Nonlinear Self-consistent Theory Research Articles

Investigation on Ku-Band Dual-State Gyro-TWT

This article presents the development of a dual-state Ku -band gyrotron traveling-wave tube (gyro-TWT) dual-state curved-profile magnetic injection gun (MIG) generating high-quality electron beams, in which the pitch factor is up to 1.2 and 1.35 for the pulse wave (PW) state and the continuous wave (CW) state, separately. A multiobjective genetic algorithm (MOGA) is applied in the profile optimization. Meanwhile, the parametric sensitivity is also discussed in detail. A periodic dielectric-loaded interaction circuit is adopted to suppress oscillations. Furthermore, thermal analyses of the interaction circuit under different duty cycles are also elaborated. The interaction circuit is analyzed in accordance with the proposed nonlinear self-consistent theory and particle-in-cell (PIC) codes. The results of hot experiments show that the dual-state tube obtains the output power of 150/30 kW corresponding to a saturated gain of 40/41 dB and the maximum efficiency of 25%/21% within the bandwidth of 2.0/1.1 GHz for the PW/CW state, respectively.

Development of High-Efficiency Gyro-TWT With a Nonuniform Dielectric-Loaded Circuit

This paper presents the development of highly efficient gyrotron traveling-wave tube (gyro-TWT) with a nonuniform dielectric-loaded interaction circuit. The high-quality electron beam has been generated by curved-profile magnetron injection gun (MIG). With regard to the profile optimization, simulated annealing algorithm (SAA) and genetic algorithm (GA) are applied. An electron beam with a pitch factor of 1.6 and low-axial velocity spread of 0.9182% have been obtained. The parametric sensitivity is discussed in detail. A nonuniform dielectric-loaded circuit has been employed to suppress both global oscillations and local oscillations. Different thicknesses of dielectric materials have been manufactured and measured, demonstrating the circuit loss of oscillation modes that are enough for stable operation. The interaction circuit is analyzed under the guidance of nonlinear self-consistent theory and particle-in-cell (PIC) codes. The tube achieves a saturated peak output power of 36.24 kW at 93 GHz, corresponding to a saturated gain of 54 dB and a maximum efficiency of 45.3% within a 3-dB saturated bandwidth of 5 GHz.

Design and Simulation of a Broadband <inline-formula> <tex-math notation="LaTeX">$Ka$ </tex-math> </inline-formula>-Band Gyrotron Traveling-Wave Tube With a Fully Dielectric-Loaded Circuit

This paper presents the design and simulation of a broadband Ka -band gyrotron traveling-wave tube operating in the $\text {TE}^{d}_{\text {02}}$ mode at the fundamental cyclotron harmonic with a fully dielectric-loaded circuit. Through loading loss-free dielectric on the entire circuit, the dispersion properties of the circuit are changed to maintain resonance condition at a wide frequency band. A sliced lossy dielectric-loaded structure is employed to provide the required loss for stable operation. The interaction circuit is analyzed under the field matching theory, the nonlinear self-consistent theory, and particle-in-cell codes. A saturated peak output power of 100 kW is achieved at 29 GHz, corresponding to a saturated gain of 44 dB and an efficiency of more than 15% within a 3-dB saturated bandwidth of 6.1 GHz (20% relative bandwidth).

Theory and Experiment Investigate of a 400-kW Ku-Band Gyro-TWT With Mode Selective Loss Loading Structure

A high-power Ku-band TE01 mode gyro-traveling wave tube (gyro-TWT) with a loss loading structure is designed, fabricated, and tested. A high beam quality magnetron injection gun generating 68-kV, 20–30-A electron beam is optimized to provide a high power radiation. A novel lossy ceramic loaded structure with mode selective attenuation ability is proposed to suppress the potential backward wave oscillation. The interaction circuit is analyzed by linear, nonlinear self-consistent theory, and experiment. An improved wideband input structure design is proposed accordingly. In the hot test, the proposed gyro-TWT produces a 420-kW maximum peak power, about 35-dB saturated gain, 23% efficiency, and more than 1.6 GHz (10%)−1-dB bandwidth in a stable operating condition.

