用谐振子网络近似加速器阻抗
Approximating Accelerator Impedances with Resonator Networks
AI总结：
本文提出利用福斯特正则谐振子网络和偏导数下降优化综合谐振子网络，以近似加速器元件阻抗，并结合解析尾场解简化束流动力学模拟。
摘要：
在加速器领域，通常使用加速器元件的阻抗来描述频域中的尾场相互作用。然而，对于非高斯性质的激励，通常希望在时域中以一般方式理解这种尾场相互作用。传统方法是对元件阻抗进行逆傅里叶变换，得到格林函数，然后将其与所需的激励分布进行卷积。这种方法在数值上可能很繁琐，因为每当需要尾场函数时，必须对每个时间点计算卷积积分。另一种方法是解析计算尾场函数，这样可以避免重复积分。然而，只有少数情况足够简单，使得这种方法可行。其中一种情况是所考虑的元件是RLC谐振子，它具有闭合形式的解析尾场函数解。这意味着可以用谐振子表示的元件可以利用这一解。事实上，常见的网络综合技术可用于将任意阻抗分布映射到RLC谐振子网络，而加速器领域尚未利用这一点。在本工作中，我们将使用福斯特正则谐振子网络和偏导数下降优化来开发一种综合谐振子网络的技术，该网络能很好地近似真实加速器元件的阻抗。我们将把这种综合与闭合形式的谐振子尾场函数解联系起来，从而产生一个强大的工作流程，可用于简化束流动力学模拟。
英文摘要：
It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. The conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.
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