CN111781477A - Method for analyzing working state electron beam motion state of space traveling wave tube - Google Patents

Method for analyzing working state electron beam motion state of space traveling wave tube Download PDF

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CN111781477A
CN111781477A CN202010505084.XA CN202010505084A CN111781477A CN 111781477 A CN111781477 A CN 111781477A CN 202010505084 A CN202010505084 A CN 202010505084A CN 111781477 A CN111781477 A CN 111781477A
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孙小菡
汪锦言
沈长圣
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Southeast University
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Abstract

The invention discloses a method for analyzing the motion state of an electron beam in a working state of a space traveling wave tube, which is characterized in that a fan-shaped thin disk model for electron beam shape analysis and a fan-shaped ring thin disk model for electron beam speed analysis are provided based on motion data of electrons obtained by a finite element method, and the changes of the electron beam shape and the speed along the slow wave structure of a spiral line of the space traveling wave tube are obtained. The invention solves the problems that the prior art can not accurately quantify the form of the electron beam and can not analyze the radial velocity change and the section velocity distribution of the electron beam.

Description

Method for analyzing working state electron beam motion state of space traveling wave tube
Technical Field
The invention belongs to the technical field of vacuum electronics, and particularly relates to a method for analyzing the motion state of a working electron beam of a space traveling wave tube.
Background
Space traveling wave tubes (S-TWTs) are key components of the transmitting components of satellite communication systems. Since the size and weight of the launching assembly are greatly limited due to the space environment, the S-TWT needs to have the characteristics of high efficiency, long service life, high reliability, miniaturization, and the like. Improving the S-TWT efficiency is one of the core technologies for ensuring the quality of the satellite communication system. The power amplification effect of the S-TWT is from the interaction of electron beam in the tube and wave beam of high-frequency signals, the energy transferred to the high-frequency signals by the electrons in a deceleration field determines the amplification effect, and is closely related to the efficiency of the S-TWT. In the literature of the currently reported improvement of the S-TWT efficiency, no analysis about the influence of the electron beam motion state and the velocity distribution thereof on the efficiency is found. Therefore, an effective electron beam analysis model needs to be established, the change rule of the motion state of the electron beam along the spiral slow wave structure is detected, and the influence of the working electron beam on the S-TWT efficiency is researched.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a method for analyzing the motion state of an electron beam in a working state of a space traveling wave tube.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a method for analyzing the motion state of an electron beam in a working state of a space traveling wave tube comprises the following steps:
(1) analyzing the wave-injection interaction of the space traveling wave tube by using a finite element method, and simultaneously setting a group of two-dimensional monitors which are uniformly distributed along a spiral slow wave structure to record the position vector and the speed vector of the electron beam section macro-electrons under a rectangular coordinate system;
(2) establishing a fan-shaped thin disc model for analyzing the electron beam form, longitudinally dividing the electron beam into thin discs, dividing the thin discs into a plurality of fan-shaped discs in an angular equal division manner, and defining the electron beam radius, the electron dispersion, the electronic beam radius angular fluctuation and the electron beam center drift according to the fan-shaped thin disc model;
(3) establishing a fan ring thin disc model for analyzing the electron beam speed, dividing the electron beam thin disc into a plurality of fan rings in the radial direction and the angular direction, and representing the motion speed of the fan rings by the average speed of all electrons on the fan rings;
(4) and reading the analysis result of the electronic motion state data, obtaining the evaluation parameters of the electron beam form and the calculation result of the velocity component according to the fan-shaped thin disk model and the fan-shaped ring thin disk model, storing the evaluation parameters and the calculation results into a database, and displaying the change diagram of the electron beam form and the electron beam velocity along the slow wave structure through a data visualization program.
Further, in step (2), the electron beam is divided equally into m sectors at an angle per radian phi, and the radius R of the electron beam is expressed as follows:
Figure BDA0002526244660000021
in the above formula, RsIs the radius of the s-th sector,
Figure BDA0002526244660000022
dsthe distance between the centroid of the s-th sector and the center of the electron beam disk,
Figure BDA0002526244660000023
(xs,ys) Is the centroid coordinate of the s-th sector, (x)o,yo) The coordinates of the center of the electron beam disk are shown.
Further, in step (2), the expression of the electron dispersion ρ is as follows:
Figure BDA0002526244660000024
in the above formula, neNumber of electrons outside the thin disk, riThe distance between the ith electron outside the thin disk and the center of the electron beam thin disk is shown.
