A method for calculating micro-discharge of microwave components under linear frequency modulation signal

Abstract

A method for calculating micro-discharge of microwave components under linear frequency modulation signals comprises the following steps: firstly, the probability density function of secondary electron emission speed and angle is discretized, the linear frequency modulation signal is discretized, the discharge area is equally divided into mutually parallel thin layers, the discrete trajectory of electron motion is obtained by combining with a parallel plate structure, the surface charge of a medium and the charge of a space thin layer (each layer) are updated according to each movement and collision of electrons, the surface charge of a medium and the charge of a space thin layer after the updated charge are used to calculate the electric field distribution, the electric field of the discrete value of the linear frequency modulation signal is combined to accelerate the electrons, the secondary electron emission coefficients of metal and dielectric materials are respectively called when colliding, the number of secondary electrons is updated, the number of secondary electrons is weightedly calculated in the entire iterative process, and the evolution process of micro-discharge of microwave components under the condition of linear frequency modulation signals is obtained.

Description

Technical Field

[0001] The invention relates to a method for calculating micro-discharge of microwave components under linear frequency modulation signals, and belongs to the field of micro-discharge of microwave devices. Background Art

[0002] With the development of satellite microwave remote sensing technology, the resolution is required to be higher and higher, which puts higher requirements on the micro-discharge power capacity of microwave components. However, the microwave components in remote sensing satellites usually work in linear frequency modulation signal mode. Different from single carrier, the frequency of linear frequency modulation signal changes linearly with time, and the traditional micro-discharge calculation method for single frequency signal is not applicable.

[0003] Statistical theory is an effective method for analyzing micro-discharge. It determines the motion trajectory equation of electrons based on the excitation signal and device structure, constructs the joint probability density function of electron transit time, emission phase and displacement through the probability density function of secondary electron emission, and obtains the change process of the number of electrons over time. However, traditional statistical theory requires the derivation of an analytical expression for the motion trajectory of electrons, which can only be obtained for single-frequency signals, and cannot be obtained for linear frequency modulation signals. Therefore, traditional statistical theory is not suitable for the calculation of micro-discharge of microwave components under linear frequency modulation signals.

[0004] With the improvement of satellite functions, the volume requirements for high-power microwave components are getting higher and higher. Filling with dielectrics can effectively reduce the volume of microwave components and achieve miniaturization. The introduction of dielectrics causes microwave components to accumulate charges on the surface of the dielectric when micro-discharge occurs, which will generate a DC electric field. Electrons are affected by the combined effects of the RF field and the DC electric field. At the same time, in order to calculate the entire evolution process of dielectric micro-discharge, the space charge effect needs to be considered, making traditional statistical theories inapplicable to the calculation of dielectric microwave component micro-discharge.

[0005] Another method to calculate microdischarge is the numerical calculation method, which can effectively simulate the effect of electromagnetic fields on electrons and the electron multiplication process. However, in order to effectively simulate the evolution of microdischarge, it is necessary to use the Monte Carlo method to generate a large number of secondary electrons to simulate its statistical characteristics. During the simulation of microdischarge, the number of electrons will increase rapidly and even exceed the computing power of the computer, resulting in calculation failure. Summary of the invention

[0006] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a method for calculating the micro-discharge of microwave components under a linear frequency modulation signal, taking into account the linear variation of the excitation signal frequency with time, taking into account the influence of the surface charge and space charge of the medium, and realizing the calculation of the micro-discharge of microwave components under a linear frequency modulation signal.

[0007] The technical solution of the present invention is: a method for calculating the micro-discharge of microwave components under a linear frequency modulation signal, which is achieved by:

[0008] Discretize the probability density function of the secondary electron emission velocity and angle, and the linear frequency modulation signal;

[0009] The discharge area is divided into parallel thin layers, electron injection is initialized, and the following iterations are performed until the simulation duration reaches the preset duration:

[0010] The discrete trajectory of electron movement is obtained by combining the parallel plate structure, the charge of the thin layer is updated according to each movement and collision of the electron, and the electric field distribution at the current iteration moment is calculated using the updated thin layer charge; the parallel plate structure includes two upper and lower metal plates, and the discharge area is between the upper and lower metal plates;

[0011] The electric field distribution calculated above is combined with the electric field of the discrete value of the linear frequency modulation signal as the total electromagnetic field, and the total electromagnetic field is used to accelerate the electrons, update the positions of all emitted electrons at all times before the current iteration, and determine whether they have hit the surfaces of the upper and lower metal plates, and calculate the secondary electron emission coefficient when the collision occurs;

[0012] According to the secondary electron emission coefficient combined with the probability density function of the secondary electron emission velocity and angle after discretization, the weights of all emitted electrons at the current iteration moment are calculated;

[0013] According to the weights of all the above-mentioned emitted electrons, the total number of spatial electrons and the spatial electron data of each thin layer are updated to complete one iteration.

