CN111625946B - Output signal mode component decomposition method for three-dimensional conformal full-electromagnetic particle simulation - Google Patents
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Abstract
The invention discloses an output signal mode component decomposition method for three-dimensional conformal full-electromagnetic particle simulation, which solves an equation based on a numerical eigenvalue, solves an eigenvector with orthogonality in an output waveguide, is used for mode decomposition of numerical diagnostic data, and has consistency in the method; the invention adopts a more general mode to construct related parameters for solving the mode to be solved, including the amplitudes and phases of the forward wave and the backward wave, and can complete the decomposition analysis of a plurality of modes by a group of diagnosis data.
Description
Technical Field
The invention belongs to the technical field of simulation of vacuum electronics devices, and particularly relates to an output signal mode component decomposition method for three-dimensional conformal full-electromagnetic particle simulation.
Background
For vacuum electronic devices that are high power or operate in high frequency bands, designers often employ overmode structures to increase power capacity or reduce processing difficulty, which may require consideration of mode selection, mode competition, and mode rejection issues in the device.
In the development process of vacuum electronic devices, numerical simulation becomes an indispensable means, so that the development and design cost of the devices can be reduced, and the development period of the devices can be shortened. Among these numerical simulations, the particle simulation technique is a relatively well-established and widely used numerical simulation method. At present, common full electromagnetic particle simulation software such as Karat, UNIPIC, magic does not have a mode decomposition function, but cannot obtain output mode components by directly observing field distribution in a device
Disclosure of Invention
The present invention is directed to a method for decomposing output signal mode components for three-dimensional conformal full electromagnetic particle simulation, so as to solve the above-mentioned problems.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the output signal mode component decomposition method for three-dimensional conformal full-electromagnetic particle simulation comprises the following steps:
step 1, establishing a vacuum electronic device model to be simulated and calculated by adopting three-dimensional modeling software;
step 2, performing discrete subdivision on the three-dimensional model in a three-dimensional Cartesian orthogonal grid system, and performing conformal reconstruction on the model in the discrete grid system by adopting a local filling method;
step 3, setting diagnostic parameters for mode analysis in the output waveguide section, wherein the diagnostic parameters comprise: a frequency point of diagnosis, a position of a diagnosis section, and a center point of a diagnosis time period, and thereby determining a time interval in which diagnosis data is recorded;
step 4, calculating to obtain feature vectors corresponding to different modes on the diagnosis surface according to the eigenvalue, wherein the feature vectors have orthogonality;
step 5, starting a conformal full-electromagnetic particle simulation main program, simulating a calculation model, and recording electric field and magnetic field values at the space points and in the time intervals defined in the step 3 in the calculation process, and taking the electric field and magnetic field values as diagnostic values;
step 6, filtering the recorded signals, and performing orthogonal decomposition on the filtered signals;
step 7, establishing equations at different time and different positions, and constructing a linear equation set to obtain the amplitudes of the forward wave and the backward wave of the single mode signal;
step 8, repeating step 6 and step 7, decomposing and analyzing other patterns based on the same set of data recorded by step 5.
Further, in step 3, the diagnosis position and diagnosis time are selected in the following manner (z i ,t i )，i＝1,2,3,4：
z 3 ＝z 1
t 2 ＝t 1
Wherein omega r For the dominant frequency, k, of the current diagnosed signal after filtering r ＝2π/ω r 。
Further, in step 4, the eigen equation is derived from the following equation:
discrete wave equation using electric field on port face as variableThe equation is converted to the frequency domain, resulting in the following eigen equation:
wherein,
discrete wave equation with the field at the port face as a variable:the conversion to the frequency domain yields the following eigen equation:
wherein,
further, in a discrete grid system, a discrete passive Maxwell system of equations is shown by the following equation:
further, the eigenvalue is the cut-off angle frequency of the waveguide, the eigenvector corresponds to the mode distribution, and the eigenvectors are mutually orthogonal, namely, the eigenvector meets the following conditions:
the mode decomposition in the output signal is achieved by using the orthogonality given by the above equation.
