The continuous operation of a tokamak fusion reactor requires, among other things, a means of providing continuously the toroidal current. Such operation is preferred to the conventional pulsed operation, where the plasma current is induced by a time-varying magnetic field. A variety of methods have been proposed to provide continuous current, including methods that utilize particle beams or radio-frequency waves in any of several frequency regimes. Currents as large as half a mega-amp have now been produced in the laboratory by such means, and experimentation in these techniques has now involved major tokamak facilities worldwide.

/pdf/theory-of-current-drive-in-plasmas-1ahksixqgt.pdf

Theory of current-drive in plasmas

A theory for the generation of current in a toroidal plasma by radio‐frequency waves is presented. The effect of an opposing electric field is included, allowing the case of time varying currents to be studied. The key quantities that characterize this regime are identified and numerically calculated. Circuit equations suitable for use in ray‐tracing and transport codes are given.

Current in wave-driven plasmas

The current drive by HF waves in a tokamak with longitudinal electric field is studied on the basis of the two-dimensional kinetic equation for electrons. Analytical formulas for current and current drive efficiency are obtained for a low level of absorbed power. Numerical methods are used to solve the kinetic equation at high HF power level. It is shown that the dependence of the efficiency on the effective charge of the plasma changes with increasing power absorption. The existence of trapped particles reduces current drive efficiency. An analysis of the calculation results leads to simple approximate expressions for current and efficiency, convenient for comparisons with the experiments.

Toroidal and electric field effects on current drive in tokamaks by lower hybrid and electron cyclotron waves

Computing of RF heating and current drive in Tokamaks

The problem of quasilinear diffusion of plasma electrons, resonantly interacting with waves in lower-hybrid range of frequency launched from the exterior, is examined within a self-consistent one-dimensional homogeneous model. An analytical solution is obtained, which allows the derivation of a simple formula for the plasma current in terms of the parameters characterizing the spectral distribution of the RF power source. The major outcome is a dramatic sensitivity of the plasma current to the presence of a small, high-N/sub /// component in the RF power source spectral distribution, in agreement with previous numerical calculations.

Generation of Superthermal Electrons Interacting with Waves in Lower-Hybrid Range of Frequency Revisited

The present understanding (May 1983) of current drive by lower hybrid waves in Tokamak plasmas is reviewed with particular stress on the theory. First, the classical model of Fisch and its variants are discussed in light of recent experimental data. It is argued that these simple models do not account for most of the features of the results obtained. Next, effects of runaways on current generation are considered. It is shown that runaways, resulting from a residual ohmic electric field, may play an important role. Further, the mechanism of runaway-current sustainment, as proposed by LIU et al. (1982b) is re-examined. It is shown that, for a realistic range of parameters, this mechanism does not allow a significant current to be sustained. Finally, some results of a recently-developed numerical code, which include the evolving electron distribution function, ray tracing and transport, are briefly noted. It is concluded that none of the existing theories can be used to interpret satisfactorily all the experimental observations.

https://iopscience.iop.org/article/10.1088/0032-1028/25/12/301/pdf

Runaway and wave-induced currents

The combined effects of an electric field and externally driven magnetized Langmuir waves on the tail of an electron distribution function are studied analytically. The runaway production rate is enhanced by many orders of magnitude if the source, even though weak, drives waves with parallel phase velocities around the critical velocity. A practical formula to quantify this phenomenon is derived. Depending on the source strength two different regimes may occur: one is stable and linear with the RF power, whilst the other, which saturates, may be unstable. Connections with lower-hybrid current-drive experiments are discussed.

A Theory of Electron Tail Induced by Radio-Frequency Waves

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Runaway and wave-induced currents

A Theory of Electron Tail Induced by Radio-Frequency Waves