Cavity Gyrotron Research Articles

Ion Compensation for Space Charge in the Helical Electron Beams of Gyrotrons

We solve analytically the problem about ion compensation for the space charge of a helical electron beam in a gyrotron operated in the long-pulse regime. Elementary processes, which take place during ionization of residual gas in the tube under typical pressures of 10−6–10−7 mm Hg, are considered. It is shown that distribution of the space charge is affected mainly by the electrons of the initial beam and slow-moving ions produced by ionization of the residual gas. Steady-state density of ions in the operating space of the gyrotron after the end of the transitional processes is found, as well as the electron density profile in the channel of electron beam transportation. The results obtained allow us to evaluate the pitch-factor variations caused by partial compensations for the potential “sagging” in the gyrotron cavity, thus being useful for analysis of starting currents, efficiency, and mode competition in high-power gyrotrons.

Selectivity Properties of Coaxial Gyrotron Cavities With Mode Converting Corrugations

Longitudinally corrugated inserts have been proposed as an additional mean to enhance the selectivity properties of coaxial gyrotron cavities. However, when increasing the frequency and the output power, the corrugated insert may not be sufficient to ensure mode stability. Vane loaded cavities with corrugated inserts seem to have the potential for superior mode selectivity and could be employed to facilitate the development of multimegawatt gyrotrons. In this paper, a numerical code based on the spatial harmonics method is used to study the spectrum rearrangement of a typical coaxial cavity with corrugated insert in which additional wedge-shaped corrugations are introduced on the outer wall. A general design procedure for the upgrade of the mode selectivity is presented. Its merits are demonstrated for a 140-GHz gyrotron cavity.

The nonlinear simulation, design and experiments on 0.42 THz gyrotron with gradually tapered complex cavity

Gyrotron oscillators are one of promising sources to generate high power terahertz radiation. To achieve high power at high frequency, gyrotrons have to operate at high order modes to alleviate the problem of wall heating and the miniaturization of interaction structures at these frequencies. Due to high order modes, the mode spectrum is very dense and the electron beam is likely to interact with several modes. Mode competition is a major hurdle in achieving stable and efficient operation of a gyrotron at cyclotron harmonics. The gradually tapered complex cavity could suppress mode competition by locking a pair of operating modes in two single cavities. Starting from the general transmission line equations with an electron beam, self-consistent nonlinear simulations on the second harmonic complex cavity gyrotron operating at 0.42 THz are presented. The influences of the electron beam parameters on the interaction efficiency are analyzed. The experimental results show that the designed complex cavity gyrotron is operationally stable at TE17.4 with pulse output power of 22.25 kW when the beam current is 4.8 A, beam voltage is 45 kV, and applied magnetic field is 8.185 T. The corresponding frequency and interaction efficiency are 421.60 GHz and 10.27%, respectively.

Investigations and advanced concepts on gyrotron interaction modeling and simulations

In gyrotron theory, the interaction between the electron beam and the high frequency electromagnetic field is commonly modeled using the slow variables approach. The slow variables are quantities that vary slowly in time in comparison to the electron cyclotron frequency. They represent the electron momentum and the high frequency field of the resonant TE modes in the gyrotron cavity. For their definition, some reference frequencies need to be introduced. These include the so-called averaging frequency, used to define the slow variable corresponding to the electron momentum, and the carrier frequencies, used to define the slow variables corresponding to the field envelopes of the modes. From the mathematical point of view, the choice of the reference frequencies is, to some extent, arbitrary. However, from the numerical point of view, there are arguments that point toward specific choices, in the sense that these choices are advantageous in terms of simulation speed and accuracy. In this paper, the typical monochromatic gyrotron operation is considered, and the numerical integration of the interaction equations is performed by the trajectory approach, since it is the fastest, and therefore it is the one that is most commonly used. The influence of the choice of the reference frequencies on the interaction simulations is studied using theoretical arguments, as well as numerical simulations. From these investigations, appropriate choices for the values of the reference frequencies are identified. In addition, novel, advanced concepts for the definitions of these frequencies are addressed, and their benefits are demonstrated numerically.

Theoretical study on mode competition between fundamental and second harmonic modes in a 0.42 THz gyrotron with gradually tapered complex cavity

In this paper, the nonlinear dynamics of mode competition in the complex cavity gyrotron are studied by using multi-frequency, time-dependent theory with the cold-cavity longitudinal profile approximation. Based on the theory, a code is written to simulate the mode competition in the gradually tapered complex cavity gyrotron operating at second harmonic oscillation. The simulations tracking seven competition modes show that single mode oscillation of the desired mode TE17.4 at 150 kW level can be expected with proper choice of operating parameters. Through studying on mode competition, it is proved that the complex cavity has a good capability for suppressing the mode competition. Meanwhile, it is found that TE17.3 could be excited in the first cavity as a competition mode when the gyrotron operating at large beam current, which leads to that TE17.3 and TE17.4 with different frequencies can coexist stably in the complex cavity gyrotron with very close amplitudes. Thus, the complex cavity might be used for multi-frequency output gyrotron.

