Proton and alpha particle thermal energetics in the solar wind
Numerical simulations indicate that proton and alpha particle thermal energetics in the solar wind are importantly influenced by kinetic instabilities.
The proton thermal energetics in the solar wind is rather complex. Helios 1 and 2 data indicate that protons need to be heated in the perpendicular direction with respect the ambient magnetic field from 0.3 to 1 AU. In the parallel direction protons need to be cooled at 0.3 AU with a cooling rate comparable to the corresponding perpendicular heating rate; between 0.3 and 1 AU the required cooling rate decreases until a transition to heating occurs: by 1 AU the protons require parallel heating, with a heating rate comparable to that required to sustain the perpendicular temperature. The heating/cooling rates (per unit volume) in the fast and slow solar are comparable (
Hellinger et al., JGR, 2011, 2013).
Results of a 2D hybrid expanding box simulation of a plasma system with three ion populations, beam and core protons, and alpha particles (drifting with respect to each other) with a strictly radial magnetic field suggest that the observed proton parallel cooling is connected with kinetic instabilities driven by the proton beam-core relative drift. Moreover, kinetic instabilities driven by the relative drift between (core) protons and alpha particles may importantly contribute to the proton heating (
Hellinger and Travnicek, JGR, 2013).
The first figure shows a comparison between heating rates estimated from the Helios 1 and 2 observations and 2D hybrid expanding box simulation. The left panels show the parallel, perpendicular and total proton heating rates as functions of the radial distance from the sun
R estimated from Helios in situ observations in units of the ratio between the proton kinetic energy and the expansion time
QE = np kB Tp / tE (where
np is the proton number density,
kB is the Boltzmann constant,
Tp is the proton temperature, and
tE=vsw / R,
vsw being the solar wind velocity) for the (black) slow (v
sw < 400 km/s) and (red) fast (v
sw > 600 km/s) solar wind. The right panels shows the parallel, perpendicular and total proton heating rates as functions of time from 2D hybrid expanding box simulation in units of
QE.
The ion velocity distribution function is strongly modified during the nonlinear evolution of the system. The second figure shows the proton (left) and alpha particle (right) velocity distribution functions f=f(vperp,vpar) at the end of the simulation as color scale plots. The theoretical double-adiabatic expectation is shown as dotted contours.