Further, in step 6 and step 7, specifically:
to achieve a pattern decomposition of the output signal, first, a general expression form of the output signal is given; without loss of generality, the transverse electric/transverse magnetic field distribution across the cross section at the coordinate z in the output waveguide can be broken down into a superposition of different modes, in the form,
wherein q j To obtain q corresponding to a certain mode by decomposing the orthogonality of the field line integral vector corresponding to the mode j on the diagnosis surface i The expression can be:
wherein k is j The axial wave number representing mode j is represented,and->A vector formed for the magnitude of the field integral over the geometric element; for a certain mode, the field distribution over the cross-section is expressed as a function of the coordinates over the cross-section f (x, y); then, a vector is determinedAnd->And +.>And->The solution calculation of (a) is converted into solving for +.o on the geometric element with the largest amplitude>And->And assume that the corresponding field value is q j From the above formula, q j The expression can be as follows:
in the above-mentioned method, the step of,and->Are all unknown, and to solve these 4 unknowns, a system of equations is constructed from the above equation at 4 different (t, z) coordinate points to solve:
substituting the time interval for recording the diagnostic data determined in step 3 into the above four formulas, defining the following intermediate variables,
from the three equations above, 4 different (t, z) coordinate points are transformed into:
from the above equation, solveAnd->The method further comprises the following steps:
for different modes, the same set of diagnostic data changesK in (a) j And carrying the above formula to complete the solution of the amplitude values of different modes; for k j To say, the cut-off frequencies of different modes are obtained through the solution of the eigen equation, namely the transverse wave number corresponding to the cut-off frequency can be obtained, and the axial wave number k corresponding to the diagnosed frequency can be obtained j 。
Compared with the prior art, the invention has the following technical effects:
the method solves an equation based on the eigenvalue on the numerical value, solves the eigenvector with orthogonality in the output waveguide, is used for mode decomposition of numerical diagnostic data, and has consistency on the method; the invention adopts a more general mode to construct related parameters for solving the mode to be solved, including the amplitudes and phases of the forward wave and the backward wave, and can complete the decomposition analysis of a plurality of modes by a group of diagnosis data. It has the following advantages:
first: in the three-dimensional conformal particle simulation, in order to realize loading of a specific injection wave mode of a straight waveguide, a software code is often required to realize the construction of an eigen equation based on a wave equation to solve each orthogonal mode in the straight waveguide, and the invention provides a mode decomposition algorithm of an output signal on the basis, which is easy to realize, has universality and avoids the problem of unmatched algorithm systems depending on third-party software;
second,: according to the invention, analysis and calculation of modes are realized based on the eigenvalue, and the basis vectors of all modes obtained by the eigenvalue are mutually orthogonal, so that the proposed mode decomposition algorithm can strictly decompose and analyze the output signals, and can accurately obtain the power duty ratio of all modes in the output signals;
third,: in the mode decomposition algorithm, the invention adopts a general diagnosis parameter setting mode, the setting of the relative interval between the diagnosis time point and the diagnosis position point is determined by the frequency to be diagnosed, is irrelevant to the mode to be analyzed, and can quantitatively decompose and analyze a plurality of groups of modes simultaneously based on one group of diagnosis parameters.
Drawings
FIG. 1 is a three-dimensional full electromagnetic simulation calculation flow after addition mode diagnosis;
FIG. 2 is a schematic decomposition calculation flow;
fig. 3 is a schematic diagram of a mode converter.
Detailed Description
The following is a further explanation of embodiments of the invention by way of examples.
Step 1, a mode converter in a high-power microwave device shown in fig. 3 is built by adopting three-dimensional modeling software. In FIG. 3, R 1 And theta 1 Respectively represent the radius and radian of the first section and the third section of bent waveguide, R 2 And theta 2 Respectively representing the radius and radian of the second curved waveguide. In this model, since the injection power is high, ionization occurs at the curved waveguide, generating charged particles, so that the operation performance of the mode converter is changed, and thus it is necessary to determine the influence of ionization on the performance of the mode converter by decomposing and analyzing the output mode;
and 2, performing discrete subdivision on the model shown in the figure 3 in a three-dimensional Cartesian orthogonal grid system, and performing conformal reconstruction on the model in the discrete grid system by adopting a local filling method.
