CN102298658A - Method for simulating dominant wave interaction of traveling wave tubes - Google Patents

Abstract

The invention belongs to a traveling wave tube simulation technology and discloses a method for simulating the dominant wave interaction of traveling wave tubes. Specific to the problems existing in the process of simulating the dominant wave interaction of various traveling wave tubes with the conventional semi-analytical and semi-numerical parameter theoretical model, high-frequency field distributions in high-frequency structures of traveling wave tubes are obtained with a pure numerical method in the method, and simultaneous differential equations are established by combining a high-frequency field equation, a particle phase equation and a motion equation, so that a dominant wave interaction parameter theoretical model suitable for various traveling wave tubes is established. The method can be used for simulating the dominant wave interaction processes in various traveling wave tubes, has high efficiency of the parameter theoretical model, and can be applied to numerical simulation of the interactions of electron beams and high-frequency fields in various traveling wave tubes with periodic high-frequency structures.

Description

A kind of travelling-wave tube is annotated the analogy method of ripple interaction

Technical field

The invention belongs to the travelling-wave tube analogue technique, be specifically related to the analogy method that a kind of travelling-wave tube is annotated the ripple interaction.

Background technology

Travelling-wave tube is to use one of vacuum electron device the most widely, is widely used in fields such as satellite communication, radar, electronic countermeasure.At present, (Computer Aided Design, CAD) technology is to save cost, improves design and improves one of main means of travelling-wave tube overall performance to adopt computer-aided design (CAD).In the travelling-wave tube cad technique, analyze significant with the interaction (promptly annotating the ripple interaction) of electromagnetic field of high frequency to electronics notes in the travelling-wave tube.Notes ripple interaction in the travelling-wave tube be one from being in harmony process: the space charge field that electromagnetic field of high frequency in the travelling-wave tube high-frequency structure and particle clustering produce promotes particle movement, particle movement forms high-frequency current, and high-frequency current encourages the electromagnetic field of high frequency in the high-frequency structure conversely.

At present, mainly contain the notes ripple interaction process in the two class methods simulation travelling-wave tube, the one, the particle simulation method of pure values, the 2nd, utilize the parameter theory model of partly resolving the half value.The particle simulation method of pure values has versatility, can simulate the notes ripple interaction process of all kinds of travelling-wave tube, but it calculates length consuming time, and memory consumption is many, and ripple interaction process is once annotated in calculating often needs a few hours even a couple of days.The parameter theory Model Calculation is once annotated ripple interaction process only needs a few minutes even tens seconds to get final product.Yet to dissimilar travelling-wave tube, as helix TWT, coupled-cavity TWT, folded waveguide travelling-wave tube etc., the difference of its high-frequency structure has caused inconsistent electromagnetic field to distribute, thereby need set up different notes ripple interaction parameter theoretical models.For some travelling-wave tube, can't set up effective notes ripple interaction parameter theoretical model with complicated high-frequency structure such as coupler structure, folded waveguide structure.

Summary of the invention

The objective of the invention is to annotate the problem that ripple interaction process exists, proposed the analogy method that a kind of travelling-wave tube is annotated the ripple interaction in order to solve existing all kinds of travelling-wave tube of parameter theory modeling of partly resolving the half value.

Technical scheme of the present invention is: a kind of travelling-wave tube is annotated the analogy method of ripple interaction, may further comprise the steps:

A. obtain the radio-frequency field equation according to the broad sense radio-frequency field expression formula in the travelling-wave tube high-frequency structure;

B. utilize the method for pure values to obtain radio-frequency field distribution passive in the travelling-wave tube high-frequency structure;

C. computer memory charge field;

D. utilize Lorentz force equation to promote particle movement, obtain the phase equation and the equation of motion of particle;

E. utilize the radio-frequency field equation that steps A, B, C, D obtain, the phase equation and the equation of motion of particle, set up and describe the differential equation group that travelling-wave tube is annotated ripple interaction process, the interaction starting condition is set, find the solution the differential equation group of foundation, finish up to annotating the ripple interaction, can finish the simulation of once annotating ripple interaction process.

