Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Propagation of ultrastrong femtosecond laser pulses in PLASMON-X   The derivation is presented of the nonlinear equations that describe the
propagation of ultrashort laser pulses in a plasma, in the Plasmon-X device. It
is shown that the Plasmon-X scheme used for the electron acceleration uses a
sufficiently broad beam ($L_\bot\sim 130\,\,\mu{\rm m}$) that justifies the use
of the standard stationary 1-D approximation in the electron hydrodynamic
equations, since the pulse width is sufficiently bigger than the pulse length
($\sim 7.5\,\,\mu{\rm m}$). Furthermore, with the laser power of $W\leq 250$ TW
and the $130\,\,\mu{\rm m}$ spot size, the dimensionless laser vector potential
is sufficiently small $|A_{\bot_0}|^2/{2} =
({W}/{c^2\epsilon_0})({\lambda^2}/{8 \pi^2 c})({4}/{\pi L_\bot^2})({e}/{m_0
c})^2 \sim 0.26$, the nonlinearity is sufficiently weak to allow the power
expansion in the nonlinear Poissons's equation. Such approximation yields a
nonlinear Schr\" odinger equation with a reactive nonlocal nonlinear term. The
nonlocality contains a cosine function under the integral, indicating the
oscillating wake. For a smaller spot size that is used for the Thomson
scattering, $L_\bot = 10\,\, \mu$m, the length and the width of the pulse are
comparable, and it is not possible to use the 1-D approximation in the
hydrodynamic equations. With such small spot size, the laser intensity is very
large, and most likely some sort of chanelling in the plasma would take place
(the plasma gets locally depleted so much that the electromagnetic wave
practically propagates in vacuum).

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The categories of this paper are: hep-ph
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The categories of this paper are: stat
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph