Phase-space single electron-hole acceleration

Single electron-hole dynamics in a one-dimensional plasma composed of two species, electrons and protons, with reduced mass ratio, is investigated through numerical kinetic Vlasov–Maxwell simulations. The electron-hole's growth of phasetrophy and acceleration are systematically studied as a function of different plasma and electron-hole parameters such as electron drift velocity vd, initial hole velocity δvh, electric potential amplitude ϕ0, and gradients of the distribution functions fe,h′ and fi,h′. A first parameter scan shows two different regimes of positive exponential increase for the electron-holes growth-rate at both positive and negative gradient sides of the electron distribution function. Linear growth of an electron-hole is observed as a function of both ion and electron distribution functions. Moreover, two power laws are measured as a function of the electric potential amplitude in both low- and high-amplitude regimes. Finally, a qualitative agreement between measurements of phasetrophy growth-rate against an effective gradient is found, the latter considering variations and effects of the electron distribution function gradient over the electron-hole's width.