Self-consistent Nonlinear Theory Research Articles

Analysis and calculation of beam-wave interaction in 220GHz gyrotron resonator

In this paper, the beam-wave interaction of the 220GHz gyrotron resonator is analyzed. The design scheme of the physical structure of the TE36,17 cylindrical open resonator is given. According to the beam-wave coupling coefficient, the center radius of the electron beam guidance of the resonator is obtained, and the working parameters of the resonator are determined by the start current. The single-mode self-consistent nonlinear theory in the frequency domain of the resonator is deduced, and the output characteristics of the resonator are studied by using MATLAB.

Nonlinear adiabatic electron plasma waves: I. General theory and nonlinear frequency shift

This paper provides a complete self-consistent nonlinear theory for electron plasma waves, within the framework of the adiabatic approximation. The theory applies whatever the variations of the wave amplitude provided that they are slow enough, and it is also valid when the plasma is inhomogeneous and non-stationary. Moreover, it accounts for: (i) the geometrical jump in action resulting from separatrix crossing; (ii) the continuous change in phase velocity making the wave frame non-inertial; (iii) the harmonic content of the scalar potential; (iv) a non-zero vector potential; (v) the transition probabilities from one region of phase space to the other when an orbit crosses the separatrix; and (vi) the possible change in direction of the wavenumber. The relative importance of each of the aforementioned effects is discussed in detail, based on the derivation of the nonlinear frequency shift. This allows us to specify how the general formalism may be simplified, depending on the value of the wavenumber normalized to the Debye length. Specific applications of our theory are reported in Paper II.

Effects of the Magnetic Field Taper on a Continuously Frequency-Tunable Gyrotron

Generally, the magnetic field profile in the gyrotron beam-wave interaction section is usually considered to be constant in the theoretical investigation, but actually it is approximately linearly tilted slightly due to the limitation of the superconducting magnet coils. The effects of the weak operating magnetic field taper on the operating frequency, the beam-wave interaction efficiency, and the frequency-tuning range for a continuously frequency-tunable gyrotron are investigated with a self-consistent nonlinear beam-wave interaction theory. It is found that the tapered operating magnetic field has a significant effect on the operating frequency, the frequency tuning bandwidth, and the beam-wave interaction efficiency. In addition, the effect of the weak operating magnetic field taper on the starting current is studied based on the linear theory. It is found that the values of not only the starting current but also the operating magnetic field are obviously different from those when the tapered operating magnetic field is taken into account. With the increase in the slope of the tapered operating magnetic field, the operating frequency and the frequency-tuning range are decreased, but the beam-wave interaction efficiency is increased. When the slope of the tapered operating magnetic field is negative, the variations in the operating frequency, the frequency-tuning range, and the beam-wave interaction efficiency are more obvious. The effects of the tapered magnetic field on different order axial modes are different, and the effect on a higher order axial mode is more notable.

Stability properties of a thin relativistic beam propagation in a magnetized plasma

A self-consistent nonlinear hydrodynamic theory is presented of the propagation of a long and thin relativistic electron beam through a plasma that is relatively strongly magnetized, $|\Omega_e|\sim\omega_{pe}$ and whose density is much bigger than that of the beam. In the regime when the parallel phase velocity in the comoving frame is much smaller than the thermal speed and the beam electrons are thermalized, a stationary solution for the beam is found when the electron motion in the transverse direction is negligibile and the transverse localization comes from the nonlinearity of its 3-D adiabatic expansion. Conversely, when the parallel phase velocity is sufficiently large to prevent the heat convection along the magnetic field, a helicoidally shaped stationary beam is found whose transverse profile is determined from a nonlinear dispersion relation and depends on the transverse size of the beam and its pitch angle.

