From 5d5566446f12fd3a039a5c5cf110131484f3a580 Mon Sep 17 00:00:00 2001 From: Viktoria Keusch Date: Wed, 4 Sep 2024 10:24:38 +0200 Subject: [PATCH] Final corrections --- summary/Sections/01_Introduction.tex | 2 +- summary/Sections/02_Coils.tex | 27 +++++++++--------- summary/Sections/03_Design.tex | 6 ++-- summary/Sections/04_Diagnostics.tex | 42 ++++++++++++++-------------- summary/Sections/05_Heating.tex | 25 +++++++++-------- summary/Sections/06_Vacuum.tex | 22 +++++++-------- summary/Sections/07_Conclusion.tex | 4 +-- 7 files changed, 65 insertions(+), 63 deletions(-) diff --git a/summary/Sections/01_Introduction.tex b/summary/Sections/01_Introduction.tex index 44a1a30..86884a7 100644 --- a/summary/Sections/01_Introduction.tex +++ b/summary/Sections/01_Introduction.tex @@ -1,7 +1,7 @@ \section{Introduction} The following report documents the progress and intermediate results of "Fusion Reactor Design", a joint course between Graz University of Technology and the Technical University of Munich, supported by Proxima Fusion. It consists of a student project where the goal is to design a fusion reactor with stellarator geometry, with priority given to the following properties: \begin{itemize} - \item \textbf{Size}: The reactor should be able to fit through a small door, imposing an upper size limit of 190x90 cm. + \item \textbf{Size}: The reactor should be able to fit through a small door, imposing an upper size limit of (190x90)~cm. \item \textbf{Aspect ratio and plasma volume:} While there is no hard limit here, the stellarator should have a high plasma volume, and thus the aspect ratio should be as low as possible without compromising other properties (stability, alpha particle losses, island reduction). \item \textbf{Coil simplicity:} The coils should be possible for a group of students to understand and theoretically construct. Realistically, this means that the number of coils and, more importantly, the number of coil types, should be kept at a minimum. diff --git a/summary/Sections/02_Coils.tex b/summary/Sections/02_Coils.tex index 39ac09b..3c1dc27 100644 --- a/summary/Sections/02_Coils.tex +++ b/summary/Sections/02_Coils.tex @@ -19,10 +19,9 @@ \subsection{Requirements and Tasks} It follows from these requirements that the coils have to be manufactured very precisely, stiff and robust as well as mounted very precisely within the vacuum chamber. - \subsection{Outcome} \subsubsection{Structure} -In order to meet the design requirements the overarching structure of a coil is made up of a multitude of water cooled double pancake coils separated by a thin insulator material. +In order to meet the design requirements, the overarching structure of a coil is made up of a multitude of water cooled double pancake coils separated by a thin insulator material. The whole coil structure is then embedded into a steel casing in order to avoid contamination of the vacuum from the used adhesives and material combinations. %\todo{Sketch of the coil structure - we need to make clear how the product looks like before we describe it in more detail} @@ -38,24 +37,24 @@ \subsubsection{Manufacturing} \end{itemize} While 3D printers can achieve high purity prints, with effective conductivities being close to 99\% of pure copper, current manufacturing methods do not allow us to print the geometries in the necessary dimensions and with a suitable internal surface smoothness. The internal roughness is of special concern, since water has to flow through the windings without too much pressure loss. -Additionally the powder used during manufacturing remains in the channels and can be difficult do remove from the manufactured coils. +Additionally the powder used during manufacturing remains in the channels and can be difficult to remove from the manufactured coils. Due to this it was decided to use conventional manufacturing methods. -While the manufacturing of the complex geometries might prove challenging for future teams the advantages of off the shelf copper conductors, especially high performance conductors, cannot be overstated. +While the manufacturing of the complex geometries might prove challenging for future teams, the advantages of off the shelf copper conductors, especially high performance conductors, cannot be overstated. As mentioned above the coils are designed to be inside a casing, which addresses both outgassing concerns, a well as the feedthroughs for water and current. For the casing of the coils, electron beam sintering could be considered in addition to 5-axis milling in order to achieve the necessary accuracy. The casings are flanged to the walls of the vacuum chamber, such that the inside of the casings are not under vacuum, which makes the design of the winding pack easier.\\ -(for more: \href{https://cloud.tugraz.at/index.php/apps/onlyoffice/s/XBeMB6XiRDt3L2p?fileId=1032740140}{"Isolation and 3D Printing" Powerpoint presentation}). +(for more: \href{https://cloud.tugraz.at/index.php/apps/onlyoffice/s/XBeMB6XiRDt3L2p?fileId=1032740140}{"Isolation and 3D Printing" PowerPoint presentation}). \subsubsection{Insulation} The windings within a coil have to be insulated from each other. -The best option seems to be fibre glass reinforced epoxy, as it be bought in pre-impregnated rolls and further improves stability. +The best option seems to be fibre glass reinforced epoxy, as it can be bought in pre-impregnated rolls and further improves stability. The epoxy has to be hardened for which the coil might have to cooled, using the already in place water-cooling. -However, then the epoxy can withstand the applied temperature and forces and it should be around \SI{0.5}{mm} to \SI{1.0}{mm} thick. +Then the epoxy can withstand the applied temperature and forces and it should be around \SI{0.5}{mm} to \SI{1.0}{mm} thick. In order to prevent outgassing of the coils into the vacuum chamber, they are to be enclosed with a stainless steel casing of \SI{2.0}{mm} thickness, which could either be 3D printed or manufactured by arc welding sheet metal.\\ \subsubsection{Optimization} A python script was developed in order to explore the space of possible configurations. -In the beginning rough estimates for the magnetic field and size were used, they were later replaced by the actual currents supplied by the optimization team and the size of the vacuum chamber. +In the beginning rough estimates for the magnetic field and size were used, later they were replaced by the actual currents supplied by the optimization team and the size of the vacuum chamber. The overall goal was to reduce both power loss and pressure loss, while staying within some reasonable bounds for voltage and current. This was done for different winding configurations and pipe diameters. Figure \ref{fig:both} shows an example output. The simulation is based on double pancakes, meaning, that two neighbouring coils are paired and supplied with water separately. @@ -70,20 +69,20 @@ \subsubsection{Optimization} \begin{subfigure}[b]{0.3\textwidth} \centering \includegraphics[width=0.9\textwidth]{Images/02_Coils/pressure.png} - \caption{pressure drop} + \caption{Pressure drop} \label{fig:pressure} \end{subfigure} - \caption{6x1mm pipe configuration and 6x1mm pipe pressure drop calculation for different configurations} + \caption{(6x1)~mm pipe configuration and (6x1)~mm pipe pressure drop calculation for different configurations} \label{fig:both} \end{figure} -A design with rectangular pipes and circular holes for water, greatly improves the power loss and pressure loss characteristics. %\todo{Where is an image of it?@Mimo please run the simulation for conductors with the square outer cross section that we can display it} -While these pipes exist and a re-used for high current applications, it is unclear if there are suppliers which could be contacted. %\todo{Cite Luvato and the sketchy supplier}\\ +A design with rectangular pipes and circular holes for water greatly improves the power loss and pressure loss characteristics. %\todo{Where is an image of it?@Mimo please run the simulation for conductors with the square outer cross section that we can display it} +While these pipes exist and are used for high current applications, it is unclear if there are suppliers which could be contacted. %\todo{Cite Luvato and the sketchy supplier}\\ (for more see \href{https://github.com/LiigaSoolane/coil}{Github})\\ In order to validate these results an experiment was designed. However, due to problems with the delivery of equipment, the test has not yet been conducted.\\ \subsubsection{3D Modeling} -The filaments, created by the optimization team have been imported into fusion 360, however the program was not able to process the actual extrusion process, as especially constructed coordinate systems had to be used in order to ensure the coils not touching. +The filaments, created by the optimization team, have been imported into Autodesk Fusion 360. However, the program was not able to process the actual extrusion process, as especially constructed coordinate systems had to be used in order to ensure the coils are not touching. For this purpose Python and CadQuery were used. %\todo{citation of CadQuery} Furthermore, Python scripts for the determination of the maximum dimension as well as the minimum distance between coil filaments were created. This was then also used to determine the scaling factor for the optimization teams data (it was set to be 0.33). @@ -92,7 +91,7 @@ \subsubsection{3D Modeling} %\textcolor{red}{Daniel: Add pictures of the coils model} A mount for the coils was conceptually drawn and constructed in Autodesk Fusion as can be seen in figure \ref{fig:mount}. -It enables the coils to be mounted to the vacuum chamber and to be adjusted and aligned them from outside the chamber. +It enables the coils to be mounted to the vacuum chamber and for them to be adjusted and aligned from outside the chamber. Additionally it serves as port for the electrical cables and the water hoses. In order to allow for movement through the walls of the vacuum chamber a bellow has to be used. %\todo{The drawing should use the same colors as the crosssection on the left} diff --git a/summary/Sections/03_Design.tex b/summary/Sections/03_Design.tex index 27cfe9b..a235277 100644 --- a/summary/Sections/03_Design.tex +++ b/summary/Sections/03_Design.tex @@ -8,7 +8,7 @@ \subsection{Requirements and Tasks} \subsection{Outcome} -After searching the \href{https://quasr.flatironinstitute.org/}{QUASR} data base it was decided that \cite{QUASR} a design with 3 distinct coil types and an aspect ratio of about 4 shall serve as the base, with the possibility of further optimizations being performed on it using \href{https://github.com/hiddenSymmetries/simsopt}{SIMSOPT}, \href{https://github.com/PrincetonUniversity/STELLOPT}{STELLOPT}, and \href{https://github.com/itpplasma/SIMPLE}{SIMPLE} (for alpha particle tracing). +After searching the \href{https://quasr.flatironinstitute.org/}{QUASR} data base it was decided that \cite{QUASR}, a design with 3 distinct coil types and an aspect ratio of about 4 shall serve as the base, with the possibility of further optimizations being performed on it using \href{https://github.com/hiddenSymmetries/simsopt}{SIMSOPT}, \href{https://github.com/PrincetonUniversity/STELLOPT}{STELLOPT}, and \href{https://github.com/itpplasma/SIMPLE}{SIMPLE} (for alpha particle tracing). \autoref{tab:conffrac} shows the calculated alpha particle losses for certain magnetic flux surfaces, both for the small model and a scale-up. \begin{table}[H] @@ -81,7 +81,7 @@ \subsection{Outcome} \label{fig:poincare_shifted_coils} \end{figure} -Further results on the influence of manufacturing and positioning errors of the coils can be found at \href{https://github.com/itpplasma/reactor24}{this Github repository}\cite{design_repo}. +Further results on the influence of manufacturing and positioning errors of the coils can be found at \href{https://github.com/itpplasma/reactor24}{this Github repository} \cite{design_repo}. \subsection{Outlook} Further optimization could yield an even lower aspect ratio. @@ -89,5 +89,5 @@ \subsection{Outlook} Continuing to optimize the $\iota$ parameter towards a steeper profile (similar to LHC) or flatter (similar to W7X) profile may also be of interest to improve stability against errors. \subsection{Learnings} -Even if small disturbances seem to have disastrous consequences for the vacuum field, the real world application will not be affected as much due to plasma fields. Theory results in much more pessimistic outcomes than the actual experiment.\\ +Even if small disturbances seem to have disastrous consequences for the vacuum field, the real world application will not be affected as much due to plasma fields. Theory results have much more pessimistic outcomes than the actual experiment.\\ Additionally, if scaled to "proper" reactor sizes, the model performs much better than the small version with a major radius of about $0.33~\unit{m}$. For example, the confined alpha particle fraction after $0.1~\unit{s}$ calculated via \href{https://github.com/itpplasma/SIMPLE}{SIMPLE} goes from around $40\%$ for the small reactor to around $70\%$. See \autoref{tab:conffrac}. diff --git a/summary/Sections/04_Diagnostics.tex b/summary/Sections/04_Diagnostics.tex index 160253e..3c24478 100644 --- a/summary/Sections/04_Diagnostics.tex +++ b/summary/Sections/04_Diagnostics.tex @@ -7,8 +7,8 @@ \section{Diagnostics} % \textit{At first, please introduce your Team and why it's needed for designing a fusion reactor} -Diagnostics are needed to validate the calculated magnetic field as well as measure the densities and currents. We, Felix, Michael and Lukas, designed an interferometer, a 2D-manipulator for the Langmuir probe in the y-z-direction, with a changeable probe tip, a fluorescence rod, a concept for -a Rogowski coil measurement, concept for a diamagnetic coil measurement and a price comparison for different types of lock-in amplifier for a low temperature stellarator which has a configuration of $B=87~\unit{mT}$, $n_e < 10^{18}~\unit{m^{-3}}$ and $T_e=10~\unit{eV}$ under supervision of Gregor Birkenmeier. +Diagnostics are needed to validate the calculated magnetic field as well as measure the densities and currents. For this, the diagnostics team designed an interferometer, a 2D-manipulator for the Langmuir probe in the y-z-direction, with a changeable probe tip, a fluorescence rod, a concept for +a Rogowski coil measurement, concept for a diamagnetic coil measurement and a price comparison for different types of lock-in amplifier for a low temperature stellarator which has a configuration of $B=87~\unit{mT}$, $n_e < 10^{18}~\unit{m^{-3}}$ and $T_e=10~\unit{eV}$. % With these we can measure... @@ -16,18 +16,19 @@ \subsection{Requirements and Tasks} % \textit{What are the requirements your system has to fulfill to build the small reactor? What do other teams require from you? What are the topics you first had to investigate on? Please include your tasks, what you did as a Team during the semester. What did you look into? What implementations did you consider (but maybe rejected later)?}\\ -The interferometer measures the change in phase of a wave due to the plasma and relates it with the line integrated electron density of the plasma. We first need to know the maximum magnetic field and density, see above, to determine the maximum electron cyclotron and electron plasma frequency. We can show that when we send a wave into a magnetized plasma in such a way that the direction of propagation is perpendicular to the magnetic field, the ordinary wave, which has an oscillating electric field parallel to the magnetic field has a an index of refraction of $N = \sqrt{1 - \frac{\omega_\mathrm{pe}^2}{\omega^2 }}$. This means that we need to send in the wave at a right angle to the magnetic field and with a frequency higher than the electron plasma frequency, which for our values is $9$ GHz. When writing the resulting phase shift as a function of the frequency we use the simplification that $\omega \gg \omega_\mathrm{pe}$ meaning we want a frequency $f \gg$ 9 GHz. Using Gaussian beams it was possible to derive the optimal dimensions of the mirror reflecting the wave. It is based on the frequency used and the distance between horn antenna and mirror which depends on the plasma diameter. Depending on the geometry of the vacuum vessel we can put the horn antenna that sends the wave as well as the horn antenna that receives the reflected wave inside the vacuum chamber. For this we need to know the geometry and the space available inside the chamber to calculate the positions of the horn antenna as well as the reflecting mirror. +The interferometer measures the change in phase of a wave due to the plasma and relates it with the line integrated electron density of the plasma. First the maximum magnetic field and density need to be known, see above, to determine the maximum electron cyclotron and electron plasma frequency. Then it was shown that when a wave is sent into a magnetized plasma in such a way that the direction of propagation is perpendicular to the magnetic field, the ordinary wave, which has an oscillating electric field parallel to the magnetic field has a an index of refraction of $N = \sqrt{1 - \frac{\omega_\mathrm{pe}^2}{\omega^2 }}$. This means that the wave needs to be sent in at a