It has been known since the early days of plasma physics research that superthermal electrons are generated during beam-plasma laboratory experiments. Superthermal electrons (the $\kappa$ distribution) are also ubiquitously observed in space. To explain such a feature, various particle acceleration mechanisms have been proposed. However, self-consistent acceleration of electrons in the context of plasma kinetic theory has not been demonstrated to date. This Letter reports such a demonstration. It is shown that the collisionality, defined via the “plasma parameter” $g=1/\widehat{n}{\lambda }_{\mathrm{D}}^3$, plays a pivotal role. It is found that a small but moderately finite value of $g$ is necessary for the superthermal tail to be generated, implying that purely collisionless ($g=0$) Vlasov theory cannot produce a superthermal population.

• Received 11 July 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.215003