Ardavan H
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Aug;62(2 Pt B):3010-3. doi: 10.1103/physreve.62.3010.
The criticism made by Hannay [preceding Comment, Phys. Rev. E 62, 3008 (2000)] is unfounded since the steps, familiar from the subluminal regime, that are taken in his argument are not mathematically permissible when the distribution pattern of the source is moving and has volume elements that approach the observer with the speed of light and zero acceleration along the radiation direction. In the superluminal regime, the retarded time is a multivalued function of the observation time and so the retarded potential for the radiation from a localized source cannot be represented, as Hannay assumes, by an integral over all space whose integrand entails a differentiable retarded distribution of the source density. Contrary to what is claimed by Hewish [Comment in this issue, Phys. Rev. E 62, 3007 (2000)], moreover, there is no discrepancy between conventional antenna theory and the analysis that appears in Phys. Rev. E 58, 6659 (1998). The characteristics of the new type of emission predicted by this analysis, and received from pulsars, differ from those of the radiation that is produced by known leaky waveguides because there are at present no antennas in which the emitting electric current is both volume-distributed and has the time dependence of a traveling wave with an accelerated superluminal motion.
汉内（[《物理评论E》62卷，3008页（2000年），前文评论]）所提出的批评是没有根据的，因为他论证过程中采用的那些在亚光速情形下常见的步骤，当源的分布模式在移动且其体积元沿辐射方向以光速趋近观测者且加速度为零时，在数学上是不允许的。在超光速情形下，推迟时间是观测时间的多值函数，所以如汉内所假定的那样，来自局域源的辐射的推迟势不能由对整个空间的积分来表示，该积分的被积函数包含源密度的可微推迟分布。此外，与休伊什（[本期评论，《物理评论E》62卷，3007页（2000年）]）所声称的相反，传统天线理论与《物理评论E》58卷，6659页（1998年）中出现的分析之间不存在差异。这种分析所预测并从脉冲星接收到的新型辐射的特性，与已知漏波导所产生的辐射特性不同，因为目前不存在这样的天线，其发射电流既是体分布的，又具有加速超光速运动的行波的时间依赖性。