right angle to the magnetic field and with a frequency higher than the electron plasma frequency, which for our values is $9$ GHz. When writing the resulting phase shift as a function of the frequency, the simplification that $\omega \gg \omega_\mathrm{pe}$ was used, meaning a frequency $f \gg$ 9 GHz. Using Gaussian beams it was possible to derive the optimal dimensions of the mirror reflecting the wave. It is based on the frequency used and the distance between horn antenna and mirror which depends on the plasma diameter. Depending on the geometry of the vacuum vessel the horn antenna, which sends the wave, as well as the horn antenna that receives the reflected wave, can be placed inside the vacuum chamber. For this the geometry and the space available inside the chamber need to be known to calculate the positions of the horn antenna as well as the reflecting mirror. \\ -The magnetic diagnostics has to extract the plasma currents out of a large background noise. In this project, the magnetic diagnostics consists of two diamagnetic coils, one Rogowski coil, and signal -processing equipment. The diamagnetic coils measure the poloidal plasma current. The Rogowski -coil measures the toroidal plasma current. The signal processing -equipment consists of several lock-in amplifiers, low- and band-passes and D/A converters. They filter out the background -noise, and amplify the plasma current signals. +The magnetic diagnostics has to extract the plasma currents out of a large background noise. In this project, the magnetic diagnostics consists of two diamagnetic coils, one Rogowski coil, and signal processing equipment. +The diamagnetic coils measure the poloidal plasma current. +The Rogowski coil measures the toroidal plasma current. +The signal processing +equipment consists of several lock-in amplifiers, low- and band-passes and D/A converters. They filter out the background noise, and amplify the plasma current signals. \\ + +For the Langmuir probe it is needed to scan the cross-section of the plasma to measure the $I-V$-characteristic of the plasma. With this characteristic plasma parameters are fitted (the floating potential $\Phi_\mathrm{fl}$, the plasma potential $\Phi_\mathrm{p}$, the electron current $I_\mathrm{e}$, the ion current $I_\mathrm{i}$, the electron saturation current $I_\mathrm{e,sat}$, the ion saturation current $I_\mathrm{i,sat}$ and the electron plasma density $n_\mathrm{e}$). -For the Langmuir probe we need to scan the cross-section of the plasma to measure the $I-V$-characteristic of the plasma. With this characteristic we fit plasma parameters like the floating potential $\Phi_\mathrm{fl}$, the plasma potential $\Phi_\mathrm{p}$, the electron current $I_\mathrm{e}$, the ion current $I_\mathrm{i}$, the electron saturation current $I_\mathrm{e,sat}$, the ion saturation current $I_\mathrm{i,sat}$ and the electron plasma density $n_\mathrm{e}$. In the left image of Figure~\ref{fig:probe characteristics and CAD_Interferometer and CAD_changeable_probe_tip} we can see that the electron saturation current has different curve shapes for different probe tips, for example for a spherical, cylindrical or a flat tip. The flat tip has the \emph{sharpest} bend of all the tip geometries. -The floating potential is the root of the $I-V$-characteristic which occurs when the ion current and electron current are equal, negating each other resulting in zero current. -The saturation currents exists because when we charge the probe one way, for example positive, all electrons in a region around the probe fly towards the probe. However, due to Debye shielding the created depletion region cannot grow indefinitely. Once it reaches its maximum the current saturates and only thermal electrons outside the region enter the probe. The corresponding voltages are the plasma potential and the floating potential. With following equation you can determine the current of the probe: +The floating potential is the root of the $I-V$-characteristic, which occurs when the ion current and electron current are equal, negating each other resulting in zero current. +The saturation currents exists because when the probe is charged one way, for example positive, all electrons in a region around the probe fly towards the probe. However, due to Debye shielding the created depletion region cannot grow indefinitely. Once it reaches its maximum the current saturates and only thermal electrons outside the region enter the probe. The corresponding voltages are the plasma potential and the floating potential. With following equation the current of the probe can be determined: \begin{equation} I=I_i+I_e=enS \sqrt{\frac{T_e}{2 \pi m_e}} @@ -39,18 +40,17 @@ \subsection{Requirements and Tasks} \begin{equation} I^*_{e,sat} =I_{e,sat}\Biggr[1+ \frac{e(U-\Phi_p)}{T_e}\Biggl]^{\gamma_{om}} \end{equation} -where $\gamma_{om}= 1/2$ is for cylindrical probe tips and $\gamma_{om}= 1$ is for spherical probe tips.