[0014] A method for calculating micro-discharge of microwave components under linear frequency modulation signal is implemented in the following way:

[0015] Discretize the probability density function of the secondary electron emission velocity and angle, and the linear frequency modulation signal;

[0016] The discharge area is divided into parallel thin layers, electron injection is initialized, and the following iterations are performed until the simulation duration reaches the preset duration:

[0017] The discrete trajectory of electron movement is obtained by combining a parallel plate structure, and the surface charge of the medium and the thin layer are updated according to each movement and collision of the electrons. The electric field distribution at the current iteration moment is calculated using the updated surface charge of the medium and the thin layer charge in space. The parallel plate structure includes two upper and lower metal plates, a medium is placed on the lower metal plate, and a discharge area is between the medium and the upper metal plate.

[0018] The electric field distribution calculated above is combined with the electric field of the discrete value of the linear frequency modulation signal as the total electromagnetic field, and the total electromagnetic field is used to accelerate the electrons, update the positions of all emitted electrons at all times before the current iteration, and determine whether they have hit the metal plate surface and the medium surface, and calculate the secondary electron emission coefficient when the collision occurs;

[0019] According to the secondary electron emission coefficient combined with the probability density function of the secondary electron emission velocity and angle after discretization, the weights of all emitted electrons at the current iteration moment are calculated;

[0020] According to the weights of all the above-mentioned emitted electrons, the total number of spatial electrons, the accumulated charge data on the medium surface and the spatial electron data of each thin layer are updated to complete an iteration.

[0021] Preferably, the simulation iteration step length Δt is 1 / 100 to 1 / 50 of the period corresponding to the initial frequency.

[0022] Preferably, the principle of dividing the discharge area thin layer is: divide the discharge area into n c Each thin layer is located at the center of each equally divided area, and the thickness of the equally divided area is not greater than 0.05mm.

[0023] Preferably, the electron injection initialization includes

[0024] Label the initial electron as e 0 , the initial electrons and secondary electrons both represent a type of electrons with the same motion state. The actual number of electrons contained is called its weight. The weight of the initial electron is set to w 0 = 1, the secondary electron emission coefficient σ of the initial collision is calculated based on the speed and angle of the incident electron 0 ;

[0025] Calculate t according to the following formula 1 =The weight of the secondary electrons emitted at time 0.

[0026]

[0027] The subscript 1 represents t 1 Moment, 2 refers to the collision with the lower plate, i.e., the surface of the medium or the surface of the lower metal plate;

[0028] Initialization: When the parallel plate structure contains a medium, assume that t 1 = 0, an electron is emitted from the surface of the medium, so Q surface (t 1 )=-e, the emitted electron enters the nth c The electron thin layer of the layer, c=1,2,…n c ; When there is no medium in the parallel plate structure, assuming t 1= 0, an electron is emitted from the lower metal surface, so Q surface (t 1 )=0, the emitted electron enters the nth c The electron thin layer of the layer, c=1,2,…n c

[0029] Where e represents the electron charge, n c is the total number of thin layers.

[0030] Preferably, the total electromagnetic field calculation formula is as follows:

[0031] E total (t i )=E rf (t i )+E surface (t i )+E space (t i )

[0032] Among them, E rf (t i ) is t i The RF field in the parallel slab waveguide,

[0033] E surface (t i ) is the Coulomb field of the dielectric surface charge, ε r is the relative dielectric constant of the medium, h is the thickness of the medium, d is the distance between the medium and the upper metal plate, A is the area of ​​the medium facing the upper metal plate, Q surface (t i-1 ) is t i-1 The surface charge of the medium at the moment; ε 0 is the dielectric constant of vacuum. When there is no medium in the parallel plate structure, E surface (t i ) takes the value of 0;

[0034] E space (t i ) is the space charge Coulomb field, which is the sum of the electric fields of all thin layers:

[0035] E space (t i )=E sheet,1 (t i )+E sheet,2 (t i )+…E sheet,nc (t i ).

