Effect of Hall current on the instability of an anisotropic plasma jet

The modified Chew—Goldberger—Low (CGL) equations are applied to the effect of Hall current on the instability of an incompressible plasma jet surrounded by non-conducting, compressible matter. The dispersion relation is obtained and discussed. The following is found. (i) When λ (the ratio of plasma density to the density of surrounding medium) is much greater than unity, the plasma jet is unstable for all wavenumbers for which k * = K üα < [(4 R 2 2 – 1)ü(1 + V 2 α )], where R 2 = p ∥ / p ⊥ , V 2 α = H 2 /4αρ, K = ( l 2 + α 2 ) ½ . Also, the jet is unstable for R 2 > 1 + V 2 α . (ii) When λ ≪ 1, the critical wavenumber ratio for the instability to set in is k * < [( V 2 α + 3 R 2 )ü(1 + V 2 α ) ½ . Also, the jet becomes unstable for R 2 < ⅓. (iii) When either l = 0 or α= 0, we must have R 2 > 1 + V 2 α for instability. It is established that the Hall current has a destabilizing effect for certain wave- numbers. The dispersion relation for the incompressible plasma jet in cylindrical geometry is solved numerically on a computer.