\include{fusion}
\def\fig#1#2#3#4{
\begin{figure}[h]
\centering
\includegraphics[width=#1\textwidth, height=!]{#2}\caption{#3}\label{#4}
\end{figure}}
\def\bi{\begin{itemize}\setlength{\itemsep}{-5pt}}\def\ei{\end{itemize}}\def\im{\item}
\def\ig{\includegraphics}
\def\tw\textwidth
\def\ChamberResistivity{10 m$\Ohm$} %Podle Honzy Stockela 2009
\def\ChamberResistivity_{5.7 m$\Ohm$} %Podle Ivana Durana 2009
\def\ChamberResistivity_{5.49 m$\Ohm$} %Podle Jany Brotankove 2009
\def\golemstory{According to Jewish folklore narrative, Judah chief rabbi Loew created a golem out of the clay in the late 16th century to defend the Prague ghetto from anti-Semitic attacks. Golem was brought to life through Jewish rituals \cite{wiki-golem}. As this golem became increasingly violent and spreading fear, it was deactivated and from this time his enormous energy lies without benefit somewhere in Prague.
Modern culture brings a new versions of the golem story, among others it is possible to trace up the pursuit of a lot of people to find him and try to activate to get the great armament over the all the word. On the other hand some people are trying to direct the golem energy to "bake the bread''.
{\bf The fusion is a kind of enormous energy potential which is relativelly easy possible to misuse to get dominancy somewhere, on the other hand, there is a enormous strength of humankind to use this energy to "bake the bread''. }}
\def\history
{
\bi
\im {\bf TM1-TH (1960-1974)}, tokamak was created in Kurchatov institut, Moscow
\im {\bf CASTOR (1977-2007)}, tokamak was operated as scientific device in the Institute of plasma physics, Czech Academy of Sciences, Prague. New chamber was installed
\im {\bf GOLEM (2008-)}, tokamak was moved to Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Prague as a educational device for a new teaching specialization "Physics and Technology of Thermonucear Fusion''
\ei
}
\def\originalengscheme
{
\bi
\im Vacuum system,
\im toroidal field generation,
\ei
}
\def\proposedexperiments
{
\bi
\im {\bf Tokamak technology}
\bi
\im Vacuum technology and measurement.
\im Magnetic field in a coil.
\im RLC circuits.
\im Transformer action.
\im Data acquisition.
\im Feedback stabilization.
\ei
\im {\bf Tokamak operation}
\im {\bf Elementary diagnostics} of global plasma discharge parameters, like plasma density, electron and ion temperature, loop voltage, plasma current and plasma radiation on selected $H_\alpha$ and CIII energies.
\im {\bf Probe diagnostics} offers detailed information about plasma edge physics.
\bi
\im Arrays of Langmuir probes are planned to space-time monitoring of turbulence structures.
\im Emissive Ball pen probe to measure plasma potential.
\im Ion flows measured by oriented probes.
\im Fast ion aned electron temperature measurement by tunnel probes.
\ei
\im Radiation
\ei
}
\def\tokamakgolem
{
GOLEM is a small size tokamak with the circular poloidal cross-section. Main parameters are:
\bi
\im{Major radius of the vacuum vessel $R=0.4$ m.}
\im{Minor radius of the vacuum vessel $r=0.1$ m.}
\im{Radius of poloidal limiter $a = 0.085$ m.}
\ei
Principal engineering scheme (see fig \ref{EngScheme}) has five principal parts:
\fig{0.9}{figs/MainSchemaMarkovic/schema3.png}{Principal engineering scheme of the tokamak}{EngScheme}
\bi
\im {$B_t$ toroidal magnetic field generation circuit (blue color) with the aim to confine the plasma, consisting of a set of capacitors with the total capacity $C_B=10.8$ mF charged up to $U_{C_B}=2$ kV, which is triggered by PC controlled thyristor into a set of 28 magnetic field coils, altogether having inductance $L_B=2.76$ mH. This LC circuit together with the thyristor produce one harmonic current pulse in the coils which generates the required toroidal magnetic field $B_t$. }
\im {$E_t$ toroidal electric field generation circuit (green color) with the aim to generate, heat the plasma and to drive the plasma current, consisting of a set of capacitors with the total capacity $C_E=3.6$ mF charged up to $U_{C_E}=600$ V, which is triggered by PC controlled thyristor into a primary winding of the transformer. This LC circuit generate through the time changing magnetic flux in the transformer core the appropriate toroidal electric field $E_t$ which firstly generate and consequently heat the plasma. $E_t$ generates current both in plasma and in the tokamak chamber, which resistance $R_{chamber}\approx 10\ m\Omega$}
\im {Vacuum system, consisting of a rotary vacuum pump, valves, a turbomolecular pump and a measurement system, alltogether aiming to reach the preassure $\approx 5\cdot 10^{-4}$ Pa.}
\im {Gas handling system providing hydrogen with working preassure $\approx 5\cdot 10^{-2}$ Pa.}
\im {Backing system, which serves to clean the tokamak chamber.}
\ei
}
\def\das{
At the moment, the GOLEM tokamak is equipped by following diagnostics
\bi
\item A single loop around the transformer core measures the loop voltage $U_{loop}$.