\cite{Stroth_Plasmaphysik} +where $\gamma_{om}= 1/2$ is for cylindrical probe tips and $\gamma_{om}= 1$ is for spherical probe tips. \cite{Stroth_Plasmaphysik} \subsection{Outcome} %\textit{What's the outcome of your study? What does your design look like in the end? What did you decide on and why? Maybe include some parameters, please include finalized designs \& CAD models} -Having evaluated the basic parameters for the interferometer the schematic of the circuit was designed. The difficulty lies in measuring a phase shift occurring at a GHz frequency. For this purpose we mix the signals with a Gunn diode ring modulator used to function as a downconverter. We run the local oscillator (LO) with a frequency $\omega$ and the reference oscillator (RO) with the frequency $\omega + \Delta \omega$, see the right image of Figure~\ref{fig:2D-manipulator and probe tip and interferometer_circuit_schematic}. With two mixers and amplifiers and band-pass filters we manage to get a signal with the frequency $\Delta \omega$. When we use a $\Delta \omega$ in the MHz range we can detect the phase shift with a phase detector. If there is not enough space inside the vacuum space an alternative design with Teflon lenses was also explored, see~\cite{2012JInst...7C1107C}. A python script was written with which one can calculate the ideal distances for every geometry and frequency. +Having evaluated the basic parameters for the interferometer the schematic of the circuit was designed. The difficulty lies in measuring a phase shift occurring at a GHz frequency. For this purpose mixing the signals with a Gunn diode ring modulator is used to function as a downconverter. The local oscillator (LO) is run with a frequency $\omega$ and the reference oscillator (RO) with the frequency $\omega + \Delta \omega$, see the right image of Figure~\ref{fig:2D-manipulator and probe tip and interferometer_circuit_schematic}. With two mixers and amplifiers and band-pass filters we manage to get a signal with the frequency $\Delta \omega$. When we use a $\Delta \omega$ in the MHz range we can detect the phase shift with a phase detector. If there is not enough space inside the vacuum space an alternative design with Teflon lenses was also explored, see~\cite{2012JInst...7C1107C}. A python script was written with which one can calculate the ideal distances for every geometry and frequency. \\ -The basic principles of the Rogowski coil were explored. The -diamagnetic effect in linear pinches was shortly reviewed. -Different options regarding the lock-in amplifiers were examined. +Reagrding the Rogowski coil, the basic principles of the coil were explored. The +diamagnetic effect in linear pinches was shortly reviewed, and different options regarding the lock-in amplifiers were examined. Simple CAD-models of the Rogowski and diamagnetic coils were created. \begin{figure}[h] @@ -58,7 +58,7 @@ \subsection{Outcome} \includegraphics[width=0.3\linewidth]{Images/04_Diagnostics/probe characteristic.png} \includegraphics[width=0.3\linewidth]{Images/04_Diagnostics/CAD_Interferometer.png} \includegraphics[width=0.3\linewidth]{Images/04_Diagnostics/CAD_changeable_probe_tip.png} - \caption{Left: I-V-characteristic of a Langmuir probe\cite{Stroth_Plasmaphysik}. Middle: plasma CAD of the interferometer for a certain frequency and distance. Right: 3D-model of the changeable probe tip with a union nut.} + \caption{Left: I-V-characteristic of a Langmuir probe \cite{Stroth_Plasmaphysik}. Middle: plasma CAD of the interferometer for a certain frequency and distance. Right: 3D-model of the changeable probe tip with a union nut.} \label{fig:probe characteristics and CAD_Interferometer and CAD_changeable_probe_tip} \end{figure} @@ -78,7 +78,7 @@ \subsection{Outcome} -The outcome at the measurement of the magnetic flux lines was to design a fluorescence rod which has a coating of zinc-oxide (ZnO:Zn). The design for the rod was implemented to the changeable probe holder which has the same plug. Also a electron gun was designed. +The outcome at the measurement of the magnetic flux lines was to design a fluorescence rod which has a coating of zinc-oxide (ZnO:Zn). The design for the rod was implemented to the changeable probe holder which has the same plug. Also an electron gun was designed. \subsection{Outlook} @@ -91,7 +91,7 @@ \subsection{Outlook} Refine the preliminary CAD models of the Rogowski and diamagnetic coil. After deciding an oscillator with a certain frequency once can fix the geometry of the mirror and work on the mounting of the mirror. Similarly the circuit can be refined and the powers and voltages can be calculated. Finally, the appropriate hardware can be looked into and acquired. -The observation window can be used for passive spectroscopy and additional diagnostics tools could also be designed to compliments the current instruments. It is necessary to choice the right material and a possible wall thickness for the vacuum chamber of the 2D-manipulator and the dimension. To design a 1000~mm manipulator for the 2D-manipulator on the side. The evaluation of the measurement and implement to LabVIEW. Designing an electron gun. +The observation window can be used for passive spectroscopy and additional diagnostics tools could also be designed to compliment the current instruments. It is necessary to choose the right material and a possible wall thickness for the vacuum chamber of the 2D-manipulator and the dimension. To design a 1000~mm manipulator for the 2D-manipulator on the side. The evaluation of the measurement and implement to LabVIEW. Designing an electron gun. \subsection{Learnings} @@ -100,5 +100,5 @@ \subsection{Learnings} Some basic properties of a static plasma configurations were learned. Concepts behind the lock-in technique were reviewed. -Great difficulties were encountered in using the \emph{Fusion} CAD software. -In order to understand the interferometer we learned plasma wave physics as well as the propagation of a wave in a waveguide and in the horn antenna. Furthermore we learned about signal processing, however we did not have much experience in that regard so we had to learn a lot about it and we are still not sure if we chose the ideal circuit or if there are complications we have not thought of. A new 3D-CAD software and implement movements in the assembly group. Design movement parts in vacuum and use the right bearings. Design layout of different plasma measurement systems. Concepts behind the Langmuir probe measurement and the measuring of a closed magnetic flux field. Cross-team collaboration. +Great difficulties were encountered in using the Autodesk Fusion CAD software. +In