Step 3, setting diagnostic parameters for mode analysis in the output waveguide section, wherein the diagnostic parameters comprise: 1) Frequency points of diagnostic mode, 2) position of diagnostic section (z) 1 ，z 2 ，z 3 And z 4 ) The method comprises the steps of carrying out a first treatment on the surface of the 3) Calculating a time zone for recording diagnostic data, which time zone covers a time point (t 1 ，t 2 ，t 3 And t 4 ) The basis for determining the time interval is as follows: when the recorded signal is subjected to a filtering operation using a bandpass filter function, (t) 1 ，t 2 ，t 3 And t 4 ) Diagnostic values at time points ensure validity. Wherein t is 1 ，t 2 ，t 3 And t 4 ) And (z) 1 ，z 2 ，z 3 And z 4 ) The expression (23) to (27).
And 4, calculating eigenvectors corresponding to different modes on the diagnosis surface by using eigenvectors given by the equation (12) and the equation (14), wherein the eigenvectors have orthogonality as shown by the equation (15) and the equation (16).
And 5, starting a conformal full-electromagnetic particle simulation main program, simulating a calculation model, and recording electric field and magnetic field values at the space points and in the time intervals defined in the step 3 in the calculation process, and taking the electric field and magnetic field values as diagnostic values.
Step 6, filtering the recorded signal, performing orthogonal decomposition on the filtered signal by the equation (15) and the equation (16), and describing the signal by the form defined by the equation (18).
And 7, establishing equations of different time and different positions defined by the formulas (23) to (27), constructing a linear equation set, solving 4 unknowns in the formula (18), and obtaining the amplitudes of the forward wave and the backward wave of the single mode signal given by the formulas (35) and (36).
Step 8, repeating step 6 and step 7, decomposing and analyzing other patterns based on the same set of data recorded by step 5.
In the above example implementation steps, the flowcharts of step 1 to step 5 are shown in fig. 1, and the calculation flows of step 6 to step 8 are shown in fig. 2.
Regarding numerical calculations, the following are specifically implemented:
1) Solving of feature vectors corresponding to the pattern:
in the full electromagnetic particle simulation, an FIT method is adopted for electromagnetic field propulsion, and the FIT method is established on a composite grid system consisting of an initial grid and a dual grid, and the establishment mode is as follows: the grid nodes of the initial grid system are the centers of gravity (barycenters) of the cells of the dual grid system and vice versa.
The electric field vector and the magnetic field vector are integrated on basic geometric elements (line elements and surface elements) in the discrete grid to define the voltage drop and flux of the electric field and the magnetic field on the grid, and the voltage drop and the flux are used as variables in the solution process of the FIT method. In the FIT method, all variables are defined as follows:
wherein L is i ，S i And V i Is an edge element, a face element and a body element on the initial grid system G;and->Is a dual grid system->Edge elements, face elements and body elements on the table. In addition, set up the surface element S in the initial grid system i Reference numerals of (2) and line elements in the dual system intersecting with them->The reference numerals of the lines L in the initial grid system are the same, and the line L in the initial grid system can be set i Reference numerals of (2) and the face elements in the dual system intersecting with them->The reference numerals of which are identical.
In a discrete grid system, a discrete passive Maxwell's system of equations is shown by the following equation:
wherein, the matrix C is used for the matrix,discrete rotation operators in an initial grid system and a dual grid system respectively; the matrix S is provided with a matrix S,discrete divergence operators in the initial grid system and the dual grid system, respectively. Vector->The definition of (c) is given by:
wherein N and N' are the number of effective line elements and surface sources in the discrete grid system respectively.And->And +.>And->The constitutive relation of (2) is as follows:
wherein M is ε ，M μ And M ε And M μ Is a discrete matrix of material, given by the following equation,
wherein D is S Matrix representing original grid bin area, D L A matrix representing the edge length of the original grid,and->Corresponding to the amount on the dual grid. The material parameters epsilon and mu on each original grid are constant values. Matrix D ε And->The size of the element in the initial grid corresponds to the line element (or the face element in the dual grid), and the size of the element is obtained by a method of taking the average value of the dielectric constants of all initial grids sharing the line element and the inverse of the dielectric constants according to the area weight; and D is μ And->The elements in the pair-wise grid (or the surface elements in the initial grid) are corresponding to the line elements, and the size of the line elements is obtained by averaging the magnetic permeability and the reciprocal of the magnetic permeability on all the initial grids sharing the line elements according to the length weight.
