arXiv 1501.010052015-01-05physics.opticsmath-phmath.MP

无功电磁能量在无功时间内的守恒

Conservation of reactive electromagnetic energy in reactive time

Gerald Kaiser

备注：: 2 pages, no figures, paper submitted by invitation to special session on Fundamental Considerations of Electromagnetic Energy and Interactions: Theory and Applications at IEEE APS/URSI 2015 Symposium http://www.2015apsursi.org

摘要：

将复坡印廷定理（CPT）推广到正则时间尺度域$(t,s)$ .时间谐波相量被一般场的正频率部分所取代，其解析地延伸到复时间$t+is$，其中$s>0$被解释为时间分辨率尺度。扩展CPT的实部在$t$中给出时间平均场能量的守恒，虚部在$s$中给出时间平均无功能量的守恒。在这两种情况下，平均窗口由宽度为$Δt\sim \pm s$的柯西核确定。这就完成了时谐CPT，它的虚部一般被假定为与无功能量模糊地“相关”，而没有给出无功能量的守恒定律，甚至没有给出无功能量的表达式。将$s$解释为无功时间，跟踪与存储的电容性和电感性能量相关的超前和滞后，给出了测量无功功率的伏安无功（var）单位的简单解释：var简单地说就是1焦耳/无功秒。相关的“复辐射阻抗密度”被引入来表示场的局部辐射磁阻。

英文摘要：

The complex Poynting theorem (CPT) is extended to a canonical time-scale domain $(t,s)$. Time-harmonic phasors are replaced by the positive-frequency parts of general fields, which extend analytically to complex time $t+is$, with $s>0$ interpreted as a time resolution scale. The real part of the extended CPT gives conservation in $t$ of a time-averaged field energy, and its imaginary part gives conservation in $s$ of a time-averaged reactive energy. In both cases, the averaging windows are determined by a Cauchy kernel of width $Δt\sim \pm s$. This completes the time-harmonic CPT, whose imaginary part is generally supposed to be vaguely `related to' reactive energy without giving a conservation law, or even an expression, for the latter. The interpretation of $s$ as reactive time, tracking the leads and lags associated with stored capacitative and inductive energy, gives a simple explanation of the volt-ampere reactive (var) unit measuring reactive power: a var is simply one Joule per reactive second. The related 'complex radiation impedance density' is introduced to represent the field's local reluctance to radiate.

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