order to understand the interferometer we learned plasma wave physics as well as the propagation of a wave in a waveguide and in the horn antenna. Furthermore we learned about signal processing, however we did not have much experience in that regard so we are still not sure if we chose the ideal circuit or if there are complications we have not thought of. A new 3D-CAD software and implement movements in the assembly group. Design movement parts in vacuum and use the right bearings. Design layout of different plasma measurement systems. Concepts behind the Langmuir probe measurement and the measuring of a closed magnetic flux field. Cross-team collaboration. diff --git a/summary/Sections/05_Heating.tex b/summary/Sections/05_Heating.tex index 19f8bc1..988dc23 100644 --- a/summary/Sections/05_Heating.tex +++ b/summary/Sections/05_Heating.tex @@ -34,8 +34,8 @@ \subsubsection{Power balance} % Matthias %It becomes clear that the lower the neutral density $n_\mathrm{neu}$, the lower the achievable electron densities. Another outcome is that the higher the heating power, the higher the input density. -From a preliminary 0D simulation implemented as described in \cite{plasmaParameterLimitsLechte2002}, it became clear, that the lower the neutral density $n_\mathrm{neu}$, the lower the achievable electron densities. -Another outcome was, that the higher the heating power, the higher the input density. +\noindent From a preliminary 0D simulation implemented as described in \cite{plasmaParameterLimitsLechte2002}, it became clear that the lower the neutral density $n_\mathrm{neu}$, the lower the achievable electron densities. +Another outcome was that the higher the heating power, the higher the input density. \\ A 1D simulation, using the approach described in \cite{birkenmaierModeling2008}, was then performed. Here, the major difference was, that the the plasma parameters were a function of the minor radius $r$. @@ -44,14 +44,17 @@ \subsubsection{Power balance} % Matthias For the diffusivities and neutral densities, the parameters from the TJ-K experiment in Stuttgart were used, as shown in \autoref{tab:parameters}. \begin{table}[H] - \caption{1D simulation parameters} + \caption{1D simulation parameters. \\ + $D$ ... particle diffusivity \\ + $\chi$ ... heat diffusivity \\ + $n_new$ ... neutral density} \centering \begin{tabular}{lSS} & {Helium} & {Argon} \\ \hline $D$ / $\si{\meter\squared\per\second}$ & 8.5 & 6 \\ $\chi$ / $\si{\meter\squared\per\second}$ & 200 & 8 \\ - $n_\mathrm{neu}$ & 2.30 $\times 10^{18}$ & 2.32 $\times 10^{17}$ \\ + $n_\mathrm{new}$ & 2.30 $\times 10^{18}$ & 2.32 $\times 10^{17}$ \\ \end{tabular} \label{tab:parameters} \end{table} @@ -67,7 +70,7 @@ \subsubsection{Power balance} % Matthias % \end{figure} \begin{figure}[H] - \center{\includegraphics[width=12cm]{Images/05_Heating/1d_volume04435_argon.png}} + \center{\includegraphics[width=14cm]{Images/05_Heating/1d_volume04435_argon.png}} \captionof{figure}{1D equilibrium radial profiles for Argon.} \label{fig:1d_volume04435_argon} \end{figure} @@ -85,9 +88,9 @@ \subsubsection{Heating processes} % Diogo In order to recreate how the heating would occur, a series of theoretical approximations were made. To start with, even though this is a design of a stellarator, a toroidal symmetry was assumed. Then, the density profile was assumed to be parabolic and poloidally centred and the magnetic field to decay with $1/r$. -It was also assumed that the frequency of the wave sent into the plasma was much higher than the ion cyclotron (IC) frequency ($\omega >> \omega_{ci}$), so the dynamics of the ions, which are much slower than the electrons, was overall neglected. +It was also assumed that the frequency of the wave sent into the plasma was much higher than the ion cyclotron (IC) frequency ($\omega >> \omega_{ci}$), so the dynamics of the ions, which are much slower than the electrons, was overall neglected. \\ -Given that the interest is to have an overdense plasma, $\omega_{pe} > \omega_{ce}$ everywhere, making it impossible to heat up the plasma only by exciting the electron cyclotron resonance (ECR). +The interest is to have an overdense plasma, $\omega_{pe} > \omega_{ce}$ everywhere, making it impossible to heat up the plasma only by exciting the electron cyclotron resonance (ECR). This is because the incoming wave will be reflected at the critical density, where the wave reaches $\omega_{pe}$. There will also have to be excitation of the upper-hybrid resonance (UHR), but, when plasmas are overdense, the R-wave that permits this heating method is also reflected back at the $\omega_R$ cut-off before reaching this mode. These frequency profiles can be seen in \autoref{fig:freq_profiles}. @@ -99,7 +102,7 @@ \subsubsection{Heating processes} % Diogo \begin{figure}[H] \centering - \includegraphics[width=0.6\textwidth]{Images/05_Heating/freq_profiles.png} + \includegraphics[width=0.8\textwidth]{Images/05_Heating/freq_profiles.png} \caption{Frequency profiles for ECRH and UHRH for non overdense (top) and overdense (bottom) plasma. The resonant frequencies $\omega_{ce}$ and $\omega_{UH}$ and the cut-off frequencies $\omega_{pe}$ and $\omega_R$ are displayed.