A minimal model of parallel electric field generation in a transversely inhomogeneous plasma

We study the generation of parallel electric fields by virtue of propagation of ion-cyclotron (IC) waves (with frequency 0.3 ωci) in the plasma with a transverse density inhomogeneity. Using two-fluid, cold plasma linearized equations, we show for the first time that Eparallel generation can be understood by an analytic equation that couples Eparallel to the transverse electric field of the driving IC wave. We prove that the minimal model required to reproduce previous kinetic results on Eparallel generation is the two-fluid, cold plasma approximation in the linear regime. In this simplified model, the generated Eparallel amplitude e.g. for plausible solar coronal parameters attains values of ∼90 V m-1 for the mass ratio mi/me = 262, within a time corresponding to three periods of the driving IC wave. By considering the numerical solutions we also show that the cause of Eparallel generation is electron and ion flow separation (which is not the same as electrostatic charge separation) induced by the transverse density inhomogeneity. The model also correctly reproduces the previous kinetic results in that only electrons are accelerated (along the background magnetic field), while ions do not accelerate substantially. We also investigate how Eparallel generation is affected by the mass ratio and find that amplitude attained by Eparallel decreases linearly as the inverse of the mass ratio mi/me, i.e. Eparallel ∼ 1/mi. This result contradicts the earlier suggestion by Genot et al (1999 J. Geophys. Res. 104 22649; 2004 Ann. Geophys. 6 2081) that the cause of Eparallel generation is the polarization drift of the driving wave, which scales as ∼mi. Also, for a realistic mass ratio of mi/me = 1836 our empirical scaling law produces Eparallel = 14 V m-1 (for solar coronal parameters). Increase in mass ratio does not have any effect on the final parallel (magnetic field aligned) speed attained by electrons. However, parallel ion velocity decreases linearly with the inverse of the mass ratio mi/me, i.e. the parallel velocity ratio of electrons and ions scales directly as mi/me. These results can be interpreted as follows: (i) ion dynamics plays no role in the Eparallel generation; (ii) decrease in the generated parallel electric field amplitude with the increase of the mass ratio mi/me is caused by the fact that ωd = 0.3ωci ∝ 1/mi is decreasing, and hence the electron fluid can effectively 'short-circuit' (recombine with) the slowly oscillating ions, hence producing smaller Eparallel which also scales exactly as 1/mi