\item A Rogowski coil, surrounding the tokamak chamber measures the sum of the plasma and chamber current $I_{p+ch}$.
\item A small pick-up coil placed on the tokamak chamber measures the toroidal magnetic field $B_t$.
\item A photocell facing a glass port of the tokamak measures the plasma radiation in the visible part of the spectra.
\ei
Experimental data from these diagnostics are digitized by the sampling frequency 100 kHz and stored by PC.
\fig{1.0}{kresby/planek/das.pdf}{Diagnostic system of the tokamak GOLEM}{das}
}
%%%%%%%%%%%%%%%%%%%% EXPERIMENTS %%%%%%%%%%%%%%%
\def\minimum{
Start to charge capacitor sets both the $U_E$ and $U_B$ up to 600 V with the $p_{H_2}$ preassure at $\approx 2\cdot 10^{-2}$ Pa and time delay $\tau_{BE}\approx 2$ ms beetween $U_B$ thyristor trigger and $U_E$ thyristor trigger. Find the minimumvalues of $U_E, U_B, p_{H_2}, \tau_{BE}$ parameters to get the plasma discharge.
}
\def\safetyfactor{
The safety factor $q$ (see e.g. \cite[J. Brot\'ankov\'a Ph.D.]{BrotancePhD}) describes a helicity of a resulting magnetic field in the tokamak as a superposition of a toroidal $B_t$ and poloidal $B_p$ magnetic field components. In the first approximation for the GOLEM like tokamaks, it can be expressed as: $$q(r)=\frac{r}{R}\frac{B_t}{B_p(r)}.$$ Measure the safety factor and find two regimes (by changing $U_E, U_B, p_{H_2}, \tau_{BE}$ ) with the most different values of the safety factor.
}
\def\habilitace
{
\documentclass[12pt]{article}
\usepackage{graphicx}
\topmargin -3cm\oddsidemargin -1.5cm\textwidth 19cm\textheight 27cm
\begin{document}
\title{GOLEM}\author{Vojt\v ech Svoboda}\maketitle
\section{Introduction}
\golemstory
\subsection{History}
\history
\section{..}
\originalengscheme
\proposedexperiments
\end{document}
}
\def\sumtraic09
{
\documentclass[12pt,pdftex]{article}
\usepackage{graphicx}
\topmargin -3cm\oddsidemargin -1.5cm\textwidth 19cm\textheight 25cm
\begin{document}
\title{SUMTRAIC at GOLEM}\author{Vojt\v ech Svoboda}\date{\today\\http://golem.fjfi.cvut.cz/sumtraic}\maketitle
\section{Tokamak GOLEM}
\tokamakgolem
\section{Available diagnostics}
\das
\section{Proposed laboratory experiments}
\bi
\im \minimum
\im \safetyfactor
\ei
\nocite{BrotancePhD}
\nocite{wwwgolem}
\bibliographystyle{plain}
\bibliography{/home/svoboda/Work/Stale/Bibtex/biblio}
\end{document}
}
\def\praktikaFTTF09
{
\documentclass[12pt,pdftex]{article}
\usepackage{graphicx}
\topmargin -3cm\oddsidemargin -1.5cm\textwidth 19cm\textheight 25cm
\begin{document}
\title{FTTF practicum at GOLEM}\author{Vojt\v ech Svoboda}\date{\today\\http://golem.fjfi.cvut.cz}\maketitle
\section{Tokamak GOLEM}
\tokamakgolem
\section{Available diagnostics}
\das
\section{Proposed laboratory experiments}
\bi
\im \minimum
