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Approximate analytical solutions for continuously focused beams and single-species plasmas in thermal equilibrium
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10.1063/1.2896229
/content/aip/journal/pop/15/4/10.1063/1.2896229
http://aip.metastore.ingenta.com/content/aip/journal/pop/15/4/10.1063/1.2896229

Figures

Image of FIG. 1.
FIG. 1.

Numerical calculation of scaled density vs scaled radial coordinate for the values of indicated.

Image of FIG. 2.
FIG. 2.

Fractional errors of approximate solution are plotted as a function of for the indicated values of for (a) weak space-charge (large ), and (b) strong space-charge (small ). Curves are cutoff at values of where .

Image of FIG. 3.
FIG. 3.

Normalized error plotted as a function of for values of satisfying , , , , , and as indicated on the curves. Here, and .

Tables

Generic image for table
Table I.

Scaled variables in the transformed Poisson equation. In both formulations, and are the nonrelativistic plasma frequency and Debye length formed from the on-axis density .

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/content/aip/journal/pop/15/4/10.1063/1.2896229
2008-04-02
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Approximate analytical solutions for continuously focused beams and single-species plasmas in thermal equilibrium
http://aip.metastore.ingenta.com/content/aip/journal/pop/15/4/10.1063/1.2896229
10.1063/1.2896229
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