Charles F. F. Karney

Long-time correlations in the stochastic regime

The phase space for Hamiltonians of two degrees of freedom is usually divided into stochastic and integrable components. Even when well into the stochastic regime, integrable orbits may surround small stable regions or islands. The effect of these islands on the correlation function for the stochastic trajectories is examined. Depending on the value of the parameter describing the rotation number for the elliptic fixed point at the center of the island, the long-time correlation function may decay as t/sup -5/ or exponentially, but more commonly it decays much more slowly (roughly as t/sup -1/). As a consequence these small islands may have a profound effect on the properties such as the diffusion coefficient, of the stochastic orbits.

Numerical studies of current generation by radio‐frequency traveling waves

By injecting radio‐frequency traveling waves into a tokamak, continuous toroidal electron currents may be generated. This process is studied by numerically solving the two‐dimensional Fokker–Planck equation with an added quasi‐linear term. The results are compared with the one‐dimensional analytic treatment of Fisch, which predicted a reduced plasma resistivity when high‐phase‐velocity waves are employed. It is shown that two‐dimensional velocity space effects, while retaining the predicted scaling, further reduce the ratio of power dissipated to current generated by about 40%. These effects enhance the attractiveness of steady‐state tokamak reactors utilizing this method of current generation.

Fokker-Planck and quasilinear codes

Abstract The interaction of radio-frequency waves with a plasma is described by a Fokker-Planck equation with an added quasilinear term. Methods for solving this equation on a computer are discussed.

Efficiency of current drive by fast waves

The Rosenbluth form for the collision operator for a weakly relativistic plasma is derived. The formalism adopted by Antonsen and Chu can then be used to calculate the efficiency of current drive by fast waves in a relativistic plasma. Accurate numerical results and analytic asymptotic limits for the efficiencies are given.

Current in wave-driven 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.

Conductivity of a relativistic plasma

The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. In this formulation the collision operator is expressed in terms of five scalar potentials that are given by one‐dimensional integrals over the distribution function. This formulation is used to calculate the electrical conductivity of a uniform electron–ion plasma with infinitely massive ions.

Effect of noise on the standard mapping

Abstract The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term proportional to the reciprocal of the variance of the noise term. At large values of the stochasticity parameter, the accelerator modes exhibit a universal behavior. As a result the dependence of the diffusion coefficient on the stochasticity parameter also shows some universal behavior.

Nonlinear evolution of lower hybrid waves

The two‐dimensional steady‐state distribution of lower hybrid waves is governed by the complex modified Korteweg–deVries equation, vτ+vξξξ+(‖v‖2v)ξ=0, where v is proportional to the electric field and ξ and τ are two spatial coordinates. The equation is studied numerically. Two types of solitary waves can arise; one is a constant phase pulse, whereas the other is an envelope solitary wave. These solitary waves are not solitons. The occurrence of the constant phase pulses points to the possibility of internal reflections due to scattering off ponderomotive density fluctuations. This necessitates solving the equation as a boundary value problem. With typical fields for lower hybrid heating of a tokamak, it is found that large reflections can occur close to the edge of the plasma.

Differential form of the collision integral for a relativistic plasma

A differential formulation for the Beliaev and Budker relativistic collision integral is presented. This permits the rapid numerical evaluation of the collision integral. The decomposition into spherical harmonics allows the collision operator to be expressed in terms of one-dimensional integrals for simple background distributions. This is useful in carrying out analytical work. It also provides a convenient method for calculating the boundary conditions for the potentials. 6 refs.

Coupling of Parallelized DEGAS 2 and UEDGE Codes

Benchmarks of DEGAS 2 against EIRENE yield agreement to within 5% and comparable single processor run times. DEGAS 2 demonstrates a nearly linear increase in processing speed with the number of parallel processors. That speed is put to practical use here in the first runs of UEDGE coupled to DEGAS 2. The results of the coupled codes match those of coupled UEDGE and EIRENE. Additional algorithmic improvements such as use of the correlated sampling technique promise to make runs of the coupled UEDGE - DEGAS 2 codes practical for everyday use.