方位对称光束中的空间电荷场：积分格林函数方法
Space charge fields in azimuthally symmetric beams: integrated Green's function approach
摘要：
相对论束流中空间电荷感应的电磁场在加速器物理中发挥着重要作用。它们导致发射度增长、切片能量变化和微聚束不稳定性。通常情况下，这些影响的数值模拟，因为简单的描述只存在于大规模或小规模的电流变化的限制。在本文中，我们考虑一个轴对称的带电光束内的圆形管道，并找到解决方案的空间电荷问题是有效的，在整个范围内的电流变化。我们表示的解决方案的领域的分量的格林函数，这是完全由一个单一的功能。然后我们发现，该函数是一个轴上的潜力，从一个带电盘在一个圆形管道，与横向电荷密度$ρ_\perp(r)$，它有一个紧凑的解析表达式。最后，我们提供了一个集成的格林函数为基础的方法，有效的数值计算的情况下，当横向电荷密度保持不变沿光束。
英文摘要：
Electromagnetic fields induced by the space charge in relativistic beams play an important role in Accelerator Physics. They lead to emittance growth, slice energy change, and the microbunching instability. Typically, these effects are modeled numerically since simple description exists only in the limits of large- or small-scale current variations. In this paper we consider an axially symmetric charged beam inside a round pipe and find the solution of the space charge problem that is valid in the full range of current variations. We express the solution for the field components in terms of Green's functions, which are fully determined by just a single function. We then find that this function is an on-axis potential from a charged disk in a round pipe, with transverse charge density $ρ_\perp(r)$, and it has a compact analytical expression. We finally provide an integrated Green's function based approach for efficient numerical evaluation in the case when the transverse charge density stays the same along the beam.
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