CN104679920B - Waveguide device microwave gas discharge method for numerical simulation - Google Patents
Waveguide device microwave gas discharge method for numerical simulation Download PDFInfo
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Abstract
The invention discloses a kind of waveguide device microwave gas discharge method for numerical simulation, this method establishes the fluid model of microwave gas discharge in waveguiding structure, accurate numerical analysis has been carried out for electron density, electronic fluid speed and mean electron energy during gas breakdown, can obtain the rule that the electric-field intensity of different given viewpoints changes over time with electron density in the case of gas discharge in the labyrinth waveguide device of different geometric shapes.The present invention is based on time domain spectral element method, it is possible to achieve the modeling of arbitrarily complicated structured waveguide device；The mass matrix of generation is that block diagonal matrix can directly obtain inverse matrix, greatly reduces and calculates the time；Internal electric field distribution and the electron density of experiment acquisition waveguide device repeatedly can be avoided passing through using the method for numerical simulation simultaneously, obtain breakdown threshold, shorten the design cycle, design cost is saved, is highly suitable for realizing the effective design of Simulation and numerical simulation to the complicated waveguide device with discontinuous structure.
Description
Technical field
The invention belongs to the electromagnetic property emulation technology of multiple physical field, particularly a kind of analysis waveguiding structure microwave device
The New Type of Numerical emulation mode of part gas discharge breakdown.
Background technology
With making rapid progress for space technology, the circuit level more and more higher of electronic equipment, the work frequency of microwave device
Rate improves constantly；Simultaneously tens Gw number is can reach with the continuous maturation of high-power pulse generator technology, its power output
Magnitude.Microwave device microwave breakdown to the space waveguiding structure of gas with various filling and the numerical analysis of gas discharge phenomenon with
Computer simulation is paid attention to by scientific research institution increasingly, be current space technology with high power pulse field hot it
One.Research to the problem contributes to the design and protection of microwave device, has higher application value and realistic meaning.At present
Using numerical method simulation analysis, such problem has the advantages that cost minimization, design optimization, cycle time, increasingly into
For antenatal design and the important means of prognosis modelling.It is related to multiple physical field, complexity in this one kind using numerical method simulation analysis
Nonlinear problem when, how efficiently to carry out quick full wave analysis and key Design threshold value accurately ask for it is most important.Phase
To be grown compared with the laboratory facilities cycle, cost is high, is faced with using numerical method prediction and solves object structure complexity, nonlinearity,
The solution calculating time is longer, the difficult point such as not high problem of computational accuracy.
It is mainly at present to use the time-domain finite in differential equation class method with gas discharge analysis means to microwave breakdown
Calculus of finite differences, such as document 1.Yee, Jick H., et al, " Propagation of intense microwave pulses in
Air and in a waveguide, " IEEE Transactions on Antennas and Propagation, 39.9
(1991), pp:1421-1427. and limited bulk point-score, such as document 2.Adnane Hamiaz, et al, " Finite Volume
Time Domain modelling of microwave breakdown and plasma formation in a
Metallic aperture, " Computer Physics Communications 183 (2012), pp:On 1634-1640.
State and delivered document and be used to analyze the two-dimensional gas electric discharge problem of simple structure, although can provide the electric field of simple problem with
The numeric distribution of electron density and prediction, but have model simple, accuracy is not high, calculate the time it is longer the shortcomings of.Time Domain Spectrum
First method uses hexahedral element discrete grid block, can approach the contour structures of target to be solved, the moment of mass generated well
Battle array be diagonal matrix, and inversion process is simple, and it is shorter to calculate the time, is discharged this kind of multiple physical field, non-analyzing microwave gas breakdown
There is larger advantage in terms of linear problem.There has been no carry out waveguiding structure gas discharge phenomenon using time domain spectral element method to imitate at present
Genuine document report.
