Theory of Turbulent Heating in Ion Acoustic Turbulence

We present the energy-conservation relation in the presence of an ion acoustic wave. An energy-transfer collision frequency is given in terms of the energy spectrum of the ion acoustic wave. It will be shown that this satisfies the relation ${\nu }_E\simeq \left(\frac{v_0{c}_s}{{v_e}^2}\right){\nu }_{\mathrm{eff}}$, and that electron heating is realized when $v_i\ll c_s\ll v_0\ll v_e$.