A fast point charge interacting with the screened VlasovPoisson system
Abstract
We consider the longtime behavior of a fast, charged particle interacting with an initially spatially homogeneous background plasma. The background is modeled by the screened VlasovPoisson equations, whereas the interaction potential of the point charge is assumed to be smooth. We rigorously prove the validity of the stopping power theory in physics, which predicts a decrease of the velocity $V(t)$ of the point charge given by $\dot{V} \sim V^{3} V$, a formula that goes back to Bohr (1915). Our result holds for all initial velocities larger than a threshold value that is larger than the velocity of all background particles and remains valid until (i) the particle slows down to the threshold velocity, or (ii) the time is exponentially long compared to the velocity of the point charge. The longtime behavior of this coupled system is related to the question of Landau damping which has remained open in this setting so far. Contrary to other results in nonlinear Landau damping, the longtime behavior of the system is driven by the nontrivial electric field of the plasma, and the damping only occurs in regions that the point charge has already passed.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 arXiv:
 arXiv:2205.00035
 Bibcode:
 2022arXiv220500035H
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 35Q83;
 35B40
 EPrint:
 55 pages, comments welcome