No abstract
The relativistic expression for the dielectric tensor obtained by Trubnikov is simplified in the very weakly relativistic limit at and near electron cyclotron harmonics. Wavenumbers parallel to magnetic field are included, leading to relativistic damping when this wavenumber is minute and to cyclotron damping when it is sufficiently large. The transition to the nonrelativistic Z function is shown and the regions of validity of the various functions are indicated. Collisional damping is neglected. The dielectric elements given here are also applicable to cases of complex ω and real k. An example of such a situation arises in Alouette cyclotron harmonic reception when one is concerned with an initial time value problem. For this application the analytic continuation of a complicated function is provided, and the tracks where it is real for complex ω are investigated.
A new generalized pair of space-correlation and wave-number spectrum functions, which has properties indicated by fluid dynamics and by intuition, is proposed. In contrast with previously used combinations, both are analytic functions and smooth and cover the complete range of their arguments. For example, the spectrum form can apply to all wave numbers rather than to any limited portion, such as the inertial range. Whenever convolution is necessary, it becomes a routine computer calculation. Furthermore, the correlation function has a zero first derivative and a negative second derivative at the origin, giving both an integral scale and a microscale for the turbulence. The spectrum function can have an inertial region with some power-law decay for intermediate wave numbers and has an exponential decay for very large wave numbers. There are three adjustable parameters, determined by experiment, namely, the spectral power-law decay index, the turnover point where this power law starts, and the turnover point where the power dependence changes to an exponential decay. A library of such spectrum functions is not required, since the single proposed function, with its adjustable parameters, can be made to fit most data. One can also allow any even power of wave number for the spectral dependence in the limit of zero wave number. Simple anisotropic functional forms can readily be incorporated. It is indicated that two inertial falloffs with different power laws can be provided and the resultant correlation function is derivable by convolution. The results are applied to simplified versions of plasma electron density fluctuations and to velocity fluctuations of the background fluid. Various scales of turbulence and the related pressure-correlation function are derived. Expressions of correlation functions of amplitude and phase over parallel-line-of-sight propagation paths are also deduced.The proposed pair of functions should only be considered as a generalized model of Tatarski's form, which allows easy conversion from the correlation to the spectrum function and vice versa. Perhaps even more realistic forms can be invented.
A detailed investigation is presented on the ability of combined ray-tracing and Fokker–Planck calculations to predict the hard x-ray (HXR) emission during lower-hybrid (LH) current drive in tokamaks when toroidally induced ray stochasticity is important. A large number of rays is used and the electron distribution function is obtained by self-consistently iterating the appropriate power deposition and Fokker–Planck calculations. It is shown that effects due to radial diffusion of suprathermal electrons and to radiation scattering by the inner wall can be significant. The experimentally observed features of the HXR emission are fairly well predicted, thus confirming that combined ray-tracing and Fokker–Planck codes are capable of correctly modeling the physics of LH current drive in tokamaks.
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