CN115630466A - High-frequency and magnetic field distribution collaborative design method for curve profile gyrotron traveling wave tube - Google Patents
High-frequency and magnetic field distribution collaborative design method for curve profile gyrotron traveling wave tube Download PDFInfo
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Abstract
The invention discloses a collaborative optimization design method for a high-frequency structure and magnetic field distribution of a curved-profile gyrotron traveling wave tube, and belongs to the technical field of millimeter waves and terahertz. The method comprises the steps of firstly establishing a mapping relation between performance parameters and high-frequency structure parameters of a curve contour gyrotron traveling wave tube, then calculating the energy distribution and the phase distribution of the optimal pre-clustered electron beams by utilizing the dispersion relation and the propagation characteristic of a linear high frequency band, finally establishing a fitness function to evaluate the performance of the gyrotron traveling wave tube, and carrying out cooperative optimization on the gyrotron traveling wave tube through a global optimization algorithm. According to the invention, through the matching design of the multi-solenoid coil magnet and the high-frequency structure with gradually changed calibers, the design freedom degree is improved; a global optimization algorithm is introduced, so that the electron beam and the high-frequency field are subjected to maximum matching transduction in a broadband, and finally, the cooperative optimization design of the high-frequency structure and the magnetic field distribution of the curve profile gyrotron traveling wave tube under the condition of given performance indexes is realized.
Description
Technical Field
The invention belongs to the technical field of millimeter waves and terahertz, and particularly relates to a collaborative optimization design method for a high-frequency structure and magnetic field distribution of a curve profile gyrotron traveling wave tube, which is applied to design of a broadband high-efficiency gyrotron traveling wave tube amplifier.
Technical Field
gyro-TWT (gyro-TWT) is an electronic device that performs amplification based on the electron cyclotron stopple instability mechanism. In the millimeter wave band, the gyrotron traveling wave tube amplifier has the advantages of high broadband, high power and the like. With the development of high-speed communication, electronic countermeasure, advanced radar and other systems, a new generation system puts more stringent requirements on the comprehensive performance indexes such as the working frequency, bandwidth and efficiency of a high-power source device. In general, the bandwidth and efficiency of the amplifier are constrained to each other, and it is difficult to achieve a synchronous boost. The bandwidth of a hundred-kilowatt millimeter wave gyrotron travelling wave tube reported internationally is only 8% at most, the in-band efficiency is lower than 20%, and the existing structure is difficult to obtain further improvement (A.A. Bogdashov et al, IEEE Electron Device Letters,42 (1): 98-101, jan.2021, doi.
The gyrotron traveling wave tube high-frequency structure with the curve profile comprises: an input modulation section, and a high-frequency structure (the high-frequency structure is composed of a linear high-frequency section and a nonlinear high-frequency section; a multi-solenoid magnet is arranged at the periphery, and the multi-solenoid magnet determines the magnetic field distribution of the injection-wave interaction). Generally, when a gyrotron traveling wave tube is designed and optimized, parameters of a linear high-frequency band and a nonlinear high-frequency band are designed integrally, even if the nonlinear high-frequency band is designed, the whole high-frequency structure still needs to be calculated repeatedly, parameters of related medium materials are numerous, and calculation is complex. When the gyrotron traveling wave tube is optimally designed, the requirement of high comprehensive performance indexes is difficult to meet.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a collaborative optimization design method for a high-frequency structure and magnetic field distribution of a curved-profile gyrotron traveling wave tube. The method provides a large-signal method for high-frequency design of a gradient-caliber gyrotron traveling wave tube, establishes a mapping relation between performance influence parameters of the gyrotron traveling wave tube and form and position parameters and high-frequency structure parameters of a multi-solenoid magnet, improves the degree of freedom of design through matching design of the multi-solenoid magnet and a high-frequency structure with a gradient caliber, introduces a global optimization algorithm to enable electron beams and a high-frequency field to carry out matching transduction to the maximum extent in a broadband, and finally realizes cooperative optimization design of a curve profile gyrotron traveling wave tube high-frequency structure and magnetic field distribution under a given performance index condition.
The technical scheme adopted by the invention is as follows:
a high-frequency and magnetic field distribution collaborative design method for a curve profile gyrotron traveling wave tube is characterized by comprising the following steps:
s1, establishing a mapping relation between performance parameters and high-frequency structure parameters of the curve profile gyrotron traveling wave tube.
