a non-parallel plate structure includes the following steps:

[0283] Step 1: Initial parameter setting

[0284] The non-parallel plate structure model is expressed using cylindrical coordinates (r, θ, and z):

[0285] x=r*cosθ, y=r*sinθ, z=z,

[0286] Where r is the distance from the calculation point to the origin of the coordinate system, and θ is the angle between the cathode metal plate and the anode dielectric plate. Based on the relationship of the parameter equation given above, we can transform it into the following equation relationship:

[0287]

[0288] The charge density is zero outside a given effective emission region:

[0289]

[0290] In the formula, r, θ c , J(r, θ c ), R and W represent the polar coordinate radius value corresponding to each point on the cathode plate, the polar angle value corresponding to the cathode plate, and the coordinate (r, θ c ), the distance from the middle point of the cathode metal plate emission area to the coordinate origin, and the width of the emission area.

[0291] Step 2: Calculate the injected charge

[0292] Given two smaller current density values ​​J1 and J2 as inputs to the Poisson trajectory process (intermediate iteration), the amount of charge injected per unit time, the distribution of charge density ρ, the cathode emission current density J, and the potential difference V between the two plates are calculated. g As with the traditional particle-point grid method (PIC), the relationship between charge density and charge is calculated by weighting the particle trajectory and position:

[0293]

[0294] Where dV is the unit volume element, dQ is the charge per unit volume element, and the current flowing through the unit area element dS is I. The relationship between I and current density J is:

[0295] I=J*dS,

[0296] And because the relationship between dQ and current is:

[0297] dQ=I*dt,

[0298] In cylindrical coordinates, the equations for the unit area element dS and the unit volume element dV in cylindrical coordinates are as follows:

[0299] dS=dr*dz, dV=r*dθ*dr*dz,

[0300] Combining the above equations, we can get:

[0301]

[0302] Step 3: Internal iteration (finite difference method)

[0303] First, use the cylindrical coordinate form to express the Poisson equation, giving the following form:

[0304]

[0305] Assuming that electrons are emitted uniformly in the z direction, we can obtain:

[0306]

[0307] So the Poisson equation simplifies to:

[0308]

[0309] Assume that the polar angle corresponding to the surface boundary of the dielectric anode is 0, and the polar angle corresponding to the surface boundary of the metal cathode is θ c , the boundary conditions for solving Poisson's equation are as follows:

[0310] V(r,θ)=0 for θ=θ c ,

[0311] V(r,θ)=V g for θ=0,

[0312]

[0313] In order to facilitate numerical calculation using the finite difference method (internal iteration), the Poisson equation is converted into a discrete difference equation form, which is as follows:

[0314]

[0315] The above equation is computationally simplified to obtain the expression for updating V(i, j).

[0316] Step 4: Intermediate iteration (Poisson trajectory process)

[0317] For the first iteration of the Poisson trajectory process, the finite difference method is used to solve the Laplace equation:

[0318]

[0319] Thus, the vacuum potential distribution is obtained. The electric field at each point is solved according to the electric field definition. These vacuum electric fields are used to calculate the electron trajectory by solving Newton's equations of motion. Assume that the electric fields along the x and y directions are E x and E y , then Newton's equation of motion is as follows:

[0320]

[0321] Assume that the electric fields along the r direction and the θ direction are E r and E θ , then the electric field transformation relationship between the Cartesian coordinate system and the cylindrical coordinate system is as follows:

[0322]

[0323] Taking the partial derivatives of x and y with respect to r and θ respectively, we get:

[0324]

[0325] In the process of solving the electron trajectory in the vacuum electric field for the first Poisson trajectory iteration, we deposit the particle charge weighted calculation onto the grid through the particle point grid method (PIC) to obtain the initial charge density distribution ρ old , which is a function of r and θ. This initial charge density is then used to iterate the Poisson trajectory to solve the Poisson equation to obtain an updated potential field. This updated potential field will give an updated electric field, which is then used to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ * Repeat the Poisson trajectory iteration until convergence, and obtain the updated charge density ρ before each iteration new :

[0326] ρ new =0.9*ρ old +0.1*ρ * .

