  Whether tidal disruption events (TDEs) circularise or accrete directly as a
highly eccentric disc is the subject of current research and appears to depend
sensitively on the disc thermodynamics. In a previous paper we applied the
theory of eccentric discs to TDE discs using an $\alpha-$prescription for the
disc stress, which leads to solutions that exhibit extreme, potentially
unphysical, behaviour. In this paper we further explore the dynamical vertical
structure of highly eccentric discs using alternative stress models that are
better motivated by the behaviour of magnetic fields in eccentric discs. We
find that the presence of a coherent magnetic field has a stabilising effect on
the dynamics and can significantly alter the behaviour of highly eccentric
radiation dominated discs. We conclude that magnetic fields are important for
the evolution of TDE discs.
