Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T07:19:36.072Z Has data issue: false hasContentIssue false
  • English
  • Français

Theory and simulation of heavy ion stopping in plasma

Published online by Cambridge University Press:  19 June 2009

Günter Zwicknagel
Günter Zwicknagel*
Affiliation:
Institut für Theoretische Physik, Department Physik, Universität Erlangen-Nürnberg, Erlangen, Germany
*
Address correspondence and reprint requests to: G. Zwicknagel, Institut für Theoretische Physik, Department Physik, Universität Erlangen-Nürnberg, Staudtstrasse 7, D-91058 Erlangen, Germany E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The theoretical description of the energy loss of heavy ions in fully ionized matter is considered, where we focus on the many–body and plasma physics aspects of the stopping of point like projectiles with a fixed charge by free electrons, disregarding the atomic physics of the projectile and the target ions. This starts by identifying different coupling regimes for a heavy ion which passes through an electron plasma, and continues with a discussion of the available and appropriate analytical and numerical treatments of the energy loss and their applicability in these various regimes. Special attention is given to a nonlinear coupling regime with significant strong coupling effects on the projectile-target energy transfer where standard perturbative approaches cease to be valid. More advanced theoretical treatments, which are required for this regime, are presented, discussed and evaluated by comparison with simulation results.

Keywords

Energy lossNonideal plasmaNonlinear couplingParticle simulationsStopping power
Type
Research Article
Information
Laser and Particle Beams , Volume 27 , Issue 3 , September 2009 , pp. 399 - 413
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arista, N.R. & Brandt, W. (1984). Dielectric response of quantum plasmas in thermal equilibrium. Phys. Rev. A 29, 1471–1480.CrossRefGoogle Scholar
Barkas, W.H., Dyer, J.N. & Heckman, H.H. (1963). Resolution of the Σ−-Mass Anomaly. Phys. Rev. Lett 11, 26–28.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. (2008). Mermin dielectric function versus local field corrections on proton stopping in degenerate plasmas. Laser Part. Beams 26, 389–395.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. & Potekhin, A.Y. (2006). Proton stopping in plasmas considering e −-e − collisions. Laser Part. Beams 24, 553–558.CrossRefGoogle Scholar
Bethe, H. (1930). Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie. Ann. Physik 5, 325–400.CrossRefGoogle Scholar
Bloch, F. (1933). Zur Bremsung rasch bewegter Teilchen beim Durchgang durch Materie. Ann. Physik 16, 285–320.CrossRefGoogle Scholar
Bohr, N. (1913). Phil. Mag. 25, 10; (1915). Phil. Mag. 30, 581.CrossRefGoogle Scholar
Bohr, N. (1948). The penetration of atomic particles through matter. Kgl. Dan. Vidensk. Selsk. Mat. Fys. Medd. 18, 1–144.Google Scholar
Deutsch, C., Fromy, P. & Zwicknagel, G. (1996). Correlated ion stopping in a classical dense plasma. Laser Part. Beams 14, 699–712.CrossRefGoogle Scholar
Deutsch, C. & Popoff, R. (2006). Low velocity ion stopping of relevance to the US beam-target program. Laser Part. Beams 24, 421–425.CrossRefGoogle Scholar
Eisenbarth, S., Rosmej, O.N., Shevelko, V.P., Blazevic, A. & Hoffmann, D.H.H. (2007). Numerical simulations of the projectile ion charge difference in solid and gaseous stopping matter. Laser Part. Beams 25, 601–611.CrossRefGoogle Scholar
