CN110781581B - Method for analyzing space electron fluctuation in medium single-surface micro-discharge process - Google Patents

Method for analyzing space electron fluctuation in medium single-surface micro-discharge process Download PDF

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CN110781581B
CN110781581B CN201910950630.8A CN201910950630A CN110781581B CN 110781581 B CN110781581 B CN 110781581B CN 201910950630 A CN201910950630 A CN 201910950630A CN 110781581 B CN110781581 B CN 110781581B
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申发中
王新波
崔万照
冉立新
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Abstract

The invention discloses an analytic method of space electron fluctuation in a medium single-surface micro-discharge process. High-energy particles are incident to the surface of the medium to generate secondary electrons, and the probability density function of the transit time of the secondary electrons and the emission transfer rate of the secondary electrons are calculated according to the probability density function of the emission speed, the emission polar angle and the emission azimuth angle of the secondary electrons; calculating the emissivity and incidence rate of secondary electrons on the surface of the medium according to the probability density function of the transition time of the secondary electrons and the emission transfer rate of the secondary electrons, and finally processing to obtain a fluctuation function of the number of the space electrons in the micro-discharge process of the single surface of the medium so as to obtain an analytic result of the fluctuation of the space electrons. The invention has no relation with the number of space electrons, solves the difficulty that the Monte Carlo method has larger and larger calculation amount along with the increase of the number of micro-discharge electrons, and has accurate and reliable result.

