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One-dimensional self-consistent kinetic models as Vlasov equation solutions

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  02 October 2017

Helen Y. Barminova Open the ORCID record for Helen Y. Barminova [Opens in a new window]
Helen Y. Barminova*
Affiliation:
Plasma Physics Department, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, 115409, Russian Federation
*
†Email address for correspondence: [email protected]
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Abstract

One-dimensional self-consistent kinetic models may describe some states of intense charged particle beams. In the collisionless approximation, which is appropriate for the short current pulse duration, the kinetic distribution function may be built as a function of the motion integrals. Two situations are considered corresponding to the wide charged particle flux with the sharp front and to the sheet continuous beam freely propagating in space. In both cases, one-dimensional Vlasov equation solutions are shown to exist, which are based on algebraic functions of the motion invariants.

Keywords

intense particle beams
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 5 , October 2017 , 705830501
Copyright
© Cambridge University Press 2017 

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References

Barminova, E. E. & Chikhachev, A. S. 1991 Three-dimensional problem of emittance transformation of charged-particle bunches in nonuniform magnetic field. Radiophys. Quant. Electron. 34 (9), 818; 1991 Three-dimensional problem of emittance transformation of charged particle bunches in nonuniform magnetic field. Izvest. Vysh. Uchebn. Zaved. Radiofiz. 34 (9), 1041.CrossRefGoogle Scholar
Barminova, E. E. & Chikhachev, A. S. 1992 Non-stationary process of charged particle acceleration in a flat diode. Radiotekhn. Elektron. 37 (11), 2097.Google Scholar
Barminova, H. Y. 2014 On nonlinear dynamics of a sheet electron beam. Eur. Phys. J. D 68 (8), 221.Google Scholar
Barminova, H. Y. & Chikhachev, A. S. 2012 Nonstationary process of ion bunch acceleration in flat diode. Rev. Sci. Instrum. 83 (2), 02B505.CrossRefGoogle ScholarPubMed
Barminova, H. Y. & Chikhachev, A. S. 2013 Dynamics of a three-dimensional charged particle dense bunch. Phys. Rev. Spec. Top.-Accel. Beams 16 (5), 050402.Google Scholar
Bertrand, P., Albrecht-Marc, M., Reveille, T. & Ghizzo, A. 2005 Vlasov models for laser–plasma interaction. Transp. Theory Stat. Phys. 34, 103.CrossRefGoogle Scholar
Besse, N., Elskens, Y., Eskande, D. F. & Bertrand, P. 2011 Validity of quasilinear theory: refutations and numerical confirmations. Plasma Phys. Control. Fusion 53 (2), 025012.CrossRefGoogle Scholar
Chikhachev, A. S. 1984 Equilibrium relativistic electron beam in a magnetic quadrupole system. Sov. Phys. Tech. Phys. 29 (1), 57.Google Scholar
Courant, E. D. & Snyder, H. D. 1958 Theory of the alternating-gradient synchrotron. Ann. Phys. 3, 1.Google Scholar
Danilov, V., Cousieau, S., Henderson, S. & Holmes, J. 2003 Self-consistent time dependent two dimensional and three dimensional space charge distributions with linear force. Phys. Rev. Spec. Top.-Accel. Beams 6 (9), 74.Google Scholar
Feix, M. R. & Bertrand, P. 2005 A universal model: the Vlasov equation. Transp. Theory Stat. Phys. 34, 7.Google Scholar
Ghizzo, A. & Bertrand, P. 2013 On the multistream approach of relativistic Weibel instability. I. Linear analysis and specific illustrations. Phys. Plasmas 20, 082109.Google Scholar
Inglebert, A., Ghizzo, A., Reveille, T., Del Sarto, D., Bertrand, P. & Galifano, F. 2011 A multi-stream Vlasov modeling unifying relativistic Weibel-type instabilities. Eur. Phys. Lett. 95 (4), 45002.Google Scholar
Kapchinsky, I. M. & Vladimirsky, V. V. 1959 Limitations of proton beam current in a strong focusing linear accelerator associated with the beam space charge. In Proceedings of the Conference on High Energy Accelerators and Instrumentation, CERN, Geneva, p. 274.Google Scholar
Neuffer, D. 1979 Longitudinal motion in high current ion beams – a self-consistent phase space distribution with an envelope equation. IEEE Trans. Nucl. Sci. 26 (3), 3031.Google Scholar
Reiser, M. 2008 Theory and Design of Charged Particle Beams, 2nd edn. Wiley-VCH.Google Scholar
Yarkovoi, O. I. 1966 Nonstationary self-consistent model of charged particle azimuthal uniform ring in external electromagnetic field. Sov. Phys. Tech. Phys. 36 (6), 988.Google Scholar