Limitations of Stationary Vlasov-Poisson Solvers in Probe Theory

For ep = 0 (cylindrical probe), the orbits of the ions are regular (integrable configuration) and the boundary that separates trapped and non-trapped ions in velocity space is a smooth curve. For ep ≠ 0, some orbits are chaotic (non-integrable configuration) and the boundary that separates trapped and non-trapped ions in velocity space has a fractal structure.

The data also highlights the role of the numerical parameter Ntr, which control the number of loops around the probe that an ion should perform to be considered as trapped by the Vlasov-Poisson solver.