Range of validity of the Rayleigh hypothesis.
Range of validity of the Rayleigh hypothesis.
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DOI：
10.1103/physreve.69.056606
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发表时间：
2004-05
期刊：
影响因子：
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通讯作者：
T. Watanabe;Y. Choyal;K. Minami;V. Granatstein
中科院分区：
文献类型：
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作者：
T. Watanabe;Y. Choyal;K. Minami;V. Granatstein
本文用数值方法研究了光栅的瑞利假设（RH）适用于分析高功率返波振荡器的参数范围。从严格的数学观点来看，RH仅适用于慢波结构（SWS）的浅周期，使得h K 0 <0.448;这里，h和K 0分别是正弦平面光栅中周期性的振幅和波数。我们数值分析的电磁场的轴对称SWS与不使用RH。对于给定的k（z），利用高阶隐式差分法（Higher Order Implicit Difference Method，HIDM）对慢波系统的场型和本征频率进行了数值求解。结果表明，对于深磁层，h K 0 =5 × 0.448，虽然Floquet谐波展开不能正确地表示磁层内部的场型，但利用RH仍然可以得到色散关系。因此，在使用RH获得色散关系的有效性和在SWS中各处FHE的精确收敛性之间存在差异。
The parameter range over which the Rayleigh hypothesis (RH) for optical gratings might be validly applied to analysis of high power backward wave oscillators has been investigated numerically. It had been pointed out that from a rigorous mathematical viewpoint, RH was only valid for a shallow corrugation of slow wave structure (SWS) such that h K0 <0.448; here, h and K0 are, respectively, the amplitude and wave number of the periodicity in a sinusoidal planar grating. We numerically analyze the electromagnetic fields in the axisymmetric SWS with and without use of RH. The field patterns and eigenfrequency for the SWS are solved numerically for a given k(z) by using the code HIDM (higher order implicit difference method) that is free from the RH. It is found that, for a deep corrugation, h K0 =5 x 0.448, using RH is still valid for obtaining the dispersion relation, although the Floquet harmonic expansion (FHE) fails to correctly represent the field patterns inside the corrugation. Accordingly, there exists a discrepancy between the validity of using RH for obtaining dispersion relations and for an exact convergence of FHE everywhere in the SWS.