[0327] Step 5: Perform polynomial fitting to solve the electric field E at each point

[0328] After the Poisson trajectory process converges, the potential distribution V is obtained after considering the space charge effect under the corresponding input current density. Then, according to the definition of the electric field, the electric field E at each point is solved by polynomial fitting through the extrapolation process:

[0329] E(θ)=Aθ 2 +Bθ+C,

[0330] In the formula, A, B, and C are all unknown coefficients. Therefore, three electric field values closest to the cathode are required to determine the values of A, B, and C. This extrapolation process obtains the potential values at the three closest grid points from the cathode surface, where the electric field value is defined as the electric field value in the middle of two adjacent nodes:

[0331]

[0332] E(θ c -Δθ) = A(θ c -Δθ) 2 +B(θ c -Δθ)+C,

[0333]

[0334] By using the above fitting function, the electric field value is calculated for each grid point of the cathode, and the electric field distributions E1 and E2 at the cathode boundary can be obtained;

[0335] Step Six. External Iteration (Secant Method)

[0336] For the electron emission model of an infinite electron emission source, it is assumed that the metal plate cathode can provide a high enough current density to push the electric field strength to zero in all electron emission regions (R - W / 2 < r < R + W / 2), that is:

[0337]

[0338] Use the secant method (external iteration) to obtain the updated current density J * :

[0339]

[0340] Repeat the external iteration until the current density J converges. Before each iteration, obtain the updated charge density:

[0341] J new = 0.9*J old + 0.1*J * .

[0342] J * is the predicted current density value. Through the above iteration formula, the current density is predicted for each grid point of the cathode to obtain the cathode current density distribution. Repeat the whole process until the current density converges and output the current density J.

[0343] In summary, compared with the prior art, the method of this embodiment has the following advantages and beneficial effects:

[0344] (1) The embodiment of the present invention provides a method for calculating the space charge limited current of a non-parallel plate structure, uses the particle point grid method (PIC) as an intermediate iteration to solve the electron motion trajectory, and explores the motion law of particles under the influence of space charge.

[0345] (2) The embodiment of the present invention can solve the double boundary problem in space charge limited current by self-consistently updating the current density to meet the given boundary conditions without analytically solving the nonlinear Poisson equation in multiple dimensions.

[0346] This embodiment also provides a space charge limited current calculation method and device, including:

[0347] at least one processor;

[0348] at least one memory for storing at least one program;

[0349] When the at least one program is executed by the at least one processor, the at least one processor implements Figure 2 The method shown.

[0350] A space charge limited current calculation method device of this embodiment can execute a space charge limited current calculation method provided by the method embodiment of the present invention, can execute any combination of implementation steps of the method embodiment, and has the corresponding functions and beneficial effects of the method.

[0351] The present application also discloses a computer program product or a computer program, which includes a computer instruction stored in a computer-readable storage medium. A processor of a computer device can read the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes Figure 2 The method shown.

[0352] This embodiment also provides a storage medium storing instructions or programs that can execute a method for calculating a space charge limited current provided by an embodiment of the method of the present invention. When the instructions or programs are run, any combination of implementation steps of the method embodiment can be executed, and the corresponding functions and beneficial effects of the method can be obtained.

[0353] In some selectable embodiments, the function / operation mentioned in the block diagram may not occur in the order mentioned in the operation diagram. For example, depending on the function / operation involved, the two boxes shown in succession can actually be executed substantially simultaneously or the boxes can sometimes be executed in reverse order. In addition, the embodiment presented and described in the flow chart of the present invention is provided by way of example, for the purpose of providing a more comprehensive understanding of technology. The disclosed method is not limited to the operation and logic flow presented herein. Selectable embodiments are expected, wherein the order of various operations is changed and the sub-operation of a part for which is described as a larger operation is performed independently.

