D. A. Hitchcock

Quasi-linear diffusion and radial transport in tokamaks

An important difference between the classical collision operator, C(f), and Kaufman’s quasi‐linear diffusion operator in action space, D(f), is that only the former conserves particles, momentum, and energy at each spatial point. The nonlocal character of action‐space diffusion allows all transport fluxes to be expressed directly in terms of appropriate moments of D. Thus, a general description of quasi‐linear diffusion and convection across flux surfaces in any collisionless, axisymmetric toroidal system is obtained, in terms of scale factors relating the invariant surfaces to the flux surfaces. Several analogues to the neoclassical problem are apparent, including the collisionless version of the Ware–Galeev pinch effect, whose derivation in action space is especially straightforward. Toroidicity modifies not only particle orbits but also the spatial structure of the fluctuations, and both modifications affect the resulting transport in an important way. The use of appropriate action‐angle variables auto...

Uniqueness and inversion of the ballooning representation

Scale‐separation arguments underlying the balloning representation are employed to demonstrate that its coefficients are uniquely determined by the original function, contrary to certain suggestions in the literature. An explicit formula for inverting the series is displayed.

Unified kinetic theory in toroidal systems

A kinetic theory for toroidal systems which includes the effects of collisions as well as instabilities is constructed. This yields a pair of evolution equations; one for the spectrum and one for the distribution function. In addition, this theory yields a toroidal generalization of the usual collision operator which is shown to have many similar properties, conservation laws, and H theorem, to the usual collision operator.

Quasilinear momentum and energy transport

The equations of quasilinear momentum and energy transport are studied to show that a suprathermal level of low‐frequency fluctuations can cause highly enhanced electron energy transport without effectively changing the plasma resistivity.

Parametric dependence of the ion cyclotron instability in a two‐energy‐component system

The excitation of the ion cyclotron wave and the harmonic ion cyclotron waves by injection of a neutral beam is studied as a function of beam injection energy and angle. The fundamental mode is found to be stable for parameters similar to the current and future neutrally injected tokamaks. The harmonic cyclotron waves are found to have growth rates of a few percent of the ion cyclotron frequency when the thermal ion temperature is below a critical level. The results of these calculations are compared to several current experiments.

Runaway electron instability in the high‐density (ωpe/Ωe>0.5), low‐electric‐field (E/ED<0.05) regime

The characteristics of the runaway instability are studied for the high‐density (ωpe/Ωe>0.5) and low‐electric‐field (E/ED<0.05) cases. For this experimentally relevant case, the wave oscillation frequency as well as the growth rate are calculated for a variety of plasma parameters.

Enhanced current penetration in tokamaks

The rate at which current penetrates to the interior of a plasma during the current rise phase of a discharge is found to be greatly enhanced by anomalous viscosity due to electromagnetic turbulence.

Neutral beam driven convective loss cone instability in toroidal geometry

When a neutral beam is injected into a tokamak obliquely to the magnetic field, a region where ∂Fb/∂v2⊥≳0 may develop which can drive the convective loss cone instability. From a slab model with magnetic shear, low thresholds (nb/ne∼10−3) and substantial growth rates are found for parameters of interest for present and future tokamaks.

Destabilization of the electron Bernstein modes by runaway electrons

It is shown that the electromagnetic finite k∥ electron Bernstein mode can be destabilized by the runaway electron distribution which results from the quasilinear action of the magnetized plasma oscillation. This mechanism is shown to yield growth rates of the order of 108 sec−1 and is suggested as a mechanism for the enchanced cyclotron harmonic emission in the presence of runaway electrons.

RF INSTABILITIES DRIVEN BY NEUTRAL BEAM INJECTION

The parametric dependence of the beam driven RF instabilities is reviewed with particular emphasis given to the low harmonic cyclotron waves. Anomalous slowing of the fast ion distribution is investigated along with an analysis of the spatial structure of the modes in toroidal systems.