Thermal Conductivity and Low Frequency Waves in Collisional Plasmas

Abstract

Thermal fluctuations and heat flow terms are retained in the two-fluid equations which are used to derive a localized dispersion relation for low-frequency electrostatic waves in a nonuniform collisional plasma. A slab plasma immersed in a uniform magnetic field is assumed. The Nyquist analysis shows two unstable waves: the collisional drift instability and a new overstability of the entropy wave. The collisional drift wave is most easily excited for parallel wavenumbers given by k‖2 = 0.15 α2(me/mi)1/2 where α ≡ |≇ In n| (all quantities in cgs units). The stability condition at this k| is B/k⊥ < 104 (min/κTe|α|)1/2 G-cm. These are in markedly improved agreement with the experimental data. Heat transport reduces the maximum growth rate, especially at high density. A small equilibrium temperature gradient tends to stabilize the drift waves in the large magnetic field region. The entropywave instability propagates along ion drift direction and is found in the range 0.4 ≤ d¯ ≤ 2 with d¯ ≈ 0.15 (k⊥κ2Ti/Ωi2mi)2νiiνeime/k‖κ2Te. The maximum growth rate of entropy wave is roughly k‖(κTi/mi)1/2(k⊥κ2Te/miΩi2)(mi/me)1/4, and occurs around d¯ = 0.6 ∼ 1The ion thermal conductivity and temperature gradient are not sigificant for both instabilities.