Rayleigh-Taylor instability with finite current relaxation

In this work, we explore the influence of perturbative wavelengths, shorter than those usually considered, on the growth rate of the Rayleigh-Taylor modes. Therefore, we adopt an extended form of Ohm's law which includes a finite relaxation time of the current density due to inertial effects of charged species in the plasma. The restoring force density that acts upon charged species close to the mode rational surface takes into account a new term which is usually neglected with respect to the motional electromotive force. We find that the width of the resistive layer can be interpreted in terms of the “height” of free fall in a constant gravitational field, in the Alfvén time interval. We also show that the charged species must fall “down” in the constant gravitational field in order that the static state of equilibrium of the system becomes unstable to the linear perturbation. Through the principle of conservation of energy, we find a general formula which gives the growth rate γ of the Rayleigh-Taylor modes. When the new term becomes negligible with respect to the motional electromotive force, we recover the standard result of the Rayleigh-Taylor instability, which establishes that γ scales with the plasma resistivity η as γ ∼ η 1 / 3 . However, in the opposite limiting situation, we find that γ does not depend any longer on the plasma resistivity and scales now with the electron number density n e as γ ∼ n e − 1 / 2 . Further developments of our theory may contribute to improve our understanding on the excitation mechanisms of resistive plasma instabilities by transient phenomena such as shock waves.