Limitations of Stationary Vlasov-Poisson Solvers in Probe Theory

The goal of the data is showing the structure of the ion distribution function around a negatively polarized Langmuir probe with an elliptical cross section of eccentricity e<sub>p</sub>. For e<sub>p</sub> = 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 e<sub>p</sub> ≠ 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 N<sub>tr</sub>, which control the number of loops around the probe that an ion should perform to be considered as trapped by the Vlasov-Poisson solver.