The boltzmann folder contains methods for solving a Boltzmann-Poisson coupled system. equation. Such methods typically take the distribution function and the electric field computed at a given time $t$, and return the value of the distribution function and the electric field at a time $t+dt$, where $dt$ is the timestep of the simulation. A Boltzmann equation refers to an advection equation in phase space with sources. In the simplified 1D geometry in space and velocity it has the general form
$\partial_t f + v \partial_x f + E/m\partial_v f = S(f)$
Where $f$ is the distribution function, $x$ and $v$ are the space and velocity variables respectively, $E$ is the electric field and $m$ is the mass of the considered plasma species. The $S(f)$ operator refers to any source terms (including collisions). A Quasi-Neutrality equation is of the form
$-\varepsilon_0 \nabla E = \rho$
Where $\rho$ is the charge density.
The implemented time integrators are: