Nonlocal theory of the Rayleigh-Taylor instability in the limit of unmagnetized ions

A nonlocal theory of the Rayleigh-Taylor instability is developed that applies to both magnetized and unmagnetized ion systems. The distinction between these two regimes is the time scale of the instability: for γ<Ω_i the ions can be considered to be magnetized, and for γ>Ω_i the ions can be considered to be unmagnetized, where γ is the growth rate and Ω_i is the ion gyrofrequency. Both analytical and numerical results are presented that contrast the behavior of the Rayleigh-Taylor instability in these two regimes. In the long wavelength limit (k_yL_n≪1, where k_y is the wavenumber and L_n is the density gradient scale length), it is found that the growth rate of the Rayleigh-Taylor instability in the unmagnetized ion limit is γ≂(k_yg/A)^1/2, where A is the Atwood number; this is quite different from the growth rate in the magnetized ion limit which is γ=(k_ygA)^1/2. Another distinction between the two limits is that in the unmagnetized ion regime the fastest growing mode is not the lowest-order mode; again this is different from the magnetized ion regime in which the fastest growing mode is the lowest order mode. Finally, these results are applied to recent experimental observations (e.g., AMPTE [J. Geophys. Res. 92, 5777 (1987)], NRL laser experiment [Phys. Rev. Lett. 59, 2299 (1987)]).