Abstract
The numerical noise inherent to particle-in-cell (PIC) simulation of 3d anisotropic high intensity bunched beams in periodic focusing is compared with the analytical model by Struckmeier [Part. Accel. 45, 229 (1994)]. The latter assumes that entropy growth can be related to Markov type stochastic processes due to temperature anisotropy and the artificial “collisions” caused by using macro-particles and calculating the space charge effect. The PIC simulations are carried out with the tracewin code widely used for high intensity beam simulation. The resulting noise can lead to growth of the six-dimensional rms emittance. The logarithm of the latter is shown to qualify as rms-based entropy. We confirm the dependence of this growth on the bunch temperature anisotropy as predicted by Struckmeier. However, we also find a grid and focusing dependent component of noise not predicted by Struckmeier. Although commonalities exist with well-established models for collision effects in PIC-simulation of extended plasmas, a distinctive feature is the presence of a periodic focusing potential, wherein the beam one-component plasma extends only over relatively few Debye lengths. Our findings are applied in particular to noise in high current linac beam simulation, where they help for optimization of the balance between the number of simulation particles and the grid resolution.6 MoreReceived 15 July 2014DOI:https://doi.org/10.1103/PhysRevSTAB.17.124201This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society
Highlights
In modeling of high intensity beams by particle-in-cell (PIC) computer simulation it is of importance to understand whether any observed emittance growth or beam loss is caused by real physical processes, or by nonphysical processes like numerical discretization and grid effects from the Poisson solver, which can be seen as pseudocollisions with the grid charge distribution
Our emphasis is on the numerical noise generated by the discreteness of the spatial grid used for the Poisson solver, collision effects between simulation super-particles and the presence of a periodic focusing potential
We have explored space charge and grid induced noise in 3d PIC simulation with the TRACEWIN code, and compared results with the analytical rms entropy growth equation by Struckmeier based on a purely collisional approach
Summary
In modeling of high intensity beams by particle-in-cell (PIC) computer simulation it is of importance to understand whether any observed emittance growth or beam loss is caused by real physical processes, or by nonphysical processes like numerical discretization and grid effects from the Poisson solver, which can be seen as pseudocollisions with the grid charge distribution. Significantly different, if grid heating effects play a role It is one of the challenges of high intensity beam simulation to be able to distinguish between physical and numerical growth effects. A significant step ahead in this direction has been the noise and entropy growth model by Struckmeier [5,6,7], which provides a useful theoretical framework based on second order moments of the Vlasov-Fokker-Planck equation. In a forthcoming companion paper to the present study by Boine-Frankenheim et al [13] the collision and noise effects in 2d isotropic beams with space charge and their connection with entropy and noise, on the basis of Struckmeier’s equations, has been given detailed consideration
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