} \label{fig:freq_profiles} \end{figure} @@ -109,13 +112,13 @@ \subsubsection{Heating processes} % Diogo \subsubsection{Hardware} % Joe -The 2.45GHz microwaves will be generated by a magnetron, and transported to the plasma by WR340 waveguides (86.36mm x 43.18mm). This size was chosen to maintain polarization by only allowing the TE1 mode to propagate. Upon reaching the vacuum chamber, the microwaves will be focused using an optimum horn antenna. It is important for effective heating, that the wider H-plane flare is oriented along the vertical axis perpendicular to the containment B-field. +The 2.45\,GHz microwaves will be generated by a magnetron, and transported to the plasma by WR340 waveguides (86.36 x 43.18)\,mm. This size was chosen to maintain polarization by only allowing the TE1 mode to propagate. Upon reaching the vacuum chamber, the microwaves will be focused using an optimum horn antenna. It is important for effective heating, that the wider H-plane flare is oriented along the vertical axis perpendicular to the containment B-field. Further RF components must be added along the waveguides to minimize feedback into the magnetron. A circulator and a directional coupler are added to remove any returning waves. A 3-stub tuner is added before the horn antenna to maximize the heating system's efficiency. \subsection{Outlook} In the end, further developments can still be made. In regard to the cross-sectional wave resonance and cut off profiles, only the example of a tokamak was studied. This was enough to understand what will qualitatively happen, upon heating of the plasma, but the quantitative study is not applicable to a stellarator design. -Further work on this could then consist in figuring out which cross section of the stellarator is most ideal to perform heating on, depending on its shape. +Further work on this could then consist of figuring out which cross section of the stellarator is most ideal to perform heating on, depending on its shape. % Still missing: Joe & Matthias @@ -123,7 +126,7 @@ \subsection{Outlook} \subsection{Learnings} % Matthias -One of the main learnings from the simulations were that the major two parameters to achieve are higher densities are heating power, but also the neutral density $n_\mathrm{neu}$. +One of the main learnings from the simulations were that the major two parameters to achieve are higher densities are heating power, but also the neutral density $n_\mathrm{new}$. A more technical learning was, that while \cite{birkenmaierModeling2008} employed the Crank-Nicelson scheme for numerical implementation, a naïve fully-explicit scheme works as well. The only downside was, that around 500 times more steps were needed. But the python/numpy-based implementation still took less than 5 minutes per case (depending on number of radial points). diff --git a/summary/Sections/06_Vacuum.tex b/summary/Sections/06_Vacuum.tex index 7e02973..e1eb71b 100644 --- a/summary/Sections/06_Vacuum.tex +++ b/summary/Sections/06_Vacuum.tex @@ -2,14 +2,14 @@ \section{Vacuum} \subsection{Requirements and Tasks} The main task of the vacuum team is to design a vacuum chamber that can be used for a small table top stellarator. -For this the maximum size of the chamber was given, so it can fit through a standard door of $\SI{90}{\centi\meter}$ times $\SI{200}{\centi\meter}$. +For this the maximum size of the chamber was given, so it can fit through a standard door of (90 x 200)~cm. Thus this are the maximum dimensions of the individual parts of the chamber. The necessary requirements for the chamber are: (a) The chamber should be large enough to fit the coils for the stellarator as well as all other devices to generate and measure the plasma, (b) needs to be able to withstand pressures $<\SI{e-8}{\milli\bar}$, when evacuated, (c) should be able to encounter different types of noble gases to create the plasma, -(d) should be able to withstand the radiation of the plasma as well the microwave radiation of the heating. +(d) should be able to withstand the radiation of the plasma as well the microwave radiation of the heating. \\ In order to achieve these requirements, the focus is on the design of the vacuum chamber, the vacuum system, and the radiation protection. This is described in more detail in the full \href{https://www.overleaf.com/3861427278qpnrdmbhknty#518852}{\emph{Vacuum Team Report}}. @@ -23,12 +23,12 @@ \subsubsection{Vacuum chamber} The design of the vacuum chamber, which was finalized, is shown in \autoref{fig:Kammer_all}. It has a dome shaped lid as well as a dome shaped base. This allowed to increase the size of the chamber as the base and the lid are both removable and can be placed together inside a laboratory. -The given specifications of the size were given, that the chamber need to fit through a standard door, with the size of $\SI{90}{\centi\meter}$ times $\SI{200}{\centi\meter}$. +The given specifications of the size were given, that the chamber need to fit through a standard door, with the size of (90 x 200)~cm. Also other configuration were considered, for example with a flat base and a flat lid, but the dome shaped design was chosen as it was the most rigid one. -The rigidity is needed to prevent the chamber from bending when evacuated to a pressure of $<\SI{e-8}{\milli\bar}$. +The rigidity is needed to prevent the chamber from bending when evacuated to a pressure of~$<\SI{e-8}{\milli\bar}$. For the sake of simplicity, all flange connections were chosen to have the same size. -Only the connections for the Pirani-Bayard-Alpert pressure measurement and the quadrupole spectrometer were chosen differently, as little previous knowledge of specific flange sizes was known. +Only the connections for the Pirani-Bayard-Alpert pressure measurement and the quadrupole spectrometer were chosen differently, as little was previously known of specific flange sizes. The universal fange connections chosen for the versatile connection is the same flange used as for the TMP (DN 320 ISO-F). This flange size was chosen because if a second TMP is needed, it can be easily added to the chamber using a knee. Also the relative large size of the flange allows to connect other flanges to it using adapters. @@ -37,9 +37,9 @@ \subsubsection{Vacuum chamber} This makes is easier for the future use of the chamber, as retrofitting extra ports is not necessary. Also adding ports from the