Ohmic Losses During Scattering of a Plane Electromagnetic Wave by a Metal Corrugated Surface

We estimate the ohmic losses in the case of scattering of a plane electromagnetic wave by a metal corrugated surface. Comparative analysis of the losses is performed for different regimes of wave incidence and scattering (self-collimation and different incidence angles), and their dependence on the amplitude and shape of the corrugation profile is studied. The study is based on numerical solving of the integral equation which describes the diffraction of a plane electromagnetic wave by a corrugated interface between two dielectrics. Metal is regarded as a dielectric with purely imaginary dielectric permittivity of a great value which is determined by metal conductivity. The waves with E polarization (i.e., the waves with the electric-field vector directed along the grooves), which are used in echelette gyrotron cavities, are studied in detail.

Effects of electron beam parameters and velocity spread on radio frequency output of a photonic band gap cavity gyrotron oscillator

In this paper, the effects of electron beam parameters and velocity spread on the RF behavior of a metallic photonic band gap (PBG) cavity gyrotron operating at 35 GHz with TE041–like mode have been theoretically demonstrated. PBG cavity is used here to achieve a single mode operation of the overmoded cavity. The nonlinear time-dependent multimode analysis has been used to observe the beam-wave interaction behavior of the PBG cavity gyrotron, and a commercially available PIC code “CST Particle Studio” has been reconfigured to obtain 3D simulation results in order to validate the analytical values. The output power for this typical PBG gyrotron has been obtained ∼108 kW with ∼15.5% efficiency in a well confined TE041–like mode, while all other competing modes have significantly low values of power output. The output power and efficiency of a gyrotron depend highly on the electron beam parameters and velocity spread. The influence of several electron beam parameters, e.g., beam voltage, beam current, beam velocity pitch factor, and DC magnetic field, on the PBG gyrotron operations has been investigated. This study would be helpful in optimising the electron beam parameters and estimating accurate RF output power of the high frequency PBG cavity based gyrotron oscillators.

A Long Cavity With Reduced Diffraction <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> for Subterahertz and Terahertz Gyrotrons

A promising modification of the gyrotron cavity with a little bit wider and fairly long insertion (drift section) into the regular cylindrical part has been studied, both analytically and numerically, by means of both solution of the well-known nonuniform string equation and direct solution of Maxwell equations based on the CST Microwave Studio code. It has been shown that relatively low ohmic losses and an axial field structure that is favorable for the achievement of a high gyrotron efficiency can, in principle, be provided in such a sectioned cavity in the cases of transparent and strongly reflecting drift sections. The decrease in ohmic losses is stronger for the second case because of the smaller amplitude of the wave with a high group velocity in the drift section, but the separation between the operating mode and the closest spurious axial mode is larger for the first case.

An Improved Broadband Boundary Condition for the RF Field in Gyrotron Interaction Modeling

Gyrotrons are the only RF sources providing significantly high output powers at continuous-wave operation in the sub-terahertz frequency range. A prerequisite for a proper study of gyrotron behavior is the accurate time-dependent self-consistent simulation of the interaction between the electron beam and the RF wave inside the interaction region (cavity). That requires an accurate description of the RF fields at the boundaries of the interaction region. In this work, an improved broadband boundary condition is proposed. Based on polynomial series expansion of the load impedance and of the wavenumber, this boundary condition not only features a significantly improved broadband matching, but also allows a customizable frequency-dependent reflection coefficient at the boundaries. The boundary condition has a general formulation, i.e., it does not rely on a special numerical method. For the case of perfect matching, the new formulation is validated through comparing the numerically calculated reflection coefficients with those obtained by the state-of-the-art matched gyrotron broadband boundary condition, whereas the validation in the case of a given frequency-dependent reflection is done by comparing the numerically calculated reflection with the prescribed one. Although this concept is initially intended for the simulation of gyrotron cavities, it can be easily extended to any other open-cavity resonators, for which proper definition of the boundary conditions is required.

