High Order Numerical Integrators for Relativistic Charged Particle Tracking

Explicit symplectic integrator for particle tracking in s-dependent static electric and magnetic fields with curved reference trajectory

We describe a method for symplectic tracking of charged particles through static electric and magnetic fields. The method can be applied to cases where the fields have a dependence on longitudinal as well as transverse position, and where the reference trajectory may have non-zero curvature. Application of the method requires analytical expressions for the scalar and vector potentials: we show how suitable expressions, in the form of series analogous to multipole expansions, can be constructed from numerical field data, allowing the method to be used in cases where only numerical field data ar…

Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines

Symplectic tracking of beam particles using point magnets is achieved using a reference orbit made of circular arcs and straight lines that join smoothly with each other. For this choice of the reference orbit, results are given for the transfer functions, transfer matrices, and the transit times of the magnets and drift spaces. These results provide a symplectic integrator, and allow the linear orbit parameters to be computed by multiplying transfer matrices. It is shown that this integrator is a second-order integrator, and that the transfer functions can be derived from a hamiltonian.

Accurate and efficient spin integration for particle accelerators

Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate th…

高阶时间积分器用于磁四极子中带电粒子运动的模拟

High order time integrators for the simulation of charged particle motion in magnetic quadrupoles

本文研究了如何通过高阶时间积分器提高磁四极子中带电粒子运动模拟的稳定性与效率，分析了不同高阶积分方法的精度和效率，并探讨了矢量势插值对粒子跟踪精度的影响。

Modeling and Particle Tracking through Longitudinal Gradient Bending Magnets

This report documents the development of a versatile model for longitudinal gradient bending magnets (LGB's) and its implementation in particle tracking simulations. The model presented below may be used to represent an arbitrary magnetic field profile, and was successfully implemented to represent two different LGB's. After building a symplectic integrator for our model, we were able to perform particle tracking studies. By producing phase space plots which depicted stable trajectories, we were able to demonstrate that we had in fact correctly implemented our symplectic integration scheme. In…

Symplectic Particle Tracking in a Thick Nonlinear McMillan Lens for the Fermilab Integrable Optics Test Accelerator (IOTA)

The McMillan system is a novel method to increase the tune spread of a beam without decreasing its dynamic aperture due to the systems integrability. While the ideal system is based on an infinitely thin kick, the physical design requires a thick electron lens, including a solenoid. Particle transport through the lens is difficult to simulate due to the nature of the force on the circulating beam. This paper demonstrates accurate simulation of a thick McMillan lens in a solenoid using symplectic integrators derived from Yoshidas method.