colours imply higher densities.[]{data-label="eqnden"}](figure2.eps){height="8cm"}

Comparison with Simulation Results {#SIM}
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As it is not possible to directly confirm the effectiveness of this method for determining the plasma $\beta$ of a prominence, it is important to apply it to simulations results to provide some validation. We apply it to the results of @HILL2011 and @HILL2012, where a full description of the simulations are presented. In this section we apply Equation \[dendist\] to solve the forward problem, i.e. we use the parameters of the simulation - including the plasma $\beta$ - to see how well the density distribution around the plume head can be reproduced.

The simulation used in this paper is of the 3D magnetic Rayleigh-Taylor instability in the Kippenhahn-Schülter prominence model. To destabilise the Kippenhahn-Schülter prominence model, a low density tube (density of 30% of the prominence) was placed inside the model. The boundary between this tube and the dense material was subjected to a random velocity perturbation allowing the magnetic Rayleigh-Taylor instability to develop. A 3D rendering of the initial conditions of this simulation are shown in Figure \[INIT\].

![3D rendering of the initial conditions of the simulation. The blue isosurface shows the density and the lines show the 