Study on the Effect of Electron Beam Quality on a Continuously Frequency-Tunable 250-GHz Gyrotron

The effect of the electron beam quality, including the variation of the velocity spread, the guiding center radius spread, and the pitch factor when the operating frequency of a 250-GHz TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">52</sub> mode continuously frequency-tunable gyrotron used for dynamic nuclear polarization (DNP) enhanced nuclear magnetic resonance (NMR) spectroscopy is tuned by changing the operating voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> or the operating magnetic field B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , on the operating frequency, the frequency-tunable range and the beam-wave interaction efficiency, has been studied based on a selfconsistent nonlinear beam-wave interaction theory. It is found that the velocity spread changes from 2.2% to 7.3% and the guiding center radius spread varies from 0.6% to 1.5%, when the operating voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> changes between 8 and 15 kV at an operating magnetic field of 9.24 T, the velocity spread varies from 4.1% to 6% and the guiding center radius spread changes from 0.8% to 1.4%, when the operating magnetic field B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> changes between 9 and 9.3 T at an operating voltage of 10.1 kV. The variation of the velocity spread and guiding center radius spread with respect to the operating voltage or the magnetic field have a significant effect on the beam-wave interaction efficiency and the frequency-tunable range of the 250-GHz TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">52</sub> mode continuously frequency-tunable DNP/NMR gyrotron,and the effect of the variation of the velocity spread and the guiding center radius spread should be taken into account in a frequency-tunable gyrotron design.

Linear and Nonlinear Analyses of a 0.34-THz Confocal Waveguide Gyro-TWT

In this paper, the dispersion relation of the beam wave interaction of the confocal waveguide gyrotron-traveling-wave tube (confocal gyro-TWT) is derived from kinetic theory for the first time; according to this dispersion relation, we can make the linear analysis of confocal gyro-TWT as well as the cylindrical waveguide gyro-TWT. At the same time, a numerical code based on the self-consistent nonlinear theory is written to simulate the behavior of electron beam and electromagnetic wave during beam wave interaction. When neglecting the spread of velocity and guiding center, the gain and growth rate calculated by the nonlinear theory code makes great agreement with that of linear theory in the small-signal region.

Self consistent hydrodynamic description of the plasma wake field excitation induced by a relativistic charged-particle beam in an unmagnetized plasma

A self-consistent nonlinear hydrodynamic theory is presented of the propagation of a long and thin relativistic electron beam, for a typical plasma wake field acceleration configuration in an unmagnetized and overdense plasma. The random component of the trajectories of the beam particles as well as of their velocity spread is modelled by an anisotropic temperature, allowing the beam dynamics to be approximated as a 3D adiabatic expansion/compression. It is shown that even in the absence of the nonlinear plasma wake force, the localisation of the beam in the transverse direction can be achieved owing to the nonlinearity associated with the adiabatic compression/rarefaction and a coherent stationary state is constructed. Numerical calculations reveal the possibility of the beam focussing and defocussing, but the lifetime of the beam can be significantly extended by the appropriate adjustments, so that transverse oscillations are observed, similar to those predicted within the thermal wave and Vlasov kinetic models.

The Nonlinear Designs and Experiments on a 0.42-THz Second Harmonic Gyrotron With Complex Cavity

Terahertz (THz) and sub-THz science and technology are very hot today. However, it is difficult to obtain high-power source of THz wave. Gyrotrons are well known as one of the most promising source for powerful THz radiation. In this paper, a 0.42-THz second harmonic gyrotron with complex cavity operating at TE17.4 is numerically simulated and designed by adopting self-consistent nonlinear theory with the first-order transmission line equations. Meanwhile, the mode competitions in the designed gyrotron have been investigated carefully by using time-dependent multimode nonlinear theory. It is proved that the operating mode can be first excited and other competing modes are well suppressed in the complex cavity. Based on these numerical simulations, the designed complex cavity gyrotron has been manufactured and measured in the Terahertz Science and Technology Research Center at the University of Electronic Science and Technology of China. The measured results show that the designed gyrotron can stably operate at TE17.4 with pulsed output power of 19.3 kW when the beam current ${I}_{{0}}$ is 4.4 A, beam voltage ${U}_{{0}}$ is 51 kV, and magnetic field ${B}_{{0}}$ is 8.03 T. The corresponding frequency and interaction efficiency are 421.645 GHz and 8.6%, respectively.