A comparative study on the modeling of dynamic after-cavity interaction in gyrotrons

There are cases where gyrotron interaction simulations predict dynamic After-Cavity Interaction (ACI). In dynamic ACI, a mode is excited by the electron beam at a dominant frequency in the gyrotron cavity and, at the same time, this mode is also interacting with the beam at a different frequency in the non-linear uptaper after the cavity. In favor of dynamic ACI being a real physical effect, there are some experimental findings that could be attributed to it, as well as some physical rationale indicating the possibility of a mode being resonant with the beam at different frequencies in different regions. However, the interaction codes used in dynamic ACI prediction up to now are based on simplifications that put questions on their capability of correctly simulating this effect. In this work, the shortcomings of the usual simplifications with respect to dynamic ACI modeling, namely, the trajectory approach and the single-frequency boundary condition, are identified. Extensive simulations of dynamic ACI cases are presented, using several “in-house” as well as commercial codes. We report on the comparison and the assessment of different modeling approaches and their results and we discuss whether, in some cases, dynamic ACI can be a numerical artifact or not. Although the possibility of existence of dynamic ACI in gyrotrons is not disputed, it is concluded that the widely used trajectory approach for gyrotron interaction modeling is questionable for simulating dynamic ACI and can lead to misleading results.

A Numerical Study on Finite-Bandwidth Resonances of High-Order Axial Modes (HOAM) in a Gyrotron Cavity

Finite-bandwidth resonances of high-order axial modes (HOAM) in an open gyrotron cavity are studied numerically using the GYROSIM problem-oriented software package for modelling, simulation and computer-aided design (CAD) of gyrotron tubes.

On the theory of longitudinally inhomogeneous waveguides with impedance walls

The Maxwell equations for longitudinally inhomogeneous (irregular) waveguides with impedance walls are reduced equivalently to a system of ordinary differential equations by applying transverse expansions. The obtained system of equations for amplitudes of the coupled modes is used to analyze gyrotron cavities. Specifically, the effect of mode conversion and ohmic losses on the eigenfrequencies, quality factors, and field distributions in the gyrotron cavities operating in the submillimeter range is investigated.

Research on a 170 GHz, 2 MW coaxial cavity gyrotron with inner-outer corrugation

In this paper, a coaxial cavity gyrotron with inner-outer corrugation is researched. The electron kineto-equations and the first order transmission line equations of the gyrotron are derived from Lorentz force equation and the transmission line theory, respectively. And then, a 2 MW, 170 GHz coaxial cavity gyrotron with inner-outer corrugation is designed. By means of numerical calculation, the beam-wave interaction of the coaxial cavity gyrotron with inner-outer corrugation is investigated. Results show that the efficient and the outpower of the gyrotron are 42.3% and 2.38 MW, respectively.

Study of Dynamic After Cavity Interaction in Gyrotrons—Part II: Influence of a Nonuniform Magnetic Field

Spurious oscillations, particularly dynamic after cavity interaction (ACI) in high-power gyrotrons gained attention as an influencing factor on the overall gyrotron performance. Numerical investigations are a main pillar for a deeper understanding of this phenomenon. The Karlsruhe Institute of Technology in-house self-consistent, time-dependent self-consistent multimode code was modified to accommodate the influence of an axial variation of the external magnetic field on the after cavity dynamics. Inclusion of the influence of the nonuniform distribution of the magnetic field in the time-dependent gyrotron beam-wave interaction differential equations is necessary to make proper numerical investigations in terms of the appearance of the dynamic ACI particularly in the output waveguide section (uptaper), where the nonuniform distribution of the magnetic field is more significant. We evaluate the importance of this for modeling of three different high-power gyrotron cavities, where partially undesired weak interactions in the up-taper/launcher region have been observed.

Study of Dynamic After Cavity Interaction in Gyrotrons—Part I: Adiabatic Approximation

In recent years, the after cavity interaction (ACI) in high-power gyrotrons operating in the 100-200 GHz range gained special attention as an influence factor on overall efficiency. While investigations concentrated on ACI as a stationary effect until now, recent simulations show that undesired interactions in the output waveguide region (uptaper) can also result in additional parasitic oscillations. In this paper, such nonstationary, dynamic processes are investigated in first simulations and results are described using the self-consistent time-dependent Karlsruhe Institute of Technology multimode code. In this paper, results are generated along with the assumption of constant B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> (z) = B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (maximum magnetic field) as well as with the implementation of the adiabatic approximation in the case of varying magnetic field for determination of the axial velocity of each particle. The simulations show weak parasitic/spurious oscillations in the uptaper of the gyrotron cavity that may be attributed to the occurrence of dynamic ACI.

