Skip to main content Accessibility help

Dynamic screening and charge state of fast ions in plasma and solids

  • E. Nardi (a1), Y. Maron (a1) and D.H.H. Hoffmann (a2)


This paper addresses the effect of target plasma electrons on the charge state of energetic ions, penetrating a target composed of bound as well as plasma electrons. Dynamic screening of the projectile Coulomb potential by the plasma electrons brings about a depression in the ionization energy of the ionic projectiles, as has been verified experimentally. This in turn makes the ionization cross-sections larger, while making the recombination cross-section smaller, thereby causing an increase in the ion charge state compared to the case of a gas target. The effect of the plasma environment, where the valence electrons are treated as plasma, is illustrated here for a 2 MeV carbon beam penetrating amorphous carbon targets of varying densities.


Corresponding author

Address correspondence and reprint requests to: E. Nardi, Weizmann Institute of Science, Faculty of Physics, Rehovot, Israel. E-mail:


Hide All
Andersen, J.U., Gruner, F., Ryabov, V.A. & Uguzzoni, A. (2002). On transverse cooling of channeled ions by electron capture and loss. Nucl. Instr. & Meth. Phys. Res. B 193, 118127.
Barriga-Carrasco, M.D. (2008). Mermin dielectric function versus local field corrections on proton stopping in degenerate plasmas. Laser Part. Beams 26, 389395.
Betz, H.D. & Grodzins, L. (1970). Charge states and excitation of fast heavy ions passing through solids: A new model for density effect. Phys. Rev. Lett. 25, 211.
Betz, H.D. (1983). Applied Atomic Collision Physics. New York: Academic Press.
Bohr, N. & Lindhard, J. (1954). Electron capture and loss by heavy ions penetrating through matter. Mat. Fys. Medd. Dan. Vid. Selsk. 28, 131.
Brandt, W. (1975). Atomic Collisions in Solids. New York: Plenum.
Chevallier, M., Clouvas, A., Faria, N.V.D., Mazuy, B.F., Gaillard, M.J., Poizat, J.C., Remillieux, J. & Desesquelles, J. (1990). Evidence for a velocity threshold for the binding of the 3p state of fast He+ ions inside solids. Phys. Rev. A 41, 17381740.
Cook, R.C., Kozioziemski, B.J., Nikroo, A., Wilkens, H.L., Bhandarkar, S., Forsman, A.C., Haan, S.W., Hoppe, M.L., Huang, H., Mapoles, E., Moody, J.D., Sater, J.D., Seugling, R.M., Stephens, R.B., Takagi, M. & Xu, H.W. (2008). National Ignition Facility target design and fabrication. Laser Part. Beams 26, 479487.
Deutsch, C., Maynard, G., Bimbot, R., Gardes, D., Dellanegra, S., Dumail, M., Kubica, B., Richard, A., Rivet, M.F., Servajean, A., Fleurier, C., Sanba, A., Hoffmann, D.H.H., Weyrich, K. & Wahl, H. (1989). Ion beam-plasma interaction: A standard model approach. Nucl. Instr. & Meth. Phys. Res. A 278, 3843.
Dietrich, K.G., Hoffmann, D.H.H., Boggasch, E., Jacoby, J., Wahl, H., Elfers, M., Haas, C.R., Dubenkov, V.P. & Golubev, A.A. (1992). Charge state of fast heavy-ions in a hydrogen plasma. Phys. Rev. Lett. 69, 3623–366.
Ebeling, W., Kraeft, W.D. & Kremp, D. (1976). Theory of bound states and ionization equilibrium in plasmas and solids. In Ergebnisse der Plasmaphysik und der Gaselektronik, Band 5. Berlin: Akademie-Verlag.
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, 601611.
Eliezer, S., Murakami, M. & Val, J.M.M. (2007). Equation of state and optimum compression in inertial fusion energy. Laser Part. Beams 25, 585592.
