Polarization vector formalism of plasma weak turbulence

Peter H Yoon

doi:10.1063/5.0070559

Abstract

This paper formulates the plasma weak turbulent theory based on the unit electric field polarization vector. This concept is not intrinsically new, and partial formulations of weak turbulence processes based on the polarization vector approach are found in the literature. However, the present paper applies such a method uniformly to all the relevant processes for the first time, thus unifying the existing formalisms. The present result potentially provides many advantages including the fact that it facilitates the complex manipulations of various tensor coupling coefficients that dictate the wave–wave and nonlinear wave–particle interactions. To demonstrate its validity, the limit of unmagnetized plasmas is considered, and it is shown that the known results are recovered. The present formalism can be extended to more complex situations including magnetized plasmas, which is a subject of future work.

Highlights

The weak turbulence theory is a useful and venerable research tool in plasma physics with numerous applications in the laboratory and space environment
In writing down the above results, we have considered that the weak turbulence theory in unmagnetized plasmas pertains to Langmuir wave turbulence
Note that the present formalism leads to what is known as the “Vlasov” weak turbulence theory in that the effects due to discrete particles, namely, spontaneous emission and spontaneous scattering, which comes about when one adopts the Klimontovich formalism, are not included in this paper

Summary

INTRODUCTION

The weak turbulence theory is a useful and venerable research tool in plasma physics with numerous applications in the laboratory and space environment. This point will be discussed more fully later, but the important point is that by expressing the electric field vector associated with the plasma normal mode by Eαk = ∣Eαk∣eα(k), the complicated tensor products in the displacement electric field reduce to tensor multiplications involving the nonlinear response tensorial functions and unit electric field vector so that if one can compute the vector eα(k) from the linear wave theory, it may facilitate the formulation of the problem That is, in this approach, once we have an appropriate description of the linear wave properties, which leads to the concrete expressions for eα(k), the tensor manipulations can be done one piece at a time, the precise meaning of which will become clear as we expound on the theoretical development in the remainder of the present paper. A series of Appendices supplement some intermediate steps in the main body of the present paper

GENERAL WAVE KINETIC EQUATION

POLARIZATION VECTOR FORMALISM OF WAVE KINETIC EQUATION

UNMAGNETIZED PLASMA

SUMMARY AND DISCUSSION