So I'd to make some changes to the Newton iterative method, but it's
working now. It's not giving noise, it converges, and with these
conditions the case reproduces the Diko's peak.
Okay, so after going to Cartesian coordinantes, going back to spherical
coordinates, reviewing Poisson and Vlasov equations in spherical
coordinates (be careful on how you write Vlasov grad.(v f)).