The content of the invention
It is an object of the invention to provide gas in a kind of complicated microwave device to waveguiding structure based on time domain spectral element method
The numerical method that body punch-through is emulated, this method consider the mutual of gaseous medium and strong electromagnetic pulse in waveguide device
Effect, mainly including avalanche ionization, electronic molecules collision, electronic and ionic complex effect, electronic molecules adhesion effect, it can simulate
Simplify the discharge physicses process in waveguide device, meanwhile, the lead time is greatly shortened, reduces R＆D costs, can using the present invention
The Threshold Analysis and analogue simulation of punch-through suitable for all kinds of waveguide devices.
The technical scheme for realizing the object of the invention is：
The first step, the geometry subdivision model of device to be analyzed is established using Ansys softwares, according to the several of complicated waveguiding structure
What size, is modeled with cad tools, object module is entered using the hexahedral element based on GLL basic functions
Row subdivision, the geological information for obtaining target and positional information and application driving source that driving source is set；
Second step, by given atmospheric pressure, the original state of numerical simulation is provided, it is close to set electronics in waveguide device
The initial value of degree；
3rd step, according to the initial shape set in the geological information and second step of the device to be analyzed obtained in the first step
State, the differential equation group of description nonlinear gas electric discharge phenomena, the GLL basic functions pair that will be selected are established using time domain spectral element method
Five unknown electric field, magnetic field, electron density, velocity of electrons and mean electron energy known variables approximate expansions, then distinguish
The partial differential equations being made up of maxwell equation group and electronic fluid mechanical equation group are substituted into, finally select GLL basic functions
As weighting function, by the gold test of gal the Liao Dynasty, the surplus for making each differential equation under weighted average meaning is zero, thus will be continuous
Differential equation group be converted to Matrix division, obtain the unknown quantity information of each GLL points in space；
4th step, according to the Matrix division obtained by the 3rd step, using centered Finite Difference Methods, each moment is calculated successively,
The magnetic field intensity of each node, velocity of electrons, electric-field intensity, electron density, mean electron energy, are obtained at diverse location in space
The rule that above-mentioned variable changes over time；
5th step, the mean electron energy obtained according to the 4th step, renewal ionization parameter, repeat step three to step 4,
Untill the default calculating time is reached；
6th step, electromagnetic field value and electron density that each moment is calculated are exported, obtains electromagnetism in waveguide device
The rule that field changes over time with electron density, thus can calculate various electromagnetic property parameters, complete to waveguide device microwave
The analysis process of gas discharge phenomenon.
Compared with prior art, its remarkable advantage is the present invention：
（1）The fluid model that microwave gas breakdown is discharged in waveguide device is established, in waveguide device in gas discharge
The electromagnetic field of each node in portion has carried out numerical simulation calculation with electron density, velocity of electrons, mean electron energy, can quantify
The known variables at any unknown point are provided, can be with using the waveguide device microwave gas discharge method for numerical simulation of the present invention
The gas breakdown threshold value that experiment repeatedly obtains waveguide device is avoided passing through, shortens the design cycle, saves design cost, realize to band
There are the effective protection simulation of the complicated waveguide device of discontinuous structure and antenatal design；
（2）A kind of waveguide device microwave gas discharge method for numerical simulation proposed by the present invention, using time domain spectral element method as base
Plinth, using hexahedron subdivision unit can be to arbitrarily complicated structured waveguide device modeling so as to realizing 3 D complex construction geometry
The modeling of information with it is discrete；It can directly be inverted for block diagonal matrix using the mass matrix of spectral element method generation, dropped significantly simultaneously
The low calculating time, calculating cost is reduced, shortens the design cycle；
（3）In waveguide device microwave gas discharge numerical model proposed by the present invention, it is contemplated that gaseous state is situated between in waveguide device
The interaction of matter and strong electromagnetic pulse, mainly including avalanche ionization, electronic molecules collision, electronic and ionic complex effect, electronics
Molecule adhesion effect, the discharge physicses process in simplified waveguide device can be simulated, employ improved Electron energy distribution letter
Number method for solving, in each time step, according to the mean electron energy tried to achieve, updates the ionization parameter of each point, solves
The close coupling problem of Maxwell equation and electronic fluid mechanical equation, it is ensured that the accuracy of ionization parameter renewal, improve
The accuracy of fluid model.
