Three-dimensional simulation of ultrarelativistic charged beams dynamics: study of initial and boundary conditions

V. A. Vshivkov ; M. A. Boronina

Matematičeskoe modelirovanie, Tome 24 (2012) no. 2, pp. 67-83.

Résumé

We consider problems of initial and boundary conditions in the mathematical modeling of full three-dimensional charged beam dynamics applicable to colliders of new generation. In this case high values of relativistic factors ($10^3$–$10^6$) lead to high gradients of electromagnetic fields, requiring special attention to the computation of initial and boundary conditions. We present new methods for the computation of initial and boundary conditions, their analysis and comparison with standard methods. The algorithms presented are also applicable to other problems addressed by the particle-in-cell-method with high relativistic factors.

Détail

Keywords: particle-in-cell method, ultrarelativism, numerical simulation, charged particle beams, Maxwell equations, beam beam effects, electromagnetic fields.
Mots-clés : Vlasov equation

Bibliographie

[1] Raimondi P., “Towards Higher Luminosities in B and Phi Factories”, Proceedings of EPAC 2004, 2004, 286–289

[2] Seeman J., Cai Y., Ecklund S., et al., Parameters Of A Super-B-Factory Design, SLAC-PUB-11726, 2005

[3] Yokoya K., ILC Conceptual Design and R D Status, Talk on the 8th ICFA Seminar on “Future Perspectives in High Energy Physics”, Daegu, Korea, 2005

[4] Schulte D., Study of Electromagnetic and Hadronic Background in the Interaction Region of the Tesla Collider, Tesla Reports, Hamburg, 1996 (v. 97-08)

[5] Le Meur G., Touze F., Alabau M., Bambade Ph., Dadoun O., Rimbault C., Schulte D., Development and improvement of the Guinea-Pig beam-beam simulation, European LC Workshop, Daresbury, 2007

[6] Anderson E.B., Banks T I., Rogers J.T., ODYSSEUS: A Dynamic Strong-Strong Beam-Beam Simulation for Storage Rings, International Computational Accelerator Physics Conference, 1998

[7] Furman Miguel A., Beam-Beam Simulations with the Gaussian Code TRS, SLAC-AP 119, LBNL 42669/CBP, CBP 272, 1999

[8] Bassetti M., Erskine G., Closed Expression for the Electric Field of a Two-Dimensional Gaussian Charge, CERNISR-ISR-TH/80-06, 1980

[9] Krishnagopal S., “Luminosity-Limiting Coherent Phenomena in Electron-Positron Colliders”, Physical Review Letters, 76:2 (1996), 235–238 | DOI

[10] Krishnagopal S., Furman M.A., Turner W.C., “Studies of the beam-beam interaction for the LHC”, Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

[11] Raimondi P., “Crabbed Waist Collisions in DAFNE and Super-B Design”, Proceedings of EPAC08, Genoa, Italy, WEXG02, 2008, 1898–1902

[12] Boronina M.A., Vshivkov V.A., Levichev E.B., Nikitin S.A., Snytnikov V.N., “Algoritm dlya trekhmernogo modelirovaniya ultrarelyativistskikh puchkov”, Vychislitelnye metody i programmirovanie, 8:2 (2007), 203–210 | Zbl

[13] Boronina M.A., Vshivkov V.A., Levichev E.B., Nikitin S.A., Simonov E.A., Snytnikov V.N., “3D-kod dlya modelirovaniya ultrarelyativistskikh puchkov”, Vychislitelnye tekhnologii, 14:5 (2009), 18–30 | MR

[14] Boronina Marina, Vshivkov Vitaly, Levichev Evgeny, Nikitin Sergei, Snytnikov Valery, “3D PIC Method Development for Simulation of Beam-Beam Effects in Supercolliders”, Proceedings of Particle Accelerator Physics 2007, Albuquerque, New Mexico, USA, 3366–3368

[15] Boronina M.A., Snytnikov V.N. and Vshivkov V.A., “3D Beam-Beam Effects Simulation Algorithm”, 5th European Congress on Computational Methods in Applied Sciences and Engineering, Venice, Italy, 2008

[16] Khokni R., Istvud Dzh., Chislennoe modelirovanie metodom chastits, Mir, M., 1962

[17] Berezin Yu.A., Vshivkov V.A., Metod chastits v dinamike razrezhennoi plazmy, Nauka. Sib. otdelenie, Novosibirsk, 1980

[18] Zholents A.A., Beam-beam effects in electron-positron storage rings, Preprint IYaF SO AN SSSR, 1991 (91-18)

[19] Villansenor J., Buneman O., “Rigorous Charge Conservation for Local Electromagnetic Field Solvers”, Computer Physics Communications, 69 (1992), 306–316 | DOI