[0036] Preferably, Where c = 1, 2, ... nc , n c is the total number of thin layers; z′ is the position of the cth electron thin layer, z is the position of the electric field to be solved, Q sheet,c (t i-1 ) The charge of the cth electron layer, E sheet,u (t i ) is the electric field above the cth electron layer, E sheet,d (t i ) The electric field below the cth electron layer, E sheet,m (t i ) is the electric field at the location of the cth electron layer.

[0037] Preferably, the Boolean function is calculated to determine whether the emitted electron has hit the plate surface. and The calculation formula is as follows:

[0038]

[0039]

[0040] In the formula, t i All emitted electrons e at all times before time i',j,k,l,h (where i'=1,2,…,i) position z i′,j,k,l,h ;

[0041] d is the height of the discharge area; Used to determine whether there is a collision with the upper metal plate. Used to determine whether a collision occurs with the lower metal plate or the medium surface.

[0042] Preferably, t i The weight w of all emitted electrons at the moment i,j,k,l,h The calculation formula is as follows:

[0043]

[0044] P v,k , P θ,l , represent the secondary electron emission speed v e , polar angle θ e and azimuth φ e The probability density function of v e ,θ e and φ e The probability corresponding to the discretized p, q and s discrete values, where k = 1…p, l = 1…q, h = 1…s. p, q, s are the number of discrete values ​​of the velocity, polar angle and azimuth angle of the secondary electron emission, respectively.

[0045] Preferably, t i The total number of electrons in space at time N(t i ) and the number of space electrons N in each thin layer sheet,c (t i ):

[0046]

[0047]

[0048] In the formula, is a Boolean-valued function representing the electron e i′,j,k,l,h In t i Whether the moment is located in the cth thin layer, is a Boolean-valued function representing the electron e i′,j,k,l,h In t i And whether the upper plate or the lower plate has been hit at some time before.

[0049] Preferably, t i The total number of electrons in space at time N(t i ) and the number of charges accumulated on the dielectric surface N surface (t i ) and the number of space electrons N in each thin layer sheet,c (t i ).

[0050]

[0051]

[0052]

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) The method of the present invention discretizes the probability density function of the secondary electron emission velocity and angle, uses a numerical calculation method to determine the motion trajectory of the particles, and obtains the evolution process of micro-discharge under the excitation of linear frequency modulation signals, which provides an effective means for the calculation of micro-discharge of microwave components under linear frequency modulation signals;

[0055] (2) The present invention uses a multi-layer charge model to simulate the distribution of dielectric surface charge and space charge, accurately calculates the self-extinguishing effect caused by dielectric surface charge and the saturation effect caused by space charge, and realizes accurate calculation of micro-discharge of dielectric microwave components. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of the present invention;

[0057] Figure 2Schematic diagram of medium loading parallel plates in an embodiment of the present invention;

[0058] Figure 3 The linear frequency modulation signal waveform in the embodiment of the present invention;

[0059] Figure 4 is the secondary electron emission velocity v in the embodiment of the present invention e , polar angle θ e and azimuth Definition of;

[0060] Figure 5 An equivalent multi-layer charge model of space electrons in an embodiment of the present invention;

[0061] Figure 6 The figure shows the evolution process of micro-discharge of microwave components under linear frequency modulation signal in the embodiment of the present invention. DETAILED DESCRIPTION

[0062] The specific implementation modes of the present invention are described in detail below with reference to the accompanying drawings.

