The formulas given in C.3.7 do not apply when outside the limiting regime or when particles are emitted from the surface or when the spherical symmetry condition is not fulfilled. The problem can be resolved by solving the complete Vlasov-Poisson system of equations
where F stands for the force applied on the species described by the distribution function.
In case of spherical symmetry the Turning Point formulation method can be used to solve this system (see e.g. [1]). In the more general case, current can be computed via Particle-in-Cell simulations codes. Example of two of them are PicUp3D and SPIS (see [3]).