#### Simulation

### Numerical Simulations

Numerical simulations of the experiment are used to achieve a better understanding of the experiment and to seperate
the acting processes. Global aspects as well as seperated parts are studied. The results of such simulations allow not
only to predict parameter dependencies but also to forecast expected measurements. Modifications to the experimental
setup can be investigated numerically before they are finally applied.

Throughout numerical simulation it is posible to evaluate serveral aspects of the experiment and vice versa the experiment
provides new information to improve the simulation.

(To scale the picture on the left to maximum, please click on it.)

### Magneto-hydrodynamical Equations

The simulation of the FlareLab experiment uses a fluid plasma description, the magneto-hydrodynamical (MHD) model. The
equations showed above describe the temporal evolution of the plasma density, the plasma bulk velocitiy and the magnetic
field.

### Initial Conditions

Two dipoles located beneath the electrodes provide the initial conditions
for the magnetic field. In addition to this potential field we include
a ring current, therefor we do not simulate the formation of the current arc.

To save computation time as well as computer memory we use an adaptive
mesh, which has its highest resolution at the current channel. The simulations
are performed parallel on the TP1 cluster "euler" as well as on the
JUMP
supercomputer at Jülich, Germany. The software package
racoon
is the base for our calculations.

The figure on the shows our initial conditions. The current density is gray and
some magnetic field lines are displayed in green. The blocks represent the adaptive
grid and each block contains 8x8x8 computation points.

### Kinkinstability

To identify various processes, seperated and reduced setups, thus less complex, are studied to achive a general
understanding of each of these processes. Exemplary the result of a simulation of a kink mode.

The kinkinstability plays a central role in the amalysis of the results. The wavemode as well as the growth rate
depend in this dynamical setup not only on the current and the guiding field, but for example also on the viskosity.
An existing viskosity dumps the fast growing short kink modes, leaving only the long kink modes.

(To scale the picture on the left to maximum, please click on it.)

### Effect of the plasma density

The above images show three characteristic situations for three choosen density models. From left to right:
i) the initial density is constant and the continuity equation is used, ii) the Alfven velocity is kept constant
(i.e. the plasma density is proportional to the magnetic energy) and at least iii) the plamsa density is
generated by a simple ionization and recombinization model. Up to now the plasma density distribution is
not measured in the experiment, yet. The second model shows qualitatively the best correlation to the observed
structures.

(To scale the pictures to maximum, please click on the one demanded.)