[0063] like Figure 1 Shown is a flow chart of the present invention, comprising Figure 1 It can be seen that the present invention provides a method for calculating the micro-discharge of microwave components under linear frequency modulation signals. Figure 2 The parallel plate structure shown in the figure is used as an example to illustrate. Figure 2 The parallel plate structure includes two metal plates, the lower one and the lower one. The dielectric is placed on the lower metal plate, and the discharge area is between the dielectric and the upper metal plate. The main steps of the method are as follows:

[0064] (1) Given the secondary electron emission coefficients of dielectric materials and metal materials, the relative dielectric constant of the medium is ε r , the dielectric thickness is h, the distance between the dielectric and the upper plate is d, and the dielectric area facing the upper metal plate is A;

[0065] (2) Apply a linear frequency modulation signal V to the two metal plates rf (t)

[0066]

[0067] Where V 0 is the amplitude, f is the initial frequency of the linear FM signal, B w is the bandwidth, τ is the pulse width, and the repetition period of the linear frequency modulation signal is T, that is,

[0068] V rf (t) = V rf (t+T) (2)

[0069] The ratio of pulse width to period is called duty cycle η, i.e. η = τ / T;

[0070] (3) In the aforementioned linear frequency modulation signal V rf (t), the RF electric field in the vacuum region is

[0071]

[0072] Where d is the vacuum gap, h is the dielectric layer thickness, ε r is the relative dielectric constant of the medium;

[0073] (4) Electrons are incident on the surface of the electrode to generate secondary electrons. According to the emission speed v of the secondary electrons e , polar angle θ e and azimuth The probability density function f v 、f θ and Put v e Discretized into probabilities P v,1 ,P v,2 ,…,P v,p p values ​​v e,1 ,v e,2 ,…,v e,p . Similarly, θ e Discretized into probabilities P θ,1 ,P θ,2 ,…,P θ,q The q values ​​of θ e,1 ,θ e,2 ,…,θ e,q , Discretized into probabilities are s values ​​of

[0074] The velocity ve, polar angle θe and azimuth angle of secondary electron emission All of them are random, and their definitions are as follows Figure 4 As shown, they are independent random variables, and their probability density functions fv, fθ and They are

[0075]

[0076] f θ (θ e )=cosθ e (5)

[0077]

[0078] where v t is the heat diffusion rate, which is determined by the material properties and is usually given by the heat diffusion energy W t It means that the relationship between the two is Where m is the mass of the electron, e is the absolute value of the electron charge, W t =2eV.

[0079] Since the field distribution of the parallel plate waveguide is a uniform field, the secondary electron emission azimuth is symmetrical in all directions. The number of discrete emission azimuths is s = 1, and the number of discrete emission speeds and polar angles is p = 20, q = 10. (5) The simulation time is T s , set the simulation time T s The time interval Δt is much smaller than the excitation signal period, usually 1 / 50 of the period corresponding to the initial frequency of the linear frequency modulation signal. Set the initial electron incident upper plate or lower plate, as well as the speed and angle of the incident electron.

[0080] The initial electron is marked as e 0 Here, the initial electron and the subsequent secondary electrons represent a class of electrons with the same motion state, rather than a single electron. The actual number of electrons it contains is called its weight. The weight of the initial electron is set to w 0 =1, calculate the secondary electron emission coefficient σ of this collision based on the speed and angle of the incident electron 0 Calculate t according to the following formula 1 =The weight of the secondary electrons emitted at time 0.

[0081]

[0082] w 1,2,k,l,h Middle 1 finger t 1 At this moment, the 2nd finger hits the lower plate (i.e. the dielectric surface)

[0083] Initialization: Due to t 1 = 0, an electron is emitted from the surface of the medium, so Q surface (t 1 )=-e, c=1,2,…n c , n c =20

[0084] Where e represents the electron charge, set the loop variable i = 2, and enter the following loop:

[0085] (6) Calculate t i The RF field E in the parallel plate waveguide at the moment rf (t i ), surface charge and space charge Coulomb field E surface (t i ), space charge Coulomb field E space (t i ), whose sum is the total electromagnetic field.

[0086] E total (t i )=E rf (t i )+E surface (t i )+E space (t i ) (8)

[0087]

[0088]

[0089]

[0090] (7) Update t i All emitted electrons e at all times before time i',j,k,l,h (where i'=1,2,…,i) position z i′,j,k,l,h , to determine whether they have hit the plate surface, and calculate the Boolean function according to the following formula and

[0091]

[0092] (8) Electronic i',j,k,l,h If it hits the plate, calculate the secondary electron emission coefficient σ of this collision based on its incident speed and angle i',j,k,l,h , at any time t i , there may be multiple electrons colliding with the same plate at the same time. The total weight of all emitted electrons after the collision is equal to the sum of the weights of all incident electrons at this moment multiplied by their secondary electron emission coefficients, that is,

[0093]

[0094] Calculate t according to the following formula i The weight w of all emitted electrons at the moment i,j,k,l,h .

