标题： 一个与屏蔽的Vlasov-Poisson系统相互作用的快速点电荷 显示英文标题

标题： A fast point charge interacting with the screened Vlasov-Poisson system

摘要： 我们考虑一个快速带电粒子与初始空间均匀背景等离子体相互作用的长时间行为。 背景由屏蔽的Vlasov-Poisson方程建模，而点电荷的相互作用势被假设为光滑的。 我们严格证明了物理学中的\emph{停止功率理论}的有效性，该理论预测了点电荷的速度$V(t)$的减少，其由$\dot{V} \sim -|V|^{-3} V$给出，这一公式可以追溯到玻尔（1915年）。 我们的结果适用于所有大于阈值速度的初始速度，该阈值速度大于所有背景粒子的速度，并且在（i）粒子减速至阈值速度，或（ii）时间相对于点电荷的速度呈指数长的情况下仍然有效。 该耦合系统的长时间行为与Landau阻尼问题有关，而这个问题在此设定下一直未得到解决。 与其他非线性Landau阻尼的结果不同，该系统长时间的行为是由等离子体的非平凡电场驱动的，而且阻尼仅发生在点电荷已经经过的区域。 显示英文摘要

摘要： 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 \emph{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 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 non-trivial electric field of the plasma, and the damping only occurs in regions that the point charge has already passed.