Gericke, D.O., Schlanges, M. & Kraeft, W.D. (1997). T-matrix approximation of the stopping power. Laser Part. Beams 15, 523–531.CrossRefGoogle Scholar
Gericke, D.O. & Schlanges, M. (1999). Beam-plasma coupling effects on the stopping power of dense plasmas. Phys. Rev. E 60, 904–910.CrossRefGoogle ScholarPubMed
Goldstein, H. (1980). Classical Mechanics. New York: Addison Wesley Pub.Co.Google Scholar
Gouedard, C. & Deutsch, C. (1978). Dense electron-gas response at any degeneracy. J. Math. Phys. 19, 32–38.CrossRefGoogle Scholar
Gould, H.A. & DeWitt, H.E. (1967). Convergent kinetic equation for a classical plasma. Phys. Rev. 155, 68–74.CrossRefGoogle Scholar
GSI (2007). Facility for antiproton and ion research. http://www.gsi.de/fair/.Google Scholar
Hahn, H.-S., Mason, E.A. & Smith, F.J. (1971). Quantum transport cross sections for ionized gases. Phys. Fluids 14, 278–287.CrossRefGoogle Scholar
Hoffmann, D.H.H., Blazevic, A., Ni, P., Rosmej, O., Roth, M., Tahir, N.A., Tauschwitz, A., Udrea, S., Varentsov, D., Weyrich, K. & Maron, Y. (2005). Present and future perspectives for high energy density physics with intense heavy ion and laser beams. Laser Part. Beams 23, 47–53.CrossRefGoogle Scholar
Jacoby, J., Hoffmann, D.H.H., Laux, W., Müller, R.W., Wahl, H., Weyrich, K., Boggasch, E., Heimrich, B., Stöckl, C., Wetzler, H. & Miyamoto, S. (1995). Stopping of heavy ions in a hydrogen plasma. Phys. Rev. Lett. 74, 1550–1553.CrossRefGoogle Scholar
Jacoby, J., Bickes, C., Flierl, H.-P., Hoffmann, D.H.H., Dornik, M., Weyrich, K., Stöckl, C. & Wetzler, H. (1996). Interaction of heavy ions with plasmas. Nucl. Instr. Meth. Phys. Res. B 115, 7–13.CrossRefGoogle Scholar
Koresheva, E.R., Aleksandrova, I.V., Koshelev, E.L., Nikitenko, A.I., Timasheva, T.P., Tolokonnikov, S.M., Belolipetskiy, A.A., Kapralov, V.G., Sergeev, V.Yu., Blazevic, A., Weyrich, K., Varentsov, D., Tahir, N.A., Udrea, S. & Hoffmann, D.H.H. (2009). A study on fabrication, manipulation and survival of cryogenic targets required for the experiments at the Facility for Antiproton and Ion Research: FAIR. Laser Part. Beams 27, 255–272.CrossRefGoogle Scholar
Lindhard, J. (1954). On the properties of a gas of charged particles. K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 28, 1–58.Google Scholar
Mahan, G.D. (1990). Many Particle Physics. New York: Plenum Press.CrossRefGoogle Scholar
Maynard, G. & Deutsch, C. (1985). Born random phase approximation for ion stopping in an arbitrarily degenerate electron fluid. J. Physique 46, 1113–1122.CrossRefGoogle Scholar
Maynard, G., Katsonis, K., Zwicknagel, G., Mabong, S., Chabot, M., Gardes, D. & Kurilenkov, Yu.K. (1998). Nonlinear effects in stopping of partially ionized swift heavy ions. Nucl. Instr. Meth. A 415, 687–692.CrossRefGoogle Scholar
Maynard, G., Katsonis, K., Deutsch, C., Zwicknagel, G., Chabot, M. & Gardes, D. (2001 b). Modeling of swift heavy ions interaction with dense matter. Nucl. Instr. Meth. Phys. Res. A 464, 86–92.CrossRefGoogle Scholar
Maynard, G., Zwicknagel, G., Deutsch, C. & Katsonis, K. (2001 a). Diffusion transport cross section and stopping power of swift heavy ions. Phys. Rev. A 63, 052903/1–14.CrossRefGoogle Scholar
Möller, S.P., Uggerhój, E.H., Bluhme, H., Knudsen, H., Mikkelsen, U., Paludan, K. & Morenzoni, E. (1997). Direct measurements of the stopping power for antiprotons of light and heavy targets. Phys. Rev. A 56, 2930–2939.CrossRefGoogle Scholar
Nardi, E., Maron, Y. & Hoffmann, D.H.H. (2009). Dynamic screening and charge state of fast ions in plasma and solids. Laser Part. Beams 27, 355–361.CrossRefGoogle Scholar
