Pseudo-three-dimensional turbulence in magnetized nonuniform plasma

Abstract

A simple nonlinear equation is derived to describe the pseudo-three-dimensional dynamics of a nonuniform magnetized plasma with Te≫Ti by taking into account the three-dimensional electron, but two-dimensional ion dynamics in the direction perpendicular to B0. The equation bears a close resemblance to the two-dimensional Navier–Stokes equation. A stationary spectrum in the frequency range of drift waves is obtained using this equation by assuming a coexisting large amplitude long wavelength mode. The ω-integrated k spectrum is given by k1.8(1+k2)−2.2, while the width of the frequency spectrum is proportional to k3(1+k2)−1, where k is normalized by cs/ωci. The result compares well with the recently observed spectrum in the ATC tokamak.

Fundamental statistical descriptions of plasma turbulence in magnetic fields

“…Accumulated evidence from many years of computer simulations has shown that they are important constituents of plasma microturbulence as well. This could be expected from the close analogy between Rossby waves and drift waves (Horton and Hasegawa, 1994), and indeed was anticipated by Hasegawa and Mima (1978). Zonal flows are theoretically interesting because they are nonlinearly driven and very weakly damped, and their self-generated (random) shear can be expected to play a role in the dynamics of the modes (which will be called drift waves for short) that drive them.…”

“…Although extensive research on the NSE in the presence of forcing and dissipation shows that actual turbulent steady states are far from equilibrium, statistical methods have made substantial inroads. A fundamental difficulty with the statistical approach is that nonlinear systems can also display a tendency toward self-organization (Hasegawa, 1985). Certain fluid equations admit the possibility of soliton solutions; in plasmas, the Vlasov equation can support Bernstein-Greene-Kruskal (BGK) modes (Bernstein et al, 1957).…”

“…The original derivation of the HME (Hasegawa and Mima, 1978) proceeded from fluid equations expressed in particle coordinates [often referred to in plasma physics as the equations of Braginskii (1965)]. However, it is far more concise and elegant to proceed from the GKE (29a) (Dubin et al, 1983).…”

“…(43) with a particular model of dissipative effects were discussed by Liang et al (1993). At the other extreme, if the nonadiabatic contributions are neglected both linearly and nonlinearly, 51 one arrives at the equation of Hasegawa and Mima (1978) 52 :…”

“…In the last three decades a huge literature on both the theory and numerical simulation of drift and related instabilities has blossomed with the increasing appreciation of their relevance to turbulent transport in magnetically confined fusion plasmas. From the involved practical details of realistic devices have been distilled some simple generic models such as those of Hasegawa and Mima (1978), Terry and Horton (1982), and Hasegawa and Wakatani (1983). The statistical theory of strong turbulence has been proven capable of making quantitatively accurate predictions for some key features of such nonlinear models, including the steady-state turbulent flux and spectral shape.…”