Beneficial effect of the present invention: method of the present invention obtains radio-frequency field passive in the travelling-wave tube high-frequency structure by the method for utilizing pure values and distributes, and in conjunction with the radio-frequency field equation, the phase equation of particle and the equation of motion, make up differential equation group, promptly set up the notes ripple interaction parameter theoretical model that is applicable to all kinds travelling-wave tube, method of the present invention can be simulated the notes ripple interaction process in all kinds of travelling-wave tube, and the high efficiency with parameter theory model, the electronics that can be used in all kinds of travelling-wave tube with periodical high-frequency structure is annotated and the interactional numerical simulation of radio-frequency field

Description of drawings

Fig. 1 is the schematic flow sheet of the inventive method.

Fig. 2 is that the present invention and Christine theoretical model are found the solution the power of the first-harmonic 5GHz of helix TWT and harmonic wave 10GHz along the axle distribution schematic diagram.

Fig. 3 utilizes method of the present invention to find the solution coupled-cavity TWT saturation output power and test result comparison synoptic diagram.

Embodiment

The invention will be further described below in conjunction with the drawings and specific embodiments.

The schematic flow sheet of the analogy method of travelling-wave tube notes ripple of the present invention interaction comprises the steps: as shown in Figure 1

A. the broad sense radio-frequency field expression formula according to the travelling-wave tube high-frequency structure obtains the radio-frequency field equation.

In having the travelling-wave tube high-frequency structure of axial cyclic, the broad sense electromagnetic field of high frequency can be expressed as formula (1.1)

$\left\{\begin{array}{c}{E}_{\mathrm{rf}}(x_{\&perp;},z,t)=a\left(z\right)/\sqrt{\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000084077250000012.png,HDA0000084077250000021.png"\; state="\{\{state\}\}">p</figure-callout>}}_0}}e(x_{\&perp;},z)\exp (-\mathrm{i\&omega;t})\\ H_{\mathrm{rf}}(x_{\&perp;},z,t)=a\left(z\right)/\sqrt{\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000084077250000012.png,HDA0000084077250000021.png"\; state="\{\{state\}\}">p</figure-callout>}}_0}}h(x_{\&perp;},z)\exp (-\mathrm{i\&omega;t})\end{array}\right.$ Formula (1.1)

First formula is high-frequency electric field E in the formula (1.1) _RfExpression formula, second formula is high frequency magnetic field H _RfExpression formula; Wherein, vector x representation space position vector, subscript " ⊥ " expression cross stream component, variable z and t represent axial location and time respectively.

A (z) is the radio-frequency field amplitude, is the complex function of axial location variable z; According to radio-frequency field amplitude a (z), utilize relational expression p (z)=| a (z) | ²Can obtain power. Be intrinsic power, e (x _⊥, z) and h (x _⊥, z) be respectively the passive high-frequency electric field and the distribution function of high frequency magnetic field, satisfy passive Maxwell equation group.I is the imaginary number factor, and ω=2 π f are angular frequency, and f represents eigenfrequency.

High-frequency electric field in the formula (1.1) and high frequency magnetic field expression formula are applied to active Maxwell equation group, utilize Poynting's theorem, in a high-frequency structure cycle l and period of time T=2 π/ω, be averaged simultaneously, obtain the satisfied radio-frequency field equation of radio-frequency field amplitude a (z) at last:

$[\frac{d}{\mathrm{dz}}+\mathrm{\&sigma;}\left(z\right)]a\left(z\right)=-\frac{1}{2\sqrt{\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000084077250000012.png,HDA0000084077250000021.png"\; state="\{\{state\}\}">p</figure-callout>}}_0}}}\underset{z}{\overset{z+l}{\&Integral;}}\frac{\mathrm{dz}}{l}\underset{t}{\overset{t+T}{\&Integral;}}\frac{\mathrm{dt}}{T}\underset{S}{\&Integral;\&Integral;}\mathrm{dsj}(x_{\&perp;},z)\&CenterDot;e^{*}(x_{\&perp;},z)\exp \left(\mathrm{i\&omega;t}\right)$ Formula (1.2)

Wherein, Be differentiating about axial location z.σ (z) is the damping capacity of unit length radio-frequency field, i.e. attenuation coefficient; L is the axial-periodic length of high-frequency structure, and T=2 π/ω is and the corresponding time cycle of signal frequency,

Expression is along high-frequency structure xsect integration.J (x _⊥, z) be electric current distribution, obtain by the motion state of particle.Subscript " ^*" expression gets conjugation, identical in the physical meaning of other symbol and the formula (1.1).

Formula (1.2) has versatility, is applicable to the travelling-wave tube of various dissimilar high-frequency structures, just to dissimilar high-frequency structures, and passive high-frequency electric field distribution e (x _⊥, z) have different distributional patterns.

B. utilize the method for pure values to obtain radio-frequency field distribution passive in the travelling-wave tube high-frequency structure.

Know by steps A, find the solution the radio-frequency field equation, need to obtain passive high-frequency electric field distribution e (x in the travelling-wave tube periodic structure _⊥, z).Yet the high-frequency structure difference that dissimilar travelling-wave tube adopt causes the passive high-frequency electric field distribution e (x of high-frequency structure inside _⊥, z) do not have unified analytical expression.So the numerical value field distribution that consideration utilizes the method for pure values to obtain in any travelling-wave tube high-frequency structure replaces resolving field distribution e (x _⊥, z), make this theoretical model have versatility.

The method of the pure values here can realize by the experiment test of passive radio-frequency field in 3 D electromagnetic Flow Field Numerical simulation software or the high-frequency structure.

The travelling-wave tube complex structure, interaction zone is long, and the passive radio-frequency field that obtains in the whole interaction zone of the experiment test by 3 D electromagnetic Flow Field Numerical simulation software or passive radio-frequency field distributes individually, and resource consumptions such as internal memory and time are big.

Here, as a preferable scheme, can utilize the periodic characteristics of travelling-wave tube high-frequency structure, distribute by the numerical value radio-frequency field in axial-periodic of experiment test acquisition travelling-wave tube high-frequency structure of 3 D electromagnetic Flow Field Numerical simulation software or passive radio-frequency field, the numerical value radio-frequency field that utilizes the Fu Luokui theorem to obtain optional position in the travelling-wave tube high-frequency structure then distributes.

According to the Fu Luokui theorem, in periodic structure

E (x _⊥, z)=e (x _⊥, ρ) exp[(n-1) and i φ] formula (1.3)

In the formula (1.3), φ represents and the corresponding monocycle phase shift of angular frequency; Integer n is represented the residing high-frequency structure periodicity of current axial location z, and ρ represents the offset of z and z place space periodic reference position, and satisfy between each physical quantity: z=(n-1) l+ ρ, wherein, l is the axial-periodic length of high-frequency structure.

C. computer memory charge field;

In the present embodiment, adopt space charge wave Model Calculation space charge field.

Under the one-dimensional case, the axial space charge field can be got real part by m space charge wave summation and obtain, promptly

$E_{\mathrm{sc},z}=-\mathrm{Re}\underset{m}{\mathrm{\&Sigma;}}\frac{8I_{b}i}{{\mathrm{\&omega;}}_m(r_{\mathrm{bo}}^2-r_{\mathrm{bi}}^2)}{R}_m<e^{\mathrm{im\&omega;t}}>e^{-\mathrm{im\&omega;t}}$ Formula (1.4)

In the formula (1.4), E _{Sc, z}Be the axial space charge field; M is the number of times of space charge wave, ω _mAngular frequency for m space charge wave satisfies ω _m=m ω; r _BiAnd r _BoBe respectively electronics and annotate inside radius and electronics notes external radius; I _bBe the beam current size; I is the imaginary number factor; R _mThe plasma frequency that is the m time space charge wave reduces the factor, satisfies

$R_m=1-\frac{2}{(r_{\mathrm{bo}}^2-r_{\mathrm{bi}}^2)}\left\{\right[r_{\mathrm{bo}}{K}_1\left({\mathrm{\&gamma;}}_m^{\left(e\right)}{r}_{\mathrm{bo}}\right)+r{I}_1\left({\mathrm{\&gamma;}}_m^{\left(e\right)}r\right){|}_{r_{\mathrm{bi}}}^{r_{\mathrm{bo}}}{K}_0\left({\mathrm{\&gamma;}}_m^{\left(e\right)}{r}_s\right)/I_0\left({\mathrm{\&gamma;}}_m^{\left(e\right)}{r}_s\right)].$ Formula (1.5)

$\left[r{I}_1\left({\mathrm{\&gamma;}}_m^{\left(e\right)}r\right){|}_{r_{\mathrm{bi}}}^{r_{\mathrm{bo}}}\right]-r_{\mathrm{bi}}{I}_1\left({\mathrm{\&gamma;}}_m^{\left(e\right)}{r}_{\mathrm{bi}}\right)\left[r{K}_1\left({\mathrm{\&gamma;}}_m^{\left(e\right)}r\right){|}_{r_{\mathrm{bi}}}^{r_{\mathrm{bo}}}\right]\}$

In the formula (1.5), r is radial position, I ₀() and I ₁() is respectively zeroth order and single order first kind modified Bessel function, K ₀() and K ₁() is respectively zeroth order and the single order second class modified Bessel function.