Description

Method for analyzing space electron fluctuation in medium single-surface micro-discharge process
Technical Field
The invention relates to a medium single-surface micro-discharge analysis method, in particular to an analysis method of space electron fluctuation in a medium micro-discharge process in a high-power vacuum microwave device.
Background
Dielectric microdischarge is a space electron avalanche effect based on secondary electron emission that occurs on the surface of a medium in a high power vacuum microwave component. It seriously threatens the long-term stability of microwave components in the application fields of space, accelerators and the like. Accurate analysis of the microdischarge process is important in order to predict and suppress the occurrence of microdischarges in the medium.
The analytic expression of the medium microdischarge process is quite complex. Compared with metal microdischarge, the medium microdischarge is significantly different in that a large amount of static charges can be accumulated on the surface of the medium, and the generated static electric field can significantly influence the emission of secondary electrons, so that the phenomena of medium single-surface microdischarge, space charge saturation, oscillation and the like can occur.
The traditional approach to study dielectric microdischarges is particle simulation based on the monte carlo method. The monte carlo method requires a large amount of computational resources and computational time due to the need to track each particle. In order to solve the problem, a steady-state statistical model is recently proposed and used for resolving the dielectric single-surface micro-discharge threshold, however, the method cannot obtain the fluctuation rate of the number of space electrons in the micro-discharge process. At present, an unsteady state statistical model for metal waveguide micro-discharge can be obtained by processing electron number fluctuation rate, but cannot be used for medium micro-discharge, and the model only considers the randomness of secondary electron emission speed, ignores the randomness of secondary electron emission angle, and has certain influence on accuracy.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides an analytical method of space electron fluctuation in a medium single-surface micro-discharge process, which can also be used as a suppression mode of medium single-surface micro-discharge, the method takes the randomness of the velocity, polar angle and azimuth angle of secondary electron emission into consideration, the precision is high, the calculation time is irrelevant to the number of space electrons, and the accuracy of micro-discharge result test is improved.
The invention adopts the specific technical scheme that:
1) high-energy particles are incident on the surface of the medium to generate secondary electrons according to the emission speed v of the secondary electronseAngle of emission pole thetaeAnd azimuth of transmission
Figure GDA0002988137050000011
Probability density function fv(ve)、fθ(θe) And
Figure GDA0002988137050000012
calculating the probability density function f of the transit time of the secondary electronsτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2)，t1And t2Respectively representing the starting time and the ending time of the secondary electron emission transfer;
the surface of the single surface of the medium is the surface of the medium. In a specific implementation, the medium is arranged in the waveguide and is used as a medium window of the waveguide.
Applied RF field E according to surface area of mediumrfcos (ω t) and DC field EdcCalculating the escape time, the speed, the polar angle and the azimuth angle as t respectivelye、ve、θeAnd
Figure GDA0002988137050000021
calculating the time t of re-incidence on the surface of the mediumiVelocity viAnd polar angle thetai。
2) Then according to the probability density function f of the transit time of the secondary electronsτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2) Calculating emissivity E of secondary electrons on medium surfacem(t) and incidence rate ImAnd (t) and t represents time, and finally, the fluctuation function N (t) of the number of space electrons in the medium single-surface micro-discharge process is obtained through reprocessing, so that the analysis result of the space electron fluctuation is obtained.
The calculation amount and the calculation time of the method are independent of the number of space electrons.
The calculation of the probability density function and the emission transfer rate comprises three calculation methods: consider ve、θeAnd
Figure GDA0002988137050000022
method for calculating randomness of three components only considering veAnd thetaeBoth randomness calculation method and only considering veAnd (4) a calculating method of randomness.
The step 1) is selected as one of the following three calculation methods:
a) the emission velocity v according to the secondary electronseAngle of emission pole thetaeAnd azimuth of transmission
Figure GDA0002988137050000023
The randomness of the three is calculated by adopting the following formula to obtain the probability density function and the emission transfer rate of the secondary electrons:
Figure GDA0002988137050000024
Figure GDA0002988137050000025
a) the emission velocity v according to the secondary electronseAngle of emission pole thetaeThe randomness of the two is calculated by adopting the following formulas to obtain the probability density function and the emission transfer rate of the secondary electrons:
Figure GDA0002988137050000026
Figure GDA0002988137050000027
a) the emission velocity v according to the secondary electronseRandomness, and calculating the probability density function and the emission transfer rate of the secondary electrons by adopting the following formulas:
fτ(τ)＝(adc/2)fv(adcτ/2)
CEE(te,ti)＝fτ(ti-te)σ(vi,θi)
wherein f isτ(τ) probability density function representing the transit time τ of the secondary electrons, CEE(te,ti) Represents the emission transfer rate of secondary electrons; τ denotes the transit time of the secondary electrons, teAnd tiRespectively indicate the time when the secondary electrons are emitted from the surface of the medium and the time when the secondary electrons are emitted and then enter the surface of the medium again, ti、viAnd thetaiRespectively representing the incidence time, incidence speed and incidence polar angle of secondary electrons incident to the surface of the medium; a isdcRepresenting the acceleration of the secondary electrons, fv(ve) Represents the secondary electron emission velocity veIs determined by the probability density function of (a),
Figure GDA0002988137050000031
indicating the azimuth of secondary electron emission
Figure GDA0002988137050000032
Of the probability density function of σ (v)i,θi) Indicating the velocity v of the secondary electronsiPolar angle of incidence thetaiCorresponding secondary electron emission coefficient, f, incident on the surface of the mediumv(adcτ/2) represents the secondary electron emission velocity ve＝adcTau/2 time veProbability density of fτ(ti-te) Denotes when the transit time τ is ti-teProbability density of time τ.
The step 2) is specifically as follows:
2.1) probability density function f according to the transit time of the secondary electronsτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2) Calculating the exitance E of the surface electrons of the mediumm(t) and incidence rate Im(t)：
Figure GDA0002988137050000033
Figure GDA0002988137050000034
Wherein, CEE(t ', t) represents a secondary electron emission transfer rate from time t ' to time t, t ' and t represent a start time and an end time of the secondary electron emission transfer, respectively, Em(t ') represents the secondary electron emission rate of the dielectric surface at time t', and δ (t) represents the secondary electron emission rate applied to the dielectric surface;