[0095]

[0096] (9) Calculate t according to the following formula i The total number of electrons in space at time N(t i ) and the number of charges accumulated on the dielectric surface N surface (t i ) and the number of space electrons N in each thin layer sheet,c (t i ).

[0097]

[0098] in is a Boolean-valued function representing the electron e i′,j,k,l,h In t i And whether it has hit the upper plate or the lower plate at a certain moment before, the calculation method is

[0099]

[0100]

[0101]

[0102] in is a Boolean-valued function representing the electron e i′,j,k,l,h In t i Whether the moment is located on the cth thin layer is calculated as follows:

[0103]

[0104] (10) i plus 1, to determine whether the simulation time reaches T s If it is reached, exit the loop; if it is not reached, go to step 6.

[0105] (11) Finally, we get the fluctuation function of the number of electrons in space during micro-discharge: N(t i ), thereby obtaining the analytical results of spatial electron fluctuations.

[0106] The above method is applicable to the case of micro-discharge calculation of dielectric loaded parallel plate under linear frequency modulation signal. Here, the implementation process of this method is introduced by taking the parallel plate loaded with a certain dielectric by a silver metal plate as an example. The SEY parameters of silver are Wmax=165, δmax=2.22; the SEY parameters of a certain dielectric material are Wmax=327, δmax=1.86, and the dielectric constant ε r is 9.4, d = 1 mm, h = 1 mm, and the area of ​​the medium facing the upper metal plate is A = 4 cm 2 The starting frequency f of the linear frequency modulation signal is 1GHz, the bandwidth Bw is 10MHz, the pulse width τ is 10ns, the repetition period T is 20ns, the duty cycle η is 50%, and the waveform of the linear frequency modulation signal is as follows Figure 3 As shown. t =2eV. The number of emission azimuth discretizations is s=1, the number of emission velocity and polar angle discretizations is p=20, q=10. The space electrons are divided into n c = 20 layers, such as Figure 5 As shown in FIG. 1 , Ts is 60ns, and Δt is 0.02ns.

[0107] When the voltage is 54V, 56V and 58V respectively, the micro-discharge calculation results of the linear frequency modulation signal with different excitation voltages are as follows Figure 6 shown.

[0108] Example 2

[0109] The present invention is also applicable to the case where the parallel plate structure only includes two upper and lower metal plates, and the discharge area between the upper and lower metal plates does not include a dielectric. In this case, the method implementation steps are slightly different from those of Example 1, which are specifically reflected in the following aspects:

[0110] 1. Electron injection initialization includes:

[0111] Label the initial electron as e 0 , the initial electrons and secondary electrons both represent a type of electrons with the same motion state. The actual number of electrons contained is called its weight. The weight of the initial electron is set to w 0 = 1, the secondary electron emission coefficient σ of the initial collision is calculated based on the speed and angle of the incident electron 0 ;

[0112] Calculate t according to the following formula 1 =The weight of the secondary electrons emitted at time 0.

[0113]

[0114] The subscript 1 represents t 1 Moment, 2 refers to the collision with the lower plate, i.e., the surface of the medium or the surface of the lower metal plate;

[0115] Initialization: Assume t 1 = 0, an electron is emitted from the lower metal surface, so Q surface (t 1 )=0, the emitted electron enters the nth c The electron thin layer of the layer, c=1,2,…n c

[0116] Where e represents the electron charge, n c is the total number of thin layers.

[0117] 2. The total electromagnetic field calculation formula is as follows:

[0118] E total (t i )=E rf (t i )+E surface (t i )+E space (t i )

[0119] Among them, E rf (t i ) is t i The RF field in the parallel slab waveguide,

[0120] E surface (t i ) takes a value of 0.

[0121] 3. Determine whether the emitted electron has hit the plate surface by calculating the Boolean function. and The calculation formula is as follows:

[0122]

[0123]

[0124] In the formula, t i All emitted electrons e at all times before time i',j,k,l,h (where i'=1,2,…,i) position z i′,j,k,l,h ;

[0125] d is the height of the discharge area; Used to determine whether there is a collision with the upper metal plate. Used to determine whether there is a collision with the lower metal plate.