Brief description of the drawings
Fig. 1 is band slot-waveguide configuration diagrammatic cross-section.
Fig. 2 is that the first other side cone midpoint point of observation electric-field intensity changes over time rule figure.
Fig. 3 is that the first other side cone midpoint point of observation electron density changes over time rule figure.
Fig. 4 is the flow chart of the present invention.
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
The present invention proposes a kind of waveguide device microwave gas discharge method for numerical simulation.Below in conjunction with the accompanying drawings, with Fig. 1 institutes
Exemplified by showing band slot-waveguide configuration device, the specific steps of the present invention are described in further detail.
Band slot-waveguide configuration diagrammatic cross-section shown in Figure 1, model geometric size are as follows：Using BJ-100 wave guide modes
Type, inside filling argon gas, pressure 3.9Torr, waveguide long side a=22.86mm, waveguide short side b=10.16mm, waveguide overall length l=
27.45mm, resonant element centre distance are 9.15mm, and sparking electrode is a pair of cuboid policies, length of side a1=1.0mm；Diaphragm is wide
Spend m=8.0mm, height b=10.16mm, thickness 1.0mm, intermediate gap height h1=1.0mm.According to the institute of analysis chart 1 of the present invention
Show the microwave gas discharge method for numerical simulation with slot-waveguide configuration, its concrete operation step is as follows：
The first step, the physical dimension with slot-waveguide configuration according to Fig. 1, is modeled using Ansys softwares to it,
Subdivision is carried out to band slot-waveguide configuration using the hexahedral element based on GLL basic functions, that is, obtains gap waveguiding structure with seam
The coordinate information of unknown quantity number and node, can be according to band gap waveguide junction for the boundary information with slot-waveguide configuration
Structure and size, four sides rectangular waveguide wave guide wall being set to desired metallic, transmission direction two sides is set to absorbing boundary condition to handle,
And the positional information of driving source is set；
Second step, according to the atmospheric pressure of given working environment, the original state of numerical simulation is provided, sets wave guide
The initial value of electron density is 10 in part6m-3；
3rd step, according to the original state set in geological information and second step with slot-waveguide configuration, during use
Domain spectral element method establishes the differential equation group of description nonlinear gas electric discharge phenomena, and the GLL basic functions that will be selected are to unknown electricity
Five field, magnetic field, electron density, velocity of electrons and mean electron energy known variables approximate expansions, are then substituted into by wheat respectively
The partial differential equations that Ke Siwei equation groups are formed with electronic fluid mechanical equation group, GLL basic functions are finally selected as weighting
Function, by the gold test of gal the Liao Dynasty, the surplus for making the equation under weighted average meaning is zero, thus turns continuous differential equation group
Matrix division is changed to, such as formula（1）It is shown：
Wherein, the subscript of T expressions mass matrix, S expression stiffness matrix, mass matrix and stiffness matrix is respectively with deploying base
It is corresponding with test base.R and F represents boundary integral matrix and source vector matrix, νi、νa、νcAnd QlRepresented respectively for ionization parameter
Ionization rate, adhesive rate, collision rate and rate of energy loss；
4th step, according to the Matrix division obtained by the 3rd step, using centered Finite Difference Methods, each moment is calculated successively,
The magnetic field intensity H of each node, velocity of electrons u, electric-field intensity E, electron density n, mean electron energy in spaceObtain difference
The rule that the above-mentioned variable of opening position changes over time.The display format such as following formula of each each time step iteration of variable（2）It is shown：
Wherein, Δ t represents time step, and subscript k represents time step number；
5th step, the mean electron energy obtained according to the 4th step, renewal ionization parameter：
1st, according to following formula（3）Obtain ionization rate：
ν in formulaiFor ionization rate, NgasFor gas number density, meFor electron mass, εeFor electron energy, σiIonization cross section is accumulated,
f(εe) it is electron energy distribution functions；
2nd, the electron energy distribution functions in above formula needed for integral term are solved and are expressed as mean electron energyFunction：
Wherein ξ1=3/ (2 χ), ξ2=5/ (2 χ), χ take 6.5 corresponding argon gas
The situation of filling,
3rd, according to the functional relation and the 4th counted average electron of step of above-mentioned ionization parameter and mean electron energy
Energy value, using the method for interpolation, after being updated in space each location point ionization parameter, substitute into and carry out subsequent cycle
Interative computation, repeat step three to step 4, untill the default calculating time is reached；
6th step, electric field value and electron density that each moment is calculated are exported, obtain band slot-waveguide configuration device
The rule that electric-field intensity changes over time with electron density in part.
