Plasma heating during the chiral plasma instability

The presence of a chiral asymmetry in a relativistic plasma opens a tachyonic instability toward the growth of a helical magnetic field. We study the transfer of energy from the chiral asymmetry into the magnetic field during the development of this chiral plasma instability. We find that there is more energy stored in the initial chiral asymmetry than goes into growing magnetic field and that the excess energy is transferred to the thermal bath. Consequently, we find that the chiral plasma instability is accompanied by a heating of the plasma, and the temperature increase is parametrically $\delta T \sim \mu_5^2 / T$ if the ratio of chemical potential to temperature is small, i.e. $\mu_5/T \ll 1$. We briefly remark on possible observable implications for early universe cosmology.