Non-degenerate plasma

A model of confined atoms in an arbitrary static electric field, which can also be solved analytically, will then be discussed in some detail. Contact will be made with results on atomic ions in non-degenerate plasmas, with illustrative examples being presented. A brief treatment follows of the time-dependent uniform electric field Feynman propagator. 

In the above study, the aim was first to present a soluble model for a confined assembly of independent electrons subjected to a static electric field of arbitrary strength F. These workers achieved the confinement by imposing a harmonic force in addition to the electric field. They aimed, secondly, to relate their results to atomic ions in hot, non-degenerate plasma. 

Sections 13-1.5 are then concerned with relating the above model to atomic ions in a hot, non-degenerate plasma in an external electric field. The first step is to add an atomic-like potential energy V(r) to the model. Strictly, V(r) should be calculated self-consistently as a function of p, F and the plasma density. While this has not been achieved numerically at the time of writing, a model potential F(r) is incorporated into the treatment of Sect. 7.3 by means of the semiclassical Thomas-Fermi approximation. The second step taken by Amovilli et al. [41] is to connect the strength of the harmonic potential with the plasma density (Sect. 7.4). 

This definition of the force constant will be employed below in some illustrative examples. The division of the volume of the plasma into these small cells is best applicable in the case of dense plasmas. The model described above is restricted in the density range because of the assumption of a non-degenerate plasma, but using Fermi-Dirac statistics instead of Maxwell-Boltzmann the range of applicability of this approach could be widened to embrace very high densities ( 10 particles per cc). 

Here, some numerical examples will be presented from Amovilli et al. [41]. As far as possible, bearing in mind the limitations of the model, the examples are designed for conditions which can be achieved in laboratory experiments. However only non-degenerate plasmas will be considered, this then implying the constraint that the ionic number density n,- satisfies... 

Nevertheless, it seems likely that the model treatment of atomic ions in hot, non-degenerate plasmas presented in this work, is well worth further study, the intermediate Fermi-Dirac degeneracy being of obvious importance. Under these conditions, an appropriate starting point to introduce the potential would be the elevated temperature Thomas-Fermi theory [46]. 

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