Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T17:59:32.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Stopping power of a heterogeneous warm dense matter

Published online by Cambridge University Press:  08 April 2016

D. Casas ,
A.A. Andreev ,
M. Schnürer ,
M.D. Barriga-Carrasco ,
R. Morales  and
L. González-Gallego
D. Casas*
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain Max Born Institute, Max Born Str. 2a D-12489, Berlin, Germany
A.A. Andreev
Affiliation:
Max Born Institute, Max Born Str. 2a D-12489, Berlin, Germany
M. Schnürer
Affiliation:
Max Born Institute, Max Born Str. 2a D-12489, Berlin, Germany
M.D. Barriga-Carrasco
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain
R. Morales
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain
L. González-Gallego
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain
*
Address correspondence and reprint requests to: D. Casas, E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The stopping power of warm dense matter (WDM) is estimated by means of the individual contributions of free electrons and bound electrons existing in this special kind of matter, located between classical and degenerate plasmas. For free electrons, the dielectric formalism, well described in our studies, is used to estimate the free electron stopping power. For bound electrons, the mean excitation energy of ions is used. Excitation energies are obtained through atomic calculations of the whole atom or, shell by shell in order to estimate their stopping power. Influence of temperature and density is analyzed in case of an impinging projectile. This influence becomes important for low projectile velocities and is negligible for high ones. Using free and bound electron analysis, the stopping power of an extended WDM is inferred from a dynamical calculation of energy transferred from the projectile to the plasma, where the stopping range is calculated. Finally, this theoretical framework is used to study a typical plasma density profile of a WDM heated by lasers.

Keywords

Partially ionized plasmasStopping powerWarm dense matter
Type
Research Article
Information
Laser and Particle Beams , Volume 34 , Issue 2 , June 2016 , pp. 306 - 314
Copyright
Copyright © Cambridge University Press 2016 

