%<*Tools>
The GOLEM tokamak, $U_{l}$ wire, $B_{t}$ coil, Rogowski coil, photodiode with $\mathrm{H}_{\alpha}$ filter, oscilloscope RIGOL, coaxial cables with BNC connectors, device for remote tokamak operation (e.g. laptop).
%</Tools>
%<*ToolsRemote>
The GOLEM tokamak, basic GOLEM diagnostics ($U_{l}$ wire, $B_{t}$ coil, Rogowski coil, photodiode with $\mathrm{H}_{\alpha}$ filter), RIGOL oscilloscope, device for remote tokamak operation (e.g. laptop).
%</ToolsRemote>
%<*WarningRemote>
Note: {\bf It is highly recommended that students complete task 1 \underline{before} the experiment begins.} Tokamaks are complex machines and GOLEM data access and processing cannot be done without due preparation. We therefore implore students to designate sufficient time (approx. 3 hours) to prepare for the class by completing task 1 beforehand. If a student comes to the class unprepared, it will cost him/her excruciating difficulties with experimental data processing after the class and losing more than the said amount of time desperately trying to understand what is required of him/her in tasks 2-5.
%</WarningRemote>
%<*Task1:Preparation>
\underline{Homework before the measurements}: Learn how to access and manipulate the remote data files from GOLEM measurements according to \cite{gw:KFpraktdopr}. Then use the link at \cite{gw:KFpraktdopr} to access the web-based virtual control room and get familiar with the web interface. Finally, bring at least one laptop per group to the measurement, with the remote file access already set up and tested.
%</Task1:Preparation>
%<*Task1:PreparationRemote>
\underline{Homework before the measurements}: Learn how to access and manipulate the remote data files from GOLEM measurements according to \cite{gw:KFpraktdopr}. Then use the link at \cite{gw:KFpraktdopr} to access the web-based virtual control room and get familiar with the web interface. At least one group member must have the remote file access already set up and tested when the experiment begins.
%</Task1:PreparationRemote>
%<*Task2:MeetGOLEM>
\underline{In the tokamak laboratory}, have a look at the GOLEM tokamak and identify its basic elements described in this document (tokamak chamber, toroidal field coils, transformer core and primary winding, vacuum pumps etc.). With the help of an assistant, test the function of the following individual components of the tokamak facility:
\begin{itemize}
\item Turn the vacuum pumping off and on again.
\item Fill the tokamak vacuum vessel with the working gas.
\item Test the pre-ionisation system ("electron gun" / light bulb wire).
\end{itemize}
%</Task2:MeetGOLEM>
%<*Task2:OscilloscopeSetupRemote>
Connect to the web control interface of your group's oscilloscope (the link will be provided to you on the spot) and set up your oscilloscope for measurement. Use \cite{OscilloscopeManual} as a reference.
%</Task2:OscilloscopeSetupRemote>
%<*Task3:TestDischargeRemote>
Using the remote control room, execute a test tokamak discharge with arbitrary values of $U_B$, $U_{CD}$ and $p_0$, pre-ionisation on. Plot the time traces of the individual diagnostic signals:
\begin{itemize}
\item loop voltage $U_l$ (channel 1)
\item voltage induced on the small $B_t$ measuring coil (channel 2)
\item voltage induced on the Rogowski coil (channel 3)
\item voltage of the photodiode with an $\mathrm{H}_{\alpha}$ filter measuring the plasma radiation intensity (channel 4)
\end{itemize}
%</Task3:TestDischargeRemote>
%<*Task3:InstallDiagnostics>
\underline{In the tokamak laboratory}, install 4 basic diagnostic tools on the tokamak: a wire measuring the loop voltage $U_{l}$, a small coil measuring the toroidal magnetic field $B_{t}$, a Rogowski coil measuring the sum of chamber and plasma current $I_{ch+p}$, and a photodiode with an $\mathrm{H}_{\alpha}$ filter measuring the plasma radiation intensity. Connect all of these diagnostics to the 4-channel oscilloscope RIGOL (or dedicated data acquisition channels). Then execute a tokamak discharge with preset values of $U_B$, $U_{CD}$ and $p$, pre-ionisation on, and record the time trace of the individual diagnostic signals.
%</Task3:InstallDiagnostics>
%<*Task4:Calibration>
\underline{Using the remote control room}, run the following exploratory experiments:
\begin{enumerate}
\item \label{task:4a} \textbf{$B_t$ coil calibration.} Create a discharge with toroidal magnetic field $B_{t}$ only ($U_B>0$, $U_{CD}=0$, $p=0$, pre-ionisation off), and record the time trace of the $B_t$ coil voltage $U_{B_t}(t)$. Compare the time-integrated $U_{B_t}$ to the signal \texttt{torodial\_field}, stored within the GOLEM database, and calibrate your $B_t$ measuring coil according to equation \eqref{eq:CBt} (e.g. specify $C_{B_t}$).
