Edge plasma emissivity profile reconstruction by forward modelling of diode bolometer signals at ASDEX Upgrade
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UNIVERSITY OF PADOVA Department of Physics and Astronomy "G. Galilei" Master's Degree in Physics Edge plasma emissivity profile reconstruction by forward modelling of diode bolometer signals at ASDEX Upgrade Student: Pietro Vincenzi Supervisor: Prof. Piero Martin External reviewer: Dr. Enrico Conti Tutor: Prof. Dr. Hartmut Zohm Tutor: Dr. Thomas Eich Tutor: Matthias Bernert ACADEMIC YEAR 2011-2012 1 INTRODUCTION 1.1 the energy problem The present energy scenario and the forecast for the next future reveal an increasing energy demand . Moreover, the actual global energy supply is based on fossil fuels for 81%, while just for 13% on different forms of renewable energy (biomass, hydroelectric, combustible waste, etc). The rest relies on nuclear ﬁssion . Considering the decreasing availability of fossil resources, the development of alternative and renewable energy sources has become a crucial challenge. Through a continuous research, new ways have been explored, solutions have been suggested, and some possible answers have been found ﬁrst in nuclear ﬁssion, then in investing more in "green en- ergy". It seems anyway more logical to imagine a future where the energy demand is sustained by different sources, in order to maintain a stable en- ergetic and economic system. Energy from sun, wind or similar renewable resources cannot sustain the whole energy demand, being bound to partic- ular environmental conditions. Anyway they can be considered a good and environmentally-friendly alternative to the dependence on main energy re- sources as, for instance, the current coal, gas or ﬁssion power plants. But now the main challenge is thus to ﬁnd a new main energy source: hope- fully long lasting, eco-friendly and inherently safe. A promising candidate fulﬁlling these conditions is fusion. 1.2 a possible solution to the increasing energy demand: fusion Generally speaking, fusion is a nuclear process in which two light nuclei merge to form a heavier element. In order to reach a fusion reaction, two positive charged nuclei have to overcome the mutual Coulomb repulsion. They have hence to be closer than a distance in the order of 10 -15 m . A vast knowledge about fusion comes from stars, which are the oldest and biggest fusion "plants" existing. Studying the sun, the proton-proton fusion chain has been discovered. In this reaction helium is formed out of hydro- gen, releasing an energy of26.7MeV for each reaction. In the sun, this fusion process is possible due to the high core density (~10 31particles m 3 ), sustained by the gravitational force. This is not attainable on earth, since densities in this range cannot be reached. In order to exploit fusion processes on earth, the most feasible reaction is employing two hydrogen isotopes, namely deu- terium and tritium (reaction1). They are used because of their cross section, which is larger compared to other possible reactions (reactions 2,3,4, see ﬁgure 1). 2 D+ 3 T! 4 He+ 1 n+17.6MeV (1) 2 D+ 2 D! 3 He+ 1 n+3.27MeV (2) 1 2 introduction 2 D+ 2 D! 3 T + 1 H+4.03MeV (3) 2 D+ 3 He! 4 He+ 1 H+18.3MeV (4) Figure 1.: Cross-sections for the reactions D-T, D-D andD- 3 He. The D-D curve is the sum of the cross sections of the two D-D reaction listed in reactions 2 and 3. . As shown in ﬁgure1, the D-T curve has a maximum around a particle en- ergy of ~100keV . Actually, the mean temperature needed to have a sufﬁcient number of reactions in a future fusion reactor is 10keV . At this temperature there are enough high energetic ions lying in the high energy tails of the Maxwell distribution of the particles which can reach fusion. A concise way to express the condition needed to achieve fusion is that of the Lawson cri- teria: temperature (T), density (n) and energy conﬁnement time ( E ) have to satisfy the relation 5. Figure 2 shows the ignition curve, as function of triple product parameters. Ignition means a self-sustaining burning plasma heated without any external system, but just with the energy coming from fusion reactions. nT E >3 10 21 keVs m 3 (5) The temperature required is about ten times the core temperature of the sun: at this temperature atoms are ionized. The state of this hot, ionized gas is called "plasma": it consists in a globally neutral system of many charged particles, which is characterized by presenting collective properties (some- how as a ﬂuid). Fusion with D-T fuel is very advantageous in terms of energy density: compared with fossil and ﬁssion fuels, it shows its great potential. fossil ﬁssion fusion 10 6 tonne oil 0.8 tonne uranium 0.14 tonne deuterium Table 1.: Comparison of energy equivalence among different resources . Deuterium is a stable isotope of hydrogen and is widespread in nature (0,015% of the total hydrogen). Tritium on the contrary, is radioactive and has a half-life of approximately 12 years. For this reason it does not occur 1.3 thermonuclear fusion by magnetic confinement 3 Figure 2.: The value ofn E required to obtain ignition, as a function of temperature . in nature and it has to be produced directly inside the reactor. Neutrons coming from the fusion reactions in the plasma will be used to breed tritium out of lithium (with reactions 6, 7). 