The performance parameters of the curve profile high-frequency gyrotron traveling wave tube comprise: high frequency field power distribution P (z), efficiency distribution η (z) at different frequency points, where z represents the normalized longitudinal position of the high frequency structure.
The high-frequency structural parameters include: a curved high frequency profile r (z) and a multi-solenoid magnet controlled magnetic field profile B (z).
Transverse wave number distribution k in nonlinear high frequency band with slowly gradually changed caliber t (z) and normalized value κ (z) and longitudinal wavenumber distribution k thereof z (z) and its normalized value h (z) are:
in the above formula, k is the electromagnetic wave number, x mn Is the derivative J 'of the mth order Bessel function' m (x) The nth square root of =0, h (z) is the normalized longitudinal wave number.
Establishing a mapping relation of injection-wave interaction under the conditions of a curve high-frequency profile r (z) and a magnetic field distribution B (z):
where ξ (z) is the normalized lamor radius, w (z) is the normalized electron energy variation, θ (z) is the phase slowness variable, θ (z) is the normalized electron energy variation 0 For the initial phase lag, F (z) is the normalized high frequency field amplitude, L s (z) is a structural factor, L * s (z) is the conjugate thereof, J s (xi) is the Bessel function of order s, J s ' (ξ) is its derivative, im () represents the imaginary part of the factor, re () represents the real part of the factor, F (z) is the normalized high frequency field amplitude, Δ (z) is the normalized frequency detuning between the electron beam and the high frequency field, I 0 (z) is a current parameter, [ mu ] (z) is an influence factor of the injection-wave synchronization condition, l (z) is a coefficient related to longitudinal transduction, and the coefficient l (z) = h (z) < beta > (z) > 2 t0 /[2β z0 (1-h(z)β z0 )]，β z0 Is the initial normalized longitudinal velocity, beta t0 Is the initial normalized lateral velocity.
Normalized current parameter I 0 (z), larmor radius ξ (z) are given by the following equation:
in which I b Is the operating current, N s (z) is a quantity describing the power density of the high-frequency field, γ 0 Is the initial relativistic factor, ω is the electron cyclotron angular frequency, s is the harmonic order, c is the speed of light, e and m 0 Respectively, the electron charge and the static mass of the electrons.
The magnetic field distribution in the longitudinal direction is B (z), and the cyclotron frequency Ω (z) and the detuning amount Δ (z) of the electron are distributed as follows:
where γ (z) is a relativistic factor at different positions.
Given working magnetic field B 0 (z) and tangential point magnetic field B g (z) constraint:
in actual engineering, c is set 1 The value range is 96% -99%, c 2 The value range is 100-101%. The method can realize the strong coupling of the injection-wave interaction in consideration of proper magnetic field detuning quantity, so that the method is different from the traditional design requirement, the maximum energy exchange in the required bandwidth can be realized without setting the same strong constraint condition, and the design freedom degree of the magnetic field distribution is greatly improved.
The relationship between the normalized high-frequency field amplitude F (z) and the power distribution P (z) in the traveling wave tube is as follows:
for the nonlinear high frequency band with slowly-changing caliber, the power flows at different positions are the same, so that the position of a junction point z of two adjacent sections of infinitesimal elements is as follows:
N s (z)|F(z)| 2 ＝const. (10)
the interaction efficiency distribution η (z) is:
in the formula of U b Is the operating voltage of the device.
And S2, calculating the energy distribution w (z) and the phase distribution theta (z) of the electron beam in the optimal pre-clustering state by using the dispersion relation and the propagation characteristic of the linear high frequency band.
After entering an input modulation section of the gyrotron traveling wave tube, electrons interact with an injected high-frequency field, and pre-clustering is carried out on electron beams in a linear high-frequency band (medium loaded waveguide). The electronic pre-clustering is completed at the end of the linear high frequency band, and the optimal clustering can be realized by adjusting the input power injected into the high frequency field.
Calculating the normalized transverse wave number κ (z) and longitudinal wave number h (z) in formula (1) using formulae (4) and (6) in S1; and then, combining the formula (1), the formula (3) and the formula (11), carrying out numerical solution on the formula (2), further obtaining the energy distribution w (z), the phase distribution theta (z) and the normalized high-frequency field amplitude distribution F (z) of the electron beam, and extracting and storing the energy distribution and the phase distribution of the electron beam in the optimal pre-clustering state.
The numerical solution of the formula (2) can be carried out by adopting a Longge Kutta method, and the nonlinear high frequency band is uniformly divided into a plurality of micro-elements in the longitudinal direction for equivalent calculation.
