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Classical scattering and stopping power in dense plasmas: the effect of diffraction and dynamic screening

Published online by Cambridge University Press:  27 June 2016

M. K. Issanova ,
S. K. Kodanova ,
T. S. Ramazanov ,
N. Kh. Bastykova ,
Zh. A. Moldabekov  and
C.-V. Meister
M. K. Issanova*
Affiliation:
Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040 Almaty, Kazakhstan
S. K. Kodanova
Affiliation:
Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040 Almaty, Kazakhstan
T. S. Ramazanov
Affiliation:
Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040 Almaty, Kazakhstan
N. Kh. Bastykova
Affiliation:
Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040 Almaty, Kazakhstan
Zh. A. Moldabekov
Affiliation:
Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040 Almaty, Kazakhstan
C.-V. Meister
Affiliation:
Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstr. 9, 64289 Darmstadt, Germany Graduate School of Excellence Energy Science and Engineering, Jovanka-Bontschits-Str. 2, 64287 Darmstadt, Germany
*
Address correspondence and reprint requests to: M. K. Issanova, Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040 Almaty, Kazakhstan. E-mail: isanova_moldir@mail.ru
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Abstract

In the present work, classical electron–ion scattering, Coulomb logarithm, and stopping power are studied taking into account the quantum mechanical diffraction effect and the dynamic screening effect separately and together. The inclusion of the quantum diffraction effect is realized at the same level as the well-known first-order gradient correction in the extended Thomas–Fermi theory. In order to take the effect of dynamic screening into account, the model suggested by Grabowski et al. in 2013 is used. Scattering as well as stopping power of the external electron (ion) beam by plasma ions (electrons) and scattering of the plasma's own electrons (ions) by plasma ions (electrons) are considered differently. In the first case, it is found that in the limit of the non-ideal plasma with a plasma parameter Γ → 1, the effects of quantum diffraction and dynamic screening partially compensate each other. In the second case, the dynamic screening enlarges scattering cross-section, Coulomb logarithm, and stopping power, whereas the quantum diffraction reduces their values. Comparisons with the results of other theoretical methods and computer simulations indicate that the model used in this work gives a good description of the stopping power for projectile velocities $v\,{\rm \lesssim}\, 1.5 v_{{\rm th}}$, where vth is the thermal velocity of the plasma electrons.

Keywords

Dense plasmaDynamical screeningScattering cross-sectionCoulomb logarithmStopping power
Type
Research Article
Information
Laser and Particle Beams , Volume 34 , Issue 3 , September 2016 , pp. 457 - 466
Copyright
Copyright © Cambridge University Press 2016 

