Three-dimensional poisson solver for a charged beam with large aspect ratio in a conducting pipe

Journal Article · Thu Jan 08 00:00:00 EST 2004 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2004.03.002· OSTI ID:837240

Qiang, Ji; Gluckstern, Robert L

In this paper, we present a three-dimensional Poisson equation solver for the electrostatic potential of a charged beam with large longitudinal to transverse aspect ratio in a straight and a bent conducting pipe with open-end boundary conditions. In this solver, we have used a Hermite-Gaussian series to represent the longitudinal spatial dependence of the charge density and the electric potential. Using the Hermite-Gaussian approximation, the original three-dimensional Poisson equation has been reduced into a group of coupled two-dimensional partial differential equations with the coupling strength proportional to the inverse square of the longitudinal-to-transverse aspect ratio. For a large aspect ratio, the coupling is weak. These two-dimensional partial differential equations can be solved independently using an iterative approach. The iterations converge quickly due to the large aspect ration of the beam. For a transverse round conducting pipe, the two-dimensional Poisson equation is solved using a Bessel function approximation and a Fourier function approximation. The three-dimensional Poisson solver can have important applications in the study of the space-charge effects in the high intensity proton storage ring accelerator or induction linear accelerator for heavy ion fusion where the ration of bunch length to the transverse size is large.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Director. Office of Science. Office of High Energy and Nuclear Physics. Division of High Energy Physics, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing Project (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 837240
• Report Number(s): LBNL-54282; R&D Project: 453401; TRN: US0500936
• Journal Information: Computer Physics Communications, Vol. 160, Issue 2; Other Information: Submitted to Computer Physics Communications: Volume 160, No.2; Journal Publication Date: 07/01/2004; PBD: 8 Jan 2004
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ACCELERATORS
ASPECT RATIO
BESSEL FUNCTIONS
BOUNDARY CONDITIONS
CHARGE DENSITY
ELECTRIC POTENTIAL
ELECTROSTATICS
HEAVY IONS
INDUCTION
LINEAR ACCELERATORS
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
PROTONS
SPACE CHARGE
SPACE DEPENDENCE
STORAGE RINGS
POISSON SOLVER HERMITE-GAUSSIAN APPROXIMATION LARGE ASPECT RATIO OPEN BOUNDARY CONDITIONS