Simulation and Experiment of a Ku-Band Gyro-TWT

Design techniques and experimental results are presented on a Ku-band TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> mode gyro-traveling wave tube. The hot test of this amplifier gives more than 153-kW output power, 2.3-GHz bandwidth (14%), 41-dB saturated gain, and 20% efficiency driven by a 63 kV, 12-A electron beam with a pitch angle (v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> ) of 1.2, and velocity spread of 5%. A linear polarized TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> mode input coupler is used to introduce the input power. The stability of the amplifier from oscillation, including both the operating TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> mode and the backward wave TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> mode, has been investigated with linear codes, nonlinear selfconsistent theory, and 3-D PIC CHIPIC simulation. To suppress the potential gyro-backward wave oscillator interactions, the high frequency circuit is loaded with lossy ceramic rings. The lossy structure is optimized by nonlinear theory and 3-D PIC simulation. A low velocity spread magnetron injection gun is designed with a new structure.

On the structure of the stationary charged nearelectrode layer in a degenerate plasma

A nonlinear self-consistent theory is developed of a stationary charged near-electrode layer in the plasma in which both charged components are quantum degenerate. The theory is based on a two-liquid gas-dynamics description of the plasma with the use of equations of state for the cold Fermi-gas (in the Thomas–Fermi approximation) for both components. The generalized Bohm criterion for the existence of the stationary layer is derived together with the criterion for the formation of the structure of double-layer type in this layer. The theory is illustrated by numerical examples of various structures in the layer, including structures of single and double-layer types.

Study of a gyrotron oscillator with corrugated interaction cavity

Based on the nonlinear self-consistent theory and the three-dimensional electromagnetic simulation software CST, the beam-wave interaction of gyrotron with irregular cross section is studied. Through importing high frequency fields which are the results of CST, the beam-wave interaction efficiency, coupling coefficient and starting current can be obtained. In addition, a 0.4 THz third harmonic TE33 mode gyrotron with a corrugated interaction cavity is presented according to this approach. The gyrotron with a 40.5 kV/1 A electron beam, magnetic field of 5.09 T, and pitch factor of 1.5 can produce radiation with an output power of 3.3 kW.

Study on Nonlinear Theory and Code of Beam-Wave Interaction for Gyroklystron

A nonlinear self-consistent theory of beam-wave interaction for gyroklystron with multiple cavities is analyzed in this paper. The electron motion equations and transient electromagnetic field equations in a complex form are deduced in detail. A calculation code including a time-dependent description of the electromagnetic fields and a self-consistent analysis of the electrons is designed and the corresponding software implementation is achieved using Fortran language. An example is presented for the operation of the code, namely a four-cavity, Ka-band gyroklystron operating in the TE011 mode at the fundamental of the cyclotron frequency. The numerical results show that a maximal saturated peak output power of 330 kW, corresponding to 39% efficiency and a saturated 3-dB bandwidth of 325 MHz is achieved with a 72.8 kv, 11.8 A electron beam at a focused magnetic field of 13 kG and a beam velocity ratio of 1.63 when the speed spread is 5%. By comparison, the numerical results agree with the experimental results.

Nonlinear theory of wakefield excitation in a rectangular multizone dielectric resonator

A nonlinear self-consistent theory has been constructed and used to investigate numerically the wakefield excitation in multilayered dielectric resonators by relativistic electron bunches. Analytical expressions for solenoidal and potential components of an excited electromagnetic field have been derived. The excitation of a five-zone dielectric resonator by relativistic electron bunches was numerically investigated and comparison was made between the longitudinal distribution of an axial electric field and the results obtained previously for a corresponding problem in the waveguide formulation. The necessity of optimizing geometrical parameters of the resonator to reduce mode amplitudes nonresonant with a bunch, and to obtain a symmetric distribution of the longitudinal electric field component in the drive and accelerating channels, has been demonstrated.

On the structure of the charged near-electrode sheath in a plasma with degenerate electrons

A nonlinear self-consistent theory of a stationary charged near-electrode sheath in a plasma with a quantum-degenerate electron component is developed. The theory is based on the gasdynamic two-liquid description of the plasma, such that its degenerate component satisfies the equation of state for a cold Fermi gas (in the Thomas—Fermi approximation), while the classical component satisfies the equation of state for an ideal gas (in the isothermal approximation). A generalized Bohm criterion is derived for the existence of a stationary sheath, as well as the criterion of the formation of a double-layer-type structure in the sheath. The theory is illustrated by numerical examples of various structures (of the monolayer and the double-layer type) in the sheath.

