TY - JOUR
T1 - A PIC method for solving a paraxial model of highly relativistic beams
AU - Assous, F.
AU - Tsipis, F.
PY - 2009/5/1
Y1 - 2009/5/1
N2 - Solving the Vlasov-Maxwell problem can lead to very expensive computations. To construct a simpler model, Laval et al. [G. Laval, S. Mas-Gallic, P.A. Raviart, Paraxial approximation of ultrarelativistic intense beams, Numer. Math. 69 (1) (1994) 33-60] proposed to exploit the paraxial property of the charged particle beams, i.e the property that the particles of the beam remain close to an optical axis. They so constructed a paraxial model and performed its mathematical analysis. In this paper, we investigate how their framework can be adapted to handle the axisymmetric geometry, and its coupling with the Vlasov equation. First, one constructs numerical schemes and error estimates results for this discretization are reported. Then, a Particle In Cell (PIC) method, in the case of highly relativistic beams is proposed. Finally, numerical results are given. In particular, numerical comparisons with the Vlasov-Poisson model illustrate the possibilities of this approach.
AB - Solving the Vlasov-Maxwell problem can lead to very expensive computations. To construct a simpler model, Laval et al. [G. Laval, S. Mas-Gallic, P.A. Raviart, Paraxial approximation of ultrarelativistic intense beams, Numer. Math. 69 (1) (1994) 33-60] proposed to exploit the paraxial property of the charged particle beams, i.e the property that the particles of the beam remain close to an optical axis. They so constructed a paraxial model and performed its mathematical analysis. In this paper, we investigate how their framework can be adapted to handle the axisymmetric geometry, and its coupling with the Vlasov equation. First, one constructs numerical schemes and error estimates results for this discretization are reported. Then, a Particle In Cell (PIC) method, in the case of highly relativistic beams is proposed. Finally, numerical results are given. In particular, numerical comparisons with the Vlasov-Poisson model illustrate the possibilities of this approach.
KW - Error estimates
KW - Numerical schemes
KW - Paraxial approximation
KW - Relativistic beams
KW - Vlasov-Maxwell
KW - Vlasov-Poisson
UR - http://www.scopus.com/inward/record.url?scp=61849157326&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2008.07.022
DO - 10.1016/j.cam.2008.07.022
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AN - SCOPUS:61849157326
SN - 0377-0427
VL - 227
SP - 136
EP - 146
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1
ER -