Mixing Length Hypothesis in the Dissipative Trapped Ion Instability

Abstract

The mixing length hypothesis is investigated for the purpose of making the underlying idea of the hypothesis clear in the case of the dissipative trapped ion instability. Three different approaches are employed; 1) analogy to the ordinary turbulence in hydrodynamics, 2) a nonlinear turbulent collision theory, and 3) a quasilinear theory of the density flattening. If the isotropic turbulence is assumed, the mixing length hypothesis can be derived by the first two approaches. The formula D\simeqγ⁄k_⊥², which is usually obtained from the mixing length hypothesis, can be derived by the third approach.