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In GOLEM, part of the toroidal current always flows in the vacuum vessel, which has to be taken into account during the interpretation of experimental results. In a vacuum shot, when no plasma is formed, it is possible to determine the resistance of the vacuum vessel: all the current measured by the Rogowski-coil flows in the vessel. This is an important parameter for further evaluations.

Let us denote the loop voltage with $U_{l}$, the resistance of the chamber by $R_{ch}$, the total current (which is the chamber current ($I_{ch}$) in this case) with $I_{p+ch}$ and the inductance of the chamber by $L_{ch}$.

The circuit equation is then
\begin{equation}
	U_{l}(t)= R_{ch} \cdot I_{p+ch}(t) + L_{ch} \dfrac{d I_{p+ch}}{d t}.
\label{eq:vac}
\end{equation}

Using the loop voltage measurement and the Rogowski-coil, we have both $U_{l}$, $I_{p+ch}$ and $dI_{p+ch}/dt$ measured, so $R_{ch}$ and $L_{ch}$ can be determined. 

A simple method is the following: Just after switching on the toroidal electric field, the toroidal current is still close to zero ($I_{p+ch}\approx 0$), so $U_{l}\approx L_{ch} dI_{p+ch}/dt$, so $L_{ch}$ can be determined. On the other hand, at the flat top of the current curve ($dI_{p+ch}/dt \approx 0$) equation \eqref{eq:vac} simplifies to $U_{l}\approx R_{ch} \cdot I_{p+ch}$, so $R_{ch}$ can be estimated.

A more sophisticated method is a 2D least squares linear fit making use of all data points $(U_{l},I_{p+ch},dI_{p+ch}/dt)$. Since we have only two independent parameters $R_{ch}$ and $L_{ch}$, the fitted plane has to pass through the origin. If we divide equation \eqref{eq:vac} by $I_{p+ch}$, we can simplify the task to a 1D least squares linear fit, which can be easily implemented in MATLAB (OCTAVE), using \textit{polyfit} function.

Values of $R_{ch}$ and $L_{ch}$ should be calculated for about \textbf{5} discharges having different parameters, and the results should be compiled to a single best estimate for both parameters. Estimation should be performed by both methods described above, and the results of the method giving the more precise estimates should be used in the further steps.
}