\def\content{
A simple electrical model for the inductive current drive is a time-varying voltage source ($U_l(t)$) connected to the plasma and the vacuum chamber in parallel can be seen on Figure \ref{fig:circuit}. Both the vacuum chamber and the plasma are modeled by LR circuits. The main difference is, that while the internal inductance and resistance of the chamber are constant, and thus they can be measured separately, the parameters of the plasma differ in each discharge.

\begin{figure}[ht]
\centering
\GWincludegraphics{width=0.5\textwidth}{Diagnostics/Basic/PlasmaCurrent/circuit.pdf}
	\caption{Model of the inductive current drive circuit}
	\label{fig:circuit}
\end{figure}

The basic circuit equations are:
\begin{align}
\label{eq:chamberLR}
	U_l(t) &=  R_{ch} \cdot I_{ch}(t) + L_{ch} \dfrac{d I_{ch}(t)}{d t}\\
\label{eq:plasmaLR}
	U_l(t) &=  R_{pl}(t) \cdot I_{pl}(t) + L_{pl} \dfrac{d I_{pl}(t)}{d t}\\
	I_{tot}(t)&= I_{pl}(t) + I_{ch}(t) 
\end{align}

The chamber parameters have already been determined according to Section \ref{sec:vacuum}. Integration of the \eqref{eq:chamberLR} circuit equation using the initial condition $I_{tot}(t=0)=I_{ch}(t=0)$ is implemented in the routine GOLEM\_chamber\_current.m to arrive to $I_{ch}(t)$. This can then be used to determine the plasma current, as $I_{pl}(t)=I_{tot}(t)- I_{ch}(t)$ as shown in Figure \ref{fig:block_diagrams_current}. Plasma resistivity can be determined in turn from equation \eqref{eq:plasmaLR}.

\begin{figure}[ht]
\centering
\GWincludegraphics{trim=1cm 5cm 0cm 4cm, clip=true, width=0.5\textwidth}{Diagnostics/Basic/PlasmaCurrent/block_diagrams_current.pdf}
	\caption{Block diagram showing the steps of data processing for the plasma current measurement.}
	\label{fig:block_diagrams_current}
\end{figure}

Having calculated the plasma current, a threshold can be defined significantly exceeding the calculation accuracy to safely determine the beginning and end of the plasma discharge. Using this threshold in the "find" function, one can cut the time signals to the extent of the discharge for further processing. Time duration of the dsischarge is also an imprtant parameter.

\emph{This task needs some programming that should be done parallel to the task described in Section \ref{sec:breakdown}!}

It can be attempted to investigate the effect of the $L_{pl}\approx 0 \;\rm H$ approximation by a more careful integration of choosing $L_{pl}\approx L_{ch}$ in the time region with plasma. If significant differences are found, this latter approximation has to be implemented for all further data processing.

A suitable threshold in plasma current can be used to determine the discharge duration and cut out the interval of the measured signals relevant for plasma diagnostics.

Plasma current has to be calculated for all discharges with plasma and the maximum value and the discharge duration have to be included in the shot summary table. 
}