Simulating the dynamics and non-thermal emission of relativistic
  magnetised jets I. Dynamics
  We have performed magneto-hydrodynamic simulations of relativistic jets from
supermassive blackholes over a few tens of kpc for a range of jet parameters.
One of the primary aims were to investigate the effect of different MHD
instabilities on the jet dynamics and their dependence on the choice of jet
parameters. We find that two dominant MHD instabilities affect the dynamics of
the jet, small scale Kelvin- Helmholtz (KH) modes and large scale kink modes,
whose evolution depend on internal jet parameters like the Lorentz factor, the
ratio of the density and pressure to the external medium and the magnetisation
and hence consequently on the jet power. Low power jets are susceptible to both
instabilities, kink modes for jets with higher central magnetic field and KH
modes for lower magnetisation. Moderate power jets do not show appreciable
growth of kink modes, but KH modes develop for lower magnetisation. Higher
power jets are generally stable to both instabilities. Such instabilities
decelerate and decollimate the jet while inducing turbulence in the cocoon,
with consequences on the magnetic field structure. We model the dynamics of the
jets following a generalised treatment of the Begelman-Cioffi relations which
we present here. We find that the dynamics of stable jets match well with
simplified analytic models of expansion of non self-similar FRII jets, whereas
jets with prominent MHD instabilities show a nearly self-similar evolution of
the morphology as the energy is more evenly distributed between the jet head
and the cocoon.