6 Li+ 1 n!T + 4 He+4.8MeV (6) 7 Li+ 1 n!T + 4 He+n-2.5MeV (7) However, lithium supplies, unlike deuterium ones, could in principle rep- resent a limit . This depends on future demands and on possible new developments of new extraction processes, as for instance obtaining Li from the seawater. Anyway, by now, lithium supplies do not represent a crucial issue. Future fusion plants can also be considered inherently safe: given the strict constraints to maintain burning plasma, any accident in the reactor will lead to a stop in the reaction chain, on the contrary to ﬁssion plants. But due to the difﬁcult conditions to reach ignition, the track to commercial fusion plants is still long. 1.3 thermonuclear fusion by magnetic con- finement At the moment, two mechanisms to achieve fusion processes are being studied. The Inertial Conﬁnement Fusion (ICF) approach intends to reach a very high density and temperature of a Deuterium-Tritium target using high power lasers, causing an implosion. The other way, which is topic of this thesis, is the magnetic conﬁnement of the plasma, the most advanced concept to achieve fusion. As plasma consists of an ionized gas, it is possible conﬁne it in a device with strong magnetic ﬁelds without direct contact to any material surface. When a magnetic ﬁeld is present, the Lorentz force imposes to the particles 4 introduction Figure 3.: Helically twisted ﬁeld lines and ﬂux surfaces in a tokamak a circular motion around the ﬁeld lines ("gyro-motion"). In this way the par- ticles are strictly conﬁned to the magnetic ﬁeld. Anyway, with this kind of conﬁnement, the particles can move freely along the magnetic ﬁeld line (e.g. due to an electric ﬁeld). In a linear magnetic ﬁeld setup (e.g. a magnetic bottle conﬁguration), the particles are lost at the ends, therefore a closed conﬁguration for the magnetic ﬁeld lines has been chosen, and the devices are currently shaped as a torus. The torus is enclosed by coils, in order to generate a conﬁning toroidal magnetic ﬁeld. However this ﬁeld is not enough: to prevent the loss of the plasma to the wall due to drift effects, the magnetic ﬁeld conﬁguration is set to be helically twisted. A poloidal com- ponent is therefore added, so the main particle trajectory becomes helical, keeping most of the plasma in the central part of the torus. The magnetic ﬁelds generate nested surfaces characterized by constant magnetic ﬂux and pressure ("ﬂux surfaces"), as shown in ﬁgure 3. The pressure increases per- pendicularly to the ﬂux surfaces conﬁning the hot plasma in the centre of the torus. In the core region at the centre of the torus, it is thus possible to fulﬁll the conditions necessary to heat the plasma up to about 10keV with a density in the order of 10 20particles m 3 , as required by the triple product equation 5. Since this value of density is lower than that in the atmosphere of a factor10 6 , plasma is consequently contained in a vacuum vessel. Among magnetic conﬁned devices, three main conﬁgurations can be dis- tinguished: tokamak, reversed ﬁeld pinch (RFP , ﬁgure 4a) and stellarator (ﬁgure 4b). The ﬁrst two create the poloidal magnetic ﬁeld with induced plasma current, the latter uses complex shaping of the magnetic ﬁeld coils to generate directly helical twisted magnetic ﬁeld lines. The tokamak con- ﬁguration, subject of this thesis, will be brieﬂy presented in the following section. 1.4 tokamaks 5 (a) Reversed ﬁeld pinch (RFP) (b) Stellarator Figure 4.: Representations of helical plasma conﬁgurations in RFP (quasi-single he- licity (QSH) regime in RFX-mod, Padova ) and stellarator (Wendel- stein 7-X, Greifswald ). These are alternative magnetic conﬁgurations to tokamak. 1.4 tokamaks Figure 5.: General design of a tokamak. The plasma column is in yellow, while the magnetic ﬁeld coils are shown in red (toroidal ﬁeld) and green (vertical ﬁeld). A vertical ﬁeld is necessary to control the position of the plasma column. In the centre of the torus the transformator coil is illustrated, which is needed to generate the plasma current. The tokamak (from toroidal’naya kamera s magnitnymi katushkami - toroidal chamber with magnetic coils) design represents the most advanced fusion concept. Figure 5 shows a sketch of the tokamak design. It is the most used and studied conﬁguration, and, at the moment, the most promis- ing one for next step fusion reactors. With this conﬁguration, parameters needed for fusion have been reached, but not all at the same time for a sufﬁcient duration