A hall dynamo effect driven by two-fluid tearing instability

Abstract

A quasi-linear prediction of the two-fluid dynamo effect is analyzed with the use of tearing eigenfunctions obtained for force-free equilibrium. In the range of parameters of practical interest, the basic shear Alfvén mode is decoupled from fast compressional Alfvén and slow magneto-acoustic modes. Kinetic Alfvén modification of the shear Alfvén wave drives an instability with a growth rate ∝δ^1/3ρ ^2/3_s , where δ is the electron skin depth and ρ_s is the ion-sound gyroradius. A net dynamo effect parallel to the magnetic field is calculated at ρ _s ≫δ for large values of the stability factor $\Delta '\rho _s^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \delta ^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \gg 1$. The dynamo effect caused by the j×B Hall term dominates the contribution from the v×B term (the alpha effect) by a factor ∝(ρ_s/δ)² in the narrow electron layer, while in the broader ion layer these contributions are comparable. The results are compared with the case of a strong guiding field where ρ _s ≪δ and the tearing instability is described by resistive MHD.