Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Space-charge-limited current density for nonplanar diodes with
  monoenergetic emission using Lie-point symmetries   Understanding space-charge limited current density (SCLCD) is fundamentally
and practically important for characterizing many high-power and high-current
vacuum devices. Despite this, no analytic equations for SCLCD with nonzero
monoenergetic initial velocity have been derived for nonplanar diodes from
first principles. Obtaining analytic equations for SCLCD for nonplanar
geometries is often complicated by the nonlinearity of the problem and over
constrained boundary conditions. In this letter, we use the canonical
coordinates obtained by identifying Lie-point symmetries to linearize the
governing differential equations to derive SCLCD for any orthogonal diode.
Using this method, we derive exact analytic equations for SCLCD with a
monoenergetic injection velocity for one-dimensional cylindrical, spherical,
tip-to-tip (t-t), and tip-to-plate (t-p) diodes. We specifically demonstrate
that the correction factor from zero initial velocity to monoenergetic emission
depends only on the initial kinetic and electric potential energies and not on
the diode geometry and that SCLCD is universal when plotted as a function of
the canonical gap size. We also show that SCLCD for a t-p diode is a factor of
four larger than a t-t diode independent of injection velocity. The results
reduce to previously derived results for zero initial velocity using
variational calculus and conformal mapping.

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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex