The generation of parallel electric fields by the propagation of ion cyclotron waves ( with frequency 0.3 \omega _ { ci } ) in the plasma with a transverse density inhomogeneity was studied .
Using two-fluid , cold plasma linearised equations , it was shown for the first time that , in this particular context , E _ { \parallel } generation can be understood by an analytic equation that couples E _ { \parallel } to the transverse electric field of the driving ion cyclotron wave .
It was proven that the minimal model required to reproduce the previous kinetic simulation results of E _ { \parallel } generation [ Tsiklauri et al 2005 , Génot et al 2004 ] is the two-fluid , cold plasma approximation in the linear regime .
By considering the numerical solutions it was also shown that the cause of E _ { \parallel } generation is the electron and ion flow separation induced by the transverse density inhomogeneity .
We also investigate how E _ { \parallel } generation is affected by the mass ratio and found that amplitude attained by E _ { \parallel } decreases linearly as inverse of the mass ratio m _ { i } / m _ { e } .
For realistic mass ratio of m _ { i } / m _ { e } = 1836 , such empirical scaling law , within a time corresponding to 3 periods of the driving ion cyclotron wave , is producing E _ { \parallel } = 14 Vm ^ { -1 } for solar coronal parameters .
Increase in mass ratio does not have any effect on final parallel ( magnetic field aligned ) speed attained by electrons .
However , parallel ion velocity decreases linearly with inverse of the mass ratio m _ { i } / m _ { e } .
These results can be interpreted as following : ( i ) ion dynamics plays no role in the E _ { \parallel } generation ; ( ii ) E _ { \parallel } \propto 1 / m _ { i } scaling is caused by the fact that \omega _ { d } = 0.3 \omega _ { ci } \propto 1 / m _ { i } is decreasing with the increase of ion mass , and hence the electron fluid can effectively ” short-circuit ” ( recombine with ) the slowly oscillating ions , hence producing smaller E _ { \parallel } .