Hoefer, Richard M. and Winter, Raphael (2024) A FAST POINT CHARGE INTERACTING WITH THE SCREENED VLASOV-POISSON SYSTEM. ANALYSIS & PDE, 17 (7). ISSN 1948-206X,
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We consider the long-time behavior of a fast, charged particle interacting with an initially spatially homogeneous background plasma. The background is modeled by the screened Vlasov-Poisson 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 V (center dot) similar to -| 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 the particle slows down to the threshold velocity or the time is exponentially long compared to the velocity of the point charge. The long-time 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 long-time 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PLASMA; EQUATION; IONS; Vlasov equation; Vlasov-Poisson; stopping power |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Richard Höfer |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jul 2025 06:42 |
| Last Modified: | 23 Jul 2025 06:45 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63523 |
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