A hall dynamo effect driven by two-fluid tearing instability

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 ∝δ1/3ρ s 2/3 , where δ is the electron skin depth and ρs 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 Δ 'ρ ₛ^1 / 1 3 . - 3 δ ^1 / 1 3 . - 3 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 ∝(ρs/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.