Nersisyan, H., Toepffer, C. & Zwicknagel, G. (2007). Interactions Between Charged Particles in a Magnetic Field. Berlin: Springer.Google Scholar
Patil, S.H. (1981). Analytic scattering length for potential scattering. Phys. Rev. A 24, 3038–3043.CrossRefGoogle Scholar
Peter, T. & Meyer-ter-Vehn, J. (1991). Energy loss of heavy ions in dense plasma: I. Linear and nonlinear Vlasov theory for the stopping power. Phys. Rev. A 43, 1998–2014.CrossRefGoogle ScholarPubMed
Poth, H. (1990). Electron cooling: Theory, experiment, application. Phys. Rep. 196, 135–297.CrossRefGoogle Scholar
Redmer, R. (1997). Physical properties of dense, low-temperature plasmas. Phys. Rep. 282, 35–157.CrossRefGoogle Scholar
Rogers, F.J. (1971). Phase shifts of the static screened Coulomb potential. Phys. Rev. A 4, 1145–1155.CrossRefGoogle Scholar
Schlanges, M., Gericke, D.O., Kraeft, W.D. & Bornath, Th. (1998). Stopping power of nonideal quantum plasmas. Nucl. Inst Meth. A 415, 517–524.CrossRefGoogle Scholar
Seele, C., Zwicknagel, G., Toepffer, C. & Reinhard, P.-G. (1998). Time-dependent stopping power and influence of an infinite magnetic field. Phys. Rev. E 57, 3368–3378.CrossRefGoogle Scholar
Tahir, N.A., Udrea, S., Deutsch, C., Fortov, V.E., Grandjouan, N.Gryaznov, V., Hoffmann, D.H.H., H’ulsmann, P., Kirk, M., Lomonsov, I.V., Piriz, A.R., Shutov, A., Spiller, P., Temporal, M. & Varentsov, D. (2004). Target heating in high-energy-density matter experiments at the proposed GSI FAIR facility: Non-linear bunch rotation in SIS100 and optimization of spot size and pulse length. Laser Part. Beams 22, 485–493.CrossRefGoogle Scholar
Williams, R.H. & DeWitt, H.E. (1969). Quantum-mechanical plasma transport theory. Phys. Fluids 12, 2326–2342.CrossRefGoogle Scholar
Winkler, T., Beckert, K., Bosch, F., Eickhoff, H., Franzke, B., Klepper, O., Nolden, F., Reich, H., Schlitt, B., Spädtke, P. & Steck, M. (1996). Electron cooling force measurements for highly charged ions in the ESR. Hyp. Int. 99, 277–283.CrossRefGoogle Scholar
Winkler, T., Beckert, K., Bosch, F., Eickhoff, H., Franzke, B., Nolden, F., Reich, H., Schlitt, B. & Steck, M. (1997). Electron cooling forces for highly charged ions in the ESR. Nucl. Instr. Meth Phys. Res. A 391, 12–16.CrossRefGoogle Scholar
Wolf, A., Ellert, C., Grieser, M., Habs, D., Hochadel, B., Repnow, R. & Schwalm, D. (1994). Charge dependence of the electron cooling force for heavy ions. Beam Cooling and Related Topics, pp. 416–421, CERN 94–03, Genf: J. Bosser.Google Scholar
Zwicknagel, G., Toepffer, C. & Reinhard, P.-G. (1995). Stopping power of heavy ions in strongly coupled plasmas. Laser Part. Beams 13, 311–319.CrossRefGoogle Scholar
Zwicknagel, G. & Deutsch, C. (1996). Basic features of correlated ion stopping in plasmas. Laser Part. Beams 14, 749–763.CrossRefGoogle Scholar
Zwicknagel, G. & Deutsch, C. (1997). Correlated ion stopping in plasmas. Phys.Rev. E 56, 970–987.CrossRefGoogle Scholar
Zwicknagel, G., Toepffer, C. & Reinhard, P.-G. (1999). Stopping of heavy ions in plasmas at strong coupling. Phys. Rep. 309, 117–208. Erratum: (1999) Phys.Rep. 314, 671.CrossRefGoogle Scholar
Zwicknagel, G. (2000). Theory and Simulation of the Interaction of Ions with Plasmas, Thesis, Universität Erlangen, http://www.opus.ub.uni-erlangen.de/opus/volltexte/2008/913/.Google Scholar
Zwicknagel, G. (2002). Nonlinear energy loss of heavy ions in plasma. Nucl. Instr. Meth Phys. Res. B 197, 22–38.CrossRefGoogle Scholar
Zwicknagel, G. (2006). Electron cooling of highly charged ions in Penning traps. Non-neutral Plasma Physics VI, AIP Conference Proceedings 862, 281–291.CrossRefGoogle Scholar