\im \safetyfactor
\ei
\nocite{BrotancePhD}
\nocite{wwwgolem}
\bibliographystyle{plain}
\bibliography{/home/svoboda/Work/Stale/Bibtex/biblio}
\end{document}
}
\def\LoopVoltageModelFeb10
{
\documentclass[12pt,pdftex]{article}
\usepackage{graphicx}
\topmargin -3cm\oddsidemargin -1.5cm\textwidth 19cm\textheight 25cm
\include{defs}
\begin{document}
\title{Loop voltage model v 1.0}\author{}\date{\today}\maketitle
\section{Introduction}
Purpose of this article is to evaluate the loop voltage $U_{loop}$ at the tokamak from the equivalent RLC circuit
\section{Circuit}
\begin{figure}[h]
\centering
\includegraphics[width=0.4\textwidth]{kresby/LoopVoltageModel/obvod}
\caption{equivalent circuit }
\end{figure}
Kirchhoff's circuit laws for current $I_{pr}$ in the primary (index $_{pr}$) coil stays: $$U_C+U_R+U_L=0$$ Since the voltage drops $U_C$, $U_R$ and $U_L$ at the capacitor $C_{pr}$, resistor $R_{pr}$ and inductance $L_{pr}$ equals $U_C=Q/C_{pr}$, $U_R=R_{pr}I=R\frac{dQ}{dt}$ and $U_L=L_{pr}\frac{dI_{pr}}{dt}$. Since \be I_{pr}=\frac{dQ}{dt}=\dot Q\footnote{we will use ``dot'' notation $\frac{dQ}{dt}=\dot Q$ et vice versa}\label{IQequiv},\ee we have a second order differential equation for charge $Q$ at the capacitor $C_{pr}$:\be\frac{1}{C_{pr}}Q+R_{pr}\dot Q+L_{pr}\ddot{Q}=0\label{RLCeqQ}\ee with initial condition staying inital voltage at charged capacitor (e.g. 300 V (Golem shot No:1622)).
\section{Magnetic field $B$ evaluation}
We are looking for magnetic flux $\mathbf \Psi$. The time evolution of the charge $Q$ at the capacitor $C_{pr}$ gives the equation (\ref{RLCeqQ}) and consequently the current $I_{pr}$ through the primary coil of the transformer can be obtained with the help of the (\ref{IQequiv}) equation. Ampere law gives the proportionality between the magnetic field $\mathbf B$ and the current $I_{pr}$ (times number of primary coil loops):$$\oint_{s_{pr}} \mathbf B\cdot dl=\mu_{0}(\frac{N_{pr}}{2})I_{pr}.$$ To a first approximation we can assume $\mathbf B$, generated by the semisegment of the tokamak transformer, constant on the Ampere path (with the length in the Golem particular case $s_{pr}\approx 3.2$ m) as seen on the fig. \ref{tokamakcoils}. Then absolute value of the $\mathbf B$ is: \be B=\mu_{0}\frac{\frac{N_{pr}}{2}\ I_{pr}}{s_{pr}},\label{MagnF}\ee where $N_{pr}$ is the total number of primary coil loops at the transformer. The absolute value of the whole magnetic flux $\mathbf\Psi$ from both semisegments is then:\be\Psi = 2\ B\ A_s,\label{MagnFl}\ee where $A_s$ is the area of the central tokamak core $\approx 40\times 40\ $cm. Finally loop voltage $U_{loop}$ generated by the time change of the magnetic flux $\Psi$ gives Faraday's law of induction: $$U_{loop}=-\frac{d\Psi}{dt}$$.
