Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Electron dynamics inside a vacuum tube diode through linear differential
  equations   In this paper we analyze the motion of charged particles in a vacuum tube
diode by solving linear differential equations. Our analysis is based on
expressing the volume charge density as a function of the current density and
coordinates only, while in the usual scheme the volume charge density is
expressed as a function of the current density and electrostatic potential. Our
approach gives the well known behavior of the classical current density
proportional to the three-halves power of the bias potential and inversely
proportional to the square of the gap distance between the electrodes, and does
not require the solution of the nonlinear differential equation normally
associated with the Child-Langmuir formulation.

13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org