2.2) the method for calculating the fluctuation function N (t) of the number of space electrons along with the time in the microdischarge process is as follows:
Figure GDA0002988137050000035
wherein t represents the observation time, Im(t ') represents the absorption rate of the secondary electrons on the surface of the medium at time t'.
According to the invention, after the fluctuation condition is obtained, the discharge condition of the single surface of the medium is obtained, so that the structure and parameters of the single surface of the medium are adjusted, the micro discharge of the single surface of the medium is inhibited, and the performance of the high-power microwave vacuum device containing the medium material is improved.
The invention has the beneficial effects that:
compared with a micro-discharge space electron fluctuation analysis method based on a Monte Carlo method, the micro-discharge space electron fluctuation analysis method based on the Monte Carlo method has the advantages that analysis processing is irrelevant to the number of space electrons, and the difficulty that the calculation amount is larger and larger along with the increase of the number of micro-discharge electrons in the Monte Carlo method is solved.
The method provided by the invention covers the randomness of the velocity, the azimuth angle and the polar angle of secondary electron emission, and the analytic result is accurate and reliable.
Drawings
Fig. 1 is a schematic view of the state of motion of secondary electrons over the surface of a medium.
FIG. 2 is a probability density of transit time fτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2) Schematic diagram of the analytic principle of (1).
FIG. 3 is a diagram of analysis results and simulation results for a typical example.
Detailed Description
An implementation of the present invention is described in detail below with reference to the accompanying drawings in the embodiments of the present invention.
As shown in FIG. 1, in the micro-discharge process of a single-surface medium, space electrons are subjected to a radio-frequency electric field E parallel to the surface of the mediumrfcos (ω t) and DC electric field E perpendicular to the surface of the mediumdcUnder the action of the two electric fields, each secondary electron escaping from the surface of the medium returns to the surface of the medium again to become an incident electron under the action of the direct current electric field.
Emission time, emission speed, emitter for escape from the surface of the mediumAngle and transmitting azimuth angle are respectively te、ve、θeAnd
Figure GDA0002988137050000041
secondary electrons of (2) are incident on the surface of the medium again for an incident time tiIncident velocity viAnd polar angle of incidence thetaiRespectively as follows:
ti＝te+2(ve/adc)cosθe (1)
Figure GDA0002988137050000042
Figure GDA0002988137050000043
wherein:
adc＝eEdc/m (4)
Figure GDA0002988137050000044
Figure GDA0002988137050000045
vz,i＝-vecosθe (7)
in the formula, adcIndicating the acceleration of the secondary electrons, EdcRepresenting a direct current electric field perpendicular to the surface of the medium, m representing the mass of electrons, and e representing the electric quantity of the electrons; v. ofx,iX component representing the exit velocity of secondary electrons, ErfRepresenting the radio frequency electric field, v, parallel to the surface of the mediumy,iY component representing the initial velocity of the secondary electrons, ω the angular frequency of the radio-frequency electric field, vz,iAnd a z-component representing the exit velocity of the secondary electrons.
Transit time τ ═ ti–teFor a particular transit time τ, there isV in infinityeAnd thetaeAnd lead to different viAnd thetai. A special case is if the emitter angle thetaeFixed at zero, each particular time of flight τ corresponds to a particular ve、viAnd thetai。
Velocity v of secondary electron emissionePolar angle thetaeAnd azimuth angle
Figure GDA0002988137050000046
The probability distribution models are respectively in accordance with:
Figure GDA0002988137050000051
fθ(θe)＝cosθe (9)
Figure GDA0002988137050000052
wherein v istIs the rate of thermal diffusion, usually from the thermal diffusion energy WtShowing that the two are in the relationship of
Figure GDA0002988137050000053
Where m and e are the mass and the charge of the electrons, respectively. The secondary electron emission coefficient is expressed as σ (v)i,θi) The Vaughan model can be used. f. ofv(ve)、fθ(θe)、
Figure GDA0002988137050000054
Respectively representing the velocity vePolar angle thetaeAnd azimuth angle
Figure GDA0002988137050000055
Is determined.
FIG. 2 shows the probability density f of transit timeτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2) The principle of calculation of (1). Let us assume at t1To t1+Δt1The number of electrons emitted from the surface of the medium in the time period is N1In which N is2Electrons in t2To t2+Δt2Back to the surface of the medium for a period of time, where N2N escapes from the surface of the medium under the incidence of the electrons3An electron, then fτ(τ) and CEE(t1,t2) Is defined as follows:
Figure GDA0002988137050000056
Figure GDA0002988137050000057
and then according to the probability density function f of the transit time of the secondary electronsτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2) Calculating emissivity E of secondary electrons on medium surfacem(t) and incidence rate ImAnd (t), t represents time, and finally the fluctuation function N (t) of the number of space electrons in the medium single-surface micro-discharge process is obtained through reprocessing.
In specific implementation, the integral equation is converted into a linear matrix equation through time discretization, and numerical calculation is completed.
In the above calculation process, the secondary electron emission velocity v is consideredePolar angle thetaeAnd azimuth angle
Figure GDA0002988137050000058
Probability density function f of secondary electron transit time in different processing modes of randomnessτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2) There are three calculation methods of (1):
1) consider ve、θeAnd
Figure GDA0002988137050000059
the calculating method of the randomness of the three components has the calculating formula
Figure GDA00029881370500000510
Figure GDA00029881370500000511
2) Will be provided with
Figure GDA00029881370500000512
Fixed at 90 degrees, not considering its randomness, only considering veAnd thetaeThe calculation method of the randomness of the two is as follows
Figure GDA0002988137050000061
Figure GDA0002988137050000062
3) Will thetaeAnd
Figure GDA0002988137050000063
respectively fixed at 0 degree and 90 degrees, and only v is considered without considering randomnesseA method for calculating randomness, the calculation formula is
fτ(τ)＝(adc/2)fv(adcτ/2)
CEE(te,ti)＝fτ(ti-te)σ(vi,θi)
The experimental measurement is specifically carried out in the rectangular waveguide loaded with the dielectric window in the high-power vacuum environment, and the experimental measurement is taken as a typical example. The analysis result and the simulation result of the typical example are shown in fig. 3, and the analysis result calculation process adopts three methods, namely, v is considerede、θeAnd
Figure GDA0002988137050000064
method for randomness of three components, only considering veAnd thetaeMethod for randomness of both and only considering veThe random method adopts commercial particle simulation software CST for simulation. In simulation, the frequency of the radio frequency field is 1GHz, and the strengths of the radio frequency electric field and the direct current electric field are 1.2MV/m and 0.3MV/m respectively. FIG. 3 illustrates consider ve、θeAnd
Figure GDA0002988137050000065
the randomness method of the three is closest to the CST simulation result and is most accurate.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (1)

