Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T17:43:51.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Applying full conserving dielectric function to the energy loss straggling

Published online by Cambridge University Press:  10 February 2011

Manuel D. Barriga-Carrasco
Manuel 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, 13071, Ciudad Real, Spain. E-mail: manueld.barriga@uclm.es
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to calculate proton energy loss straggling using a full conserving dielectric function (FCDF) for plasmas at any degeneracy. This dielectric function takes into account plasma electron-electron collision considering density, momentum, and energy conservation. When only momentum conservation law is accomplished, the FCDF reproduces the well known Mermin dielectric function, when none of the conservations laws are obeyed, the random phase approximation (RPA) is recovered. Then, the FCDF is applied for the first time to the determination of the energy loss straggling. Differences among diverse dielectric functions to determine straggling follow the same behavior for all kind of plasmas then, they do not depend on the plasma degeneracy but essentially do on the value of the collision frequency. These discrepancies can rise up to 5% between FCDF values and the Mermin ones, and 2% between the FCDF ones and RPA ones for plasma with high enough collision frequency. The similarity between FCDF and RPA results is not surprising, as all conservation laws are also considered in RPA dielectric function. The fact that FCDF and RPA give similar results and the fact that FCDF considers electron-electron collisions and RPA does not, means that latter collisions are not significant for energy loss straggling calculations.

Keywords

Dielectric functionElectron collisionsEnergy loss stragglingPlasma degeneracy
Type
Research Article
Information
Laser and Particle Beams , Volume 29 , Issue 1 , March 2011 , pp. 81 - 86
Copyright
Copyright © Cambridge University Press 2010

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

Abril, I., Garcia-Molina, R., Denton, C.D., Pérez-Pérez, F.J. & Arista, N.R. (1998). Dielectric description of wakes and stopping powers in solids. Phys. Rev. A 58, 357–366.CrossRefGoogle Scholar
Arista, N.R. & Brandt, W. (1981). Energy loss straggling of charged particles in plasmas of all degeneracies. Phys. Rev. A 23, 1898–1905.CrossRefGoogle 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. (1985). Influence of damping in an electron gas on wake binding energies. Phys. Rev. B 31, 4655–4656.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
Barnes, C. & Luck, J.M. (1990). The distribution of the reflection phase of disordered conductor. J. Phys. A 23, 1717–1734.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. & Garcia-Molina, R. (2004). Simulation of the energy spectra of original versus recombined H2O molecular ions transmitted through thin foils. Phys. Rev. A 70, 032901/8.CrossRefGoogle Scholar
Barriga-Carrasco, M.D. (2006). 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. (2007). Influence of damping on proton energy loss in plasmas of all degeneracies. Phys. Rev. E 75, 016405/7.Google Scholar
Barriga-Carrasco, M.D. (2008). Target electron collisions effects on energy loss straggling of protons in an electron gas at any degeneracy. Phys. Plasma. 15, 033103.CrossRefGoogle Scholar
Bohr, N. (1948). K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 18, 1–144.Google Scholar
Deutsch, C. (1984). Atomic physics for beam-target interactions. Laser Part. Beams 2, 449–465.CrossRefGoogle Scholar
Deutsch, C. (1992). Ion cluster interaction with cold targets for ICF: Fragmentation and stopping. Laser Part. Beams 10, 217–226.CrossRefGoogle Scholar
Flowers, E. & Itoh, N. (1976). Transport properties of dense matter. Astrophys. J. 206, 218–242.CrossRefGoogle Scholar
Gerike, D.O. (2002). Stopping power for strong beam–plasma coupling. Laser Part. Beams 20, 471–474.CrossRefGoogle Scholar
Gouedard, C. & Deutsch, C. (1978). Electron gas response at any degeneracy. J. Math. Phys. 19, 32–38.CrossRefGoogle Scholar
Lampe, M. (1968 a). Transport coefficients of degenerate plasma. Phys. Rev. 170, 306–319.CrossRefGoogle Scholar
Lampe, M. (1968 b). Transport theory of a partially degenerate plasma. Phys. Rev. 174, 276–280.CrossRefGoogle Scholar
Lindhard, J. (1954). On the properties of a gas of charged particles. K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 28, 1–57.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). General response function for interacting quantum liquids. Phys. Rev. E 61, 2272–2280.CrossRefGoogle Scholar
Nersisyan, H.B. & Das, A.K. (2004). Energy loss of ions and ion clusters in a disordered electron gas. Phys. Rev. E 69, 046404/15.CrossRefGoogle Scholar
Selchow, A. & Morawetz, K. (1999). Dielectric properties of interacting storage ring plasmas. Phys. Rev. B 59, 1015–1023.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
Urpin, V.A. & Yakovlev, D.G. (1980). Thermal conductivity due to collisions between electrons in a relativistic, degenerate, electron gas. Sov. Astron. 24, 126–127.Google Scholar