beginning makes it cheaper, as not much work is needed to add them later on. -To support the support the wight of the chamber, foots are added to the side of the vessel. +To support the wight of the chamber, foots are added to the side of the vessel. This will allow to place the entire chamber on a steel scaffold. -Thus, this mounts need to be able to support the entire weight of the chamber as well as the weight of the external mounted devices. +Thus, these mounts need to be able to support the entire weight of the chamber as well as the weight of the external mounted devices. %\todo{add foot mounts of the chamber (description)} \begin{figure}[H] @@ -65,7 +65,7 @@ \subsubsection{Vacuum chamber} \subsubsection{Vacuum design} -For our Vacuum system a turbo-molecular pump is chosen, due its oil-free operation and pumping speed. +For the Vacuum system a turbo-molecular pump is chosen, due its oil-free operation and pumping speed. It is backed up by a sufficiently sized backing pump which also provides the rough vacuum before the TMP takes over. To reduce outgassing metal surfaces in the inside are polished and wires are heat and electrically isolated by using e.g. Kapton$\textsuperscript{\textregistered}$. Pressure is measured using a pressure gauge that includes a Pirani device for lower vacuum levels and a Bayard-Alpert device for higher vacuum ranges. @@ -74,15 +74,15 @@ \subsubsection{Vacuum design} \subsubsection{Radiation protection} -For our vacuum vessel, we have designed it with a thickness of $\SI{10}{\milli\meter}$, which provides adequate protection against X-ray and microwave radiation. The chosen material is austenitic stainless steel 316L. This material was selected due to its non-magnetic nature and its advantageous properties, including high strength, good availability, and overall versatility, making it an ideal choice for our application. +The vacuum vessel is designed with a thickness of $\SI{10}{\milli\meter}$, which provides adequate protection against X-ray and microwave radiation. The chosen material is austenitic stainless steel 316L. This material was selected due to its non-magnetic nature and its advantageous properties, including high strength, good availability, and overall versatility, making it an ideal choice for our application. -For the window, we designed it with a circular shape having a radius $\SI{100}{\milli\meter}$ made of quartz glass. The ideal thickness for the window is $\SI{10}{\milli\meter}$. +The window was designed with a circular shape having a radius $\SI{100}{\milli\meter}$ made of quartz glass. The ideal thickness for the window is $\SI{10}{\milli\meter}$. \subsection{Outlook} It is important to perform a detailed structural analysis to ensure the chamber can withstand external atmospheric pressure and any mechanical stresses without significant deformation or failure. -As we move forward, the design of the vacuum chamber may need to be adjusted based on the specific requirements of the other teams involved in the design process. +Moving forward, the design of the vacuum chamber may need to be adjusted based on the specific requirements of the other teams involved in the design process. The exact number and types of ports, as well as other components such as windows, gas inlets, feedthroughs, and coaxials, have not been finalized yet. Therefore, additional work will be needed to finalize these details and to ensure that the vacuum chamber design meets all necessary requirements. It is also necessary to ensure that the design meets relevant safety standards and regulations for vacuum systems and radiation protection. diff --git a/summary/Sections/07_Conclusion.tex b/summary/Sections/07_Conclusion.tex index c3f6442..6707a90 100644 --- a/summary/Sections/07_Conclusion.tex +++ b/summary/Sections/07_Conclusion.tex @@ -1,7 +1,7 @@ \section{Conclusion} -In 2024, the joint course \textit{Fusion Reactor Design} was held for the first time in a partership of TU Graz, TU Munich and Proxima Fusion GmbH. +In 2024, the joint course \textit{Fusion Reactor Design} was held for the first time in a partership of TGraz University of Technology, Technical University of Munich and Proxima Fusion GmbH. \\ -The Coils, Design, Diagnostics, Heating and Vacuum teams have each contributed and worked together to design and provide a concept for a small stellarator magnetic plasma confinement experiment in each of their respective fields of expertise. The requirements decided at the beginning of the project were prioritized and are conceptually fulfilled: 1) Size limit of 190x90 cm, 2) low aspect ratio of around 4, and 3) few (three) different coil types. As a final result, a CAD model with all the components contributed by the various teams is available.\\ +The Coils, Design, Diagnostics, Heating and Vacuum teams have each contributed and worked together to design and provide a concept for a small stellarator magnetic plasma confinement experiment in each of their respective fields of expertise. The requirements decided at the beginning of the project were prioritized and are conceptually fulfilled: 1) Size limit of (190x90)~cm, 2) low aspect ratio of around 4, and 3) few (three) different coil types. As a final result, a CAD model with all the components contributed by the various teams is available.\\ \\ As with any project of this complexity, there are various areas of possible improvement. On the theoretical end, more simulations to verify the coil structure, as well as continued optimization to improve general design stability and lowering the aspect ratio, could be performed. Additionally, refinement of the diagnostics circuits, study of the heating design for the complexities of a stellarator and structural and safety analysis of the vacuum chamber are further possibilities.\\ \\