Numerical Study of Interaction Efficiency for a 170GHz Megawatt‐Level Coaxial‐Gyrotron

The beam-wave interaction efficiency of a 170 GHz megawatt-level corrugated coaxial-gyrotron operating with TE31,12 mode was studied numerically. According to the self-consistent nonlinear theory, the efficiencies of two types of coaxial resonator were calculated and compared. Taking into account electronic velocity spread and cavity wall resistivity, the beam-wave interactions of improved cavity were investigated. The relationships between efficiency and magnetic field, voltage, current, beam radius, velocity ratio, and parameters of groove are presented. The results show that the voltage and magnetic field have great influence on efficiency, but the current and velocity spread do slightly. The optimized geometry parameters can improve efficiency, reduce the impact of velocity spread on efficiency, and achieve around 48.6% electronic efficiency and 1.7MW output power at 5% velocity spread and 6.896×10−8Ωm resistivity.

Statistical Mechanical Theory of Penetrant Diffusion in Polymer Melts and Glasses

We generalize our microscopic, force-level, self-consistent nonlinear Langevin equation theory of activated diffusion of a spherical particle in a dense hard sphere fluid to treat molecular penetrant diffusion in homopolymer melts and nonaging glasses. A coarse-grained mapping is developed where polymer chains are modeled as disconnected, noninterpenetrating Kuhn scale hard spheres (diameter, σ), and the penetrant is modeled as an effective hard sphere (diameter, d) which can be attracted to the polymer segment. The polymer mapping is a priori carried out by enforcing the effective hard sphere fluid reproduces the specific polymer liquid or glass long wavelength dimensionless collective density fluctuation amplitude. The theory predicts that penetrant diffusivity exhibits supra-Arrhenius temperature dependence in supercooled polymer melts and (near) Arrhenius temperature dependence in quenched nonequilibrium polymer glasses. Polymer–penetrant attraction slows down penetrant diffusivity to a degree that is...

Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions.

We heuristically formulate a microscopic, force level, self-consistent nonlinear Langevin equation theory for activated barrier hopping and non-hydrodynamic diffusion of a hard sphere penetrant in very dense hard sphere fluid matrices. Penetrant dynamics is controlled by a rich competition between force relaxation due to penetrant self-motion and collective matrix structural (alpha) relaxation. In the absence of penetrant-matrix attraction, three activated dynamical regimes are predicted as a function of penetrant-matrix size ratio which are physically distinguished by penetrant jump distance and the nature of matrix motion required to facilitate its hopping. The penetrant diffusion constant decreases the fastest with size ratio for relatively small penetrants where the matrix effectively acts as a vibrating amorphous solid. Increasing penetrant-matrix attraction strength reduces penetrant diffusivity due to physical bonding. For size ratios approaching unity, a distinct dynamical regime emerges associated with strong slaving of penetrant hopping to matrix structural relaxation. A crossover regime at intermediate penetrant-matrix size ratio connects the two limiting behaviors for hard penetrants, but essentially disappears if there are strong attractions with the matrix. Activated penetrant diffusivity decreases strongly with matrix volume fraction in a manner that intensifies as the size ratio increases. We propose and implement a quasi-universal approach for activated diffusion of a rigid atomic/molecular penetrant in a supercooled liquid based on a mapping between the hard sphere system and thermal liquids. Calculations for specific systems agree reasonably well with experiments over a wide range of temperature, covering more than 10 orders of magnitude of variation of the penetrant diffusion constant.