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References

REFERENCES

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
Belyaev, G., Basko, M., Cherkasov, A., Golubev, A., Fertman, A., Roudskoy, I., Savin, S., Sharkov, B., Turtikov, V., Arzumanov, A., Borisenko, A., Gorlachev, I., Lysukhin, S., Hoffmann, D.H.H. & Tauschwitz, A. (1996). Measurement of the Coulomb energy loss by fast protons in a plasma target. Phys. Rev. E 53, 2701–2707.CrossRefGoogle Scholar
Benedict, L.X., Surh, M.P., Castor, J.I., Khairallah, S.A., Whitley, H.D., Richards, D.F., Glosli, J.N., Murillo, M.S., Scullard, C.R., Grabowski, P.E., Michta, D. & Graziani, F.R. (2012). Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas. Phys. Rev. E 86, 046406.CrossRefGoogle ScholarPubMed
Cuneo, M.E., Herrmann, M.C., Sinars, D.B., Slutz, S.A., Stygar, W.A., Vesey, R.A., Sefkow, A.B., Rochau, G.A., Chandler, G.A., Bailey, J.E., Porter, J.L., McBride, R.D., Rovang, D.C., Mazarakis, M.G., Yu, E.P., Lamppa, D.C., Peterson, K.J., Nakhleh, C., Hansen, S.B., Lopez, A.J., Savage, M.E., Jennings, C.A., Martin, M.R., Lemke, R.W., Atherton, B.W., Smith, I.C., Rambo, P.K., Jones, M., Lopez, M.R., Christenson, P.J., Sweeney, M.A., Jones, B., McPherson, L.A., Harding, E., Gomez, M.R., Knapp, P.F., Awe, T.J., Leeper, R.J., Ruiz, C.L., Cooper, G.W., Hahn, K.D., McKenney, J., Owen, A.C., McKee, G.R., Leifeste, G.T., Ampleford, D.J., Waisman, E.M., Harvey-Thompson, A., Kaye, R.J., Hess, M.H., Rosenthal, S.E. & Matzen, M.K. (2012). Magnetically driven implosions for inertial confinement fusion at Sandia National Laboratories. IEEE Trans. Plasma Sci. 40, 3222–3245.CrossRefGoogle Scholar
Deutsch, C. (1977). Nodal expansion in a real matter plasma. Phys. Lett. A 60, 317–318.CrossRefGoogle Scholar
Dunn, T. & Broyles, A.A. (1967). Method for determining the thermodynamic properties of the quantum electron gas. Phys. Rev. 157, 156.CrossRefGoogle Scholar
Dzhumagulova, K.N., Shalenov, E.O. & Gabdullina, G.L. (2013). Dynamic interaction potential and the scattering cross sections of the semiclassical plasma particles. Phys. Plasmas 20, 042702.Google Scholar
Frenje, J.A., Grabowski, P.E., Li, C.K., Seguin, F.H., Zylstra, A.B., Gatu Johnson, M., Petrasso, R.D., Glebov, V.Yu & Sangster, T.C. (2015). Measurements of ion stopping around the Bragg peak in high-energy-density plasmas. Phys. Rev. Lett. 115, 205001.Google Scholar
Gericke, D.O. & Schlanges, M. (1999). Beam–plasma coupling effects on the stopping power of dense plasmas. Phys. Rev. E 60, 904–909.CrossRefGoogle ScholarPubMed
Gericke, D.O., Schlanges, M. & Kraeft, W.D. (1996). Stopping power of a quantum plasma – T-matrix approximation and dynamical screening. Phys. Lett. A 222, 241–245.CrossRefGoogle Scholar
Golubev, A. & Basko, M. (1998). Dense plasma diagnostics by fast proton beams. Phys. Rev E 57, 3363–3367.Google Scholar
Grabowski, P.E., Surh, M.P., Richards, D.F., Graziani, F.R. & Murillo, M.S. (2013). Molecular dynamics simulations of classical stopping power. Phys. Rev. Lett. 111, 215002.Google 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
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.CrossRefGoogle Scholar
Hong, W.-P. & Jung, Y.-J. (2015). Influence of quantum diffraction and shielding on electron-ion collision in two-component semiclassical plasmas. Phys. Plasmas 22, 012701.Google Scholar
Hurricane, O.A., Callahan, D.A., Casey, D.T., Celliers, P.M., Cerjan, C., Dewald, E.L., Dittrich, T.R., Doppner, T., Hinkel, D.E., Berzak Hopkins, L.F., Kline, J.L., Le Pape, S., Ma, T., MacPhee, A.G., Milovich, J. L., Pak, A., Park, H.-S., Patel, P.K., Remington, B.A., Salmonson, J.D., Springer, P.T. & Tommasini, R. (2014). Fuel gain exceeding unity in an inertially confined fusion implosion. Nature 506, 343–348.Google Scholar
Jacoby, J., Hoffmann, D.H.H., Laux, W., Muller, R.W., 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.Google Scholar
Karakhtanov, V.S., Redmer, R., Reinholz, H. & Röpke, G. (2011). Transport coefficients in dense plasmas including ion-ion structure factor. Contrib. Plasma Phys. 51, 355–360.CrossRefGoogle Scholar
Kelbg, G. (1963). Theorie des quantenplasmas. Ann. Phys. Lpz. 467, 219.Google Scholar
Khrapak, S.A., Ivlev, A.V. & Morfill, G.E. (2003). Scattering in the attractive Yukawa potential in the limit of strong interaction. Phys. Rev. Lett. 90, 22502.Google Scholar
