Thermal Conductivity and Low Frequency Waves in Collisional Plasmas

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 $k_{\Vert }^2{\text{\hspace{0.17em}=\hspace{0.17em}0.15\hspace{0.17em}α}}^2{\mathrm{(m}}_e{\mathrm{/m}}_i{)}^{\text{1/2}}$ where $\mathrm{\alpha \hspace{0.17em}\equiv \hspace{0.17em}|\ncong \; In\; n|}$ (all quantities in cgs units). The stability condition at this $k_{|}$ is ${\mathrm{B/k}}_{\perp }{\text{\hspace{0.17em}<\hspace{0.17em}104 (m}}_i{\mathrm{n/}}_{\kappa }{T}_e{\mathrm{|\alpha |)}}^{\text{1/2}}$ 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 $\text{0.4\hspace{0.17em}≤\hspace{0.17em}}\overline{d}\text{\hspace{0.17em}≤\hspace{0.17em}2}$ with $\overline{d}{{\text{\hspace{0.17em}≈\hspace{0.17em}0.15\hspace{0.17em}(k}}_{\perp }}_{\kappa }^2{T}_i{\mathrm{/\Omega }}_i^2{m}_i{)}^2{\nu }_{\mathrm{ii}}{\nu }_{\mathrm{ei}}{m}_e{{\mathrm{/k}}_{\Vert }}_{\kappa }^2{T}_e$ . The maximum growth rate of entropy wave is roughly $k_{\Vert }{(}_{\kappa }{T}_i{\mathrm{/m}}_i{)}^{\text{1/2}}{{\mathrm{(k}}_{\perp }}_{\kappa }^2{T}_e{\mathrm{/m}}_i{\Omega }_i^2{\mathrm{)(m}}_i{\mathrm{/m}}_e{)}^{\text{1/4}}$ , and occurs around $\overline{d}\text{\hspace{0.17em}=\hspace{0.17em}0.6\hspace{0.17em}∼\hspace{0.17em}1}$ The ion thermal conductivity and temperature gradient are not sigificant for both instabilities.