Heating Ions by Heating Electrons Without Collisions

In the limit of massless electrons, no energy can be exchanged via Coulomb collisions between electrons and finite mass ions in a plasma. However, ion heating is still possible due to the change in Debye shielding of the ions when the electron temperature varies, which redistributes energy between the particles and the electrostatic field. To calculate this heating, the BBGKY hierarchy is formulated in the massless-electron limit to describe the evolution of the ion distribution function. Using this formalism, a compact expression is obtained for the curious increase in ion temperature when heat is suddenly supplied to the electrons, rigorously valid for times short compared to the energy exchange timescale.