And S3, integrating the S1 and the S2, establishing a fitness function to evaluate the performance of the gyrotron traveling wave tube, and performing cooperative optimization on the gyrotron traveling wave tube through a global optimization algorithm.
The high-frequency structure of the traveling wave tube is continuous, so that the calculation complexity can be reduced by discretely calculating the quantity to be optimized when the fitness function is established. Dividing the nonlinear high-frequency band with length L into M micro-elements uniformly in longitudinal direction, and the longitudinal position of the ith micro-element is Z i = L (i-1)/(M-1) with radius R i Normalized magnetic field distribution of b i M is an integer, i =1,2.. M; and constructing a smooth nonlinear high-frequency band profile r (z) and a normalized magnetic field distribution b (z) by an interpolation mode. In the optimization process, the high-frequency caliber R is made i Gradually increase (i.e. R) i ≤R i+1 ) To reduce circuit reflections and to normalize the magnetic field distribution b i Monotonically decreasing (i.e. b) i ≥b i+1 ) To match the synchronization conditions required for broadband transduction. Actual magnetic field distribution B (z) = B 0r B (z) wherein B 0r Representing the main magnetic field value to be optimized; therefore, the nonlinear high-frequency band is total to 2M +1 variables to be optimized, including the main magnetic field value, M infinitesimal radii and M magnetic field distribution points.
And (3) inputting the energy distribution and the phase distribution of the optimal pre-clustered electron beam state stored in the S2 as condition input fitness functions, and optimizing 2M +1 variables to be optimized through a global optimization algorithm, so that the linear high-frequency band and the nonlinear high-frequency band are cooperatively optimized, and the linear high-frequency band is prevented from being repeatedly calculated during nonlinear high-frequency band calculation.
The fitness function is as follows:
g 1 ＝min{η(f 1 ),η(f 2 )...η(f Q )} (12)
or:
discretizing a given operating bandwidth into Q frequency points, η (f) q ) Is the q-th discrete frequency point f q Q =1,2, · Q; by the formula (12) or the formula (13) to B 0r 、R i And b i Optimizing to achieve a given target efficiency eta goal Maximum bandwidth below or optimal interaction efficiency within a given bandwidth.
The invention has the beneficial effects that:
(1) The invention provides a method for collaborative design of a high-frequency structure and magnetic field distribution of a gyrotron traveling wave tube for the first time on the premise of establishing mapping between magnetic field distribution and coil form and position parameters and mapping between performance indexes of the gyrotron traveling wave tube and the high-frequency structure and magnetic field distribution.
(2) The general method for solving the large signal of the nonlinear high-frequency gyrotron traveling wave tube can be used for solving a concentrated loss high frequency, a distributed loss high frequency and a combined complex high-frequency circuit (such as an electronic clustering process of inputting a modulation section and loading a high frequency and injection-wave interaction transduction calculation of curve high frequency and curve magnetic field distribution).
(3) The strong constraint condition that the magnetic field distribution is the same as the tangent point magnetic field at the corresponding position in the traditional design is effectively avoided, the design freedom of the magnetic field distribution is improved, and a theoretical basis is provided for the strong coupling transduction in the broadband.
(4) Based on the dispersion relation and the propagation characteristic of a linear high-frequency band (dielectric loaded waveguide), the energy distribution and the phase distribution of the electron beam in the optimal pre-clustering state are extracted and stored, repeated calculation and solution of the linear high-frequency band are not needed in the nonlinear high-frequency band optimization process, and the calculation amount is greatly reduced.
Drawings
Fig. 1 is a schematic diagram of a high-frequency structure of a curved-profile gyrotron traveling wave tube, wherein the reference numerals in the diagram are as follows: 1-input modulation section, 2-linear high frequency band (dielectric loaded waveguide), and 3-nonlinear high frequency band.
Fig. 2 is a schematic equivalent diagram of a discretization of a section of a curved profile gyrotron traveling wave tube.
Fig. 3 is a schematic diagram of the radius and magnetic field distribution point optimization boundary of the nonlinear high frequency band.
Fig. 4 is a phase and energy profile of a typical pre-clustered electron beam.
FIG. 5 is a graph showing the result of the high frequency profile curve and the magnetic field distribution optimization.
Fig. 6 is a frequency response curve of saturated output power and efficiency.