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

Abicht, F., Bränzel, J., Priebe, G., Koschitzki, C., Andreev, A.A., Nickles, P.V., Sandner, W. & Schnürer, M. (2014). Tracing ultrafast dynamics of strong fields at plasma-vacuum interfaces with longitudinal proton probing. Appl. Phys. Lett. 105, 034101 (1–5).Google Scholar
Andreev, A.A., Steinke, S., Sokollik, T., Schnürer, M., Ter Avetsiyan, S., Platonov, K.Y. & Nickles, P.V. (2009). Optimal ion acceleration from ultrathin foils irradiated by a profiled laser pulse of relativistic intensity. Phys. Plasmas 16, 013103 (1–9).Google Scholar
Arista, N.R. & Brandt, W. (1984). Dielectric response of quantum plasmas in thermal-equilibrium. Phys. Rev. A 29, 1471–1480.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. (2010). Proton stopping using a full conserving dielectric function in plasmas at any degeneracy. Phys. Rev. E 82, 046403 (1–5).Google Scholar
Barriga-Carrasco, M.D. (2013). PELO (Proton Energy LOss) & PELOS (Poton Energy LOss Straggling). http://www.uclm.es/area/amf/manuel/programas.htm.Google Scholar
Barriga-Carrasco, M.D. & Casas, D. (2013). Electronic stopping of protons in xenon plasmas due to free and bound electrons. Laser Part. Beams 31, 105–111.Google Scholar
Barriga-Carrasco, M.D. & Maynard, G. (2005). A 3D trajectory numerical simulation of the transport of energetic light ion beams in plasma targets. Laser Part. Beams 23, 211–217.Google Scholar
Bethe, H. (1930). The theory of the passage of rapid neutron radiation through matter. Ann. Phys. 5, 325–400.Google Scholar
Borghesi, M., Campbell, D.H., Schiavi, A., Haines, M.G., Willi, O., MacKinnon, A.J., Patel, P., Gizzi, L.A., Galimberti, M., Clarke, R.J., Pegoraro, F., Ruhl, H. & Bulanov, S. (2002). Electric field detection in laser-plasma interaction experiments via the proton imaging technique. Phys. Plasmas 9, 2214–2220.Google Scholar
Casas, D., Barriga-Carrasco, M.D. & Rubio, J. (2013). Evaluation of slowing down of proton and deuteron beams in CH2, LiH, and Al partially ionized plasmas. Phys. Rev. E 88, 033102 (1–6).Google Scholar
Chabot, M., Gardes, D., Box, P., Kiener, J., Deutsch, C., Maynard, G., Andre, V., Fleurier, C., Hong, D. & Wohrer, K. (1995). Stripping properties of a plasma medium for MeV/u chlorine ions. Phys. Rev. E 51, 3504–3510.Google Scholar
Couillaud, C., Deicas, R., Nardin, P., Beuve, M.A., Guihaume, J.M. & Renaud, M. (1994). Ionization and stopping of heavy-ions in dense laser-ablated plasmas. Phys. Rev. E 49, 1545–1562.CrossRefGoogle ScholarPubMed
Daido, H., Nishiuchi, M. & Pirozhkov, A.S. (2012). Review of laser-driven ion sources and their applications. Rep. Prog. Phys. 75, 056401 (1–71).CrossRefGoogle ScholarPubMed
Dyer, G.M., Bernstein, A.C., Cho, B.I., Osterholz, J., Grigsby, W., Dalton, A., Shepherd, R., Ping, Y., Chen, H., Widmann, K. & Ditmire, T. (2008). Equation-of-state measurement of dense plasmas heated with fast protons. Phys. Rev. Lett. 101, 015002 (1–4).Google Scholar
Garbet, X., Deutsch, C. & Maynard, G. (1987). Mean excitiation-energies for ions in gases and plasmas. J. Appl. Phys. 61, 907–916.Google Scholar
Gardes, D., Servajean, A., Kubica, B., Fleurier, C., Hong, D., Deutsch, C. & Maynard, G. (1992). Stopping of multicharged ions in dense and fully ionized hydrogen. Phys. Rev. A 46, 5101–5111.Google Scholar
Gericke, D.O. & Schlanges, M. (2003). Energy deposition of heavy ions in the regime of strong beam-plasma correlations. Phys. Rev. E 67, 037401 (1–4).Google Scholar
Golubev, A., Basko, M., Fertman, A., Kozodaev, A., Mesheryakov, N., Sharkov, B., Vishnevskiy, A., Fortov, V., Kulish, M., Gryaznov, V., Mintsev, V., Golubev, E., Pukhov, A., Smirnov, V., Funk, U., Stoewe, S., Stetter, M., Flierl, H.P., Hoffmann, D.H.H., Jacoby, J. & Iosilevski, I. (1998). Dense plasma diagnostics by fast proton beams. Phys. Rev. E 57, 3363–3367.Google Scholar
Golubev, A., Turtikov, V., Fertman, A., Roudskoy, I., Sharkov, B., Geissel, M., Neuner, U., Roth, M., Tauschwitz, A., Wahl, H., Hoffmann, D.H.H., Funk, U., Suss, W. & Jacoby, J. (2001). Experimental investigation of the effective charge state of ions in beam-plasma interaction. Nucl. Instrum. Methods Phys. Res. Sect. A-Accel. Spectrom. Dect. Assoc. Equip. 464, 247–252.Google Scholar
Gouedard, C. & Deutsch, C. (1978). Dense electron-gas response at any degeneracy. J. Math. Phys. 19, 32–38.Google Scholar
Green, A.E.S., Sellin, D.L. & Zachor, A.S. (1969). Analytic independent-particle model for atoms. Phys. Rev. 184, 1–9.Google Scholar
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, 2313–2321.CrossRefGoogle Scholar
