Quasi-Neutrality Solver
The Quasi-Neutrality solver is designed to solve the following Quasi-Neutrality equation:
\[ -\Delta \phi(x) = \sum_s \int q_s f_s(x,y,v_x,v_y) dv_x dv_y \]
This calculation is split into two parts. Firstly the charge density is calculated:
\[ \rho_{q,s}(x, y) = \int q_s f_s(x,y,v_x,v_y) dv_x v_y \]
Then the basic Poisson equation:
\[ -\Delta \phi(x) = \sum_s \rho_{q,s}(x,y) \]
is solved.
Charge Density
The charge density is calculated by integrating the distribution function.
Quasi-Neutrality Solver
The Quasi-Neutrality equation can be solved with a variety of different methods by combining Poisson solvers and charge density solvers.
These classes return the electric potential \(\phi\) and the electric field \(\frac{d \phi}{dx}\).