Abstract
Author(s): Qiang, Ji | Abstract: Space-charge effects play an important role in high intensity accelerators. These effects can be studied self-consistently by solving the Poisson equation with the dynamically evolved charge density distribution subject to appropriate boundary conditions. In this paper, two computationally efficient methods are proposed to solve the Poisson equation inside an elliptical perfectly conducting pipe. One method uses a spectral method and the other uses a spectral finite difference method. The former method has a high accuracy and the latter one has a computational complexity of O(Nlog(N)), where N is the total number of unknowns. These methods implemented in a beam dynamics tracking code enable the fast simulation of space-charge effects in an accelerator with an elliptical conducting pipe.
Highlights
The nonlinear space-charge effects play an important role in high intensity accelerators by driving beam instability, causing beam emittance growth, halo formation, and even particle loss
In the PIC method, at each time step, macroparticles that represent the phase space distribution of charged particle beam in the accelerator are transformed from the laboratory frame into the moving beam frame following the relativistic Lorentz transformation and are deposited onto a twodimensional (2D) or three-dimensional (3D) computational grid to attain the charge density distribution in spatial domain
The other uses a transverse Galerkin spectral finite-difference method and the same longitudinal spectral method. The former method has the advantage of exponential convergence of the spectral method with smooth density distribution and can be used in the simulation where high precision of the solution is needed
Summary
The nonlinear space-charge effects play an important role in high intensity accelerators by driving beam instability, causing beam emittance growth, halo formation, and even particle loss. A key issue in the PIC simulation is to solve the Poisson equation subject to appropriate boundary conditions efficiently at each time step In some accelerators such as the Proton Synchrotron at CERN, the conducting pipe that contains a train of charged particle bunches has an elliptical transverse shape.
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