Smith-Purcell radiation from a charge moving above a grating of finite length and width
Smith-Purcell radiation from a charge moving above a grating of finite length and width
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DOI：
10.1103/physrevstab.13.022804
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发表时间：
2010-02
影响因子：
--
通讯作者：
A. Kesar
中科院分区：
文献类型：
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作者：
A. Kesar
史密斯-珀塞尔辐射（SPR），当电荷通过周期性光栅上方时发出，对于太赫兹产生和无损束长诊断等应用非常重要。光栅的宽度被证明是一个重要的参数，准确地预测辐射，特别是在高度相对论制度的电荷韦克菲尔德相当大的拉伸在横向方向。采用电场积分方程（EFIE）方法对有限长、宽光栅的SPR辐射进行了严格的计算。积分方程被安排为一个多级块Toeplitz矩阵，通过使用相对于光栅周期和宽度方向的平移下的对称性。跟随巴罗维尔。（Microw。Opt. Technol. Lett. 31，28（2001）MOTLEO 0895 -247710.1002/mop. 1348]通过基本矩阵元素的矩阵到向量投影可以实现增强的计算效率。计算了一个相对论性（）、长1 mm、在10个周期、周期为2.0mm、宽度为10 mm的光栅上运动0.6mm的束团的数值例子。SPR共振关系和它的扩大，由于有限数量的凹槽是一致的封闭形式的配方。表面电流被示出为沿着光栅的中心集中，并且朝向其边缘减小。的表面电流，功率谱，和辐射能量进行了比较的EFIE制定中，假设一个无限宽的光栅。上述参数导致有限宽度和无限宽光栅假设之间高达2.5倍的相当大的差异，这意味着为了精确计算，应该考虑光栅宽度。提供了所需光栅宽度的一般规则，以实现相对于无限宽度结果的准确SPR辐射结果，以及对于大多数辐射角度的无限宽度假设的预期精度。
Smith-Purcell radiation (SPR), emitted when a charge passes above a periodic grating, is important for applications such as terahertz production and nondestructive bunch-length diagnostics. The grating width is shown to become an important parameter for accurately predicting the radiation, and especially in the highly relativistic regime where the charge wakefield considerably stretches in the transverse direction. The SPR radiation is rigorously calculated by the electric-field integral equation (EFIE) method for a grating of finite width and length. The integral equation is arranged as a multilevel block-Toeplitz matrix by using symmetry under translation with respect to the grating period and width directions. Following Barroweset al.[Microw. Opt. Technol. Lett. 31, 28 (2001)MOTLEO0895-247710.1002/mop.1348] enhanced computational efficiency can be achieved by matrix to vector projection of the essential matrix elements. A numerical example is calculated for a relativistic (), 1-mm long, bunch traveling 0.6-mm above a ten-period grating with a period of 2.0 mm and width of 10 mm. The SPR resonance relationship and its broadening due to the finite number of grooves are consistent with the closed-form formulations. The surface current was shown to be concentrated along the center of the grating and decreasing towards its edges. The surface current, power spectrum, and radiated energy were compared to the EFIE formulation in which an infinitely wide grating was assumed. The above parameters resulted in considerable difference of up to a factor of 2.5 between the finite width and the infinitely wide grating assumption, which means that for accurate calculations the grating width should be taken into consideration. A general rule for the required grating width to achieve an accurate SPR radiation result relative to the infinite width result, and the expected accuracy by the infinite width assumption for most radiation angles, is provided.