电磁惯性、无功能量和能流速度
Electromagnetic inertia, reactive energy, and energy flow velocity
摘要：
在最近一篇题为“相干电磁波及其扭曲零同余”的论文中，我定义了电磁场的局部惯性密度（I）、无功能量密度（R）和能流速度（v）。这些是相对论粒子的质量、静止能量和速度的场等价物。因此R和I是洛伦兹不变的，并且|v| <=c，当且仅当R=0时相等。具有|v| =c的特殊场被称为“相干的”，因为它们的能量与场完全协调地运动，没有留下惯性或反应能量。一般的电磁场只有在远区才变得相干。在其他地方，它们的能量以|v| <c的速度流动。本文的目的是通过研究几种常见系统中的局部能量流来证实和澄清这一说法：时谐电偶极子场，含时电偶极子场和平面驻波。对于这些场，能流（坡印廷矢量）太弱而不能带走所有的能量，因此在其尾流中留下无功能量。对于含时偶极场，我们发现能量既可以横向流动，也可以向内流动，回到源。这些现象都没有出现在通常的能量传输速度的计算中，在时间谐波的情况下，只考虑一个周期的平均值。
英文摘要：
In a recent paper titled "Coherent electromagnetic wavelets and their twisting null congruences," I defined the local inertia density (I), reactive energy density (R), and energy flow velocity (v) of an electromagnetic field. These are the field equivalents of the mass, rest energy, and velocity of a relativistic particle. Thus R and I are Lorentz-invariant and |v|<=c, with equality if and only if R=0. The exceptional fields with |v|=c were called "coherent" because their energy moves in complete harmony with the field, leaving no inertia or reactive energy behind. Generic electromagnetic fields become coherent only in the far zone. Elsewhere, their energy flows at speeds |v|<c. The purpose of this paper is to confirm and clarify this statement by studying the local energy flow in several common systems: a time-harmonic electric dipole field, a time-dependent electric dipole field, and a standing plane wave. For these fields, the energy current (Poynting vector) is too weak to carry away all of the energy, thus leaving reactive energy in its wake. For the time-dependent dipole field, we find that the energy can flow both transversally and inwards, back to the source. Neither of these phenomena show up in the usual computation of the energy transport velocity which considers only averages over one period in the time-harmonic case.
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