Then, on the basis of a discrete Maxwell equation set, an intrinsic equation on a port surface is constructed, discrete TE and TM characteristic modes on the port surface are solved, and the obtained characteristic modes are used as the basis for decomposing the output waveguide modes.
For loading of TE modes, it is necessary to solve for the characteristic frequency of the desired mode and the electric field distribution on the port face. And (3) constructing a discrete wave equation on the port surface by using the electric field on the port surface as a variable according to the TE mode field distribution characteristics and the equation (3) and the equation (4).
Converting the equation (11) to the frequency domain, resulting in the following eigen equation:
wherein,
for TM mode loading, it is also necessary to first solve for the characteristic frequency of the desired mode and the electric field distribution across the port face. Therefore, according to the distribution characteristics of TM mode fields, a discrete wave equation on a port surface is constructed by taking a magnetic field on the port surface as a variable:
converting the equation (13) to the frequency domain to obtain the following eigen equation:
wherein,
the cut-off angle frequency with the characteristic value being the waveguide can be obtained through the formula (12) and the formula (14), the characteristic vectors correspond to the mode distribution, and the characteristic vectors are mutually orthogonal, namely, the characteristic vectors meet the following conditions:
with the orthogonality given by the above equation, a pattern decomposition in the output signal can be achieved.
2) Orthogonal mode decomposition and parameter solving:
to achieve a pattern decomposition of the output signal, first, a general expression of the output signal is given. Without loss of generality, the transverse electric/transverse magnetic field distribution across the cross section at the coordinate z in the output waveguide can be broken down into a superposition of different modes, in the form,
wherein Q represents the field line integral vector on the diagnosis surface, Q j For the field line integral vector corresponding to pattern j on the diagnosis surface, the vector is formed by (15) and(16) In the formula, the orthogonality can be decomposed to obtain q corresponding to a certain mode i The expression can be:
wherein k is j The axial wave number representing mode j is represented,and->Vectors formed by the field integral magnitudes of the forward and backward wave signals over discrete geometric elements, respectively, corresponding to mode j +.>And->The forward wave phase and backward wave phase corresponding to mode j are represented, respectively. For a certain mode, the field distribution over the cross-section (maximum 1) can be expressed as a function of the coordinates over the cross-section f (x, y). Then, the vector +.>And->And +.>And->The solving calculation of (a) can be converted into solving for +.>And->And assume that the corresponding field value is q j Formula (17), q j The expression can be as follows:
in the above-mentioned method, the step of,and->All are unknown, and to solve these 4 unknowns, a system of equations is constructed from (18) at 4 different (t, z) coordinate points to solve:
to facilitate completion of the solution of the above equation and enable the algorithm to simultaneously complete decomposition analysis of multiple modes based on a set of diagnostic data; for this purpose we choose (z i ,t i )，i＝1,2,3,4：
z 3 ＝z 1 (24)
t 2 ＝t 1 (26)
Wherein omega r For the dominant frequency, k, of the current diagnosed signal after filtering r ＝2π/ω r . (z) set by the formulas (23) to (27) i ,t i ) Values are substituted into the formulas (19) to (22), the following intermediate variables are defined,
the expression (28) to the expression (30), and the expression (19) to the expression (22) are converted into:
from the above equation, it can be solved to obtainAnd->In the device design verification process, only the power duty ratio of each mode is generally concerned, that is to say, the amplitude of each mode needs to be obtained through decomposition, and the following formulas (31) to (34) can be obtained:
it can be seen that for different modes, from the same set of diagnostic data, only the changes are requiredK in (a) j And the solution of the amplitude values of different modes can be completed by bringing the above formula. For k j To be specific, we solve the above eigenequation to obtain the cut-off frequencies of different modes, that is, the transverse wave numbers corresponding to the cut-off frequencies, then the axial wave numbers k corresponding to the diagnosed frequencies can be obtained j 。
Claims (5)
1. The method for decomposing the components of the output signal mode for the three-dimensional conformal full electromagnetic particle simulation is characterized by comprising the following steps of:
step 1, establishing a vacuum electronic device model to be simulated and calculated by adopting three-dimensional modeling software;
step 2, performing discrete subdivision on the three-dimensional model in a three-dimensional Cartesian orthogonal grid system, and performing conformal reconstruction on the model in the discrete grid system by adopting a local filling method;
step 3, setting diagnostic parameters for mode analysis in the output waveguide section, wherein the diagnostic parameters comprise: a frequency point of diagnosis, a position of a diagnosis section, and a center point of a diagnosis time period, and thereby determining a time interval in which diagnosis data is recorded;
step 4, calculating to obtain feature vectors corresponding to different modes on the diagnosis surface according to the eigenvalue, wherein the feature vectors have orthogonality;
step 5, starting a conformal full-electromagnetic particle simulation main program, simulating a calculation model, and recording electric field and magnetic field values at the space points and in the time intervals defined in the step 3 in the calculation process, and taking the electric field and magnetic field values as diagnostic values;
step 6, filtering the recorded signals, and performing orthogonal decomposition on the filtered signals;
step 7, establishing equations at different time and different positions, and constructing a linear equation set to obtain the amplitudes of the forward wave and the backward wave of the single mode signal;
step 8, repeating step 6 and step 7, decomposing and analyzing other modes based on the same set of data recorded by step 5;
in the step 6 and the step 7, specifically:
to achieve a pattern decomposition of the output signal, first, a general expression form of the output signal is given; without loss of generality, the transverse electric/transverse magnetic field distribution across the cross section at the coordinate z in the output waveguide can be broken down into a superposition of different modes, in the form,
wherein q j To obtain q corresponding to a certain mode by decomposing the orthogonality of the field line integral vector corresponding to the mode j on the diagnosis surface i The expression can be:
wherein k is j The axial wave number representing mode j is represented,and->A vector formed for the magnitude of the field integral over the geometric element; for a certain mode, the field distribution over the cross-section is expressed as a function of the coordinates over the cross-section f (x, y); then, the vector +.>And->And +.>And->The solution calculation of (a) is converted into solving for +.o on the geometric element with the largest amplitude>And->And assume that the corresponding field value is q j From the above formula, q j The expression can be as follows:
in the above-mentioned method, the step of,and->Are all unknown, and to solve these 4 unknowns, a system of equations is constructed from the above equation at 4 different (t, z) coordinate points to solve:
substituting the time interval for recording the diagnostic data determined in step 3 into the above four formulas, defining the following intermediate variables,
from the three equations above, 4 different (t, z) coordinate points are transformed into:
from the above equation, solveAnd->The method further comprises the following steps:
for different modes, the same set of diagnostic data changesK in (a) j And carrying the above formula to complete the solution of the amplitude values of different modes; for k j To say, the cut-off frequencies of different modes are obtained through solving the eigen equation, and the corresponding cut-off frequencies can be obtainedTo obtain the axial wave number k corresponding to the frequency to be diagnosed j 。
2. The method for decomposing the output signal pattern components for three-dimensional conformal full electromagnetic particle simulation according to claim 1, wherein in step 3, the diagnosis position and the diagnosis time are selected by the following method (z i ,t i )，i＝1,2,3,4：
z 3 ＝z 1
t 2 ＝t 1
Wherein omega r For the dominant frequency, k, of the current diagnosed signal after filtering r ＝2π/ω r 。
3. The method of claim 1, wherein in step 4, the eigen equation is derived from the following equation:
discrete wave equation using electric field on port face as variableThe equation is converted to the frequency domain, resulting in the following eigen equation:
wherein,
discrete wave equation with the field at the port face as a variable:the conversion to the frequency domain yields the following eigen equation:
wherein,
4. a method of decomposing output signal pattern components for three-dimensional conformal full electromagnetic particle simulation according to claim 3, wherein in a discrete grid system, a discrete passive Maxwell's system of equations is represented by the following equation:
5. the method for decomposing the output signal mode components for three-dimensional conformal full electromagnetic particle simulation according to claim 3, wherein the eigenvalue is the cut-off angle frequency of the waveguide, the eigenvectors correspond to the mode distribution, and the eigenvectors are mutually orthogonal, namely, the eigenvectors satisfy the following conditions:
the mode decomposition in the output signal is achieved by using the orthogonality given by the above equation.
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