论文标题
快速点充电与筛选的弗拉索夫 - 波森系统相互作用
A fast point charge interacting with the screened Vlasov-Poisson system
论文作者
论文摘要
我们考虑了与最初的空间均匀背景等离子体相互作用的快速，带电的粒子的长期行为。背景是由筛选的vlasov-Poisson方程建模的，而点电荷的相互作用势则是平滑的。我们严格地证明了物理学中\ emph {停止功率理论}的有效性，这预测了$ \ dot {v} \ sim -sim- | v |^{ - 3} v $的速度$ v（t）$的降低。我们的结果适用于所有大于阈值大于所有背景粒子速度大的阈值的所有初始速度，并且保持有效，直到（i）粒子降低到阈值速度，或者（ii）与点电荷速度相比，时间呈指数呈指数长。该耦合系统的长期行为与Landau阻尼的问题有关，Landau阻尼的问题一直在此环境中保持开放。与非线性Landau阻尼的其他结果相反，该系统的长期行为是由等离子体的非平凡电场驱动的，并且阻尼仅发生在点电荷已经通过的区域。
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.
