Cold Cavity Approximation Research Articles

Automodulation instability in gyrotrons operating at the second cyclotron harmonic

Interest in gyrotron operation at cyclotron harmonics is motivated by the users' desire to reduce the magnetic fields required for operation at a given frequency. However, operation at harmonics is more complicated than at the fundamental resonance because in harmonic gyrotrons there are many parasitic modes at the fundamental, which can be prone to excitation. The present study is devoted to the analysis of automodulation instability in harmonic gyrotrons. Such instability may occur, for example, when in the vicinity of the desired second harmonic mode there is a pair of parasitic modes at the fundamental, for the frequencies and azimuthal indices of which some specific conditions are met. In this paper, the equations describing this instability are derived in the cold-cavity approximation. The study is then focused on a second harmonic gyrotron with the parameters optimal for efficient operation. For such a gyrotron, the region of instability is determined in the plane of frequency mismatches between the operating and parasitic modes. This treatment performed within the framework of the general theory is complemented by consideration of some gyrotrons operating in specific modes, which are surrounded by specific sideband modes at the fundamental.

Detailed Investigations on a Multisection Cavity for a Continuously Frequency-Tunable Gyrotron

The effects of the slightly up-tapered sections in a multisection gyrotron cavity on the resonant frequency and the quality factor are investigated in detail. The main role of these sections is to change the effective cavity length or the total reflection. The slightly up-tapered section near the input section plays a role of increasing the effective cavity length and the diffractive quality factor, and the increase for a higher order axial mode is more obvious. The slightly up-tapered main section plays a role of reducing the diffractive quality factor, and the decrease for a lower order axial mode is more notable. The role of the slightly up-tapered section near the output end is complicated; when the angle is small, the main role of this section is to increase the effective cavity length; however, with the increase of the angle, the main role is to reduce the reflection from the open end. In a conventional three-section gyrotron cavity, the quality factor of the low-order axial mode is dozens of times of that of the high-order axial mode, and in an optimized multisection gyrotron cavity, the quality factor for all axial modes can maintain an order of magnitude in the cold cavity approximation; it means that the operating current for all axial modes can keep an order of magnitude.

To the theory of gyrotrons with confocal resonators

In recent years, in addition to the development of traditional gyrotrons with an axially symmetric interaction space, there has been strong interest in developing gyrotrons, whose interaction space is not axially symmetric (e.g., gyrotrons with confocal resonators). The theory of such gyrotrons is presented in this paper. First, equations describing such gyrotrons in the cold-cavity approximation are formulated. Then, the linear theory is developed, which is followed by a simple, single-mode, nonlinear theory. After that, the theory describing the mode interaction in such gyrotrons is presented. Then, an alternative concept of gyrotrons with single and multicavity confocal resonators and sheet electron beams is proposed. This paper also includes the analysis of diffractive losses in confocal resonators and the estimates for curling of the ends of sheet beams of gyrating electrons caused by the space charge forces.

Saturation Effects in Frequency Pulling of Gyrotrons Operating in High-Order Axial Modes

Spectroscopic applications have stimulated strong interest in frequency tunable gyrotrons. One of the possibilities to tune gyrotron frequency is known as frequency pulling, which is based on the effect of the electron beam on the oscillation frequency. Recently, the linear theory of this effect was developed, and the results were obtained for a sequence of modes with different axial indices. This paper is intended to analyze saturation effects in such gyrotrons. The nonlinear theory describing the frequency pulling and the efficiency in gyrotrons is developed in the cold-cavity approximation. The results are obtained for the modes with different axial indices (from 1 to 4). The frequency shift and the efficiency are calculated in a wide range of the dimensionless parameters characterizing the beam current and the external magnetic field. These results related to the frequency pulling are compared with those of the linear theory. Also, comparison is made with the results of the self-consistent theory and experiments.

Competition between modes with different axial structures in gyrotrons

This study was motivated by some experiments in which it was found that during the voltage rise, instead of expected excitation of a high-frequency parasitic mode, the excitation of a lower-frequency parasitic mode takes place in a certain range of voltages. For explaining this fact, the dependence of start currents of possible competing modes on the beam voltage was carried out in the cold-cavity approximation and by using the self-consistent approach. It was found that in the case of cavities, which consist of the combination of a section of constant radius waveguide and a slightly uptapered waveguide, these two approaches yield completely different results. Thus, experimentally observed excitation of the low-frequency parasitic mode can be explained by the self-consistent modification of the axial profile of the excited field, which has strong influence on the diffractive quality factor of competing modes. This modification is especially pronounced in the case of excitation of modes with many axial variations which can be excited in the region of beam interaction with the backward-wave component of such modes.