\item \label{task:4b} \textbf{Rogowski coil calibration.} Create a discharge with toroidal electric field $E_{t}$ only ($U_B=0$, $U_{CD}>0$, $p=0$, pre-ionisation off), and record the time trace of the loop voltage $U_{l}$ and the Rogovski coil voltage $U_{RC}(t)$. Compare the time-integrated $U_{RC}$ to the signal \texttt{rogowski\_current}, stored within the GOLEM database, and calibrate your Rogowski coil according to equation \eqref{eq:CRC} (e.g. specify $C_{RC}$ and $R_{ch}$).
% \item \textbf{Chamber resistivity calculation.} Execute a vacuum discharge ($U_B>0$, $U_{CD}>0$, $p=0$, pre-ionisation off) and, from the time traces of $U_{loop}(t)$ and $I_{ch+p}(t)$ and your newly calculated $C_{RC}$, estimate the vessel resistance $R_{ch}$ according to equation \eqref{eq:Rogowski}.
\item \textbf{Test discharge.} Execute a full plasma discharge ($U_B>0$, $U_{CD}>0$, $p>0$, pre-ionisation on) and, using the measured $U_{l}(t)$ and $U_{RC}(t)$ and the previously estimated $C_{RC}$ and $R_{ch}$, calculate the time trace of the plasma current $I_{p}(t)$ using equation \eqref{eq:Rogowski}. Subsequently, calculate and plot the time trace of the electron temperature $T_{e}(t)$ according to equation \eqref{eq:SpitzerTe}.
\end{enumerate}
As you go, cross-check all the signals obtained from your improvised diagnostic system with the standard diagnostics system of the GOLEM tokamak.
%</Task4:Calibration>
%<*Task4:DischargeSeries>
\label{task:5}
Using the remote control room, execute 10 discharges with 5 different values of $U_{B}$, 2 different values of $U_{CD}$, arbitrary but constant $p_0$ and $T_{CD}$ and pre-ionisation on. This discharge series may be shared between the present groups so that the laboratory as a whole takes less time.
%</Task4:DischargeSeries>
%<*Task5:DataProcessing>
Process the oscilloscope data as described in sections \ref{part:diagnostics} and \ref{part:data_processing}. Compare standard GOLEM diagnostics output with processed oscilloscope data for one discharge.
%</Task5:DataProcessing>
%<*Task6:Scaling>
For each of the discharges, calculate the energy confinement time $\tau_E$ and the toroidal magnetic field $B_t$ during the quasi-stationary discharge phase. Plot a $(B_t, \tau_E)$ scatterplot with the errorbars representing the standard deviation (see section \ref{part:averaging}). Calculate the mean confinement time $\tau_E$ and compare it to the Neo-Alcator scaling law \cite[page 1131]{Parker1985}, which relates the ratio of the confinement time $\tau_E$ and the electron density $n_e$ to the tokamak major radius $R$ and minor radius $a$.
%</Task6:Scaling>
%<*Task5:ScalingLaws>
\label{task:5}
\underline{Using the remote control room}, execute 10 discharges with 5 different values of $U_{B}$, 2 different values of $U_{CD}$, arbitrary but constant $p$ and $T_{CD}$ and pre-ionisation on. This will facilitate a parameter scan in the toroidal magnetic field $B_t$ and the plasma current $I_p$. Estimate the energy confinement time $\tau_E$ in the quasi-stationary phase of the discharges using the mean and the standard deviation. Plot the observed confinement time $\tau_E$ (with errorbars representing the standard deviation, see section \ref{part:averaging}) versus the mean magnetic field $B_t$ in this time window. Compare the $\tau_E$ value with the Neo-Alcator scaling law
%\cite[Eq. (19)]{Yushmanov1990} and
\cite{Parker1985}, which predicts the confinement time based on the tokamak major and minor radius.
(More on scaling laws can be read in \cite{ScalingLaws}.)
%</Task5:ScalingLaws>
\subsection{Plasma breakdown}\label{sec:breakdown}
After measuring the vacuum chamber properties, we can make the next step towards creating a tokamak plasma: we can let $H_2$ gas into the chamber before initiation of the toroidal electric field. The $p_{H2}$ value, which can be set as a discharge parameter, is a control parameter for the inlet valve. The actual value of the pre-discharge gas pressure is measured by a vacuummeter $p_{ch}$.
As we will see, letting $H_2$ gas into the chamber is not always sufficient to produce a plasma. The toroidal electric field must also reach a critical value for mass ionization, in other words plasma breakdown.
The task is to plot the $p_{ch}$ against the maximum of the loop voltage spikes in the beginning of the discharge for several discharges, and indicate the plasma breakdown by the shape of the symbols. Shots should be concentrated around the critical line separating breakdown and non-breakdown shots. Detailed scan should be performed for a given magnetic field and the effect of the magnetic field should be studied with a few discharges. During this exercise the pre-ionization should be turned on to produce more reproducible results, but the effect of turning it off could also be studied. About a total of \textbf{30} discharges are available for this exercise.