Detailed Description
The technical scheme of the invention is detailed below by combining the high-frequency structure and magnetic field distribution collaborative optimization example of the G-band gyrotron traveling wave tube and the accompanying drawing:
fig. 1 shows a high-frequency structure of a generalized curve profile gyrotron traveling wave tube, which includes an input modulation section, a linear high-frequency section (dielectric loaded waveguide), and a nonlinear high-frequency section (smooth curve waveguide).
FIG. 2 is a schematic diagram of discretization equivalent of high-frequency section of a curve contour gyrotron traveling wave tube. The continuous nonlinear high-frequency band is dispersed into a plurality of infinitesimals, so that discrete iterative computation can be performed on respective nodes, and the complexity of computation is reduced.
Taking the design of a G-band gyrotron traveling wave tube as an example, the design target is a broadband high-power traveling wave tube amplifier working in the G band, and the injection-wave interaction efficiency requirement of the amplifier is more than 20%. The method comprises the following specific steps:
s1, establishing a mapping relation between performance parameters and high-frequency structure parameters of the curve profile gyrotron traveling wave tube, wherein the mapping relation is specifically shown in formulas (1) to (11). And in the nonlinear high-frequency band with the gradually changed caliber, the power flows at different positions are the same. At the same time, the working magnetic field B is given 0 (z) and tangential point magnetic field B g (z) the constraint is [96%,101%]In the interval, the design freedom degree of magnetic field distribution is improved, and strong coupling of injection-wave interaction is realized.
And S2, calculating the energy distribution w (z) and the phase distribution theta (z) of the electron beam in the optimal pre-clustering state by using the dispersion relation and the propagation characteristic of the linear high frequency band.
In a linear high frequency band, in the electron beam grouping process, medium parameters of epsilon r =6, tan delta =0.4, thickness d =0.25mm and length L are adopted loss =60mm dielectric material. The dispersion relation and the propagation characteristics of the medium loaded waveguide are utilized, including but not limited to the adoption of a field matching theory, simulation and test, so that the stability of zero drive is ensured, and the reflection instability can not be caused in a high frequency band of a curve profile. Based on the waveguide characteristics, normalized transverse and longitudinal wave number distributions κ (z) and h (z) in the formula (1) are obtained, and further, the electron beam energy distribution and the phase distribution at the end of the loading section are obtained. Setting working parameter U b ＝60kV，I b =5A, the velocity ratio α =1.2, the optimal electron beam bunching state shown in fig. 4 is obtained, as shown in the left graph, the proportion of electrons within ± 0.2 pi of the bunching center is 73.6% at the end of the linear high frequency, and the right graph in fig. 4 represents the energy distribution of the high frequency field, with the corresponding energy dispersion range being-3.34 kV to 3.23kV. Storing the energy and phase distributions of the pre-clustered electron beams as inputs in optimizing the high frequency profile of the curveAnd (4) conditions.
And S3, integrating the S1 and the S2, establishing a fitness function to evaluate the performance of the gyrotron traveling wave tube, and performing cooperative optimization on the gyrotron traveling wave tube through a global optimization algorithm.
A nonlinear high-frequency band with the length of L =62mm is evenly divided into M infinitesimals in the longitudinal direction (the larger M is, the higher the calculation precision is, M =10 can be calculated quickly in practical operation), and the longitudinal position of the ith infinitesimal is Z i = L (i-1)/(M-1) with radius R i Normalized magnetic field distribution of b i M is an integer, i =1,2.. M; and constructing a smooth nonlinear high-frequency band profile r (z) and a normalized magnetic field distribution b (z) by an interpolation mode. In the optimization process, the maximum value and the minimum value of the high-frequency contour are respectively determined by the high-side frequency band and the low-side frequency band of the required bandwidth, so that the high-frequency caliber R i Gradually increase (i.e. R) i ≤R i+1 ) To reduce circuit reflections, to normalize the magnetic field distribution b i Monotonically decreasing (i.e. b) i ≥b i+1 ) To match the synchronization conditions required for broadband transduction. Actual magnetic field distribution B (z) = B 0r B (z), wherein B 0r Representing the main magnetic field value to be optimized; therefore, the nonlinear high-frequency band is total to 2M +1 variables to be optimized, including the main magnetic field value, M infinitesimal radii and M magnetic field distribution points.
