Validation of electron temperature gradient turbulence in the Columbia Linear Machine

Abstract

The electron temperature gradient (ETG) mode, which is a universal mechanism for turbulent electron thermal transport in plasmas, is produced and verified in steady-state, collisionless hydrogen plasma of the Columbia Linear Machine. Electron temperature profiles with strong gradients are produced by DC acceleration in a remote biased mesh and subsequent thermalization. Finite amplitude $ 5%, steady-state oscillations at $ 0:3 À 0:5 MHz (in the plasma frame), with azimuthal wave numbers m $ 14À16 and parallel wave number k k $ 0:01 cm À1 are measured. The massively parallel gyrokinetic toroidal code is used to study these modes. The results show that in the linear phase, the dispersion relation is consistent with kinetic theory. In the nonlinear stage, very strong nonlinear wave coupling gives rise to an inverse cascade of the energy from the fastest growing high-m modes to low-m nonlinear oscillations, which are consistent with the measured azimuthal mode spectrum. The radial structure of the fluctuation also agrees with the experiment. An inward radial shift of the peak of the potential fluctuation occurs during the nonlinear saturation and fluctuation fingers extend radially out to the edge plasma. Three-wave coupling mechanism is involved in the saturation of ETG modes. The simulations show a power law spectrum of the turbulence which suggests that the renormalization theory is appropriate to interpret the turbulent thermal flux.

Analogous Saturation Mechanisms of the Ion and Electron Temperature Gradient Drift Wave Turbulence

“…Production and identification of slab ETG mode have been successfully demonstrated in a basic experiment in Columbia Linear Machine (CLM) [24]. This result has been recently validated by numerical simulation [25]. The first experimental scaling of electron thermal transport coefficient vs amplitude of ETG mode was also obtained [26].…”

Turbulence Theory for Drift and Alfvén Waves

“…The second region is one in which there is a cascade of enstrophy rather than energy. The energy has an inverse cascade in 2D turbulence transferring energy from high-k to low-k. A striking example is in the ETG turbulence reported in Fu, et al (2012). This is the range of greatest relevance to 2D fluid turbulence and continues down to the smallest scales where the viscous dissipation finally absorbs the vorticity of the fluctuations.…”

The study of the transition regime between slab and mixed slab-toroidal electron temperature gradient modes in a basic experiment

“…Te the experimental data points are fitted with an analytic function of the type T e ffi f ðxÞ ¼ a à tan À1 ðbx þ cÞ þ d, 26 and then we define L À1 Te j dT e dx 1 T e j. The electron temperature begins to decrease around r ¼ 1:6 cm but that the maximum of the gradient drive L À1 Te occurs around r ¼ 2.0 cm.…”

“…For typical plasma conditions, we find m $ 10 À 12 and f ExB $ 125 À 175 kHz and a true ETG mode frequency in the range of f plasma $ 400 À 700 kHz depending on plasma parameters, this agrees with prior experimental work and numerical validations. 18,26 For example, the lowest-curvature mode in Fig. 7 has h $ 100 , m $ 11, f lab $ 2:6 MHz; and f ExB $ 175 kHz and a resulting f plasma $ 650 kHz.…”