Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating Nonlinear Forces with Phase-Space Decoupling   Beam tracking software for accelerators typically falls into two categories:
fast envelope simulations limited to linear beam optics, and slower
multiparticle simulations that can model nonlinear effects. To find a middle
ground between these approaches, we introduce virtual coordinates in position
and momentum which have a cross-dependency (i.e. p=f(x) where x is an initial
position and p* is a virtual projection of momentum onto the position axis).
This technique approximates multiparticle simulations with a significant
reduction in calculation cost.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org