Further, in step (2), the expression of the angular fluctuation of the electron beam radius is as follows:
Figure BDA0002526244660000025
further, in step (2), the expression of the center shift of the electron beam is as follows:
Figure BDA0002526244660000031
further, in step (3), the velocity of the electron in each direction is calculated by the following formula:
Figure BDA0002526244660000032
Figure BDA0002526244660000033
Figure BDA0002526244660000034
in the above formula, vs、vr、vtThe transverse velocity, the radial velocity and the angular velocity of the electrons,
Figure BDA0002526244660000035
x and y are position vectors of electrons under a rectangular coordinate system in the process of wave injection interaction, and vx、vyIs the velocity vector of the electron under the rectangular coordinate system in the process of the wave injection interaction.
Adopt the beneficial effect that above-mentioned technical scheme brought:
at present, the analysis of the motion state of the S-TWT electron beam is mainly based on an electron beam envelope and a phase space diagram obtained by simulation software, the analysis mode cannot accurately quantify the form of the electron beam and cannot analyze the radial velocity change and the section velocity distribution of the electron beam.
Drawings
FIG. 1 is a flow chart of the S-TWT electron beam motion state analysis of the present invention;
FIG. 2 is a schematic diagram of an electron beam sector-shaped thin disk model according to the present invention;
FIG. 3 is a diagram of an electron beam fan ring thin disk model according to the present invention;
FIG. 4 is a graph of electron velocity vector relationships in the present invention;
FIG. 5 is a graph of electron beam shape along slow-wave structure based on a fan-shaped thin disk model;
fig. 6 is a graph of electron beam velocity along a slow wave structure based on a fan ring thin disk model.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention designs a method for analyzing the motion state of a working electron beam of a space traveling wave tube, which is shown in figure 1 and comprises the following specific processes.
1. A finite element method is used for analyzing S-TWT (two-dimensional wavelet transform) wave interaction, and meanwhile, a group of two-dimensional monitors which are uniformly distributed along a spiral line slow wave structure are arranged to record position vectors and speed vectors of electron beam section macro electrons (a large number of electron sets).
2. And establishing a fan-shaped thin disc model for analyzing the electron beam form. The electron beam is approximately circular in cross section, the electron beam is longitudinally divided into thin disc models, and when the thickness of the thin disc is small enough, the distribution state and the velocity state of each electron on the thin disc can be regarded as unchanged in the axial direction.
The electron beam shape evaluation parameters based on the fan-shaped thin disk model are defined below. The thin disk model needs to contain most of the electrons in the electron beam, which is equally divided into m sectors per radian phi at the angular direction in order to determine the radius of the thin disk, as shown in fig. 2. Defining the center O point of the electron beam disk at the average position of all n electrons on the cross section, and defining the gravity center G point of a fan shape with the average position of all electrons equally divided at each equal angle, (x)o,yo) And (x)s,ys) Coordinates of the O point and the G point are respectively expressed. In fig. 2, the distance between G, O is as follows:
Figure BDA0002526244660000041
according to the definition of the center of gravity of the fan shape, the radius R of the fan shape can be obtaineds：
Figure BDA0002526244660000042
The radius R of the electron beam is represented by the average radius of the segmented fan:
Figure BDA0002526244660000043
when the S-TWT is in operation, the electron beam may exhibit a divergence of some electrons, which are located relatively far from the electron beam disk. To represent the number and degree of deviation of these discrete electrons, the dispersion of electrons is defined:
Figure BDA0002526244660000051
wherein n iseNumber of electrons outside the thin disk, riThe distance between the ith electron outside the thin disk and the center of the electron beam thin disk is shown. When the number of discrete electrons in the electron beam thin disk is large or the distance between the discrete electrons and the thin disk is large, the electron dispersion ρ increases. ρ describes the degree and amount of discrete electrons in the electron beam disk.