[0354] In addition, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise specified, one or more of the functions and / or features described may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in separate physical devices or software modules. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the present invention. More specifically, in view of the properties, functions, and internal relationships of the various functional modules in the device disclosed herein, the actual implementation of the module will be understood within the conventional skills of the engineer. Therefore, those skilled in the art can implement the present invention set forth in the claims without excessive experimentation using ordinary techniques. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present invention, which is determined by the full scope of the appended claims and their equivalents.

[0355] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0356] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0357] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0358] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0359] In the above description of this specification, the description with reference to the terms "one embodiment / example", "another embodiment / example" or "certain embodiments / examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0360] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

[0361] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the above embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A space charge limited current calculation method, characterized in that: The following steps are involved: S1, determine the structural model between the cathode metal plate and the anode dielectric plate, and determine two initial current density values ​​J1 and J2; S2, using the two current density values ​​J1 and J2 as inputs of the Poisson trajectory process, calculating the amount of charge injected per unit time, and calculating the amount of charge in the process of calculating the electron trajectory and depositing it on the grid, iterating until the charge distribution converges; S3. After the Poisson trajectory process converges, the potential distribution V is obtained, and the electric field E at each point is solved by polynomial fitting through the extrapolation process according to the electric field definition; S4. After the Poisson trajectory process converges, the updated current density J is obtained using the secant method. * , according to the current density J * Obtain the input current density of the next Poisson trajectory process, and repeat steps S2-S3 until the current density converges; S5, output the final current density distribution J; There is a vacuum between the cathode metal plate and the anode dielectric plate. Step S2 specifically includes: In the Poisson trajectory process, the first iteration uses the finite difference method to solve the Laplace equation to obtain the vacuum potential distribution, and the vacuum electric field is obtained based on the vacuum potential distribution. Based on the vacuum electric field, the electron trajectory without considering the space charge effect is calculated by solving the Newtonian equation of motion; In the process of calculating the electron trajectory, the particle grid method is used to calculate the charge through the particle motion trajectory and position weighting and deposit it on the grid to obtain the initial charge density distribution ρ old , use the initial charge density to solve Poisson's equation in the second iteration using the finite difference method to obtain an updated potential field, which will give an updated electric field. Use the updated electric field to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ * ; In subsequent iterations, according to the charge density distribution ρ * Get the updated charge density distribution ρ new , repeat the Poisson trajectory process and the electron trajectory calculation process until the charge density distribution ρ converges.

2. A space charge limited current calculation method according to claim 1, characterized in that: The step of determining the structural model between the cathode metal plate and the anode dielectric plate comprises: Determine the length L of the plate and the width W of the emission area, extend the non-parallel cathode metal plate and anode dielectric plate in the opposite direction and intersect at point O, take point O as the origin, and the straight line where the surface of the anode dielectric plate is located as the x-axis to establish a two-dimensional Cartesian coordinate system. The angle between the two plates is recorded as θ, the distance from the midpoint of the cathode metal plate emission area to the origin of the coordinate is recorded as R, and the potential difference between the cathode metal plate and the anode dielectric plate is V g .

3. A space charge limited current calculation method according to claim 2, characterized in that: The electric field lines in the non-parallel plate structure are perpendicular to the equipotential lines. The cylindrical coordinates of the non-parallel plate structure model are expressed as: x=r*cosθ, y=r*sinθ, z=z, Where r is the distance from the calculation point to the origin of the coordinate system, θ is the angle between the cathode metal plate and the anode dielectric plate, z is the axial coordinate, and x and y are the cross-sectional coordinates of the calculation point; The transformation results in the following equation relationship: z=z, The charge density is zero outside the preset effective emission region: In the formula, θ c Indicates the polar angle value corresponding to the cathode plate, J(r, θ c ) represents the coordinates (r, θ c ), R represents the distance from the middle point of the emission area of ​​the cathode metal plate to the origin of the coordinate system, and W represents the width of the emission area.

