Plasma Physics

## A New Look at the Landau's Theory of Spreading and Damping of Waves in Collisionless Plasmas

The theory of plasma waves and Landau damping in Maxwellian plasmas, Landau's rule of pass around poles'' include doubtful statements, particularly related to an artificial constructing'' of the dispersion equation, what should allow the possibility of its solution otherwise not existing at all, and the possibility of analytical continuations of corresponding very specific ruptured functions in the one-dimensional Laplace transformation, used by Landau, what is the base of his theory. We represent, as an accessible variant, a more general alternative theory based on a two-dimensional Laplace transformation, leading to an asymptotical in time and space solution as a complicated superposition of coupled damping and {\em non-damping \/} plane waves and oscillations with different dispersion laws for every constituent mode. This theory naturally and very simply explains paradoxes of the phenomenon of plasma echo. We propose for discussion a new ideology of plasma waves (both electron and ion-acoustic waves) qualitatively different from the traditional theory of Landau damping for non-collisional as well as for low-collisional plasmas.

Plasma Physics

## A Review of Recent Developments in Atomic Processes for Divertors and Edge Plasmas

The most promising concepts for power and particle control in tokamaks and other fusion experiments rely upon atomic processes to transfer the power and momentum from the edge plasma to the plasma chamber walls. This places a new emphasis on processes at low temperatures (1-200 eV) and high densities (10^20-10^22 m^-3). The most important atomic processes are impurity and hydrogen radiation, ionization, excitation, recombination, charge exchange, radiation transport, molecular collisions, and elastic scattering of atoms, molecules and ions. Important new developments have occurred in each of these areas. The best available data for these processes and an assessment of their role in plasma wall interactions are summarized, and the major areas where improved data are needed are reviewed.

Plasma Physics

## Analytic Criteria for Power Exhaust in Divertors due to Impurity Radiation

Present divertor concepts for next step experiments such ITER and TPX rely upon impurity and hydrogen radiation to transfer the energy from the edge plasma to the main chamber and divertor chamber walls. The efficiency of these processes depends strongly on the heat flux, the impurity species, and the connection length. Using a database for impurity radiation rates constructed from the ADPAK code package, we have developed criteria for the required impurity fraction, impurity species, connection length and electron temperature and density at the mid-plane. Consistent with previous work, we find that the impurity radiation from coronal equilibrium rates is, in general, not adequate to exhaust the highest expected heating powers in present and future experiments. As suggested by others, we examine the effects of enhancing the radiation rates with charge exchange recombination and impurity recycling, and develop criteria for the minimum neutral fraction and impurity recycling rate that is required to exhaust a specified power. We also use this criteria to find the optimum impurity for divertor power exhaust.

Plasma Physics

## Calculations of Energy Losses due to Atomic Processes in Tokamaks with Applications to the ITER Divertor

Reduction of the peak heat loads on the plasma facing components is essential for the success of the next generation of high fusion power tokamaks such as the International Thermonuclear Experimental Reactor (ITER) 1 . Many present concepts for accomplishing this involve the use of atomic processes to transfer the heat from the plasma to the main chamber and divertor chamber walls and much of the experimental and theoretical physics research in the fusion program is directed toward this issue. The results of these experiments and calculations are the result of a complex interplay of many processes. In order to identify the key features of these experiments and calculations and the relative role of the primary atomic processes, simple quasi-analytic models and the latest atomic physics rate coefficients and cross sections have been used to assess the relative roles of central radiation losses through bremsstrahlung, impurity radiation losses from the plasma edge, charge exchange and hydrogen radiation losses from the scrape-off layer and divertor plasma and impurity radiation losses from the divertor plasma. This anaysis indicates that bremsstrahlung from the plasma center and impurity radiation from the plasma edge and divertor plasma can each play a significant role in reducing the power to the divertor plates, and identifies many of the factors which determine the relative role of each process. For instance, for radiation losses in the divertor to be large enough to radiate the power in the divertor for high power experiments, a neutral fraction of 10-3 to 10-2 and an impurity recycling rate of netrecycle of ~ 10^16 s m^-3 will be required in the divertor.

Plasma Physics

## 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 which 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.

Plasma Physics

An effective radiative divertor maximizes the utilization of atomic processes to spread out the energy deposition to the divertor chamber walls and to reduce the peak heat flux. Because the mixture of neutral atoms and ions in the divertor can be optically thick to a portion of radiated power, it is necessary to accurately model the magnitude and distribution of line radiation in this complex region. To assess their importance we calculate the effects of radiation transport using CRETIN, a multi-dimensional, non-local thermodynamic equilibrium simulation code that includes the atomic kinetics and radiative transport processes necessary to model the complex environment of a radiative divertor. We also include neutral transport to model radiation from recycling neutral atoms. This paper presents a case study of a high-recycling radiative divertor with a typical large neutral pressure at the divertor plate to estimate the impact of H line radiation on the overall power balance in the divertor region with consideration for line opacities and atomic kinetics.

Plasma Physics

## Electrostatic Ion Perturbations in Unmagnetized Plasma Shear Flow

The electrostatic perturbations in an unmagnetized, non-isothermal ( T i ≪ T e ) electron-ion plasma shear flow are considered. New physical effects, arising due to the non-normality of linear dynamics, are described. It is shown that the velocity shear induces the extraction of the mean flow energy by the acoustic perturbations (ion-sound waves). The influence of the medium dispersion, rising due to the violation of quasineutrality for perturbations, is examined. It is shown that in the course of the evolution ion-sound waves turn into ion plasma oscillations. New class of nonperiodic, electrostatic perturbations (with vortical motion of ion component), characterized by the intense energy exchange with the mean flow, is also described.

Plasma Physics

## Excitation of Large-ktheta Ion-Berstein Waves in Tokamaks

The mode-converted ion-Bernstein wave excited in tokamaks is shown to exhibit certain very interesting behavior, including the attainment of very small poloidal phase velocities, the reversal of poloidal direction, and up-down asymmetries in propagation and damping. Because of these effects, this wave holds promise for channeling { α -particle}\ power to ions, something that would make a tokamak fusion reactor far more attractive than presently envisioned.

Plasma Physics

## Experimental Divertor Similarity Database Parameters

A set of experimentally-determined dimensionless parameters is proposed for characterizing the regime of divertor operation. The objective is to be able to compare as unambiguously as possible the operation of different divertors and to understand what physical similarities and differences they represent. Examples from Alcator C-Mod are given.