论文标题
外部激光脉冲中亚伯拉罕 - 洛伦兹 - 迪拉克方程的非独立解决方案的非唯一性
Nonuniqueness of nonrunaway solutions of Abraham-Lorentz-Dirac equation in an external laser pulse
论文作者
论文摘要
在论文\ cite {carati95}中，表明，对于在潜在屏障的行动下的一条线上的运动中，第三阶Abraham-Lorentz-Dirac方程提出了非独立溶液的非唯一性的现象。也就是说，至少对于足够陡峭的屏障，方程的物理解决方案不取决于位置和速度的“机械状态”，也需要对初始加速度的了解。由于最近的实验和计划，在强激光脉冲与超级相对论电子之间的相互作用上，确定这种非平方现象是否扩展到后一种情况以及参数的范围是有趣的。在目前的工作中，我们将仅考虑最简单的模型，即电磁平面波的情况，此外，对于亚伯拉罕·莱伦兹 - 迪拉克方程，在非依赖性近似中处理的情况。我们发现的结果是，如果在传入波的给定频率下，场强度足够大，则会发生非唯一性现象。还给出了这种阈值的分析估计。目前尚不清楚这种现象是否也适用于全面的相对论案例，这是物理利益之一。
In the paper \cite{carati95} it was shown that, for motions on a line under the action of a potential barrier, the third-order Abraham-Lorentz-Dirac equation presents the phenomenon of nonuniqueness of nonrunaway solutions. Namely, at least for a sufficiently steep barrier, the physical solutions of the equation are not determined by the "mechanical state" of position and velocity, and knowledge of the initial acceleration too is required. Due to recent experiments, both in course and planned, on the interactions between strong laser pulses and ultra relativistic electrons, it becomes interesting to establish whether such a nonuniqueness phenomenon extends to the latter case, and for which ranges of the parameters. In the present work we will consider just the simplest model, i.e., the case of an electromagnetic plane wave, and moreover for the Abraham-Lorentz-Dirac equation dealt with in the nonrelativistic approximation. The result we found is that the nonuniqueness phenomenon occurs if, at a given frequency of the incoming wave, the field intensity is sufficiently large. An analytic estimate of such a threshold is also given. At the moment it is unclear whether such a phenomenon applies also in the full relativistic case, which is the one of physical interest.
