Alastair Rucklidge ,  University of Leeds

In strong magnetic fields, it is well known that two-dimensional convection
takes the form of narrow rolls, and can be treated in the asymptotic limit
as a nonlinear eigenvalue problem. We examine the stability of this solution
when the Prandtl number is also asymptotically small. At leading order, the
linear stability problem turns out to be the linearisation of the same
nonlinear eigenvalue problem, and as a result, it is necessary to go to
higher order to obtain a stability criterion.