The possibility of hypersonic electrostatic solitons in a plasma with turbulence heating

Here, we show that electrostatic solitons in a plasma with turbulent heating of the electrons through an accelerating electric field, can form with very high velocities, reaching up to several order of magnitudes larger than the ion-sound speed. We call these solitons hypersonic solitons. The possible parameter regime, where this work may be relevant, can be found the so-called ``dead zones'' of a protoplanetary disk. These zones are stable to magnetorotational instability but the resultant turbulence can in effect heat the electrons make them follow a highly non-Maxwellian velocity distribution. We show that these hypersonic solitons can also reach very high velocities. With electron velocity distribution described by Davydov distribution function, we argue that these solitons can be an effective mechanism for energy equilibration in such a situation through soliton decay and radiation.