Band slot-waveguide configuration device is emulated according to the method for the invention, the first other side bores midpoint point of observation
Electric-field intensity and electron density are changed over time shown in rule as Fig. 2 and Fig. 3.It can be seen that the midpoint bored in an other side,
Field strength is increased sharply, and when reaching the field strength threshold value of gas breakdown, electron concentration is exponentially increased, with the growth of electron concentration, side's cone
Plasma is generated at center, incident electric fields is produced decay, when electron concentration is by 106m-3Rise to 2.12 × 1019m-3Tend to
Stable, the electron concentration for ultimately generating plasma is 2.12 × 1019m-3.Simulation result can be explained with gap well
After complicated waveguiding structure microwave gas breakdown, electron concentration is increased sharply, a series of physical phenomenon such as incident electric fields decay, while completely
Provide the variation tendency that electron density is exponentially increased sharply after electric-field intensity reaches threshold field strength in waveguide device, can quantify
The known variables for providing given viewpoint changing rule, for waveguiding structure microwave device design with protection have it is higher
Directive significance.
Claims (3)
1. a kind of waveguide device microwave gas discharge method for numerical simulation, it is characterised in that step is as follows：
The first step, according to the physical dimension of complicated waveguiding structure, the geometry subdivision model of target is established, using based on Guass-
The hexahedral element of Lobatto-Legendre basic functions carries out subdivision to object module, obtains the geological information of target, then
The positional information of driving source is set and applies driving source；
Second step, by given atmospheric pressure, the initial value of electron density in waveguide device is set, provides waveguide device microwave
The original state of gas discharge numerical simulation；
3rd step, according to the initial value set in the geological information and second step of the target obtained in the first step, using time domain
Spectral element method establishes the differential equation group of description nonlinear gas electric discharge phenomena, and the GLL basic functions that will be selected are to unknown magnetic field
Intensity H, velocity of electrons u, electric-field intensity E, electron density n, mean electron energyFive known variables approximate expansions, Ran Houfen
The partial differential equations being made up of maxwell equation group and electronic fluid mechanical equation group are not substituted into, finally select GLL base letters
Number is used as weighting function, and by the gold test of gal the Liao Dynasty, the surplus for making each equation under weighted average meaning is zero, thus will be continuous
Differential equation group is converted to Matrix division, as shown in following formula (1)：
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Wherein, the subscript of T expressions mass matrix, S expression stiffness matrix, mass matrix and stiffness matrix is respectively with expansion base with surveying
It is corresponding to try base；R and F represents boundary integral matrix and source vector matrix, νi、νa、νcAnd QlRepresent to ionize respectively for ionization parameter
Rate, adhesive rate, collision rate and rate of energy loss；
4th step, the Matrix division (1) according to obtained by the 3rd step, using centered Finite Difference Methods, each moment is calculated successively, it is empty
Magnetic field intensity, velocity of electrons, electric-field intensity, electron density, the mean electron energy of interior each node, are obtained at diverse location
State the rule that variable changes over time；
1. the ordinary differential system shown in formula (1) is deployed using central difference schemes, the form of Algebraic Equation set is changed into, and
The final explicit iterative formula for providing five unknown quantitys, as shown in formula (2)：
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<mi>u</mi>
<mi>k</mi>
</msup>
<mo>+</mo>
<msubsup>