[0126] 4. t i The total number of electrons in space at time N(t i ) and the number of space electrons N in each thin layer sheet,c (ti):

[0127]

[0128]

[0129] In the formula, is a Boolean-valued function representing the electron e i′,j,k,l,h In t i Whether the moment is located in the cth thin layer, is a Boolean-valued function representing the electron e i′,j,k,l,h In t i And whether the upper or lower metal plate has been hit at some time before.

[0130] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for calculating micro-discharge of microwave components under linear frequency modulation signal, characterized in that This is accomplished by: Discretize the probability density function of the secondary electron emission velocity and angle, and the linear frequency modulation signal; The discharge area is divided into parallel thin layers, electron injection is initialized, and the following iterations are performed until the simulation duration reaches the preset duration: The discrete trajectory of electron movement is obtained by combining the parallel plate structure, the charge of the thin layer is updated according to each movement and collision of the electron, and the electric field distribution at the current iteration moment is calculated using the updated thin layer charge; the parallel plate structure includes two upper and lower metal plates, and the discharge area is between the upper and lower metal plates; The electric field distribution calculated above is combined with the electric field of the discrete value of the linear frequency modulation signal as the total electromagnetic field, and the total electromagnetic field is used to accelerate the electrons, update the positions of all emitted electrons at all times before the current iteration, and determine whether they have hit the surfaces of the upper and lower metal plates, and calculate the secondary electron emission coefficient when the collision occurs; According to the secondary electron emission coefficient combined with the probability density function of the secondary electron emission velocity and angle after discretization, the weights of all emitted electrons at the current iteration moment are calculated; According to the weights of all the emitted electrons mentioned above, the total number of space electrons and the space electron data of each thin layer are updated to complete one iteration; The total electromagnetic field is calculated as follows: E total (t i )=E rf (t i )+E surface (t i )+E space (t i ) Among them, E rf (t i ) is t i The RF field in the parallel slab waveguide, E surface (t i ) is the Coulomb field of the dielectric surface charge, εr is the relative dielectric constant of the medium, h is the thickness of the medium, d is the distance between the medium and the upper metal plate, A is the area of ​​the medium facing the upper metal plate, Q surface (t i-1 ) is t i-1 The surface charge of the medium at the moment; ε0 is the dielectric constant of vacuum. When there is no dielectric in the parallel plate structure, E surface (t i ) takes the value of 0; E space (t i ) is the space charge Coulomb field, which is the sum of the electric fields of all thin layers:

2. A method for calculating micro-discharge of microwave components under linear frequency modulation signal, characterized in that This is accomplished by: Discretize the probability density function of the secondary electron emission velocity and angle, and the linear frequency modulation signal; The discharge area is divided into parallel thin layers, electron injection is initialized, and the following iterations are performed until the simulation duration reaches the preset duration: The discrete trajectory of electron movement is obtained by combining the parallel plate structure, and the surface charge of the medium and the thin layer are updated according to each movement and collision of the electrons. The surface charge of the medium and the thin layer charge after the updated charge are used to calculate the electric field distribution at the current iteration moment; the above parallel plate structure includes two upper and lower metal plates, the medium is placed on the lower metal plate, and the discharge area is between the medium and the upper metal plate; The electric field distribution calculated above is combined with the electric field of the discrete value of the linear frequency modulation signal as the total electromagnetic field, and the total electromagnetic field is used to accelerate the electrons, update the positions of all emitted electrons at all times before the current iteration, and determine whether they have hit the metal plate surface and the medium surface, and calculate the secondary electron emission coefficient when the collision occurs; According to the secondary electron emission coefficient combined with the probability density function of the secondary electron emission velocity and angle after discretization, the weights of all emitted electrons at the current iteration moment are calculated; According to the weights of all the emitted electrons mentioned above, the total number of space electrons, the data of accumulated charge on the surface of the medium and the space electron data of each thin layer are updated to complete one iteration; The total electromagnetic field is calculated as follows: E total (t i )=E rf (t i )+E surface (t i )+E space (t i ) Among them, E rf (t i ) is t i The RF field in the parallel slab waveguide, E surface (t i ) is the Coulomb field of the dielectric surface charge, εr is the relative dielectric constant of the medium, h is the thickness of the medium, d is the distance between the medium and the upper metal plate, A is the area of ​​the medium facing the upper metal plate, Q surface (t i-1 ) is t i-1 The surface charge of the medium at the moment; ε0 is the dielectric constant of vacuum. When there is no dielectric in the parallel plate structure, E surface (t i ) takes the value of 0; E space (t i ) is the space charge Coulomb field, which is the sum of the electric fields of all thin layers:

3. The method according to claim 1 or 2, characterized in that: The simulation iteration step Δt is 1 / 100 to 1 / 50 of the period corresponding to the initial frequency.