Clinotron in the amplification mode

A self-consistent nonlinear theory for a clinotron model that takes into account static electron trajectories in the focusing magnetic field and the loss in the slow-wave structure, the clinotron amplification mode is analyzed for different ratios of the operating and starting currents, input signal levels, and the inclination angle of the electron beam relative to the surface of the slow-wave structure. The gain and the amplification band are calculated. It is demonstrated that the main theoretical data are qualitatively consistent with the experimental results obtained using a clinotron model operating in the five millimeter wave band.

Theoretical Study on a 0.4-THz Second Harmonic Gyrotron

In this paper, the results of theoretical study on a 0.4-THz second harmonic gyrotron operating at TE19.3 are presented. A gradually tapered cavity is adopted to alleviate the problem of parasitic mode competition. It is proved that the amplitudes of spurious modes in the gradually tapered cavity could be kept lower than that in the line-joint cavity, especially that in the line-joint cavity with large angle. Based on the self-consistent nonlinear theory, a code is written to simulate the process of beam–wave interaction. Through optimizing the operating parameters, the beam–wave interaction efficiency can reach 35% and an output power of 100 kW can be obtained. In addition, the mode competition in the designed gyrotron is studied using multifrequency time-dependent nonlinear theory. Simulations tracking five competition modes show that stable excitation of the desired operating mode TE19.3 at 100 kW level can be realized with proper choice of operating parameters.

Theory and Experiment of a W-Band Tunable Gyrotron Oscillator

A gyrotron capable of both frequency and power tuning is a promising coherent millimeter-THz wave source. A self-consistent nonlinear theory is applied to investigate the electron cyclotron interaction between electron beam and wave modes of axial nonfixed profiles in an extended W-band <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">${\rm TE}_{01}$ </tex-math></inline-formula> mode cylindrical cavity. It is revealed that tuning the magnetic field strength can excite electron cyclotron resonances on forward wave, backward wave, and even simultaneous on both waves, which makes the system operate under distinctive states, namely the gyrotron backward wave oscillation state and the gyromonotron state. In this paper, a W-band prototype gyrotron oscillator based on an extended cylindrical waveguide cavity is built, and the experiment test indicates that the system starts oscillation in a relative wide range of the operation parameters. The measured frequency spectrum reveals the system iteratively switches between the lower order instability axial modes, and it operates under nonstationary oscillation states. The experimental measurement of highest output power <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">${\sim}{\rm 8}~{\rm kW}$ </tex-math></inline-formula> is consistent with the theoretical predictions. An optimized gyrotron circuit with efficiency exceeding 20% and tunable bandwidth over 10 GHz is also presented. The free oscillation behaviors revealed in this paper provide interesting guidance for developing tunable gyrotrons in millimeter-THz wave range.

The Self-Consistent Nonlinear Theory of Charged Particle Beam Acceleration by Slowed Circularly Polarized Electromagnetic Waves

The relativistic interaction of charged particle beams with a circularly polarized electromagnetic wave propagating along a uniform guiding magnetic field in the tunneling of a dielectric medium is analyzed. The acceleration mechanism and a self-consistent nonlinear theory are presented for the interaction of relativistic charged particle beams with electromagnetic waves. Numerical results show that the beam particle can be efficiently accelerated in the interaction process.

A Study on 94 GHz Low-Voltage, Low-Current Gyrotron

A theoretical and experimental study on a 94 GHz low-voltage, low-current gyrotron is presented in this paper. In order to obtain stable radiation and make great use of the equipment in the lab, the TE6,2 mode is selected as the operating mode of the desired gyrotron. The efficiency of the electron beam interaction with RF fields under different conditions has been calculated by a code, which is based on the self-consistent nonlinear theory for gyrotrons. The gyrotron is equipped with a single-stage depressed collector and a quasi-optical mode converter. Then, a gyrotron with optimized parameters has been designed, constructed, and tested. An output power of 23 kW is obtained at an accelerating beam voltage of 31.5 kV, a beam current of 1.8 A, and a collector depression voltage of 7.4 kV, corresponding to an overall efficiency of 53%.