Be the space charge wave propagation factor, satisfy

${\mathrm{\&gamma;}}_m^{\left(e\right)}=m{[{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA0000084077250000012.png,HDA0000084077250000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2-{(\mathrm{\&omega;}/c)}^2]}^{1/2}$ Formula (1.6)

Wherein, k ₀=ω/v ₀, v ₀Be the initial axial velocity of grand particle, c is the light velocity,＜e ^{Im ω t}For axial location z place the average excitation of grand particle to the m time space charge wave arranged, satisfy

$<e^{\mathrm{im\&omega;t}}>=\frac{1}{N_{\mathrm{\&lambda;}}}\underset{v=1}{\overset{N_{\mathrm{\&lambda;}}}{\mathrm{\&Sigma;}}}{e}^{\mathrm{im\&omega;}{t}_{\mathrm{zv}}}$ Formula (1.7)

Wherein, N _λBe grand total number of particles, t _ZvV grand particle arrives the moment of axial location z.

Space charge field under two dimension or the three-dimensional situation calculates similarly, no longer is elaborated.

D. utilize Lorentz force equation to promote particle movement, obtain the phase equation and the equation of motion of particle.

Under the effect of electromagnetic field of high frequency and space charge field, promote particle movement according to Lorentz force equation, the equation of describing particle movement comprises the phase equation and the equation of motion.

Under one-dimensional case, the phase equation of v particle is:

$\frac{d{\mathrm{\&psi;}}_v}{\mathrm{dz}}=\frac{\mathrm{\&omega;}}{v_{z,v}}$ Formula (1.8)

Wherein, Be to differentiate ψ about axial location z _vBe the phase place of v particle, ω is an angular frequency, v _{Z, v}It is the axial velocity of v particle.

The equation of motion that is obtained particle under the one-dimensional case by Lorentz force equation is:

$m_0{c}^2\frac{d{\mathrm{\&gamma;}}_v}{\mathrm{dz}}=-\left|e\right|\mathrm{Re}[\frac{a\left(z\right)}{\sqrt{\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000084077250000012.png,HDA0000084077250000021.png"\; state="\{\{state\}\}">p</figure-callout>}}_0}}}{<\hat{z}\&CenterDot;e(x_{\&perp;},z)>}_{\mathrm{beam}}{e}^{-i{\mathrm{\&psi;}}_v}-\frac{8I_{b}i}{(r_{\mathrm{bo}}^2-r_{\mathrm{bi}}^2)}\underset{m}{\mathrm{\&Sigma;}}\frac{R_m}{{\mathrm{\&omega;}}_m}{e}^{-\mathrm{im}{\mathrm{\&psi;}}_v}<e^{\mathrm{im}{\mathrm{\&psi;}}_v}>]$ Formula (1.9)

Wherein, e and m ₀Be respectively the electric charge and the rest mass of electronics, γ _vRelativity factor for grand particle.

First of formula (1.9) the right is the suffered high-frequency electrical field force of grand particle,

For the mean value of axial electric field on electronics notes xsect, satisfy

${<\hat{z}\&CenterDot;e(x_{\&perp;},z)>}_{\mathrm{beam}}=\frac{1}{\mathrm{\&pi;}(r_{\mathrm{bo}}^2-r_{\mathrm{bi}}^2)}\underset{S_{\mathrm{beam}}}{\&Integral;\&Integral;}\mathrm{ds}\hat{z}\&CenterDot;e(x_{\&perp;},z)$ Formula (1.10)

Wherein, S _BeamThe expression electronics is annotated xsect, Be axial unit vector.

Second space-charge force that is subjected to for grand particle on formula (1.9) the right.