Ki, D.-H. & Jung, Y.-J. (2010). Quantum screening effects on the ion-ion collisions in strongly coupled semiclassical plasmas. Phys. Plasmas 17, 074506.CrossRefGoogle Scholar
Kilgore, M.D., Daugherty, J.E., Porteous, R.K. & Graves, D.B. (1993). Ion drag on an isolated particulate in a low-pressure discharge. J. Appl. Phys. 73, 7195–7202.Google Scholar
Kodanova, S.K., Ramazanov, T.S., Bastykova, N.Kh. & Moldabekov, Zh.A. (2015 a). Effect of dust particle polarization on scattering processes in complex plasmas. Phys. Plasmas 22, 063703.Google Scholar
Kodanova, S.K., Ramazanov, T.S., Issanova, M.K., Nigmetova, G.N. & Moldabekov, Zh.A. (2015 b). Investigation of Coulomb logarithm and relaxation processes in dense plasma on the basis of effective potentials. Contrib. Plasma Phys. 55, 271–276.Google Scholar
Kraeft, W.D. & Strege, B. (1988). Energy loss of charged particles moving in a plasma. Physica A 149, 313–322.Google Scholar
Meister, C.-V., Hoffmann, D.H.H. & Jiang, B. (2015). Thermal parameters of Super-FRagment Separator target materials. DPG Spring Conference, Plasma Physics: Theory and Modelling, p. 14.12. Bochum, 02.-05.03.15: Verhandlungen der DPG.Google Scholar
Meister, C.-V., Imran, M. & Hoffmann, D.H.H. (2011). Relative energy level shifts of hydrogen-like carbon bound-states in dense matter. Laser Part. Beams 29, 17–27.CrossRefGoogle Scholar
Meister, C.-V. & Röpke, G. (1982). Electrical conductivity of non-ideal plasmas and the ion distribution function. Ann. Phys. 39, 133–148.CrossRefGoogle Scholar
Mintsev, V.B. & Fortov, V.E. (2015). Transport properties of warm dense matter behind intense shock waves. Laser Part. Beams 33, 41–50.CrossRefGoogle Scholar
Moldabekov, Zh.A., Ludwig, P., Bonitz, M. & Ramazanov, T.S. (2015 a). Ion potential in warm dense matter: Wake effects due to streaming degenerate electrons. Phys. Rev. E 91, 023102.Google Scholar
Moldabekov, Zh.A., Ludwig, P., Joost, J.-P., Bonitz, M. & Ramazanov, T.S. (2015 b). Dynamical screening and wake effects in classical, quantum, and ultrarelativistic plasmas. Contrib. Plasma Phys. 55, 186–191.CrossRefGoogle Scholar
Moldabekov, Zh., Schoof, T., Ludwig, P., Bonitz, M. & Ramazanov, T. (2015 c). Statically screened ion potential and Bohm potential in a quantum plasma. Phys. Plasmas 22, 102104.Google Scholar
Nersisyan, H.B. & Deutsch, C. (2014). Stopping of a relativistic electron beam in a plasma irradiated by an intense laser field. Laser Part. Beams 32, 157–169.Google Scholar
Ordonez, C.A. & Molina, M.I. (2001). Evaluation of the Coulomb logarithm using cutoff and screened Coulomb interaction potentials. Phys. Plasmas 1, 2515–2517.Google Scholar
Ramazanov, T.S. & Kodanova, S.K. (2001). Coulomb logarithm of a nonideal plasma. Phys. Plasmas 8, 5049–5050.Google Scholar
Ramazanov, T.S., Kodanova, S.K., Moldabekov, Zh.A. & Issanova, M.K. (2013). Dynamical properties of non-ideal plasma on the basis of effective potentials. Phys. Plasmas 20, 112702.CrossRefGoogle Scholar
Ramazanov, T.S., Moldabekov, Zh.A. & Gabdullin, M.T. (2015). Effective potentials of interactions and thermodynamic properties of a nonideal two-temperature dense plasma. Phys. Rev. E 92, 023104.Google Scholar
Reinholz, H., Redmer, R. & Nagel, S. (1995). Thermodynamic and transport properties of dense hydrogen plasmas. Phys. Rev. E 52, 5368–5386.Google Scholar
Reinholz, H., Röpke, G., Rosmej, S. & Redmer, R. (2015). Conductivity of warm dense matter including electron–electron collisions. Phys. Rev. E 91, 043105.Google Scholar
Stanton, L.G. & Murillo, M.S. (2015). Unified description of linear screening in dense plasmas. Phys. Rev. E 91, 033104.Google Scholar
Zhang, L.-Y., Zhao, X.-Y., Qi, X., Xiao, G.-Q., Duan, W.-S. & Yang, L. (2015). Wakefield and stopping power of a hydrogen ion beam pulse with low drift velocity in hydrogen plasmas. Laser Part. Beams 33, 215–220.Google Scholar
Zwicknagel, G. (2009). Theory and simulation of heavy ion stopping in plasma. Laser Part. Beams 27, 399–413.Google Scholar
Zwicknagel, G., Toepffer, C., & Reinhard, P.-G. (1999). Stopping of heavy ions in plasmas at strong coupling. Phys. Rep. 309, 117–208.Google Scholar
Zylstra, A.B., Frenje, J.A., Grabowski, P.E., Li, C.K., Collins, G.W., Fitzsimmons, P., Glenzer, S., Graziani, F., Hansen, S.B., Hu, S.X., Gatu Johnson, M., Keiter, P., Reynolds, H., Rygg, J.R., Seguin, F.H. & Petrasso, R.D. (2015). Measurement of charged-particle stopping in warm dense plasma. Phys. Rev. Lett. 114, 215002.Google Scholar