Evans, R.G. (2008). Ion heating due to ionization and recombination. Laser Part. Beams 26, 3740.
Flippo, K., Hegelich, B.M., Albright, B.J., Yin, L., Gautier, D.C., Letzring, S., Schollmeier, M., Schreiber, J., Schulze, R. & Fernandez, J.C. (2007). Laser-driven ion accelerators: Spectral control, monoenergetic ions and new acceleration mechanisms. Laser Part. Beams 25, 38.
Gardes, D., Bimbot, R., Dellanegra, S., Dumail, M., Kubica, B., Richard, A., Rivet, M.F., Servajean, A., Fleurier, C., Sanba, A., Deutsch, C., Maynard, G., Hoffmann, D.H.H., Weyrich, K. & Wahl, H. (1988). Investigation of the transmission and stopping of light-ions passing through a plasma target. J. Phys. 49, 151157.
Gryzinski, M. (1965). Classical theory of atomic collisions. I. Theory of inelastic collisions. Phys. Rev. 138, A336A358.
Hoffmann, D.H.H., Jacoby, J., Laux, W., Demagistris, M., Boggasch, E., Spiller, P., Stockl, C., Tauschwitz, A., Weyrich, K., Chabot, M. & Gardes, D. (1994). Energy-loss of fast heavy-ions in plasmas. Nucl. Instr. & Meth. Phys. Res. B 90, 19.
Hoffmann, D.H.H., Weyrich, K., Wahl, H., Gardes, D., Bimbot, R. & Fleurier, C. (1990). Energy-loss of heavy-ions in a plasma target. Phys. Rev. A 42, 23132321.
Hora, H. (2007). New aspects for fusion energy using inertial confinement. Laser Part. Beams 25, 3745.
Jakubassa, D.H. (1977). Dynamic screening of ions passing through solids. J. Phys. C 10, 44914497.
Kojima, M., Mitomo, M., Sasaki, T., Hasegawa, J. & Ogawa, M. (2002). Charge-state distribution and energy loss of 3.2-MeV oxygen ions in laser plasma produced from solid hydrogen. Proc. 14th International Heavy Ion Inertial Fusion Symposium. Moscow, Russia.
Kraeft, W.D., Kremp, D., Ebeling, W. & Ropke, G. (1986). Quantum Statistics of Charged Particle Systems. New York: Plenum Press.
Kremp, D., Schlanges, M. & Kraeft, W.D. (2005). Quantum Statistics of Nonideal Plasmas. Berlin: Springer.
Lifschitz, A.F. & Arista, N.R. (2004). Effective charge and the mean charge of swift ions in solids. Phys. Rev. A 69, 012902/15.
Lifschitz, A.F. & Arista, N.R. (1998). Velocity-dependent screening in metals. Phys. Rev. A 57, 200207.
Lindhard, J. (1954). On the properties of a gas of charged particles. Mat. Fys. Medd. Dan. Vid. Selsk. 8, 157.
Maynard, G., Chabot, M. & Gardes, D. (2000). Density effect and charge dependent stopping theories for heavy ions in the intermediate velocity regime. Nucl. Instr. & Meth. Phys. Res. B 164, 139146.
Meister, C.-V. (1982). On the theory of conductivity and thermodynamics of nonideal plasmas. PhD. Thesis. Rostock: University Rostock.
Muller, J. & Burgdorfer, J. (1991). Dynamic thresholds for the existence of excited electronic states of fast ions in solids. Phys. Rev. A 43, 60276031.
Nagy, J. & Bergara, A. (1996). A model for the velocity-dependent screening. Nucl. Instr. & Meth. B 115, 5861.
Nardi, E. & Tombrello, T.A. (2006). Charge state of C-10 and C-5 energetic cluster ions in amorphous carbon targets: Simulations. J. Phys.-Conden. Mat. 18, 1135711370.
Nardi, E. & Zinamon, Z. (1982). Charge state and slowing of fast ions in a plasma. Phys. Rev. Lett. 49, 12511254.
Nardi, E., Fisher, D.V., Roth, M., Blazevic, A. & Hoffmann, D.H.H. (2006). Charge state of Zn projectile ions in partially ionized plasma: Simulations. Laser Part. Beams 24, 131141.
