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 waves (with frequency 0.3 w_{ci}) in the plasma with a transverse density inhomogeneity. Using two-fluid, cold plasma linearised equations, we show for the first time that E_|| generation can be understood by an analytic equation that couples E_|| to the transverse electric field of the driving ion cyclotron wave. In this simplified model, the generated E_|| amplitude e.g. for plausible solar coronal parameters attains values of 90 V/m for the mass ratio m_i/m_e=262, within a time corresponding to 3 periods of the driving ion cyclotron wave. By considering the numerical solutions we also show that the cause of E_|| 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 E_|| generation is affected by the mass ratio and found that amplitude attained by E_|| decreases linearly as inverse of the mass ratio m_i/m_e, i.e. E_|| \propto 1/m_i. This result contradicts to the earlier suggestion by Genot et al (1999, 2004) that the cause of E_|| generation is the polarisation drift of the driving wave, which scales as \propto m_i. Also, for realistic mass ratio of m_i/m_e=1836 our empirical scaling law is producing E_||=14 V/m (for solar coronal parameters).