Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Waves and instabilities in a differentially rotating disc containing a
  poloidal magnetic field   The theory of waves and instabilities in a differentially rotating disc
containing a poloidal magnetic field is developed within the framework of ideal
magnetohydrodynamics. A continuous spectrum, for which the eigenfunctions are
localized on individual magnetic surfaces, is identified but is found not to
contain any instabilities associated with differential rotation. The normal
modes of a weakly magnetized thin disc are studied by extending the asymptotic
methods used previously to describe the equilibria. Waves propagate radially in
the disc according to a dispersion relation which is determined by solving an
eigenvalue problem at each radius. The dispersion relation for a hydrodynamic
disc is re-examined and the modes are classified according to their behaviour
in the limit of large wavenumber. The addition of a magnetic field introduces
new, potentially unstable, modes and also breaks up the dispersion diagram by
causing avoided crossings. The stability boundary to the magnetorotational
instability in the parameter space of polytropic equilibria is located by
solving directly for marginally stable equilibria. For a given vertical
magnetic field in the disc, bending of the field lines has a stabilizing effect
and it is shown that stable equilibria exist which are capable of launching a
predominantly centrifugally driven wind.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con