4. The method according to claim 1 or 2, characterized in that: The principle of dividing the thin layer of the discharge area is: divide the discharge area into n c Each thin layer is located at the center of each equally divided area, and the thickness of the equally divided area is not greater than 0.05mm.

5. The method according to claim 1 or 2, characterized in that: Electron injection initialization includes: The initial electron is marked as e0. The initial electron and the secondary electron both represent a type of electron with the same motion state. The actual number of electrons contained in it is called its weight. The weight of the initial electron is set to w0 = 1. The secondary electron emission coefficient σ0 of the initial collision is calculated according to the speed and angle of the incident electron. The weight of the secondary electron emitted at time t1=0 is calculated according to the following formula: Where subscript 1 represents the time t1, and 2 refers to the collision lower plate, that is, the surface of the dielectric or the surface of the lower metal plate; Initialization: When the parallel plate structure contains a medium, assume that an electron is emitted from the surface of the medium at time t1 = 0, so Q surface (t1) = -e, the emitted electron enters the nth c layer of electrons, c=1,2,…n c ; When there is no medium in the parallel plate structure, assume that an electron is emitted from the lower metal surface at time t1 = 0, so Q surface (t1) = 0, the emitted electron enters the nth c The electron thin layer of the layer, c=1,2,…n c Where e represents the electron charge, n c is the total number of thin layers.

6. The method according to claim 1 or 2, characterized in that: Where c = 1, 2, ... n c , n c is the total number of thin layers; z′ is the position of the cth electron thin layer, z is the position of the electric field to be solved, Q sheet,c (t i-1 ) The charge of the cth electron layer, E sheet,u (t i ) is the electric field above the cth electron layer, E sheet,d (t i ) The electric field below the cth electron layer, E sheet,m (t i ) is the electric field at the location of the cth electron layer.

7. The method according to claim 1 or 2, characterized in that: By calculating the Boolean function, it is determined whether the emitted electron has hit the surface of the plate. and The calculation formula is as follows: Where, t i All emitted electrons e at all times before time i',j,k,l,h Position z i′,j,k,l,h , where i'=1,2,...,i; d is the height of the discharge area; Used to determine whether there is a collision with the upper metal plate. Used to determine whether a collision occurs with the lower metal plate or the medium surface.

8. The method according to claim 7, characterized in that: t i The weight w of all emitted electrons at the moment i,j,k,l,h The calculation formula is as follows: P v,k , P θ,l , represent the secondary electron emission speed v e , polar angle θ e and azimuth φ e The probability density function of v e ,θ e and φ e The probability corresponding to the discretization of p, q and s discrete values, where k = 1...p, l = 1...q, h = 1...s; p, q, s are the discrete numbers of the velocity, polar angle and azimuth angle of the secondary electron emission, respectively, and w i′,j′,k′,l′,h′ , σ i′,j′,k′,l′,h′ Represents t i′ The weight and secondary electron emission coefficient of secondary electrons emitted from the upper and lower plates at different emission velocities, polar angles, and azimuth angles at all times.

9. The method according to claim 7, characterized in that: t i The total number of electrons in space at time N(t i ) and the number of space electrons N in each thin layer sheet,c (t i ): In the formula, is a Boolean-valued function representing the electron e i′,j,k,l,h In t i Whether the moment is located in the cth thin layer, is a Boolean-valued function representing the electron e i′,j,k,l,h In t i and whether the upper plate or the lower plate has been hit at some point in the past, w i′,j,k,l,h Represents t i′ The weight of secondary electrons emitted from the upper and lower plates at different emission velocities, polar angles, and azimuth angles at all times.

10. The method according to claim 9, characterized in that: t i The total number of electrons in space at time N(t i ) and the number of charges accumulated on the dielectric surface N surface (t i ) and the number of space electrons N in each thin layer sheet,c (t i ).

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