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 eigen-functions 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 _s^2/3, 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 Δ′ ρ_s^1/3 δ^2/3 ≫ 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 ∝(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.