Influence of reflection of the output port on beam-wave interaction in gyrotron traveling wave amplifier

Based on the nonlinear self-consistent theory of gyrotron traveling wave amplifier (gyro-TWA)，the influence of the reflection from the tapering output port on the beam-wave interaction in the gyro-TWA is studied. The simulation results show that the amplitude and phase of the reflection coefficient resulting from the variation of the tapering angle at the output port and the beam-wave interaction length have great effect on the beam-wave interaction for a Ka band TE01 gyro-TWA. Reasonably selecting the tapering angle at the output port may increase the beam-interaction frequency bandwidth with a relatively short beam-wave interaction length while keeping the saturated output power of the gyro-TWA at almost the same level.

Influence of Reflections of the Output Port on Beam-wave Interaction in Gyrotron Traveling Wave Amplifier

Based on the nonlinear self-consistent theory of gyrotron traveling wave amplifier (gyro-TWA), the influence of the reflections of the output port with the taper on the beam-wave interaction in the gyro-TWA is studied. The simulation results show that the reflections have great effects on the TE01 mode gyro-TWA operating at the fundamental. The influence of the taper angle and the interaction length on the beam-wave interaction and the power profile is discussed and the corresponding physical mechanism is analyzed. The saturated output power keeps same approximately with the increase of the taper angle in the presence of reflection while the saturated gain decreases obviously.

Two-Stream Free Electron Lasers: Physical Analysis of the Systems with Monochromatic Pumping

Nonlinear selfconsistent theory of the Two-stream Superheterodyne Free Electron Lasers (TSFELs) is represented. The one-sectional and klystron type models of TSFEL-amplifiers are analyzed. It is shown that such systems can provide extremely high levels of amplification, and, at the same time, high levels of the input-output decoupling.

Expansion of a frequency tuning band in a gyrotron with coupled cavities

An electron frequency tuning band of a conventional high-Q cavity gyrotron approximately coincides with the unloaded cavity bandpass which usually does not exceed 0.1%. To expand the frequency tuning band we introduce a gyrotron with an RF circuit that consists of two coupled circular cavities separated by a thin iris. A nonlinear self-consistent gyrotron theory predicts a saturated efficiency of 18% and a tuning band of 1.1%. An experimental study of an X-band tube operating in the TE011 mode was carried out to test the gyrotron with the coupled cavities concept. Measurements of gyrotron performance showed a 0.96% tuning band—a tenfold increase over that of an ordinary gyrotron. Simulation results are in a good agreement with the experimental data.

Structure of a collisionless shock front with relativistically accelerated particles

A nonlinear self-consistent analytic theory is developed to describe the front structure of a strong magnetohydrodynamic (MHD) collisionless shock wave that generates accelerated particles (including ultrarelativistic particles). The theory is used to predict the degree of compression of matter at the plane front of such a wave, which can greatly exceed compression at an ordinary gas-dynamic front, and also the velocity, density, and pressure profiles. The energy spectrum of the accelerated particles, which is produced by the complex velocity profile at the shock transition, is determined self-consistently. New nonlinear effects are predicted that have not been discussed previously in the literature: a strong dependence of the particle acceleration regimes on the rate of injection; the existence of several regimes within a certain range of injected powers with differing spectra of accelerated particles, shapes of the shock transition profile, and magnitudes of compression of the medium; and the possibility of spontaneous jumps between different states of the shock transition. The question of stability of these states is discussed. For the values of the system parameters used here, the nonlinear regimes correspond to extremely low injection rates, of order 10−2–10−10 of the plasma flux density advancing into the front, and to exponents of the power-law spectra of accelerated particles between 5 and 3.