With formula (1.7) to corresponding, be of the average excitations of all grand particles, that is: to the m time space charge wave

$<e^{\mathrm{im\&omega;}{t}_{\mathrm{zv}}}>=<e^{\mathrm{im}{\mathrm{\&psi;}}_v}>=\frac{1}{N_{\mathrm{\&lambda;}}}\underset{v=1}{\overset{N_{\mathrm{\&lambda;}}}{\mathrm{\&Sigma;}}}{e}^{\mathrm{im\&omega;}{t}_{\mathrm{zv}}}=\frac{1}{N_{\mathrm{\&lambda;}}}\underset{v=1}{\overset{N_{\mathrm{\&lambda;}}}{\mathrm{\&Sigma;}}}{e}^{\mathrm{im}{\mathrm{\&psi;}}_v}$

The symbol that each formula of other symbol and front of occurring in the formula (1.9) occurs is consistent, no longer elaborates here.

Particle movement equation under two dimension or the three-dimensional situation similarly no longer is elaborated.

E. utilize the radio-frequency field equation that steps A, B, C, D obtain, the phase equation and the equation of motion of particle, set up and describe the differential equation group that travelling-wave tube is annotated ripple interaction process, be that simultaneous formula (1.2), (1.8), (1.9) are set up differential equation group, the interaction starting condition is set, find the solution the differential equation group of foundation, finish up to annotating the ripple interaction, can finish the simulation of once annotating ripple interaction process.

Here, can utilize runge kutta method progressively to find the solution the differential equation group of foundation.For finding the solution the differential equation group of foundation, starting condition must be set.The starting condition of each differential equation correspondence is provided with as follows:

To the radio-frequency field equation, the starting condition of radio-frequency field amplitude is:

$\mathrm{Rea}(z=0)=\sqrt{p_{\mathrm{in}}}\cos \left({\mathrm{\&theta;}}_{\mathrm{in}}\right)$ Formula (1.11)

$\mathrm{Ima}(z=0)=\sqrt{p_{\mathrm{in}}}\sin \left({\mathrm{\&theta;}}_{\mathrm{in}}\right)$

In the formula (1.11), p _InAnd θ _InBe respectively the power and the phase place of input signal.

Under one-dimensional case, in a high-frequency structure Cycle Length, divide N _zIndividual grid is got N on each grid _λIndividual particle, N altogether _z* N _λIndividual particle, the corresponding phase equation of each particle and an equation of motion.N on each grid _λIndividual particle, its initial phase evenly distribute in 0 to 2 π, and all particles have identical initial relativity factor, and following initial phase condition and initial relativity factor condition are promptly arranged.

The initial phase condition of particle phase equation is:

${\mathrm{\&psi;}}_v=\frac{2\mathrm{\&pi;}}{N_{\mathrm{\&lambda;}}}v,v=(\mathrm{0,1,2},...N_{\mathrm{\&lambda;}}-1)$ Formula (1.12)

Initial relativity factor condition of particle movement equation is:

${\mathrm{\&gamma;}}_0=\frac{-\left|e\right|}{m{c}^2}{U}_b$ Formula (1.13)

Wherein, U _bFor electronics is annotated voltage.

Fig. 2 is that method of the present invention and Christine theoretical model are used to simulate the power of the first-harmonic 5GHz that finds the solution when helix TWT is annotated the ripple interaction and second harmonic 10GHz along the axle distribution schematic diagram.

Fig. 3 is that the present invention finds the solution the coupled-cavity TWT saturation output power and test result compares synoptic diagram.

In Fig. 2, curve 1 is an output power of utilizing the 5GHz signal of method calculating of the present invention, curve 2 is the power that utilizes the harmonic excitation of the 10GHz that method of the present invention calculates, curve 3 is output powers of the 5GHz signal that calculates with the Christine theoretical model, and curve 4 is the power that utilizes the harmonic excitation of the 10GHz that the Christine theoretical model calculates.

In Fig. 3, curve 5 is the saturation output powers that utilize method of the present invention to calculate, and curve 6 is saturation output powers of actual coupler measurement.

Can see curve 1 and 3 by Fig. 2, curve 2 and 4 overlaps respectively, and when calculating the interaction of helix TWT notes ripple, this method is consistent with the result of calculation of Christine theoretical model.Can see that by Fig. 3 curve 5 and 6 is very approaching, difference is to be caused by factors such as fabrication errors, illustrate that this method also can be applied to the coupled-cavity TWT notes ripple interaction simulation of labyrinth, and accuracy is higher.

