Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beyond the Child-Langmuir Limit   This paper describes a new solution formulation for fully nonlinear and
unsteady planar flow of an electron beam in a diode. Using characteristic
variables - i.e., variables that follow particle paths - the solution is
expressed through an exact analytic, but implicit, formula for any choice of
incoming velocity $v_0$, electric field $E_0$ and current $J_0$. For steady
solutions, this approach clarifies the origin of the maximal current $J_max$,
derived by Child and Langmuir for $v_0=0$ and by Jaffe for $v_0>0$. The
implicit formulation is used to find (1) unsteady solutions having constant
incoming flux $J_0>J_max$, which leads formation of a virtual cathode, and (2)
time-periodic solutions whose average flux exceeds the adiabatic average of
$J_max$.

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int