Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersion Equation for Smith-Purcell FEL   For the grating, which has depth of grooves as a small parameter, the
dispersion equation of the Smith-Purcell instability was obtained. It was found
that the condition of the Thompson or the Raman regimes of excitation does not
depend on beam current but depends on the height of the beam above grating
surface. The growth rate of instability in both cases is proportional to the
square root of the electron beam current.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph