Colorado School of Mines, Golden, Colorado 80401, USA.
Phys Rev E. 2016 Apr;93:042114. doi: 10.1103/PhysRevE.93.042114. Epub 2016 Apr 14.
This paper extends the Lorentz-Abraham model of an electron (i.e., the equations of motion for a small spherical shell of charge, which is rigid in its proper frame) to treat a small, spherically symmetric charge distribution, allowing for small internal dipolar motion. This is done by dividing the distribution into thin spherical shells (in the continuum limit), and tracking the interactions between shells. Dipolar motion of each constituent spherical shell is allowed along the net dipole moment, but higher-order multipole moments are ignored. The amplitude of dipolar motion of each spherical shell is assumed to be linearly proportional to the net dipole moment. Under these assumptions, low-velocity equations of motion are determined for both the center-of-mass motion and net dipolar motion of the distribution. This is then generalized to arbitrary (relativistic) center-of-mass velocity and acceleration, assuming the motion of individual shells is completely in phase or out of phase with the net dipole moment.
本文将洛伦兹-亚伯拉罕模型（即电子的运动方程，适用于其固有框架中的小球形电荷壳）扩展到处理小的、球对称的电荷分布，允许内部小偶极子运动。这是通过将分布分割成薄的球形壳（在连续体极限下），并跟踪壳之间的相互作用来实现的。允许每个组成球形壳沿总偶极矩进行偶极子运动，但忽略更高阶的多极矩。假设每个球形壳的偶极子运动的幅度与总偶极矩成正比。在这些假设下，确定了质心运动和分布的总偶极子运动的低速度运动方程。然后将其推广到任意（相对论）质心速度和加速度，假设单个壳的运动与总偶极矩完全同相或反相。
