Ion Stopping Power in Dense Partially Degenerate Plasmas

  • Claude Deutsch
Part of the NATO ASI Series book series (volume 154)


In close connection with beam-target interaction problems encountered in inertial confinement fusion (ICF) driven by particle beams [Deutsch, 1986], we intend to solve exactly the model for the stopping of nonrelativistic pointlike and positive ions in a homogeneous, and dense electron fluid taken at any temperature. Such a model is usually considered as the simplest in providing a coherent theoretical framework with reliable estimates for the beam-target interaction parameters. The rational underlying this view is based on the observation that many, if not most, of the compressed pellet states encountered during a full compression lie in the parameter space close to weakly coupled systems indexed by a dimensionless quantity
$$ {{\rm{X}}^{\rm{2}}} = {1 \over {{\rm{\pi }}{{\rm{q}}_{\rm{F}}}{{\rm{a}}_{\rm{o}}}}} = {{{{\rm{V}}_{\rm{o}}}} \over {{\rm{m}}{{\rm{V}}_{\rm{F}}}}} = {1 \over {\rm{\pi }}}\sqrt {{{{}^{\rm{I}}{\rm{H}}} \over {{}^{\rm{k}}{\rm{B}}{}^{\rm{T}}{\rm{F}}}}} = {{{\rm{\alpha }}{{\rm{r}}_{\rm{s}}}} \over {\rm{\pi }}}, $$
with qF, VF, TF denoting Fermi wave number, velocity and temperature respectively. ao, Vo,IH refer to Bohr wavelength, velocity and energy rs = (4/3 πn)-1/3a o -1 in terms of the free electron number density n, while α = (9 π/4)-1/3. At high temperature (T » TF), eq. (1.1) becomes (Te = T/TF)
$$ {{{3_{\rm{X}}}^2} \over {{\rm{2}}{{\rm{T}}_{\rm{e}}}}} = {{{{\rm{e}}^{\rm{2}}}} \over {{\rm{\pi }}{{\rm{k}}_{\rm{B}}}{\rm{T}}{{\rm{R}}_{{\rm{ee}}}}}} = {{{\Gamma _{\rm{e}}}} \over {\rm{\pi }}}, $$
in terms of Ree = (4/3 π n)-1/3 and of the classical plasma parameter Γe. At any degeneracy (or temperature), the Random Phase Approximation (R.P.A.) is valid in a (T,n) domain defined by [Lindhard, 1954; Dar et al., 1974]
$$ {{{{\rm{X}}^2}} \over {{\rm{1 + }}{{\rm{T}}_{\rm{e}}}}} \ll 1, $$
so that the potential energy content of an electron pair located at the screening distance always remains much smaller than the kinetic energy per particle. As restricted as it looks at first sight, inequality (1.3) allows us to encompass a huge number of different systems ranging from high-temperature Tokomaks to dense and moderately hot plasmas envisioned in particle beam driven ICF.


Inertial Confinement Fusion Potential Energy Content Local Field Correction Coherent Theoretical Framework Average Atom Model 
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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Claude Deutsch
    • 1
  1. 1.Laboratoire de Physique des Gaz et des PlasmasUniversite Paris XIOrsay CedexFrance

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