<mi>T</mi>
<mrow>
<mi>u</mi>
<mi>i</mi>
<mi>u</mi>
<mi>j</mi>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msub>
<mi>S</mi>
<mrow>
<mi>u</mi>
<mi>i</mi>
<mi>e</mi>
<mi>j</mi>
</mrow>
</msub>
<msup>
<mi>E</mi>
<mi>k</mi>
</msup>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<msub>
<mover>
<mi>&epsiv;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>e</mi>
</msub>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>=</mo>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<msup>
<msub>
<mover>
<mi>&epsiv;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>e</mi>
</msub>
<mi>k</mi>
</msup>
<mo>+</mo>
<msup>
<msub>
<mi>T</mi>
<mrow>
<mi>U</mi>
<mi>i</mi>
<mi>U</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>U</mi>
<mi>i</mi>
<mi>e</mi>
<mi>j</mi>
<mi>u</mi>
<mi>k</mi>
</mrow>
</msub>
<msup>
<mi>E</mi>
<mi>k</mi>
</msup>
<mo>&CenterDot;</mo>
<msup>
<mi>u</mi>
<mi>k</mi>
</msup>
<mo>-</mo>
<mi>F</mi>
<mo>&CenterDot;</mo>
<msub>
<mi>Q</mi>
<mi>l</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, Δ t represents time step, and subscript k represents time step number；
2. in each time step, the value for successively trying to achieve a upper time step is substituted into above-mentioned explicit iterative formula (2), asked
The variate-value of next time step is obtained, and is preserved；
5th step, the mean electron energy obtained according to the 4th step, renewal ionization parameter, repeat step three to step 4, until
Untill reaching the default calculating time；
1. ionization rate is obtained according to following formula (3)：
<mrow>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>N</mi>
<mrow>
<mi>g</mi>
<mi>a</mi>
<mi>s</mi>
</mrow>
</msub>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<munderover>
<mo>&Integral;</mo>
<mn>0</mn>
<mi>&infin;</mi>
</munderover>
<msqrt>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>&epsiv;</mi>
<mi>e</mi>
</msub>
</mrow>
<msub>
<mi>m</mi>
<mi>e</mi>
</msub>
</mfrac>
</msqrt>
<msub>
<mi>&sigma;</mi>
<mi>i</mi>
</msub>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&epsiv;</mi>
<mi>e</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>d&epsiv;</mi>
<mi>e</mi>
</msub>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
ν in formulaiFor ionization rate, NgasFor gas number density, meFor electron mass, εeFor electron energy, σiIonization cross section is accumulated, f (εe)
For electron energy distribution functions；
2. solving the electron energy distribution functions in above formula needed for integral term is expressed as mean electron energyFunction：
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&epsiv;</mi>
<mi>e</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msup>
<msub>
<mi>&epsiv;</mi>
<mi>e</mi>
</msub>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</msup>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<msup>
<msub>
<mi>&epsiv;</mi>
<mi>e</mi>
</msub>
<mi>&chi;</mi>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Whereinξ1=3/ (2 χ), ξ2=5/ (2 χ),
χ is determined by the gas componant in waveguide device；
3. according to the functional relation and the 4th counted mean electron energy of step of above-mentioned ionization parameter and mean electron energy
Value, using the method for interpolation, after update in space each location point ionization parameter, substitute into the iteration of progress subsequent cycle
Computing；
6th step, magnetic field intensity, electric-field intensity and electron density that each moment is calculated are exported, is obtained in waveguide device
The rule that electromagnetic field changes over time with electron density, thus can calculate various electromagnetic property parameters.
2. waveguide device microwave gas discharge method for numerical simulation according to claim 1, it is characterised in that：The first step
In, the geological information of target refers to the coordinate information and boundary information of unknown quantity number and node.
3. waveguide device microwave gas discharge method for numerical simulation according to claim 1, it is characterised in that：In second step, lead to
Given atmospheric pressure p (Torr) is crossed, sets the initial value of electron density in waveguide device
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