Contents List of Figures

6.2 Jets as Super(magneto)sonic Collimated Plasma Flows 277
kinetic power, as well as to find self-consistent models for the particle acceleration
and flow patterns. As telescopes and analysis techniques have improved the level of
detail obtained, it has become apparent, however, that the observed properties are
not very simple and much harder to interpret than most simple models predict.
Radiative MHD with NIRVANA C: In the following we work in the one–
component approximation for the dynamical part, but include cooling for the evolution
of different atomic species [11]. The evolution of the jet plasma is given by the
continuity equation for the density ρ, the Euler equations for the momenta ρ V which
have pressure gradient and Lorentz forces as source terms. The magnetic fields B
evolve according to the induction equation, and the time evolution of the internal
energy e is determined by advection, compression and cooling (the K–term)
∂ρ
∂t + ∇ · (ρ V ) = 0 (673)
∂ρ V
∂t + ∇ · (ρ V ⊗ V ) = −∇P − 1
8π ∇ B 2 + 1
4π ( B · ∇) B (674)
∂e
∂t + ∇ · (e V ) = −P (∇ · V ) − K (675)
∂ B
∂t = ∇ × ( V × B) (676)
P = (Γ − 1)e . (677)
These equations are implemented in codes such as ZEUS3D and NIRVANA C [22],
or more modern versions based on shock capturing methods [23].
Cooling Functions for Low–Density Plasmas: Sutherland & Dopita [21] have
presented the equilibrium cooling functions for optically thin plasmas. These can
easily built into the code NIRVANA C. Some functions are terminated before reaching
10 4 K when the internal photoionization halts the cooling. The functions represent
a self-consistent set of curves covering a wide grid of temperature and metallicities
using recently published atomic data and processes. The results have implications
for phenomena such as cooling flows and for hydrodynamic modelling which
include gas components. NIRVANA C can however also handle non–equilibrium
cooling for an entire set of atomic species. Then the above equations must be supplemented
with a network of time evolution for various species. In cases, where
cooling is very rapid compared to dynamical time–scales, this network has to be
solved by means of time–implicit methods.