Electromagnetic analysis of plasma-filled waveguide structures: powerful gyrotrons, microwave waveguides :: SPE RESST

Electromagnetic analysis of plasma-filled waveguide structures: powerful gyrotrons, microwave waveguides

In order to simplify and reduce the cost of electron-cyclotron heating systems in magnetically confined fusion devices (in particular, in the project of the International Thermonuclear Experimental Reactor- ITER) the individual gyrotron must produce more than 2 MW of the output power with the efficiency higher than 30% and the pulse duration longer than 30 min. The frequency of this gyrotron must be within the range between 140 and 200 GHz. At present, it is difficult to achieve such operating performances for gyrotrons with conventional cylindrical cavities due to excessive heating of the cavity walls, mode competition, influence of the beam space-charge fields, etc. These factors limit the power of conventional gyrotrons to about 1 MW.

One way to overcome these limitations is to use coaxial gyrotron cavities with longitudinally corrugated inner conductors. The presence of the inner conductor makes it possible to alleviate the influence of the beam eigenfields and also (due to the rarefication of the frequency spectrum) the problem of mode competition, which both limit the gyrotron power. Such perspective cavity structure holds much promise for use in gyrotron with increased level of output power up to 3-5 MW.

For the analysis of such cavities, we start with the eigenvalue problem for a magnetoactive plasma-filled waveguide of arbitrary transverse cross-section.

We have developed a general approach to such kind of problems in 2013. The approach is based on the field expansion into series of basis functions, which form the complete set and are the eigenfunctions of the Dirichlet and the Neumann boundary-value problems for the Laplace operator in the waveguide cross-section.

In addition to plasma-filled waveguides, our approach can find application in waveguide structures based on various metamaterials. It is well-known that the metamaterial guides may differ in the form of cross-section and the electromagnetic properties of most metamaterials can be described by the tensors of effective permittivity and permeability.

With the increase in the gyrotron power (especially in the regime of long pulses), the probability of plasma formation in the gyrotron cavity increases rapidly. At present, it is important to investigate the effect of background plasma on the electromagnetic properties of the gyrotron cavity having coaxial geometry with longitudinal periodicity.

Dispersion properties of a dense frequency spectrum near the upper hybrid frequency w1 for a plasma-filled waveguides with losses

It has been shown, for the first time, that the upper hybrid frequency satisfies the dispersion equation of plasma-filled waveguide and can be the frequency of the waveguide modes despite the fact that these modes have an infinite value for one of the transverse wavenumbers.

Fig. 1 – Dispersion curves for ЕН_±1,1 mode

It has been found that the fields of these modes can undergo a jump discontinuity near the waveguide wall (see Fig. 2) in the case of cold collisionless plasma.


а)		б)

Fig. 2 – Field distribution for ЕН_m,1 mode: a) m = 0; b) m = 1

The necessary conditions for the existence of wave coupling between hybrid waves has been obtained, along with the hyperbola equation describing the behavior of the dispersion curves for the weakly coupled waves near the interaction point (see Fig.3).

Fig. 3 – Dispersion curves of cyclotron waves

A novel efficient numerical approach to the analysis of the loss-induced effects in waveguides with spatially inhomogeneous geometry and magnetoactive plasma filling has been developed.

Waveguide structures of non-circular cross section filled with magnetoactive plasma are often used in different technical applications. Examples are the RF structures of gyrotrons, free-electron lasers, etc. However, the theory of plasma-filled waveguide with arbitrary cross-section is little explored (as well as the theory of excitation of such waveguides). The reason is that in this case the method of separation of variables, which is generally used for plasma-filled waveguide of circular cross section, is impracticable.

The rectangular waveguide with magnetoactive plasma filling has been considered for the first time. Dispersion properties of such waveguide have not been investigated before. Computations of dispersion curves and field distribution for plasma modes have been performed (see Fig. 4).

Frequencies and fields of a rectangular waveguide with magnetoactive plasma

Fig. 4 – Frequencies and fields of a rectangular waveguide with magnetoactive plasma. The fields correspond to the frequency marked by a circular symbol

Influence of low-density background plasma on electromagnetic properties and beam instabilities in coaxial gyrotron cavities with corrugated inner conductors has been analyzed.

It has been shown that the main effect of background plasma is in the reduced difference between the frequency of the operating TE mode and that of the preceding TM mode (the so-called mode hybridization).

Our investigations for the 170-GHz 2.2-MW coaxial cavity gyrotron with the TE_34,19 operating mode have shown that the gyrotron efficiency is notable reduced (see Fig. 5), even in the case of rare plasma and negligible mode hybridization. The effect is the most evident for the high values of the accelerating beam voltage.

Fig. 5 – Measured and calculated value of output power for 170 GHz, 2.2 MW coaxial cavity gyrotron versus accelerating voltage