Nonlinear self-consistent theory of two-stream superheterodyne free electon lasers

A nonlinear self-consistent theory of superheterodyne two-stream FEL-amplifiers was developed. These FELs are based on application as a working effect two-stream instability jointly with parametric interaction mechanism traditional for FEL. It was found out possible to develop FEL-amplifiers with amplification levels of approximately 20–30 db (by amplitude) in am IR ranges at moderate requirements for REB (beam current of 4–5 A, accelerating voltage of ≤1 MV). Predicted are realization of the effect of generation of longitudinal electric field and its important role at the nonlinear stage of a signal amplifying process. It was shown that some other nonlinear effects can also be realized.

Nonlinear self-consistent theory for crossed-field devices.

A closed, nonlinear set of fluid equations that is based on the electron guiding-center orbits and is generally applicable to the analysis of crossed-field, slow-wave devices, is developed. The equations are used to model the behavior of the crossed-field amplifier. The dielectric response from the spoke charge is self-consistently included. A mean-field approximation is introduced to express the effect of the spoke charge on the rf mode profile. The dielectric modifications are then parametrized by an average amplitude factor \ensuremath{\Lambda}^ and an average phase shift \ensuremath{\psi}^ from the vacuum values. In the synchronous with the rf signal frame of reference the streamlines follow the equipotential surfaces of the transformed fields. In the steady state, the flow is incompressible. A uniform-density, constant-height electron hub feeds the current spokes. The secondary electron production at the cathode is computed self-consistently through the secondary-emission coefficient and the average impact energy. The spoke current is determined by the difference of the E\ifmmode\times\else\texttimes\fi{}B drift at the top of the hub from the rf phase velocity. At small space-charge density relative to the Brillouin density, the dielectric corrections enter as a rotation ${\mathit{e}}^{\mathit{i}\mathrm{\ensuremath{\psi}}\mathrm{^}}$ of the complex growth rate relative to the growth without spoke self-fields. The numerical solutions for arbitrary space charge are compared with previous results without spoke-field effects. An increase in the rf gain and in the anode dc current is observed at any given operation point, despite a small drop in the efficiency. It is concluded that the increase in the rf field strength in the anode-cathode space, caused by the spoke self-field, compensates for the detuning effects from the modifications on the rf mode profile. In reentrant devices, the recycling of the space charge further increases the output power and the level of noise generated by the output-input feedback.

Nonlinear self-consistent theory of superheterodyne and parametric free electron lasers

A new approach to a nonlinear self-consistent theory of superheterodyne and parametrical FEL has been formulated. The method of averaged kinetic equation was taken as a principle. Efficiency and capacity for work of the developed approach were illustrated by series of concrete examples.

High-power harmonic gyro-TWT's. I. Linear theory and oscillation study

A linear theory using Laplace transforms which is applicable to both gyrotron traveling wave amplifiers (gyro-TWTs) and gyrotron backward-wave oscillators (gyro-BWOs) is presented. The validity of the linear theory is verified by comparing it with an existing nonlinear self-consistent theory based on a different approach. In conjunction with a time-dependent multimode particle simulation code, the linear theory is applied to study the stability of harmonic gyro-TWTs. It is shown that a harmonic gyro-TWT can be made stable to all forms of spontaneous oscillations by employing a multistage interaction structure and that it can generate power levels far in excess of those possible for a fundamental gyro-TWT. The linear bandwidth of a second-harmonic gyro-TWT amplifier is also calculated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Linear and nonlinear theory of cyclotron autoresonance masers with multiple waveguide modes

The interaction of multiple waveguide modes with a relativistic electron beam in an overmoded, single-frequency, cyclotron autoresonance maser amplifier is analyzed using a nonlinear self-consistent model and kinetic theory. It is shown analytically, and confirmed by simulation, that all of the coupled waveguide modes grow at the spatial growth rate of the dominant unstable mode, but suffer different launching losses which depend upon detuning. The phases of coupled modes are locked in the exponential gain regime, and remain approximately locked for some finite interaction length beyond saturation. The saturated power in each mode is found to be insensitive to the input modal radio-frequency (rf) power distribution, but sensitive to detuning. Simulations indicate that the saturated fractional rf power in a given mode reaches a maximum at its resonant magnetic field, and then decreases rapidly off resonance. Good agreement is found between the simulations and the kinetic theory in the linear regime.