Numerical computation of high-order transfer maps for rf cavities
Numerical computation of high-order transfer maps for rf cavities
复制标题
射频腔高阶传递图的数值计算
DOI：
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发表时间：
2006
期刊：
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通讯作者：
D. Abell
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文献类型：
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作者：
D. Abell
现在存在的技术可以为非常一般的磁性元素构建精确的转移图，包括条纹和重叠场[1-3]。然而，对于射频（rf）腔，当前的建模实践通常将传输图计算为随腔相位变化的能量反冲（例如[4]）或线性图[5]。这两种方法都忽略了重要的物理学：仅使用能量反冲忽略了横向粒子动力学，例如，高梯度射频线性加速器[6，7]，包含轴向不对称的射频腔[8，9]或设计用于加速以外目的的射频腔[10-13]。在基于z的代码中使用线性映射意味着不存在二阶能量变化，这在峰值电压附近加速时很重要。这里所描述的工作的目的是把射频腔的治疗在现代非线性束流动力学代码中的磁性元件的目前治疗相同的立足点。Rosenzweig和Serafini [6]提出了一种广义的矩阵方法-广义的意义上说，相位信息包括在矩阵项-超相对论粒子的轴对称和周期性的射频腔。货车蔡茨[14]利用了汉密尔顿的机器[15]。这种方法的优点包括这样一个事实，即计算转移映射到高阶可以自动化;其他领域，从附近的磁铁或其他腔模式，可以很容易地叠加;和列入轴向不对称是直截了当的。为了计算射频腔的传输图，必须知道矢势;特别是，必须有矢势在许多纵向位置的横向展开。人们可以从轴上场及其导数构造这种展开的系数。然而，对于一个现实的腔体，轴上的字段是已知的，只有从实验测量或电磁模拟，和数值计算的衍生物变得越来越可疑的阶数增加。本文提出了一种计算横向展开系数的高阶稳健方法，
Techniques now exist for constructing accurate transfer maps for very general magnetic elements, including fringes and overlapping fields [1–3]. For radio-frequency (rf) cavities, however, current modeling practices usually compute transfer maps as either energy kicks that vary with cavity phase, e.g. [4], or linear maps [5]. Both approaches omit significant physics: Using just an energy kick ignores the transverse particle dynamics important in, for example, high-gradient rf linear accelerators [6,7], rf cavities that contain axial asymmetries [8,9], or rf cavities designed for purposes other than acceleration [10–13]. Using a linear map in a z-based code implies the absence of second-order energy variation—important when accelerating near peak voltage. The work described here aims to place the treatment of rf cavities on the same footing as the present treatment of magnetic elements in modern nonlinear beam-dynamics codes. Rosenzweig and Serafini [6] presented a generalized matrix approach—generalized in the sense that phase information is included in the matrix entries—for ultrarelativistic particles in an axisymmetric and periodic rf cavity. Van Zeijts [14] brought to bear the power of Hamilton’s machinery [15]. The advantages of this approach include the fact that computing transfer maps to high order can be automated; other fields—from nearby magnets or other cavity modes—can easily be superposed; and the inclusion of axial asymmetries is straightforward. To compute transfer maps for rf cavities, one must know the vector potential; in particular, one must have a transverse expansion of the vector potential at many longitudinal locations. One may construct the coefficients of such an expansion from the on-axis field and its derivatives. For a realistic cavity, however, the on-axis field is known only from experimental measurement or electromagnetic simulation, and numerically computed derivatives become increasingly suspect as the order increases. This paper describes a method for computing robustly and to high order the coefficients in the transverse expansion of the