A W band second harmonic gyrotron oscillator

针对谐波回旋管互作用效率低的问题, 以自洽非线性理论为基本工具, 系统地分析了三个关键因素, 即互作用腔体长度(Q值)、电子注的横纵速度比和工作电压对二次谐波互作用系统性能的影响.研究发现当工作磁场选择在硬激发区时, 通过综合调节电子注的横纵速度比和工作电压能够获得较高的互作用效率.基于自洽非线性理论优化设计了一个W波段二次谐波回旋振荡器, 粒子模拟(PIC)结果显示当电子注速度离散３％, 工作电压37 kV, 电流4 A时, 输出效率达到了39.5%.;To solve the problem of low interaction efficiency of harmonic gyrotrons, self-consistent theory was used to investigate the dependence of the interaction efficiency on three critical factors; cavity length (quality factor), electronic beam’s velocity ratio and operating voltage. It was found that high efficiency can be achieved by adjusting beam voltage and velocity ratio when the working magnetic field was located at the hard excitation region. Based on the self-consistent nonlinear theory, a W band second harmonic gyrotron oscillator was optimized. Particle in cell computation showed that the efficiency was up to 39.5% when the beam voltage and current was 37kV and 4A, respectively, with velocity spread of 3%.

Development of high-power gyrotrons with gradually tapered cavity

In high power gyrotrons, the parasitic modes coupled with the operating mode cannot be avoided in the beam-wave interaction. These parasitic modes will decrease the efficiency of the gyrotrons. The purity of the operating mode affected by different tapers should be carefully studied. The steady-state self-consistent nonlinear theory for gyrotron with gradually tapered cavity is developed in this paper. A steady-state calculation code including “cold cavity” and “hot cavity” is designed. By comparison, a time-domain model analysis of gyrotron operation is also studied by particle-in-cell (PIC). It is found that the tapers of gyrotron have different influences on the modes coupling between the operating mode and the parasitic modes. During the study, an example of 94 GHz gyrotron with pure operating mode TE03 has been designed. The purity of the operating mode in the optimized cavity is up to −77 dB, and in output waveguide of the cavity is up to −76 dB. At the same time, the beam-wave interaction in the designed cavity has been simulated, too. An output power of 120 kW, corresponding to 41.6% efficiency and an oscillation frequency of 94.099 GHz have been achieved with a 50 kV, 6 A helical electron beam at a guiding magnetic field of 3.5485 T. The results show that the power in spurious modes of the optimized cavity may be kept far below than that of the traditional tapered cavity.

Design and Experimental Demonstration of a 94-GHz Gyrotron with Complex Cavity Operating at the Second Harmonic

A systematic theoretical and experimental study on 94-GHz second-harmonic gyrotron with a superconducting magnet system is presented in this paper. A complex cavity with gradual transition is employed in the gyrotron. A self-consistent field nonlinear theory is used and numerical simulation results for electron beam interaction with TE02–TE03 modes are given. A pulse output power of 235.2 kW is obtained by simulation at a beam voltage of 60 kV with beam current of 10 A and magnetic field 17 kG, corresponding to an efficiency of 39.2 %.

Time-dependent multi-mode nonlinear theory of dual-frequency operation coaxial gyrotron with two electron beams

The nonlinear coupling between modes and electron beams of the coaxial gyrotron with two electron beams (CGTB) has been investigated by means of the self-consistent time-dependent multi-mode nonlinear theory. The effects of the currents of two electron beams on the output power of two operating modes are discussed. It has been found that CGTB can operate at two different frequencies simultaneously with the given parameters and the peaks of the output power of two operating modes appear alternately with a certain period in dual-frequency operation. Compared with the coaxial gyrotron with one beam (CGOB) with the same parameters, the corresponding average output power of two operating modes in CGTB is enhanced due to the nonlinear coupling between operating modes and electron beams.