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3D solutions of the Poisson-Vlasov equations for a charged plasma and particle-core model in a line of FODO cells. (English) Zbl 1099.82520

Summary: We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribution obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances.

MSC:

82D10 Statistical mechanics of plasmas
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
65N06 Finite difference methods for boundary value problems involving PDEs
78A35 Motion of charged particles
78A30 Electro- and magnetostatics
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[1] I.M. Kapchinsky, V.V. Vladimirsky, Proceedings 1959 International Conference High Energy Accelerators (CERN, Geneva 1959), p. 274
[2] Theory of resonance linear accelerators (Harwood Academic Publishers, New York 1985)
[3] R.L. Gluckstern, Phys. Rev. Lett. 73, 1247 (1994) · doi:10.1103/PhysRevLett.73.1247
[4] R.L. Gluckstern, W.H. Cheng, H. Ye, Phys. Rev. Lett. 75, 2835 (1995) · doi:10.1103/PhysRevLett.75.2835
[5] R.L. Gluckstern, W.H. Cheng, S.S. Kurennoy, H. Ye, Phys. Rev. E 54, 6788 (1996) · doi:10.1103/PhysRevE.54.6788
[6] H. Okamoto, M. Ikegami, Phys. Rev. 55, 4694 (1997) · doi:10.1103/PhysRevB.55.6330
[7] A. Pisent, A. Bazzani, Y. Papaphilippou, M. Communian, G. Miano, V. Vaccaro, L. Verolino, G. Turchetti, Luneburg 1977, DESY Proceedings 1998-03 (1998), p. 195
[8] A. Bazzani, M. Communian, A. Pisent, Part. Accel. 63, 79 (1999)
[9] M. Lagniel, Nucl. Instr. Meth. A 345, 405 (1994) · doi:10.1016/0168-9002(94)90490-1
[10] F. Bergamini, Non-linear effects in high intensity beams (Phys. Dep. of Bologna University, thesis 2000), unpublished
[11] G. Turchetti, A. Bazzani, F. Bergamini, S. Rambaldi, I. Hofmann, L. Bongini, G. Francheti, Nucl. Instr. Meth. 464, 551 (2001) · doi:10.1016/S0168-9002(01)00140-1
[12] K.C. Birsdall, A.B. Langdon, Plasma physics via computer simulation (McGraw Hill, New York 1985)
[13] A. Friedman, D.P. Grote, I. Haber, Phys. Fluids B 4, 2203 (1992) · doi:10.1063/1.860024
[14] R.L. Gluckstern, A.V. Fedotov, S. Kurennoy, R. Ryne, Phys. Rev. 58, 4977 (1998) · doi:10.1103/PhysRevB.58.4977
[15] D. Neuffer, IEEE Trans. Nucl. Sci. NS 26, 3031 (1979) · doi:10.1109/TNS.1979.4329929
[16] M. Communian, A. Pisent, A. Bazzani, G. Turchetti, S. Rambaldi, Physical Review Special Topics – Accelerators and Beams 4, 124201 (2001) · doi:10.1103/PhysRevSTAB.4.124201
[17] M. Reiser, Theory and design of charged particles beams (Wiley, New York 1994)
[18] R.L. Gluckstern, Proceedings of the Linac Conference, Fermilab, Batavia (1970), p. 811
[19] I. Hofmann, Phys. Rev. E 57, 4713 (1998) · doi:10.1103/PhysRevE.57.4713
[20] J. Struckmeier, Phys. Rev. E 54, 830 (1996) · doi:10.1103/PhysRevE.54.830
[21] R. Davidson, Phys. Rev. Lett. 81, 991 (1998) · doi:10.1103/PhysRevLett.81.991
[22] http://trasco.lnl.infn.it
[23] R.W. Hockney, J.W. Eastwood, Computer simulation using particles (Adam-Hilger, Bristol 1988) · Zbl 0662.76002
[24] A. Franchi, S. Rambaldi, G. Turchetti, HALODYN: documentation and users manual available from franchi@gsi.de
[25] G. Franchetti, I. Hofmann, G. Turchetti, Luneburg 1997, DESY Proceedings 1998-03 (1998) p. 183
[26] F. Bergamini, G. Franchetti, G. Turchetti, Il Nuovo Cimento A 112, 429 (1999) · doi:10.1007/BF03035854
[27] G. Kellog, Foundations of potential theory (Dover Publications, New York 1953)
[28] C. Agostinelli, Istituzioni di Fisica Matematica (Zanichelli, Bologna 1960)
[29] Bartolini, A. Bazzani, M. Giovannozzi, W. Scandale, E. Todesco, Part. Accel. 52, 147 (1996)
[30] J. Laskar, Physica D 67, 257 (1993) · Zbl 0783.58027 · doi:10.1016/0167-2789(93)90210-R
[31] C.R. Prior, Simulation with space charge Workshop in Space Charge Physics in High Intensity Hadron Rings, New York, 1998, edited by A.U. Luccio, W.T. Weng, AIP Proceedings 448, 85 (1998) · doi:10.1063/1.56783
[32] A. Friedman, D.P. Grote, D.A. Callaham, A.B. Langdon, I. Haber, Part. Accel. 37, 131 (1992)
[33] A. Franchi, private communication
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