to obtain energy gain. The largest operating tokamaks are JET in Oxford (GB), DIII-D in San Diego (USA) and ASDEX Upgrade in Garching (DE). In the tokamak conﬁguration, magnetic ﬁelds consist of an externally applied toroidal ﬁeld and a poloidal ﬁeld which is induced by a toroidal current ﬂowing through the plasma. The plasma current is generated using a voltage ramp in a central solenoid, causing a change of magnetic ﬂux in the central gap of the torus. That solenoid acts as the primary winding of a transformer with the plasma itself acting as the sec- ondary. Plasma is a conductor, and presents a resistance which varies with the temperature. The plasma current can therefore be used to heat the plasma ("ohmical heating"): as described by the Joule’s law, a current ﬂow- 6 introduction ing through a conductor generates heat. However, due to the decreasing plasma resistivity with temperature, plasma cannot be heated only ohmi- cally. For this reason it is necessary to add external heating systems, such as neutral beam injection system (NBI) or heating with electromagnetic waves. The NBI system uses neutral particle beams injected in the plasma at high energy, which release energy by scattering with plasma. The other system is based on heating plasma particles using electromagnetic waves at particular resonance frequencies connected to particles gyro-motion. Current tokamak experiments are not sufﬁciently large to provide energy gain with fusion. On the way to commercial fusion reactors, the next step is the ITER experiment  (see ﬁgure 6), under construction in Cadarache (FR). This will be the largest tokamak in the world. It has been designed to demonstrate the feasibility of a high-gain fusion reactor, with long lasting burning plasma and with effective power production, conditions achievable just with a larger experiment like ITER. It is supported by a worldwide collaboration among China, EU, India, Japan, Korea, Russia and USA. The next step after ITER is supposed to be DEMO (DEMOnstration Power Plant), the prototype of a commercial fusion reactor. According to the planned timetable (subject to change), ITER ﬁrst plasma will be created in 2019 and DEMO ﬁrst phase of operation will start from 2030 . Figure 6.: ITER tokamak design. Artist’s drawing of the entire ITER device (ITER Final Design Report.(2001). Vienna:IAEA). 1.5 the asdex upgrade tokamak (aug) The present work has been performed at the Max-Planck-Institut für Plasma- physik (IPP) in Garching (Germany), where ASDEX Upgrade tokamak (Axially Symmetric Divertor EXperiment) is operated. ASDEX Upgrade, brieﬂy AUG, went into operation in 1991. It is the largest German fusion exper- iment in operation and, in an international comparison, it is a large sized 1.5 the asdex upgrade tokamak (aug) 7 Figure 7.: The ASDEX Upgrade tokamak (AUG). The orange part is the supporting structure. Surrounding the vacuum vessel (light blue), one can see the toroidal coils (light orange) and the poloidal coils (purple). Experiment parameters AUG(maximum) AUG(typical) ITER Major plasma radius 1.6m 1.6m 6.2m Magnetic ﬁeld 3.9T 2.6T 5.3T Plasma current 2MA 1.2MA 15MA Heating power 30MW 620MW 73MW Temperature 10 8 K 10 8 K >1.5 10 8 K Table 2.: Parameters of AUG (maximum and typical ones) compared with ITER ones. Magnetic ﬁeld value is referred to the magnetic axis. tokamak. It is one of the leading fusion experiments worldwide (ﬁgure 7 and table 2 for further information). As indicated in the name, AUG is an experiment in divertor conﬁguration. This implies additional coils in order to create a null-point or X-point in the magnetic ﬁeld (there its value is zero) at the bottom or at the top of the plasma. Figure 8 shows a poloidal section of the torus. This conﬁguration causes the onset of a last closed magnetic ﬂux surface, called "separatrix" or LCFS-from last closed ﬂux surface-, which separates the conﬁned plasma from the "scrape-off layer" (SOL), the region in which plasma is in direct contact with the wall. Every ﬂux surface is labeled with a normalized radial coordinate, called poloidal ( pol ). This coordinate, depending on the magnetic ﬁelds in the plasma, is zero in the centre at the magnetic axis (see ﬁgure 8) and 1 at the LCFS. The magnetic conﬁguration is determined during the discharge by reconstruction from magnetic probes . Poloidal coordinate is calculated as following: pol = r - a s - a (8) where is the magnetic ﬂux, a is the magnetic ﬂux on the magnetic axis and s at the separatrix.
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Edge plasma emissivity profile reconstruction by forward modelling of diode bolometer signals at ASDEX Upgrade
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|Tipo:||Laurea II ciclo (magistrale o specialistica)|
|Università:||Università degli Studi di Padova|
|Facoltà:||Scienze Matematiche, Fisiche e Naturali|
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