Boltzmann solver

The boltzmann folder contains methods for solving a Boltzmann 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 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

\(\partial_t f + v \partial_x f + \frac{E}{m}\, \partial_v f = S(f)\)

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 operator \( S(f) \) represents any source terms. Different types of source terms include:

• Kinetic sources
• Krook sources

To incorporate spatial dependencies in source terms, mask functions are often used. These functions take the value 1 where the source is active and 0 otherwise. An example of such a mask function can be found in Mask with tanh.

When setting \( S(f) = 0 \), the equation is commonly referred to as the Vlasov equation.

The implemented Boltzmann solvers are:

• SplitRightHandSideSolver
• SplitVlasovSolver