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Specific resistivity of a fully ionized plasma only depends on its electron temperature ($T_e$) and effective charge number ($Z_{eff}$). This dependence is quantified by the Spitzer formula \cite{nrl_formulary}. It has to be noted that the ion temperature can be very much different from electron temperature. The effective charge number is determined by the amount, composition and state of impurities in the $H_2$ plasma, and we can take value $Z_{eff}\approx 2.5$ for GOLEM plasmas.

Center of the plasma has higher temperature, and lower resistivity with higher current density, which makes the estimation of the electron temperature ambiguous from an integrated value of resistivity ($R_{pl}(t)$). However, if we use an equilibrium temperature profile \eqref{eq:temp_prof} (Figure \ref{fig:temp_profile}), measured in more detailed measurements \cite{brotankova}, we can estimate one parameter of the profile, which is in this case the central electron temperature ($T_{e0}(t)$):
\begin{equation}
	T_{e}(r,t)=T_{e0}(t)\left( 1-\dfrac{r^2}{a^2} \right)^2
\label{eq:temp_prof}
\end{equation}

\begin{figure}[ht]
\centering
\GWincludegraphics{width=0.5\textwidth}{Diagnostics/DischargeCharacteristics/CentralElectronTemperatureSpitzerFormula/temp_profile.pdf}
	\caption{Equilibrium temperature profile used in the estimation of central plasma temperature}
	\label{fig:temp_profile}
\end{figure}

The central electron temperature ($T_{e0}$) is then calculated from equation (3.20) of \cite{brotankova}, which itself is based on Spitzer's resistivity formula:
\begin{equation}
	T_{e0}(t)=\left(\dfrac{R_0}{a^2}\dfrac{8 Z_{eff.}}{1544}\frac{1}{R_{pl}(t)}\right)^{2/3},
\end{equation}
where $R_{pl}(t)$ is in Ohms, distances are in meters and we get $T_{e0}(t)$ in electronvolts.

It has to be noted that plasma in the GOLEM tokamak is only fully ionized in the central region, $Z_{eff}$ can be estimated with large uncertainty and even the $a$ plasma small radius might change in an unmonitored way due to the lack of plasma stabilization. All these factors make the estimation of the central electron temperature quite uncertain.

Nevertheless, central electron temperature has to be calculated for all discharges with plasma and the maximum value has to be included in the shot summary table.

}