Electron Thermal Diffusivity due to the Electron Temperature Gradient Mode

Abstract

Charge neutrality breaks down in the short wavelength toroidal electron temperature gradient mode. In contrast to the ion temperature gradient mode, the wave number normalized by the Debye wave number, k/k(De), appears as a natural scale parameter, rather than the finite Larmor radius parameter k( perpendicular )rho(e). The growth rate and consequent mixing length estimate yields an electron thermal diffusivity large enough to be relevant to tokamaks.

Onqdependence of thermal transport in tokamaks

“…As explained above, charge neutrality breaks down for typical tokamak discharge parameters, and duality between the ITG and ETG modes does not hold anymore [3]. The maximum growth rate, which is of the order of the electron transit frequency ω Te = v Te /qR, occurs at k 0.7k De where k De is the Debye wavenumber.…”

“…The maximum growth rate can be found by scanning the finite Larmor radius parameter b e . When the maximum growth rate is written as γ max = √ 2T e /m e L T Rf (β * ), the function f (β * ) is approximately proportional to √ β * in the regime β * 1 relevant to tokamaks [3]. It should be noted that in tokamak stability analysis, the FLR parameter (k ⊥ ρ e ) 2 , the β factor and the…”

“…In gyro-fluid simulations of tokamak transport due to the ion temperature gradient (ITG) mode, the relationship χ i ∝ q has also been observed [2]. In a recent study on the electron temperature gradient (ETG) mode without imposing charge neutrality, the electron thermal diffusivity has been found to scale linearly with q, χ e ∝ q [3]. In an earlier study [4], it was shown that the electron thermal diffusivity in the form…”

Effects of impurity seeding and charge non-neutrality on electromagnetic electron temperature gradient modes in a tokamak

“…[2][3][4][5][6][7][8][9][10][11][12] These include several kinetic and gyrokinetic calculations which have recently been published and which explore various additional features of the ETG modes such as the linear effects due to charge non-neutrality, [6][7][8][9] finite ␤, 10 threshold, 12 and nonlinear effects due to the streamer/zonal flow excitation, 11 transport, 11 etc. These studies reveal a threshold in e = L n / L T e ; here L n and L T e are the density and temperature scale lengths, respectively.…”