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Mermin dielectric function versus local field corrections on proton stopping in degenerate plasmas

Published online by Cambridge University Press:  07 July 2008

M.D. Barriga-Carrasco
M.D. Barriga-Carrasco*
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain
*
Address correspondence and reprint requests to: Manuel D. Barriga-Carrasco, E.T.S.I. Industriales, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain. E-mail: manueld.barriga@uclm.es
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Abstract

If plasmas are considered fully ionized, the electronic stopping of a charged particle that traverses them will only be due to free electrons. This stopping can be obtained in a first view through the random phase approximation (RPA). But free electrons interact between them affecting the stopping. These interactions can be taken into account in the dielectric formalism by means of two different ways: the Mermin function or the local field corrections (LFCs). LFCs produce an enhancement in stopping before the maximum and recover the RPA values just after it. Mermin method also produces firstly a high increase at very low energies, then a small enhancement at low energies and finally decreases below RPA values before and after the maximum. Differences between the two methods are very important at very low energies and by 30% around the stopping maximum.

Keywords

Electron collisionsEnergy lossFast ignitionLocal field correction

Information

Type
Research Article
Information
Laser and Particle Beams , Volume 26 , Issue 3 , September 2008 , pp. 389 - 395
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Akhiezer, A.I. & Sitenko, A.G. (1952). O prokhozhdenii zaryazhennoi chastitsy cherez elektronnuyu plazmu. Zh. Eksp. Teor. Fiz. 23, 161–168.Google Scholar
Arista, N.R. & Brandt, W. (1984). Dielectric response of quantum plasmas in thermal equilibrium. Phys. Rev. A 29, 1471–1480.CrossRefGoogle Scholar
Ashley, J.C. & Echenique, P.M. (1987). Influence of damping in an electron gas on vicinage effects in ion-cluster energy loss. Phys. Rev. B 35, 8701–8704.CrossRefGoogle Scholar
Atwal, G.S. & Ashcroft, N.W. (2002). Relaxation of an electron system: conserving approximation. Phys. Rev. B 65, 115109.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. & Garcia-Molina, R. (2003). Vicinage forces between molecular and atomic fragments dissociated from small hydrogen clusters and their effects on energy distributions. Phys. Rev. A 68, 062902.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. & Garcia-Molina, R. (2004). Simulation of the energy spectra of original versus recombined H2+ molecular ions transmitted through thin foils. Phys. Rev. A 70, 032901.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. (2006 a). Effects of target plasma electron-electron collisions on correlated motion of fragmented H2+ protons. Phys. Rev. E 73, 026401.CrossRefGoogle ScholarPubMed
Barriga-Carrasco, M.D. (2006 b). Influence of target plasma nuclei collisions on correlated motion of fragmented H2+ protons. Laser Part. Beams 24, 211–216.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. & Maynard, G. (2006). Plasma electron-electron collision effects in proton self-retarding and vicinage forces. Laser Part. Beams 24, 55–60.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. & Deutsch, C. (2006). Plasma wake and nuclear forces on fragmented H2+ transport. Plasma Phys. Control. Fusion 48, 1787–1801.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. (2007). Influence of damping on proton energy loss in plasmas of all degeneracies. Phys. Rev. E 75, 016405.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. (2008). Target electron collisions effects on energy loss straggling of protons in an electron gas at any degeneracy. Phys. Plas. 15, 033103.CrossRefGoogle Scholar
Cassisi, S., Potekhin, A.Y., Pietrinferni, A., Catelan, M. & Salaris, M. (2007). Updated electron-conduction opacities: the impact on low-mass stellar models. Astrophys. J. 661, 1094.CrossRefGoogle Scholar
Das, A.K. (1975). The relaxation-time approximation in the RPA dielectric formulation. J. Phys. F.: Met. Phys. 5, 2035–2040.CrossRefGoogle Scholar