Method of the present invention distributes by the radio-frequency field that the method for utilizing pure values obtains in the travelling-wave tube high-frequency structure, and in conjunction with the phase equation and the equation of motion of radio-frequency field equation, particle, make up differential equation group, promptly set up the notes ripple interaction parameter theoretical model that is applicable to all kinds travelling-wave tube, method of the present invention can be simulated the notes ripple interaction process in all kinds of travelling-wave tube, and the high efficiency with parameter theory model can be used for all kinds of travelling-wave tube electronics with periodical high-frequency structure and annotates and the interactional numerical simulation of radio-frequency field.

Analogy method of the present invention also belongs to the parameter theory model of half parsing half value, computing velocity is fast, on ordinary PC, only needed several minutes can calculate the simulation of once annotating ripple interaction process, therefore can make the travelling-wave tube designer fast and effeciently carry out design optimization to various travelling-wave tube, improve the travelling-wave tube serviceability, greatly reduced R﹠D cycle and cost.

Those of ordinary skill in the art will appreciate that embodiment described here is in order to help reader understanding's principle of the present invention, should to be understood that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not break away from essence of the present invention according to these technology enlightenments disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (5)

1. a travelling-wave tube is annotated the analogy method of ripple interaction, it is characterized in that, may further comprise the steps:

A. obtain the radio-frequency field equation according to the broad sense radio-frequency field expression formula in the travelling-wave tube high-frequency structure;

B. utilize the method for pure values to obtain radio-frequency field distribution passive in the travelling-wave tube high-frequency structure;

C. computer memory charge field;

D. utilize Lorentz force equation to promote particle movement, obtain the phase equation and the equation of motion of particle;

E. utilize the radio-frequency field equation that steps A, B, C, D obtain, the phase equation and the equation of motion of particle, set up and describe the differential equation group that travelling-wave tube is annotated ripple interaction process, the interaction starting condition is set, find the solution the differential equation group of foundation, finish up to annotating the ripple interaction, can finish the simulation of once annotating ripple interaction process.

2. travelling-wave tube according to claim 1 is annotated the analogy method of ripple interaction, it is characterized in that the radio-frequency field equation described in the steps A is specially:

$[\frac{d}{\mathrm{dz}}+\mathrm{\&sigma;}\left(z\right)]a\left(z\right)=-\frac{1}{2\sqrt{\stackrel{\&OverBar;}{p_0}}}\underset{z}{\overset{z+l}{\&Integral;}}\frac{\mathrm{dz}}{l}\underset{t}{\overset{t+T}{\&Integral;}}\frac{\mathrm{dt}}{T}\underset{S}{\&Integral;\&Integral;}\mathrm{dsj}(x_{\&perp;},z)\&CenterDot;e^{*}(x_{\&perp;},z)\exp \left(\mathrm{i\&omega;t}\right),$

Wherein, Be that σ (z) is the damping capacity of unit length radio-frequency field, i.e. attenuation coefficient about the differentiating of axial location z; L is the axial-periodic length of high-frequency structure, and T=2 π/ω is and the corresponding time cycle of signal frequency,

Expression is along high-frequency structure xsect integration, j (x _⊥, z) be electric current distribution, obtain by the motion state of particle, subscript " ^*" represent to get conjugation, subscript " ⊥ " expression cross stream component, variable z and t represent axial location and time respectively, a (z) is the radio-frequency field amplitude, is the complex function of axial location variable z;

Be intrinsic power, e (x _⊥, be the distribution function of passive high-frequency electric field z), i is the imaginary number factor, and ω=2 π f are angular frequency, and f represents eigenfrequency.

3. travelling-wave tube according to claim 1 and 2 is annotated the analogy method of ripple interaction, it is characterized in that, the method of the pure values described in the step B is specially: distribute by the numerical value radio-frequency field in axial-periodic of experiment test acquisition travelling-wave tube high-frequency structure of 3 D electromagnetic Flow Field Numerical simulation software or passive radio-frequency field, the numerical value radio-frequency field that utilizes the Fu Luokui theorem to obtain optional position in the travelling-wave tube high-frequency structure then distributes.

4. travelling-wave tube according to claim 3 is annotated the analogy method of ripple interaction, it is characterized in that the described computer memory charge field of step C specifically adopts the space charge wave pattern to calculate.

5. annotate the analogy method of ripple interaction according to claim 3 or 4 described travelling-wave tube, it is characterized in that the described differential equation group of finding the solution foundation of step D specifically adopts runge kutta method.

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