The S-TWT working electron beam is generally cylindrical, but when the electron beam propagates in a slow wave structure, the electron distribution of the cross section of the electron beam cannot be kept perfectly circular due to the interaction of a magnetic field and a wave beam, and the shape is distorted. In order to describe the irregularity degree of the cross-sectional electron distribution when the electron beam propagates in the slow-wave structure, the change of the radius of the electron beam in the angular direction is used for description. The standard deviation of the electron beam radius of the m sectors of the electron beam segmentation is defined as the angular fluctuation of the electron beam radius:
Figure BDA0002526244660000052
when an electron beam is emitted from a particle emission source, the center of the electron beam is located at the center of the XOY plane (the plane in which the particle emission source is located), and as the electron beam is transmitted in the slow-wave structure, the center of the electron beam is shifted, which may affect the beam interaction. The distance between the center of the thin disk and the origin of coordinates of the XOY plane in which the section lies is defined as the central drift of the electron beam:
Figure BDA0002526244660000053
3. establishing a fan-ring thin disk model for analyzing the electron beam velocity: the electron beam disk is divided into several fan rings in radial and angular directions, as shown in fig. 3. Neglecting the rotation of the electrons, each electron beam fan ring is assumed to move axially along the slow wave structure and to have a velocity component in the radial direction, representing the moving velocity of the fan ring as the average velocity of all electrons on the fan ring. This model can describe the velocity variation of the electron beam in the radial direction. The segmentation density of the fan-ring thin disk model is related to the number of macro-electrons emitted by the particle emission source. The speed change of each region of the electron beam can be described more accurately by using more dense segmentation, but the electron beam can be divided into electrons on each fan ring, and when the number of macro-electrons of the emission source is limited, the electrons are distributed unevenly in the regions with larger electron beam dispersion, so that a dense segmentation mode cannot be adopted. The velocity of the electrons in each direction is calculated from the velocity relationship shown in fig. 4:
Figure BDA0002526244660000061
Figure BDA0002526244660000062
Figure BDA0002526244660000063
in the above formula, vs、vr、vtThe transverse velocity, the radial velocity and the angular velocity of the electrons,
Figure BDA0002526244660000064
x and y are position vectors of electrons under a rectangular coordinate system in the process of wave injection interaction, and vx、vyIs the velocity vector of the electron under the rectangular coordinate system in the process of the wave injection interaction.
4. Reading the analysis result of the electronic motion state data, compiling a calculation program according to the fan-shaped thin disc model and the fan-shaped ring thin disc model, obtaining the calculation results of the electronic note form evaluation parameters and the speed component, storing the calculation results into a database, and realizing the archiving of the currently analyzed S-TWT working state electronic note motion state data. In the process of storing data, a change diagram of the electron beam shape and the electron beam speed along the slow wave structure is displayed through a data visualization program, and a user can analyze the change characteristics of the S-TWT working state electron beam along the slow wave structure according to the change diagram, judge the focusing quality of the S-TWT electron beam under the current condition and optimize the working condition of the S-TWT or an electron beam focusing system according to the focusing quality.
A finite element method is used for analyzing the interaction of certain S-TWT (two-way wave transmission) beam, a group of two-dimensional monitor arrays which are uniformly distributed along a spiral slow wave structure are arranged to record the position vector and the speed vector of the macro electron of the section of the electron beam, and the recorded data are shown in table 1.
TABLE 1 Electron Beam section Macro-Electron position and normalized velocity (part)
Figure BDA0002526244660000065
Figure BDA0002526244660000071
In this embodiment, the number of macro electrons in the particle emission source is 104, and the number of divided sectors m is 16. According to the fan-shaped thin disk model, the change of the electron beam shape along the slow wave structure is calculated, as shown in fig. 5.
From the raw data of Table 1, the normalized velocity v/c, normalized transverse velocity v/c of each macro-electron are calculatedsC, normalized radial velocity vrC and normalized angular velocity vtAnd/c, as shown in Table 2.