Jacoby, J., Hoffmann, D.H.H., Laux, W., Muller, R.W., Wahl, H., Weyrich, K., Boggasch, E., Heimrich, B., Stockl, C., Wetzler, H. & Miyamoto, S. (1995). Stopping of heavy-ions in a hydrogen plasma. Phys. Rev. Lett. 74, 1550–1553.CrossRefGoogle Scholar
Lindhard, J. (1954). On the properties of a gas of charged particles. Matematisk-Fysiske Meddelelser Kongelige Danske Videnskabernes Selskab 28, 1–57.Google Scholar
Lindhard, J. & Scharff, M. (1953). Energy loss in matter by fast particles of low charge. Matematisk-Fysiske Meddelelser Kongelige Danske Videnskabernes Selskab 27, 1–31.Google Scholar
Macchi, A., Borghesi, M. & Passoni, M. (2013). Ion acceleration by superintense laser-plasma interaction. Rev. Mod. Phys. 85, 751–793.Google Scholar
Mackinnon, A.J., Patel, P.K., Town, R.P., Edwards, M.J., Phillips, T., Lerner, S.C., Price, D.W., Hicks, D., Key, M.H., Hatchett, S., Wilks, S.C., Borghesi, M., Romagnani, L., Kar, S., Toncian, T., Pretzler, G., Willi, O., Koenig, M., Martinolli, E., Lepape, S., Benuzzi-Mounaix, A., Audebert, P., Gauthier, J.C., King, J., Snavely, R., Freeman, R.R. & Boehlly, T. (2004). Proton radiography as an electromagnetic field and density perturbation diagnostic (invited). Rev. Sci. Instrum. 75, 3531–3536.Google Scholar
Mancic, A., Levy, A., Harmand, M., Nakatsutsumi, M., Antici, P., Audebert, P., Combis, P., Fourmaux, S., Mazevet, S., Peyrusse, O., Recoules, V., Renaudin, P., Robiche, J., Dorchies, F. & Fuchs, J. (2010). Picosecond short-range disordering in isochorically heated aluminum at solid density. Phys. Rev. Lett. 104, 035002 (1–4).CrossRefGoogle ScholarPubMed
Maynard, G. & Deutsch, C. (1985). Born random phase approximation for ion stopping in an arbitrarily degenerate electron fluid. J. De Physique 46, 1113–1122.Google Scholar
Mermin, N.D. (1970). Lindhard dielectric function in relaxation-time approximation. Phys. Rev. B-Solid State 1, 2362.Google Scholar
Mintsev, V., Gryaznov, V., Kulish, M., Filimonov, A., Fortov, V., Sharkov, B., Golubev, A., Fertman, A., Turtikov, V., Vishnevskiy, A., Kozodaev, A., Hoffmann, D.H.H., Funk, U., Stoewe, S., Geisel, M., Jacoby, J., Gardes, D. & Chabot, M. (1999). Stopping power of proton beam in a weakly non-ideal xenon plasma. Contrib. Plasma Phys. 39, 45–48.Google Scholar
Patel, P.K., Mackinnon, A.J., Key, M.H., Cowan, T.E., Foord, M.E., Allen, M., Price, D.F., Ruhl, H., Springer, P.T. & Stephens, R. (2003). Isochoric heating of solid-density matter with an ultrafast proton beam. Phys. Rev. Lett. 91, 125004 (1–4).Google Scholar
Pelka, A., Gregori, G., Gericke, D.O., Vorberger, J., Glenzer, S.H., Gunther, M.M., Harres, K., Heathcote, R., Kritcher, A.L., Kugland, N.L., Li, B., Makita, M., Mithen, J., Neely, D., Niemann, C., Otten, A., Riley, D., Schaumann, G., Schollmeier, M., Tauschwitz, A. & Roth, M. (2010). Ultrafast melting of carbon induced by intense proton beams. Phys. Rev. Lett. 105, 265701 (1–4).Google Scholar
Peter, T. & Meyer-ter-Vehn, J. (1991). Energy-loss of heavy-ions in dense-plasma .1. Linear and nonlinear Vlasov theory for the stopping power. Phys. Rev. A 43, 1998–2014.Google Scholar
Shibata, K., Sakumi, A., Sato, R., Tsubuku, K., Nishimoto, T., Hasegawa, J., Ogawa, M. & Oguri, Y. (2001). Experimental investigation of the Coulomb logarithm in beam-plasma interaction. Nucl. Instrum. Methods Phys. Res. Sect. A-Accel. Spectrom. Dect. Assoc. Equip. 464, 225–230.Google Scholar
Sokollik, T., Schnürer, M., Ter-Avetisyan, S., Nickles, P.V., Risse, E., Kalashnikov, M., Sandner, W., Priebe, G., Amin, M., Toncian, T., Willi, O. & Andreev, A.A. (2008). Transient electric fields in laser plasmas observed by proton streak deflectometry. Appl. Phys. Lett. 92, 091503 (1–3).Google Scholar
Stewart, J.C. & Pyatt, K.D. (1966). Lowering of ionization potentials in plasmas. Astrophys. J. 144, 1203.Google Scholar
Volpe, L., Batani, D., Vauzour, B., Nicolai, P., Santos, J.J., Regan, C., Morace, A., Dorchies, F., Fourment, C., Hulin, S., Perez, F., Baton, S., Lancaster, K., Galimberti, M., Heathcote, R., Tolley, M., Spindloe, C., Koester, P., Labate, L., Gizzi, L.A., Benedetti, C., Sgattoni, A., Richetta, M., Pasley, J., Beg, F., Chawla, S., Higginson, D.P. & MacPhee, A.G. (2011). Proton radiography of laser-driven imploding target in cylindrical geometry. Phys. Plasmas. 18, 012704 (1–13).Google Scholar
Ziegler, J.F. (1999). Stopping of energetic light ions in elemental matter. J. Appl. Phys. 85, 1249–1272.Google Scholar
Zwicknagel, G., Toepffer, C. & Reinhard, P.G. (1999). Stopping of heavy ions in plasmas at strong coupling. Phys. Rep.-Rev. Sec. Phys. Lett. 309, 117–208.Google Scholar