Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic Field Evolution in Neutron Stars: One-Dimensional Multi-Fluid
  Model   This paper is the first in a series aimed at understanding the long-term
evolution of neutron star magnetic fields. We model the stellar matter as an
electrically neutral and lightly ionized plasma composed of three moving
particle species: neutrons, protons, and electrons, which can be converted into
each other by weak interactions (beta decays), suffer binary collisions, and be
affected by each other's macroscopic electromagnetic fields. Since the
evolution of the magnetic field occurs over thousands of years or more,
compared to dynamical time scales (sound and Alfv\'en) of milliseconds to
seconds, we use a slow-motion approximation in which we neglect the inertial
terms in the equations of motion for the particles. We restrict ourselves to a
one-dimensional geometry in which the magnetic field points in one Cartesian
direction but varies only along an orthogonal direction. We study the evolution
of the system in three different ways: (i) estimating time scales directly from
the equations, guided by physical intuition; (ii) a normal-mode analysis in the
limit of a nearly uniform system; and (iii) a finite-difference numerical
integration of the equations of motion. We find good agreement between our
analytical normal-mode solutions and the numerical simulations. We show that
the magnetic field and the particles evolve through successive
quasi-equilibrium states, on time scales that can be understood by physical
arguments. Depending of the parameter values the magnetic field can evolve by
ohmic diffusion or by ambipolar diffusion, the latter being limited either by
interparticle collisions or by relaxation to chemical equilibrium through beta
decays. The numerical simulations are further validated by verifying that they
satisfy the known conservation laws also in highly non-linear situations.

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The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin