Feasibility of Ion-cyclotron Resonant Heating in the Solar Wind

Wave-particle interactions are believed to be one of the most important kinetic processes regulating the heating and acceleration of Solar Wind plasma. One possible explanation to the observed preferential heating of alpha ({}He⁺²) ions relies on a process similar to a second order Fermi acceleration mechanism. In this model, heavy ions are able to resonate with multiple counter-propagating ion-cyclotron waves, while protons can encounter only single resonances, resulting in the subsequent preferential energization of minor ions. In this work, we address and test this idea by calculating the number of plasma particles that are resonating with ion-cyclotron waves propagating parallel and anti-parallel to an ambient magnetic field \vec{B}₀ in a proton/alpha plasma with cold electrons. Resonances are calculated through the proper kinetic multi-species dispersion relation of Alfvén waves. We show that 100% of the alpha population can resonate with counter-propagating waves below a threshold |{Δ }U_{{α }p}/v_{A|<U_0+a(&beta_p; +&beta_0; )^b} in the differential streaming between protons and {}He⁺² ions, where U_{0=-0.532, a=1.211, &beta_0; =0.0275}, and b=0.348 for isotropic ions. This threshold seems to match with constraints of the observed {Δ }U_{{α }p} in the Solar Wind for low values of the plasma beta (β _p). Finally, it is also shown that this process is limited by the growth of plasma kinetic instabilities, a constraint that could explain alpha-to-proton temperature ratio observations in the Solar Wind at 1 AU.