Low-voltage gyrotrons

For a long time, the gyrotrons were primarily developed for electron cyclotron heating and current drive of plasmas in controlled fusion reactors where a multi-megawatt, quasi-continuous millimeter-wave power is required. In addition to this important application, there are other applications (and their number increases with time) which do not require a very high power level, but such issues as the ability to operate at low voltages and have compact devices are very important. For example, gyrotrons are of interest for a dynamic nuclear polarization, which improves the sensitivity of the nuclear magnetic resonance spectroscopy. In this paper, some issues important for operation of gyrotrons driven by low-voltage electron beams are analyzed. An emphasis is made on the efficiency of low-voltage gyrotron operation at the fundamental and higher cyclotron harmonics. These efficiencies calculated with the account for ohmic losses were, first, determined in the framework of the generalized gyrotron theory based on the cold-cavity approximation. Then, more accurate, self-consistent calculations for the fundamental and second harmonic low-voltage sub-THz gyrotron designs were carried out. Results of these calculations are presented and discussed. It is shown that operation of the fundamental and second harmonic gyrotrons with noticeable efficiencies is possible even at voltages as low as 5–10 kV. Even the third harmonic gyrotrons can operate at voltages about 15 kV, albeit with rather low efficiency (1%–2% in the submillimeter wavelength region).

Analysis of Aftercavity Interaction in European ITER Gyrotrons and in the Compact Sub-THz Gyrotron FU CW-CI

Possibilities of arising of aftercavity interaction are analyzed in the ITER 170 GHz 2 MW coaxial cavity gyrotron and the 170 GHz 1 MW cylindrical cavity gyrotron, as well as in the compact 394.5 GHz low power gyrotron FU CW-CI. Also, the simulations for the gyrotron efficiency in the presence of aftercavity interaction are performed in the cold cavity approximation. Results of the analysis illustrate the subtle interplay between the geometry of the output taper and the profile of the magnetic field.

Self-Excitation of a Tapered Gyrotron Oscillator

This paper consists of two parts. In the first part, the linear theory of a tapered gyrotron oscillator, which can operate either as a gyro-backward-wave oscillator or a gyromonotron, is developed. The formulation is done for the case of excitation near cutoff frequency. The self-excitation conditions are found in a cold-cavity approximation when the axial structure that is independent of the electron beam can be described by either the Airy function or the sinusoidal distribution in tapered and constant-radius waveguides, respectively. In the second part, results of this general treatment are used for estimating the start currents and operating parameters of a terahertz-range gyrotron oscillator. For making these estimates, an axial profile of an interaction circuit is specified, and for a chosen profile, the axial structures and quality factors of modes with different numbers of axial variations are calculated with the use of available codes. This information allows us to estimate the start current by using results of the general theory obtained in the cold-cavity approximation in the first part of the paper. Then, the start currents are determined with the use of a self-consistent set of equations. The results obtained also allow estimating the tolerances in circuit fabrication.

Multifrequency operation of a gyrotron

One specific example with the parameters close to the existing coaxial cavity gyrotron at the Forschungszentrum Karlsruhe (FZK) is analyzed in detail. Mode competition calculations are performed using the time dependent and self-consistent codes developed both at the FZK and the Institute of Applied Physics (IAP). The results are compared with the calculations performed earlier by one of the authors in the cold cavity approximation. Significant qualitative differences are found and the conclusion is drawn that it is absolutely necessary to use the self-consistent approach in analyzing advanced operation regimes of a gyrotron.

Analysis of electron trajectories in a gyrotron resonator

A detailed mathematical analysis of the equation describing the electron interaction with the high-frequency field in a gyrotron resonator is presented. Electron trajectories in the phase space are classified. It is proven that in the cold-cavity approximation when the high-frequency field is represented by a Gaussian-type function, the solutions of the gyrotron equation are asymptotically equal to the solutions of the corresponding unforced equation. This means that chaos, which, in principle, can develop in a resonator for some values of control parameters, can be only transient, i.e., electrons again follow regular trajectories once they leave the interaction space. Understanding of the distribution of electron trajectories is important, both from the theoretical and the practical point of view. As an example, detailed numerical computations of electron trajectories are performed for those values of control parameters which correspond to the maximum efficiency.

Cold-cavity and self-consistent approaches in the theory of mode competition in gyrotrons

On the basis of a generalized theory, the cold-cavity and the self-consistent methods of calculation of mode competition in gyrotrons are compared. This comparison enables the conditions when the cold cavity approximation is justified to be determined. Specific examples are presented and numerical problems are discussed. It is concluded that mode competition can be studied by neglecting the interaction of the electrons and the RF field in the output taper in those cases when the parameter of irregularity of the output taper is >15. Here, the results obtained in the cold-cavity approximation overestimate the starting current of the parasitic mode by approximately 25% in comparison with the self-consistent approach. For values of the parameter of irregularity >

On a self-consistent calculation of the self-modulation instability in gyrotrons operating in whispering gallery modes

A self—consistent calculation of the self—modulation instability in gyrotrons operating in whispering gallery modes is carried out in the cold cavity approximation for satellite modes. The approach is illustrated numerically in the case of the planned operation of the KfK gyrotron in the TE10,4 mode.

Possible operation of the KfK gyrotron at harmonics

Expected efficiencies for the possible operation of the KfK gyrotron at the first, second and third harmonics are estimated. The results obtained in the cold cavity approximation and in self-consistent calculations are compared. Mode competition between the modes operating at the fundamental and at the second harmonic is investigated. Regions of stable single-mode generation are established. Effect of the the magnetic field tapering on the mode competition is illustrated.