用缩小网格区域的方法模拟$e^+e^-$储存环的束-束效应
Simulation of the Beam-Beam Effects in $e^+e^-$ Storage Rings with a Method of Reducing the Region of Mesh
摘要：
发展了一个高精度的自洽粒子程序来模拟$e^+e^-$储存环中的束-束碰撞。它采用了一种求解开边界Poisson方程的方法。该方法由两个步骤组成：使用格林函数在有限边界上分配电势，然后使用快速泊松求解器求解边界内的电势。由于泊松方程的解是唯一的，我们的解与简单地使用格林函数得到的解完全相同。该方法允许我们选择更小的网格区域，从而提高求解器的分辨率。更好的分辨率使得更精确的计算梁的核心中的动力学。用这种方法模拟的亮度同意定量测量的PEP-II B-工厂环的线性和非线性束流制度，详细说明其预测能力。
英文摘要：
A highly accurate self-consistent particle code to simulate the beam-beam collision in $e^+e^-$ storage rings has been developed. It adopts a method of solving the Poisson equation with an open boundary. The method consists of two steps: assigning the potential on a finite boundary using the Green's function, and then solving the potential inside the boundary with a fast Poisson solver. Since the solution of the Poisson's equation is unique, our solution is exactly the same as the one obtained by simply using the Green's function. The method allows us to select much smaller region of mesh and therefore increase the resolution of the solver. The better resolution makes more accurate the calculation of the dynamics in the core of the beams. The luminosity simulated with this method agrees quantitatively with the measurement for the PEP-II B-factory ring in the linear and nonlinear beam current regimes, demonstrating its predictive capability in detail.
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