And establishing a fitness function as shown in the formula (12) or the formula (13) to evaluate the performance of the gyrotron traveling wave tube. And (3) taking the energy distribution and the phase distribution of the optimal pre-clustered electron injection state stored in S2 as condition input fitness functions, and optimizing 2M +1 variables to be optimized through a global optimization algorithm, so that the linear high-frequency band and nonlinear high-frequency band collaborative optimization is realized. Finally, the G-band gyrotron traveling wave tube high-frequency structure profile r (z) and the normalized magnetic field distribution b (z) shown in the attached figure 5 are obtained. The detailed data are shown in table 1:
TABLE 1 partial optimization parameters of traveling wave tube in G wave band
| Longitudinal position z, mm | High frequency structure profile r (z), mm | Normalized magnetic field distribution b (z) |
| 3.858 | 0.077 | 0.789 |
| 7.756 | 0.198 | 0.703 |
| 12.457 | 0.335 | 0.579 |
| 17.038 | 0.734 | 0.437 |
| 20.132 | 1.219 | 0.351 |
| 26.682 | 2.250 | 0.154 |
| 30.057 | 2.475 | 0.051 |
Notably, the target efficiency η in the optimization function is due to the relatively weak longitudinal energy exchange in the ECO effect goal May be greater than100 percent. In this case, once the fitting function reaches the maximum value, the optimization of the gyrotron traveling wave tube is finished. The frequency response results of the resulting saturated output power and interaction efficiency are shown in fig. 6. Therefore, the bandwidth of the output power of the amplifier exceeding 50kW reaches 42GHz, the working frequency range covers 195-237 GHz, the in-band injection-wave interaction efficiency is better than 20%, and the design target is completed.
The general large signal calculation scheme of the non-uniform high-frequency gyrotron traveling wave tube can be used for solving a concentrated loss high frequency, a distributed loss high frequency and a combined complex high-frequency circuit, such as an electronic clustering process for calculating an input modulation section and loading a high frequency and a nonlinear high frequency solution for curve contour.
Based on the technical solutions disclosed in the present invention, those skilled in the art can make various alterations and modifications to some technical features without creative efforts based on the disclosed technical contents, and the alterations and modifications are all within the protection scope of the present invention.
Claims (4)
1. A high-frequency and magnetic field distribution collaborative design method for a curve profile gyrotron traveling wave tube is characterized by comprising the following steps:
s1, establishing a mapping relation between performance parameters and high-frequency structure parameters of a curve profile gyrotron traveling wave tube;
the performance parameters of the curve profile high-frequency gyrotron traveling wave tube comprise: high-frequency field power distribution P (z), efficiency distribution eta (z) of different frequency points, wherein z represents the normalized longitudinal position of the high-frequency structure;
the high-frequency structural parameters include: a curved high frequency profile r (z) and a multi-solenoid magnet controlled magnetic field profile B (z);
transverse wave number distribution k in nonlinear high frequency band with slowly gradually changed caliber t (z) and normalized value κ (z) and longitudinal wavenumber distribution k thereof z (z) and its normalized value h (z) are:
in the above formula, k is the electromagnetic wave number, x mn Is the derivative J 'of the mth order Bessel function' m (x) The nth square root of =0, h (z) is the normalized longitudinal wavenumber;
establishing a mapping relation of injection-wave interaction under the conditions of a curve high-frequency profile r (z) and a magnetic field distribution B (z):
where ξ (z) is the normalized lamor radius, w (z) is the normalized electron energy variation, θ (z) is the phase slowness variable, θ (z) is the normalized electron energy variation 0 For the initial phase lag, F (z) is the normalized high frequency field amplitude, L s (z) is a structural factor, L * s (z) is the conjugate thereof, J s (xi) is the Bessel function of order s, J s ' (ξ) is its derivative, im () represents the imaginary part of the factor, re () represents the real part of the factor, F (z) is the normalized high frequency field amplitude, Δ (z) is the normalized frequency detuning between the electron beam and the high frequency field, I 0 (z) is a current parameter, [ mu ] (z) is an influence factor of the injection-wave synchronization condition, l (z) is a coefficient related to longitudinal transduction, and the coefficient l (z) = h (z) < beta > (z) > 2 t0 /[2β z0 (1-h(z)β z0 )]，β z0 Is the initial normalized longitudinal velocity, beta t0 Is the initial normalized lateral velocity;
normalized current parameter I 0 (z), larmor radius ξ (z) are given by the following equation:
in which I b Is the operating current, N s (z) is a quantity describing the power density of the high-frequency field, γ 0 Is the initial relativistic factor, ω is the electron cyclotron frequency, s is the harmonic order, c is the speed of light, e and m 0 Electron charge and the static mass of the electrons, respectively;