1. An analytical method for space electron fluctuation in a medium single-surface micro-discharge process is characterized by comprising the following steps:
1) high-energy particles are incident on the surface of the medium to generate secondary electrons according to the emission speed v of the secondary electronseAngle of emission pole thetaeAnd azimuth of transmission
Figure FDA0002988137040000015
Probability density function fv(ve)、fθ(θe) And
Figure FDA0002988137040000016
calculating the probability density function f of the transit time of the secondary electronsτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2)，t1And t2Respectively representing the starting time and the ending time of the secondary electron emission transfer;
2) then according to the probability density function f of the transit time of the secondary electronsτ(τ) and twoSecondary electron emission transfer rate CEE(t1,t2) Calculating emissivity E of secondary electrons on medium surfacem(t) and incidence rate Im(t), t represents time, and finally, the fluctuation function N (t) of the number of space electrons in the medium single-surface micro-discharge process is obtained through reprocessing, so that the analysis result of the space electron fluctuation is obtained;
the step 1) is selected as one of the following three calculation methods:
a) the emission velocity v according to the secondary electronseAngle of emission pole thetaeAnd azimuth of transmission
Figure FDA0002988137040000017
The randomness of the three is calculated by adopting the following formula to obtain the probability density function and the emission transfer rate of the secondary electrons:
Figure FDA0002988137040000011
Figure FDA0002988137040000012
a) the emission velocity v according to the secondary electronseAngle of emission pole thetaeThe randomness of the two is calculated by adopting the following formulas to obtain the probability density function and the emission transfer rate of the secondary electrons:
Figure FDA0002988137040000013
Figure FDA0002988137040000014
a) the emission velocity v according to the secondary electronseRandomness, and calculating the probability density function and the emission transfer rate of the secondary electrons by adopting the following formulas:
fτ(τ)＝(adc/2)fv(adcτ/2)
CEE(te,ti)＝fτ(ti-te)σ(vi,θi)
wherein f isτ(τ) probability density function representing the transit time τ of the secondary electrons, CEE(te,ti) Represents the emission transfer rate of secondary electrons; τ denotes the transit time of the secondary electrons, teAnd tiRespectively indicate the time when the secondary electrons are emitted from the surface of the medium and the time when the secondary electrons are emitted and then enter the surface of the medium again, ti、viAnd thetaiRespectively representing the incidence time, incidence speed and incidence polar angle of secondary electrons incident to the surface of the medium; a isdcRepresenting the acceleration of the secondary electrons, fv(ve) Represents the secondary electron emission velocity veIs determined by the probability density function of (a),
Figure FDA0002988137040000021
indicating the azimuth of secondary electron emission
Figure FDA0002988137040000022
Of the probability density function of σ (v)i,θi) Indicating the velocity v of the secondary electronsiPolar angle of incidence thetaiCorresponding secondary electron emission coefficient, f, incident on the surface of the mediumv(adcτ/2) represents the secondary electron emission velocity ve＝adcTau/2 time veProbability density of fτ(ti-te) Denotes when the transit time τ is ti-teProbability density of time τ;
the step 2) is specifically as follows:
2.1) probability density function f according to the transit time of the secondary electronsτ(τ) and Secondary Electron emission transfer Rate CEE(t1,t2) Calculating the exitance E of the surface electrons of the mediumm(t) and incidence rate Im(t)：
Figure FDA0002988137040000023
Figure FDA0002988137040000024
Wherein, CEE(t ', t) represents a secondary electron emission transfer rate from time t ' to time t, t ' and t represent a start time and an end time of the secondary electron emission transfer, respectively, Em(t ') represents the secondary electron emission rate of the dielectric surface at time t', and δ (t) represents the secondary electron emission rate applied to the dielectric surface;
2.2) the method for calculating the fluctuation function N (t) of the number of space electrons along with the time in the microdischarge process is as follows:
Figure FDA0002988137040000025
wherein, Im(t ') represents the absorption rate of the secondary electrons on the surface of the medium at time t'.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102880783A (en) * 2012-07-27 2013-01-16 西安空间无线电技术研究所 Method for determining coaxial configuration micro-discharging threshold value

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Publication number Priority date Publication date Assignee Title
CN102880783A (en) * 2012-07-27 2013-01-16 西安空间无线电技术研究所 Method for determining coaxial configuration micro-discharging threshold value

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Multipactor threshold calculation of coaxial trasmission lines in microwave applications with nonsationary statistical theory;S.Lin等;《Physics of Plasmas》;20150814;第22卷(第8期);082114 *
Nonstationary statistical theory for multipactor;S.Anza等;《Physics of Plasmas》;20100628;第17卷(第6期);062110 *
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