\begin{figure}[h]
\centering
\includegraphics[width=0.4\textwidth]{kresby/LoopVoltageModel/schema}
\caption{Principal scheme }
\label{tokamakcoils}
\end{figure}
\section{Numerical model}
Let's create discrete model of vector $(t_i,U_{C_i},U_{R_i},U_{L_i},\ddot Q_i,\dot Q_i=I_{pr_i},Q_i,B_i,\Psi_i,U_{loop_i})$ time evolution with the time step $\Delta t=10\mu$s\ \footnote{The same interval as Golem DAS system}, where $i\in \left\langle 1..3000\right\rangle $, i.e $\left\langle 0..30\right\rangle $ms. Dynamics of this vector is determined by the equation (\ref{RLCeqQ}) with parameters according the real tokamak values: $C_{pr}=8\mbox{capacitors}\times450\mu$F, $R_{pr}=5 m\Omega$ and $L_{pr}=0.02$H\footnote{V tuto chv�li hodnoty vysypane z rukavu} .Initial condition at $t=0$ is $$(t_1=0,U_{C_1}=300V,U_{R_i}=0,U_{L_i}=0,\ddot Q_i=0,\dot Q_i=I_{pr_i}=0,Q_i=C_{pr}*U_{C_1},B_i=0,\Psi_i=0,U_{loop_i}=0).$$ Situation in the next time step $t_2$ can be computed from the $t_1$ situation in this way:
\begin{eqnarray}
t_2 &=& t_1+\Delta t \nonumber \\
\ddot Q_2 &=& \frac{R_{pr}}{L_{pr}}\dot Q_1-\frac{1}{L_{pr}C_{pr}}Q_1 \ \ \ \mbox{see eq. (\ref{RLCeqQ}}) \nonumber \\
\dot Q_2 &=& \dot Q_1+\ddot Q_2\Delta t \ \ \ (\mbox{since}\ \ddot Q=\frac{d\dot Q}{dt}\Rightarrow\ddot Q=\frac{\dot Q_2-\dot Q_1}{\Delta t}) \nonumber \\
Q_2 &=& Q_1+\dot Q_2\Delta t \nonumber \\
U_{C_2} &=& Q_2/C_{pr} \nonumber \\
U_{R_2} &=& \dot Q_2R_{pr}\ \ \ (\mbox{Since}\ I_{pr}=\dot Q) \nonumber \\
U_{L_2} &=& L_{pr}\frac{\dot Q_2-\dot Q_1}{\Delta t} \ \ \ (\mbox{Since}\ U_L=L \frac{dI}{dt}) \nonumber \\
B_2 &=& \mu_0\frac{\frac{N_{pr}}{2}\dot Q_1}{s_{pr}}\ \ \ \mbox{see eq. (\ref{MagnF})} \nonumber \\
\Psi_2 &=& 2\mu_r\ B_2\ A_s \ \ \ \mbox{see eq. (\ref{MagnFl})} \nonumber \\
U_{loop_2} &=& -\frac{\Psi_2-\Psi_1}{\Delta t} \nonumber \\
\end{eqnarray}
Following time steps can be computed recurrently exactly the same way.
\bibliographystyle{plain}
\bibliography{/home/svoboda/Work/Stale/Bibtex/biblio}
\end{document}
}
\def\EPSDublin2010abstrakt
{
\documentclass{epsconf}
\usepackage{graphicx}
\usepackage{wrapfig}
\usepackage{amsmath}
\title{Remote handling}
\author{\underline{V. Svoboda}$^1$, J. St\"o ckel$^2$}
\institute{
$^1$ Association EURATOM-IPP.CR, CZ-182 21 Prague, Czech Republic.\\
$^2$ Association EURATOM-IPP.CR, CZ-115 19 Prague, Czech Republic.\\
}
\renewcommand{\baselinestretch}{1.}
\begin{document}
\maketitle
\include{defs}
\bibliographystyle{plain}
\bibliography{/home/svoboda/Work/Stale/Bibtex/biblio}
\end{document}
}
\def\firstglowdisch{
\begin{frame} \frametitle{$8^{th}$ June 2009: Golem first plasma - glow discharge }
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{figs/Golem/cimg8066}
\end{figure}
\end{frame}}
\def\firstplasma{
\begin{frame} \frametitle{$9^{th}$ July 2009: Golem first tokamak plasma }
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{figs/Golem/firstplasma}
\end{figure}
\end{frame}}
\def\batchcontrol{
\begin{frame} \frametitle{Batch tokamak control (ssh/putty)}
\footnotesize
firsttrial: \#without hydrogen
\def\indth{\hspace{1cm}}
\indth make shot Ue=400 Ub=400 Td=2000 H2filling=0 pH2=68\newline
scndtrial: \#with hydrogen
\indth make shot Ue=400 Ub=400 Td=2000 H2filling=1 pH2=66\newline
H2seq:
\indth make shot Ue=400 Ub=400 Td=2000 H2filling=0 pH2=66
\indth make shot Ue=400 Ub=400 Td=2000 H2filling=1 pH2=66
\indth make shot Ue=400 Ub=400 Td=2000 H2filling=1 pH2=68
\indth make shot Ue=400 Ub=400 Td=2000 H2filling=1 pH2=70
\indth make shot Ue=400 Ub=400 Td=2000 H2filling=1 pH2=72
\indth�make shot Ue=400 Ub=400 Td=2000 H2filling=1 pH2=100\newline
firstloop:
\indth for Ue in `seq 300 100 700`; do
\hspace{2cm}�make shot Ue=\$\$Ue Ub=400 Td=2000 pH2=68 H2filling=1;
\indth done;
\end{frame}}
\include{prednasky}