Nardi, E., Maron, Y. & Hoffmann, D.H.H. (2007). Plasma diagnostics by means of the scattering of electrons and proton beams. Laser Part. Beams 25, 489495.
Ogawa, M., Neuner, U., Kobayashi, H., Nakajima, Y., Nishigori, K., Takayama, K., Iwase, O., Yoshida, M., Kojima, M., Hasegawa, J., Oguri, Y., Horioka, K., Nakajima, M., Miyamoto, S., Dubenkov, V. & Murakami, T. (2000). Measurement of stopping power of 240 MeV argon ions in partially ionized helium discharge plasma. Laser Part. Beams 18, 647653.
Paul, H. (2004). A note on the density effect in the stopping power of positive ions. Nucl. Instr. & Meth. B 217, 711.
Perumal, A, Horvat, V, Watson, RL, Peng, Y & Fruchey, KS (2005). Cross sections for charge change in argon and equilibrium charge states of 3.5 MeV/amu uranium ions passing through argon and carbon targets. Nucl. Instr. & Meth. B 227, 251260.
Richard, P. (1985). Ion-atom collisions. In Atomic Inner Shell Processes I. New York: Academic.
Rogers, F.J., Graboske, H.C. & Harwood, D.J. (1970). Bound eigenstates of static screened coulomb potential. Phys. Rev. A 1, 15771583.
Romagnani, L., Borghesi, M., Cecchetti, C.A., Kar, S., Antici, P., Audebert, P., Bandhoupadjay, S., Ceccherini, F., Cowan, T., Fuchs, J., Galimberti, M., Gizzi, L.A., Grismayer, T., Heathcote, R., Jung, R., Liseykina, T.V., Macchi, A., Mora, P., Neely, D., Notley, M., Osterholtz, J., Pipahl, C.A., Pretzler, G., Schiavi, A., Schurtz, G., Toncian, T., Wilson, P.A. & Will, O. (2008). Proton probing measurement of electric and magnetic fields generated by ns and ps laser-matter interactions. Laser Part. Beams 26, 241248.
Rosmej, O.N., Pikuz, S.A., Korostiy, S., Blazevic, A., Brambrink, E., Fertman, A., Mutin, T., Efremov, V.P., Pikuz, T.A., Faenov, A.Y., Loboda, P., Golubev, A.A. & Hoffmann, D.H.H. (2005). Radiation dynamics of fast heavy ions interacting with matter. Laser Part Beams 23, 7985.
Roth, M., Stockl, C., Suss, W., Iwase, O., Gericke, D.O., Bock, R., Hoffmann, D.H.H., Geissel, M. & Seelig, W. (2000). Energy loss of heavy ions in laser-produced plasmas. Europhys. Lett. 50, 2834.
Schiwietz, G. & Grande, P.L. (2001). Improved charge state formulas. Nucl. Instr. & Meth. B 175–177, 125131.
Shima, K., Kuno, N., Yamanouchi, M. & Tawara, H. (1992). Equilibrium charge fractions of ions of Z = 4–92 emerging from a carbon foil. Atomic Data and Nuclear Data Tables 51, 173241.
Sigmund, P. & Narmann, A. (1995). Charge-exchange and energy-loss statistics of swift penetrating ions. Laser Part. Beams 13, 281292.
Stewart, J.C. & Pyatt, K.D. (1966). Lowering of ionization potentials in plasmas. Astrophys. J. 144, 1203.
Stockl, C., Boine Frankenheim, O., Roth, M., Suss, W., Wetzler, H., Seelig, W., Kulish, M., Dornik, M., Laux, W., Spiller, P., Stetter, M., Stowe, S., Jacoby, J. & Hoffmann, D.H.H. (1996). Interaction of heavy ion beams with dense plasmas. Laser Part. Beams 14, 561574.
Stoller, C., Suter, M., Himmel, R., Bonani, G., Nessi, M. & Wolfli, W. (1983). Charge state distributions of 1 to 7 MeV C and Be ions stripped in thin foils. IEE-NS Trans. Nucl. Sci. 30, 10741075.


Related content

Powered by UNSILO

Dynamic screening and charge state of fast ions in plasma and solids

  • E. Nardi (a1), Y. Maron (a1) and D.H.H. Hoffmann (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.