4. A space charge limited current calculation method according to claim 1, characterized in that: Charge density distribution ρ and potential difference V between the two plates g The relationship between charge density and charge is: Where dV is the unit volume element, dQ is the charge per unit volume element, and the current flowing through the unit area element dS is I. The relationship between I and current density J is: I=J*dS Because the relationship between dQ and current is: dQ=I*dt In cylindrical coordinates, the equations for the unit area element dS and the unit volume element dV in cylindrical coordinates are as follows: dS=dr*dz, dV=r*dθ*dr*dz, Combining the above equations, we can get:

5. A space charge limited current calculation method according to claim 3, characterized in that: The Poisson trajectory process and the process of calculating the electron trajectory are specifically as follows: Using cylindrical coordinates to express the Poisson equation gives the following form: Where ε0 is the dielectric constant of vacuum; Assuming that electrons are emitted uniformly in the z direction, we can obtain: Poisson's equation simplifies to: Assume that the polar angle corresponding to the surface boundary of the dielectric anode is 0, and the polar angle corresponding to the surface boundary of the metal cathode is θ c , the boundary conditions for solving Poisson's equation are as follows: In order to facilitate numerical calculation using the finite difference method, the Poisson equation is transformed into a discrete difference equation form, which is as follows: The equation is simplified computationally to obtain the expression for updating V(i, j). For the first iteration of the Poisson trajectory process, the finite difference method is used to solve the Laplace equation: The vacuum potential distribution is obtained, and the electric field at each point is solved according to the electric field definition. These vacuum electric fields are used to calculate the electron trajectory by solving Newton's equations of motion. Assume that the electric fields along the x and y directions are E x and E y , then Newton's equation of motion is as follows: Assume that the electric fields along the r direction and the θ direction are E r and E θ , then the electric field transformation relationship between the Cartesian coordinate system and the cylindrical coordinate system is as follows: Taking the partial derivatives of x and y with respect to r and θ respectively, we get: In the process of solving the electron trajectory by the first Poisson trajectory iteration in the vacuum electric field, the initial charge density distribution ρ is obtained by depositing the particle charge weighted calculation onto the grid through the particle-grid method. old , and then the initial charge density is used in the next Poisson trajectory iteration to solve the Poisson equation to obtain an updated potential field; the updated potential field will give an updated electric field, and then the updated electric field is used to solve Newton's equations of motion to obtain an updated trajectory and an updated charge density distribution ρ*; repeat the Poisson trajectory iteration until convergence, and obtain an updated charge density ρ before each iteration new : r new =0.9*ρ old +0.1*p * 。 6. A space charge limited current calculation method according to claim 3, characterized in that: After the Poisson trajectory process converges, the potential distribution V is obtained, and the electric field E at each point is solved by polynomial fitting through an extrapolation process according to the electric field definition, including: E(θ)=Aθ 2 +Bθ+C In the formula, A, B, and C are all unknown coefficients, so the three electric field values ​​closest to the cathode are needed to determine the values ​​of A, B, and C. The extrapolation process obtains the potential values ​​at the three nearest grid points from the cathode surface, where the electric field value is defined as the electric field value between two adjacent nodes: E(θ c -Δθ)=A(θ c -Dth) 2 +B(θ c -Δθ)+C, By fitting the function, the electric field value is calculated for each grid point of the cathode, and the cathode boundary electric field distributions E1 and E2 are obtained.

7. A space charge limited current calculation method according to claim 3, characterized in that: In step S4, for the electron emission model of the infinite electron emission source, it is assumed that the metal plate cathode can provide a sufficiently high current density so as to push the electric field intensity to zero in all electron emission regions, that is: Use the secant method to get the updated current density J * : Repeat the iteration until the current density J converges, and obtain the updated charge density before each iteration: I new =0.9*J old +0.1*J * J * is the predicted current density value. Through the iterative formula, the current density is predicted for each grid point of the cathode to obtain the cathode current density distribution. The whole process is repeated until the current density converges and the current density J is output.

8. A space charge limited current calculation method and device, characterized in that: include: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method according to any one of claims 1 to 7.

9. A computer-readable storage medium storing a program executable by a processor, characterized in that: The processor-executable program is used to perform the method according to any one of claims 1 to 7 when executed by the processor.

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