the magnetic field distribution in the longitudinal direction is B (z), and the cyclotron frequency Ω (z) and the amount of detuning Δ (z) of the electrons are distributed as follows:
wherein γ (z) is a relativistic factor at different positions;
given working magnetic field B 0 (z) and a tangent point magnetic field B g (z) constraint:
setting c 1 The value range is 96% -99%, c 2 The value range is 100% -101%;
the relationship between the normalized high-frequency field amplitude F (z) and the power distribution P (z) in the traveling wave tube is as follows:
for the nonlinear high frequency band with slowly-changing caliber, the power flows at different positions are the same, so that the position of a junction point z of two adjacent sections of infinitesimal elements is as follows:
N s (z)F(z) 2 ＝const. (10)
the interaction efficiency distribution η (z) is:
in the formula of U b Is the operating voltage of the device;
s2, calculating the energy distribution w (z) and the phase distribution theta (z) of the electron beam in the optimal pre-clustering state by using the dispersion relation and the propagation characteristic of the linear high frequency band;
after entering an input modulation section of a gyrotron traveling wave tube, electrons interact with an injected high-frequency field to perform pre-clustering on the electron beams in a linear high-frequency band; the electronic pre-clustering is completed at the tail end of a linear high-frequency band, and the optimal clustering can be realized by adjusting the input power injected into a high-frequency field;
calculating the normalized transverse wave number κ (z) and longitudinal wave number h (z) in formula (1) using formulae (4) and (6) in S1; then, combining the formula (1), the formula (3) -the formula (11), carrying out numerical solution on the formula (2), further obtaining the energy distribution w (z), the phase distribution theta (z) and the normalized high-frequency field amplitude distribution F (z) of the electron beam, and extracting and storing the energy distribution and the phase distribution of the electron beam in the optimal pre-clustering state;
and S3, integrating the S1 and the S2, establishing a fitness function to evaluate the performance of the gyrotron traveling wave tube, and performing cooperative optimization on the gyrotron traveling wave tube through a global optimization algorithm.
2. The method for collaborative design of high-frequency and magnetic field distribution of a curved profile gyrotron traveling wave tube according to claim 1, wherein the step S3 specifically comprises:
dividing the nonlinear high frequency band with length L into M micro-elements uniformly in longitudinal direction, the longitudinal position of the ith micro-element is Z i = L (i-1)/(M-1) with radius R i Normalized magnetic field distribution of b i M is an integer, i =1,2.. M; constructing a smooth nonlinear high-frequency-band profile r (z) and a normalized magnetic field distribution b (z) in an interpolation mode; actual magnetic field distribution B (z) = B 0r B (z) wherein B 0r Representing the value of the main magnetic field to be optimized(ii) a Therefore, the nonlinear high-frequency band is total to 2M +1 variables to be optimized, including the main magnetic field value, M infinitesimal radii and M magnetic field distribution points;
the energy distribution and the phase distribution of the optimal pre-clustered electron injection state stored in S2 are used as conditions to be input into a fitness function, 2M +1 variables to be optimized are optimized through a global optimization algorithm, and therefore linear high-frequency band and nonlinear high-frequency band collaborative optimization is achieved;
the fitness function is as follows:
g 1 ＝min{η(f 1 ),η(f 2 )...η(f Q )} (12)
or:
discretizing a given operating bandwidth into Q frequency points, η (f) q ) Is the q-th discrete frequency point f q The efficiency of interaction of (a), Q =1,2, ·, Q; by the formula (12) or the formula (13) to B 0r 、R i And b i Optimizing to achieve a given target efficiency eta goal Maximum bandwidth below or optimal interaction efficiency within a given bandwidth.
3. The method for collaborative design of high-frequency and magnetic field distribution of curved profile gyrotron traveling wave tube according to claim 2, wherein in step S3, when a smooth non-linear high-frequency band profile R (z) and a normalized magnetic field distribution b (z) are constructed in an interpolation manner, the high-frequency caliber R is made to be R i Gradually increased to reduce circuit reflection, so as to normalize magnetic field distribution b i Monotonically decreasing to match the synchronization conditions required for broadband transduction.
4. The method for collaborative design of high frequency and magnetic field distribution of curved profile gyrotron traveling wave tube according to claim 2 or 3, wherein in step S2, the numerical solution of equation (2) is as follows: and uniformly dividing the nonlinear high frequency band into a plurality of micro-elements in the longitudinal direction for equivalent calculation.
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