Validation of 3-D Time Domain Particle-in-Cell Simulations for Cold Testing a &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$W$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-Band Gyrotron Cavity

This paper evaluates the performance and reliability of a commercially available 3-D conformal finite-difference time-domain particle-in-cell (PIC) code, VSim, for cold test simulations of a gyrotron cavity. An interaction cavity for a 95-GHz gyrotron is simulated and optimized using the VSim PIC code to achieve TE6,2 mode excitation. The optimized cavity design is also studied and compared using the commercially available numerical code, CASCADE, and PIC code, MAGIC. A rigorous analysis of the simulation results obtained through VSim and MAGIC is performed using the CASCADE results as a reference. The performance of VSim is also compared with MAGIC based on its accuracy for calculating the resonant frequency and quality factor. Finally, the optimized cavity is fabricated and experimentally tested to measure the resonant frequency and the quality factor. The experimental results confirm the reliability and accuracy of the VSim cold cavity results.

Beam-wave interaction behavior of a 35 GHz metal PBG cavity gyrotron

The RF behavior of a 35 GHz photonic band gap (PBG) cavity gyrotron operating in TE041-like mode has been presented to demonstrate its single mode operation capability. In this PBG cavity gyrotron, the conventional tapered cylindrical cavity is replaced by a metal PBG cavity as its RF interaction structure. The beam-wave interaction behavior has been explored using time dependent multimode nonlinear analysis as well as through 3D PIC simulation. Metal PBG cavity is treated here similar to that of a conventional cylindrical cavity for the desired mode confinement. The applied DC magnetic field profile has been considered uniform along the PBG cavity length both in analysis as well as in simulation. Electrons energy and phase along the interaction length of the PBG cavity facilitates bunching mechanism as well as energy transfer phenomena from the electron beam to the RF field. The RF output power for the TE041-like design mode as well as nearby competing modes have been estimated and found above to 100 kW in TE041-like mode with ∼15% efficiency. Results obtained from the analysis and the PIC simulation are found in agreement within 8% variation, and also it supports the single mode operation, as the PBG cavity does not switch into other parasitic modes in considerably large range of varying DC magnetic field, contrary to the conventional cylindrical cavity interaction structure.

Effective Cavity Length of Gyrotrons

Megawatt-class gyrotron oscillators for electron cyclotron heating and non-inductive current drive (ECH&CD) in magnetically confined thermonuclear fusion plasmas have relatively low cavity quality factors in the range of 1000 to 2000. The effective length of their cavities cannot be simply deduced from the cavity electric field profile, since this has by far not a Gaussian shape. The present paper presents a novel method to estimate the effective length of a gyrotron cavity just from the eigenvalue of the operating TEm,n mode, the cavity radius and the exact oscillation frequency which may be numerically computed or precisely measured. This effective cavity length then can be taken to calculate the Fresnel parameter in order to confirm that the cavity is not too short so that the transverse structure of any mode in the cavity is the same as that of the corresponding mode in a long circular waveguide with the same diameter.

Effect of background plasma on electromagnetic properties of coaxial gyrotron cavity

We analyze the effect of the background plasma on the electromagnetic properties of coaxial resonators with a smooth and a corrugated inner conductors used in high-power gyrotrons. It is shown that the plasma produces different effects on the modes with different signs of the azimuthal index, leading to a decrease or an increase in the resonance frequencies. A modification of the distributions of electromagnetic fields and the electromagnetic energy density by the background plasma occurs in such a way that Ohmic losses decrease both on the inner and on the outer conductors. In the case of a smooth inner conductor, this is due to a decrease in the field strengths on the surface of the conductors. If the inner conductor is corrugated, the background plasma leads to an increase in the field strengths on its surface. Nevertheless, the relative Ohmic loss power decreases due to an increase in the energy density in the resonator (which is also caused by the background plasma). Calculations were mainly performed for a coaxial resonator of a gyrotron operating on the TE34.19 mode (Karlsruhe, Germany).

Design of 170 GHz, 1.5-MW Conventional Cavity Gyrotron for Plasma Heating

In this paper, an overall conceptual design of a 170 GHz, 1.5 MW, continuous wave (CW) conventional cavity gyrotron is presented for plasma heating applications in thermonuclear fusion reactors. The operating mode is carefully selected with due consideration of design constraints/goals and mode competition. The TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">36</sub> ,10 mode is selected as operating mode for the present study. A weakly tapered conventional cavity resonator is considered for the study of the RF-behavior. Single mode and multimode time dependence self-consistence calculations are carried out for power and efficiencies. In addition, the design studies of a triode type magnetic injection gun, magnetic guidance system, output system that consists of an optimized nonlinear taper, a highly efficient dimpled-wall quasi-optical launcher and a single disk Chemical Vapor Deposition diamond window are also reported. Results obtained support an output power of 1.5-MW CW power at 170 GHz with a conventional cavity gyrotron with 35% efficiency without single stage depressed collector. This device is intended to serve as heating source for international thermonuclear experimental reactorlike machines.