Analytical approach to quasiperiodic beam Coulomb field modeling

Rubtsova, Irina

doi:10.1088/1742-6596/747/1/012074

Cited by 1 publication

(1 citation statement)

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“…The questions of electromagnetic fields modeling and simulation in different focusing and accelerating systems, and corresponding beam dynamics investigation and optimization, are widely discussed. Electromagnetic fields analytical representation is often used in scientific research, in particular, [Ovsyannikov, 2012;Ovsyannikov and Altsybeyev, 2013;Rubtsova, 2014a,b;Rubtsova, 2016a;Rubtsova and Ovsyannikov, 2018;Vinogradova, Starikova and Varayun ′ , 2017;Altsybeyev et al, 2018]. Analytical field description makes possible beam dynamics optimization theory developing on the basis of analytical methods, including trajectory ensemble control methods [Ovsyannikov, 1997;Ovsyannikov et al, 2006;Ovsyannikov, 2012;Ovsyannikov and Altsybeyev, 2013;Rubtsova and Suddenko, 2012;Rubtsova, 2016b;Rubtsova and Ovsyannikov, 2018;Balabanov, Mizintseva, Ovsyannikov, 2018;Nikolskii and Belyaevskikh, 2017;Nikolskii and Belyaevskikh, 2018].…”

Section: Introductionmentioning

confidence: 99%

Electrostatic potential calculation by application of walk-on-spheres method

Vladimirova¹,

Rubtsova²,

Edamenko³

2018

CAP

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The paper is devoted to mixed boundary-value problem solving for Laplace equation with the use of walk-on-spheres algorithm. The problem under study is reduced to finding a solution of integral equation with the kernel nonzero only at some sphere in the domain considered. Ulam-Neumann scheme is applied for integral equation solving; the appropriate Markov chain is introduced. The required solution value at a certain point of the domain is approximated by the expected value of special statistics defined on Markov paths. The algorithm presented guarantees the average Markov trajectory length to be finite and allows one to take into account boundary conditions on required solution derivative and to avoid Markov paths ending in the neighborhood of the boundaries where solution values are not given. The method is applied for calculation of electric potential in the injector of linear accelerator. The purpose of the work is to verify the applicability and effectiveness of walk-on-spheres method for mixed boundary-value problem solving with complicated boundary form and thus to demonstrate the suitability of Monte Carlo methods for electromagnetic fields simulation in beam forming systems. The numerical experiments performed confirm the simplicity and convenience of this method application for the problem considered.

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