TABLE 2 normalized velocity component (part) of the macroelectrons in rectangular and cylindrical coordinates
vx/c vy/c vz/c v/c vs/c vr/c vt/c
0.005259756 0.03363792 0.1904921 0.193511 0.034047 0.001021 -0.03403
0.01220732 0.02420914 0.1915475 0.193457 0.027113 0.000856 -0.0271
-0.003250614 0.04829781 0.1875686 0.193714 0.048407 0.000503 -0.0484
-0.002442023 0.05123376 0.1868431 0.193756 0.051292 0.000473 -0.05129
-0.01500887 0.04362353 0.1881696 0.193742 0.046133 9.55E-05 -0.04613
-0.0230402 0.02751412 0.1901695 0.193526 0.035887 0.000956 -0.03587
-0.031333 0.03374991 0.1880995 0.193655 0.046052 0.000385 -0.04605
0.01835467 -0.0417591 0.1882522 0.1937 0.045615 0.000716 -0.04561
0.02262799 -0.04661941 0.1867848 0.19384 0.051821 0.000544 -0.05182
0.01803056 -0.0314923 0.1900804 0.193513 0.036289 0.000768 -0.03628
0.02219922 -0.02590296 0.1904763 0.193507 0.034114 0.000909 -0.0341
When the number of macro electrons in the emission source is limited, electrons are not uniformly distributed in a region with large electron beam dispersion, and a dense segmentation mode cannot be adopted. In this embodiment, the number of macro electrons of the particle emission source is 104, and the electron beam disk is equally divided radially by 4 and equally divided angularly by 8. The radial velocity and axial velocity of the electron beam are calculated to vary along the slow wave structure, as shown in fig. 6.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (6)

1. A method for analyzing the motion state of an electron beam in a working state of a space traveling wave tube is characterized by comprising the following steps of:
(1) analyzing the wave-injection interaction of the space traveling wave tube by using a finite element method, and simultaneously setting a group of two-dimensional monitors which are uniformly distributed along a spiral slow wave structure to record the position vector and the speed vector of the electron beam section macro-electrons under a rectangular coordinate system;
(2) establishing a fan-shaped thin disc model for analyzing the electron beam form, longitudinally dividing the electron beam into thin discs, dividing the thin discs into a plurality of fan-shaped discs in an angular equal division manner, and defining the electron beam radius, the electron dispersion, the electronic beam radius angular fluctuation and the electron beam center drift according to the fan-shaped thin disc model;
(3) establishing a fan ring thin disc model for analyzing the electron beam speed, dividing the electron beam thin disc into a plurality of fan rings in the radial direction and the angular direction, and representing the motion speed of the fan rings by the average speed of all electrons on the fan rings;
(4) and reading the analysis result of the electronic motion state data, obtaining the evaluation parameters of the electron beam form and the calculation result of the velocity component according to the fan-shaped thin disk model and the fan-shaped ring thin disk model, storing the evaluation parameters and the calculation results into a database, and displaying the change diagram of the electron beam form and the electron beam velocity along the slow wave structure through a data visualization program.
2. The method for analyzing the motion state of the electron beam in the operating state of the space traveling wave tube according to claim 1, wherein in the step (2), the electron beam is equally divided into m sectors per radian of phi at an angular direction, and then an expression of the radius R of the electron beam is as follows:
Figure FDA0002526244650000011
in the above formula, RsIs the radius of the s-th sector,
Figure FDA0002526244650000012
dsthe distance between the centroid of the s-th sector and the center of the electron beam disk,
Figure FDA0002526244650000013
(xs,ys) Is the centroid coordinate of the s-th sector, (x)o,yo) The coordinates of the center of the electron beam disk are shown.
3. The method for analyzing the motion state of the electron beam in the working state of the space traveling wave tube according to claim 2, wherein in the step (2), the expression of the electron dispersion p is as follows:
Figure FDA0002526244650000021
in the above formula, neNumber of electrons outside the thin disk, riThe distance between the ith electron outside the thin disk and the center of the electron beam thin disk is shown.
4. The method for analyzing the motion state of the electron beam in the working state of the space traveling wave tube according to claim 2, wherein in the step (2), the expression of the angular fluctuation of the electron beam radius is as follows:
Figure FDA0002526244650000022
5. the method for analyzing the motion state of the electron beam in the operating state of the space traveling wave tube according to claim 2, wherein in the step (2), the expression of the electron beam center drift is as follows:
Figure FDA0002526244650000023
6. the method for analyzing the motion state of an electron beam in a working state of a space traveling wave tube according to claim 1, wherein in the step (3), the velocity of the electron in each direction is calculated by the following formula:
Figure FDA0002526244650000024
Figure FDA0002526244650000025
Figure FDA0002526244650000026
in the above formula, vs、vr、vtThe transverse velocity, the radial velocity and the angular velocity of the electrons,
Figure FDA0002526244650000027
x and y are position vectors of electrons under a rectangular coordinate system in the process of wave injection interaction, and vx、vyIs the velocity vector of the electron under the rectangular coordinate system in the process of the wave injection interaction.
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