\documentclass{article}
\usepackage{graphicx}
\usepackage{subcaption}
\title{Calibration coefficient of ball-pen probe measurement}
\date{14.12.2017}
\author{Petr Macha}
\begin{document}
\maketitle
\section{Experimental setup}
\begin{figure}[!h]
\begin{center}
\includegraphics[height = 10cm]{setup_7_12_17_ver2}
\caption{experiment setup.}
\end{center}
\end{figure}
\section{Theory}
The aim of this work is to find calibration coefficient of ball-pen probe. To get this coefficitent, we have to use Langmuir probe to construct IV characteristics (shot to shot method) and fit them by equation 1.
\begin{equation}
\alpha = \frac{U_{float}^{bpp} - U_{float}^{lp}}{T_{e}},
\end{equation}
Where $U_{float}^{bpp}$, $U_{float}^{lp}$, $T_{e}$ are parameters via we fit. Going through all the IV characteristics can we find, how calibration coefficient depends on magnetic field.
\section{Experiment configuration}
\begin{enumerate}
\item Gas pressure 0.36 -19.93
\item Working gas: hydrogen
\item Pre-ionization: Upper el. Gun
\item $C_{Bt}$ capacitors charged to: 1300 V, triggered 5.0 ms
\item $C_{CD}$ capacitors charged to: 400 V, triggered 5.0 ms
\end{enumerate}
The numbers of shots, used for measurement are: $\# 25483$ to $\# 25490$ and $\# 25493 $ to $\# 25498$ using voltage from -134.3 to 25.5 V.
Both probes position from the vessel centre is r = 70 mm and resistance on LP was set as R = 20 Ohm.
\section{Minutes of the experiment}
\begin{enumerate}
\item The radial profile was meassured before meassurement to find best position of probes.
\item Resistance on LP was set to $20 \ \Omega$
\item Scan via $V_{bias} = \{ -12.8, -25.6, -38.3, -51.1, -63.9, -76.7, -89.4, -102.2, -134.3, -12.8, 0, 12.8, 25.5 \} \ V$
\end{enumerate}
\section{Data analysis}
IV characteristics were using equation (1). All fits are included in .zip file.
Experiment setup is given in Figure 1.
The figure 2 shows that coefficient alpha is eqaual to $\alpha = 2.2\ \pm\ 1.2$.
\begin{figure}
\begin{center}
\includegraphics[height = 8cm]{alpha_final}
\caption{final results of meassurement.}
\end{center}
\end{figure}
\section{Reproducibillity}
To get best results is it important to have good shots reproducibillity, which is shown in Figures 3, 4
\begin{figure}
\begin{center}
\includegraphics[width = 13cm,height = 7cm]{repro_voltage_2}
\caption{shows loop voltage of each shot.}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width = 13cm, height = 7cm]{repro_current_2}
\caption{shows plasma current of each shot.}
\end{center}
\end{figure}
These figures show that the reproducibillity could be better so it influences the results a lot.
\section{Fits}
At the end of the document, all fits are included.
\section{Conclusion}
To sum up, the ion saturation current is reach, because the negative voltage goes up to - 134.3, which seems to be enoght. The problem could be with reproducibillity, which is for some of the shots worse.
\begin{figure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_4}
\caption{Fit t = 6.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_5}
\caption{Fit t = 7 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_6}
\caption{Fit t = 7.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_7}
\caption{Fit t = 8 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_8}
\caption{Fit t = 8.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_9}
\caption{Fit t = 9 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_10}
\caption{Fit t = 9.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_11}
\caption{Fit t = 10 ms}
\label{fig:sfig2}
\end{subfigure}
\end{figure}
\begin{figure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_12}
\caption{Fit t = 10.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_13}
\caption{Fit t = 11 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_14}
\caption{Fit t = 11.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_15}
\caption{Fit t = 12 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_16}
\caption{Fit t = 12.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_17}
\caption{Fit t = 13 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_18}
\caption{Fit t = 13.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_19}
\caption{Fit t = 14 ms}
\label{fig:sfig2}
\end{subfigure}
\end{figure}
\begin{figure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_20}
\caption{Fit t = 14.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_21}
\caption{Fit t = 15 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_22}
\caption{Fit t = 15.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_23}
\caption{Fit t = 16 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_24}
\caption{Fit t = 16.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_25}
\caption{Fit t = 17 ms}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_26}
\caption{Fit t = 17.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_27}
\caption{Fit t = 18 ms}
\label{fig:sfig2}
\end{subfigure}
\end{figure}
\begin{figure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_28}
\caption{Fit t = 18.5 ms}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.1\linewidth]{fit_lp_final_29}
\caption{Fit t = 19 ms}
\label{fig:sfig2}
\end{subfigure}
\caption{plots of....}
\label{fig:fig}
\end{figure}
\end{document}
