# Abstracts

## XX International Linac Conference

## MOA20 (Poster)

**Presenter: **Ji Qiang (LANL)

** email: **ryne@lanl.gov

**Status: **Complete

**FullText: **
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**Eprint:** physics/0008196
# A Second Order Stochastic Leap-Frog Algorithm for
Langevin Simulation

Ji Qiang, Salman Habib (LANL)

Langevin simulation provides an effective way to study collisional
effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of
stochastic ordinary differential equations. These resulting equations usually have
multiplicative noise since the diffusion coefficients in these equations are
functions of position and time. Conventional algorithms, e.g. Euler and Heun, give
only first order convergence of moments in a finite time interval. In this paper, a
stochastic leap-frog algorithm for the numerical integration of Langevin stochastic
differential equations with multiplicative noise is proposed and tested. The
algorithm has a second-order convergence of moments in a finite time interval and
requires the sampling of only one uniformly distributed random variable per time
step. The noise may be white or colored. As an application, we apply the new
algorithm to the study of intrabeam scattering in high intensity beams.

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