矩形腔体中相干同步辐射的有效计算及其在壁面电阻加热中的应用
An Efficient Computation of Coherent Synchrotron Radiation in a Rectangular Chamber, Applied to Resistive Wall Heating
摘要：
本文研究了矩形截面真空室中的相干同步辐射（CSR），给出了一种允许任意弯曲段和直线段序列的形式。我们在频域中应用傍轴方法，在垂直坐标中进行傅立叶展开，但没有其他模式展开。本文用一种新的方法对线电荷源进行了数值处理，该方法通过改变因变量来消除奇异性方程。所得到的算法是快速的，与早期的方法相比，工程短束与复杂的结构，并产生所有六个字段组件在任何时空点。作为一个例子，我们计算切向磁场的墙壁。由此，可以对坡印廷通量进行微扰处理，以估计沉积在电阻壁中的能量。该计算的动机是LCLS-II的设计问题，即在束流压缩机的最后一个弯曲部分和随后的直段中发生多少CSR壁加热的问题。用一个真实的纵向束形式的有效值。长度$10.4~μ$ m和100 pC的电荷，我们得出结论，辐射功率非常小（在1 MHz重复率下为28 W），并且所有辐射能量都被沿直线段7 m以内的壁吸收。
英文摘要：
We study coherent synchrotron radiation (CSR) in a perfectly conducting vacuum chamber of rectangular cross section, in a formalism allowing an arbitrary sequence of bends and straight sections. We apply the paraxial method in the frequency domain, with a Fourier development in the vertical coordinate but with no other mode expansions. A line charge source is handled numerically by a new method that rids the equations of singularities through a change of dependent variable. The resulting algorithm is fast compared to earlier methods, works for short bunches with complicated structure, and yields all six field components at any space-time point. As an example we compute the tangential magnetic field at the walls. From that one can make a perturbative treatment of the Poynting flux to estimate the energy deposited in resistive walls. The calculation was motivated by a design issue for LCLS-II, the question of how much wall heating from CSR occurs in the last bend of a bunch compressor and the following straight section. Working with a realistic longitudinal bunch form of r.m.s. length $10.4~μ$m and a charge of 100 pC we conclude that the radiated power is quite small (28 W at a 1 MHz repetition rate), and all radiated energy is absorbed in the walls within 7 m along the straight section.
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