Deutsch, C. (1984). Atomic physics for beam-target interactions. Laser Part. Beams 2, 449–465.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
Fermi, E. (1940). The ionization loss of energy in gases and in condensed materials. Phys. Rev. 57, 485–493.CrossRefGoogle Scholar
Flowers, E. & Itoh, N. (1976). Transport properties of dense matter. Astrophys. J. 206, 218.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, 2313–2321.CrossRefGoogle Scholar
Hubbard, J. (1957). The description of collective motions in terms of many-body perturbation theory 2. The correlation energy of a free-electron gas. Proc. R. Soc. London, Ser. A 243, 336–352.Google Scholar
Ichimaru, I. & Utsumi, K. (1980). Analytic expression for the dielectric screening function of strongly coupled electron liquids at metallic and lower densities. Phys. Rev. B 24, 7385–7388.CrossRefGoogle Scholar
Lampe, M. (1968 a). Transport coefficients of degenerate plasma. Phys. Rev. 170, 306.CrossRefGoogle Scholar
Lampe, M. (1968 b). Transport theory of a partially degenerate plasma. Phys. Rev. 174, 276.CrossRefGoogle Scholar
Lindhard, J. (1954). On the properties of a gas of charged particles. K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 28, 1.Google Scholar
Lindhard, J. & Winther, A. (1964). Stopping power of electron gas and equipartition rule. K. Dan. Vidensk. Selsk., Mat.-Fys. Medd. 34, 1.Google Scholar
Mermin, N.D. (1970). Lindhard dielectric function in the relaxation-time approximation. Phys. Rev. B 1, 2362–2363.CrossRefGoogle Scholar
Morawetz, K. & Fuhrmann, U. (2000 a). General response function for interacting quantum liquids. Phys. Rev. E 61, 2272–2280.CrossRefGoogle Scholar
Morawetz, K. & Fuhrmann, U. (2000 b). Momentum conservation and local field corrections for the response of interacting Fermi gases. Phys. Rev. E 62, 4382–4385.CrossRefGoogle ScholarPubMed
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, 131–141.CrossRefGoogle Scholar
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, 489–495.CrossRefGoogle Scholar
Pathak, K.N. & Vashishta, P. (1973). Electron Correlations and Moment Sum Rules. Phys. Rev. B 7, 3649–3656.CrossRefGoogle Scholar
Pines, D. & Bohm, D. (1952). A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions. Phys. Rev. 85, 338–353.CrossRefGoogle Scholar
Pschiwul, T. & Zwicknagel, G. (2003). Numerical simulation of the dynamic structure factor of a two-component model plasma. J. Phys. A: Math. Gen. 36, 6251–6258.CrossRefGoogle Scholar
Roth, M., Cowan, T.E., Key, M.H., Hatchett, S.P., Brown, C., Fountain, W., Johnson, J., Pennington, D.M., Snavely, R.A., Wilks, S.C., Yasuike, K., Ruhl, K., Pegoraro, F., Bulanov, S.V., Campbell, E.M., Perry, M.D. & Powell, H. (2001). Fast ignition by intense laser-accelerated proton beams. Phys. Rev. Lett. 86, 436–439.CrossRefGoogle ScholarPubMed
Selchow, A. & Morawetz, K. (1999). Dielectric properties of interacting storage ring plasmas. Phys. Rev. B 59, 1015–1023.CrossRefGoogle Scholar
Selchow, A., Ropke, G. & Morawetz, K. (2000). The influence of electron-electron collisions on the stopping power within dielectric theory. Nucl. Instrum. Methods Phys. Res. A 441, 40–43.CrossRefGoogle Scholar
Shternin, P. S. & Yakovlev, D. G. (2006). Phys. Rev. D 74, 043004.CrossRefGoogle Scholar
Singwi, K.S., Tosi, M.P., Land, R.H. & Sjölander, A. (1968). Electron Correlations at Metallic Densities. Phys. Rev. 176, 589–599.CrossRefGoogle Scholar
Vaishya, J.S. & Gupta, A.K. (1973). Dielectric response of the electron liquid in generalized random-phase approximation: A critical analysis. Phys. Rev. B 7, 4300–4303.CrossRefGoogle Scholar
Vashishta, P. & Singwi, K.S. (1972). Electron correlations at metallic densities. V. Phys. Rev. B 6, 875–887.CrossRefGoogle Scholar
Yan, X., Tanaka, S., Mitake, S. & Ichimaru, S. (1985). Theory of interparticle correlations in dense, high-temperature plasmas. IV. Stopping power. Phys. Rev. A 32, 1785–1789.CrossRefGoogle ScholarPubMed
Zwicknagel, G., Toepffer, C. & Reinhard, P.G. (1999). Stopping of heavy ions in plasmas at strong coupling. Physi. Rep. 309, 117–208.CrossRefGoogle Scholar