Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic field in nuclear collisions at ultra high energies   The magnetic field created in proton-proton and nucleus-nucleus collisions at
ultra high energies are studied with models of point-like charges and hard
sphere for distribution of the constituents for vacuum conditions. The various
beam ions are considered from light to heavy nuclei at energies corresponded to
the nominal energies of proton beam within the projects of further accelerator
facilities high-energy Large Hadron Collider (HE-LHC) and Future Circular
Collider (FCC). The magnetic field strength immediately after collisions
reaches the value tens of GeV$^{2}$ while the approach with point-like charges
some overestimate the amplitude of the field in comparison with more realistic
hard sphere model. The absolute value of magnetic field rapidly decrease with
time and increases with growth of atomic number. The amplitude for $eB$ is
estimated at level $100$ GeV$^{2}$ in order to magnitude for quark-quark
collisions at energies corresponded to the nominal energies of proton beams.
These estimations are close to the range for onset of $W$ boson condensation.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph