Modelling of electron transport and of sawtooth activity in tokamaks

Transport phenomena in tokamak plasmas strongly limit the particle and energy confinement and represent a crucial obstacle to controlled thermonuclear fusion. Within the vast framework of transport studies, three topics have been tackled in the present thesis: first, the computation of neoclassical transport coefficients for general axisymmetric equilibria and arbitrary collisionality regime; second, the analysis of the electron temperature behaviour and transport modelling of plasma discharges in the Tokamak à Configuration Variable (TCV) ; third, the modelling and simulation of the sawtooth activity with different plasma heating conditions. The work dedicated to neoclassical theory has been undertaken in order to first analytically identify a set of equations suited for implementation in existing Fokker-Planck codes. Modifications of these codes enabled us to compute the neoclassical transport coefficients considering different realistic magnetic equilibrium configurations and covering a large range of variation of three key parameters: aspect ratio, collisionality, and effective charge number. A comparison of the numerical results with an analytical limit has permitted the identification of two expressions for the trapped particle fraction, capable of encapsulating the geometrical effects and thus enabling each transport coefficient to be fitted with a single analytical function. This has allowed us to provide simple analytical formulae for al1 the neoclassical transport coefficients valid for arbitrary aspect ratio and collisionality in general realistic geometry. This work is particularly useful for a correct evaluation of the neoclassical contribution in tokamak scenarios with large bootstrap current fraction, or improved confinement regimes with low anomalous transport and for the determination of the plasma current density profile, since the plasma conductivity is usually assumed neoclassical. These results have been included in the plasma transport code PRETOR. This code has been further extended and applied to the simulation of electron transport in TCV. In simulating the electron temperature profile of Ohmic sawtoothing plasmas, the proper description of the current density profile and the sawtooth activity play the dominant role and not the specific transport model, provided that a single parameter in the model is adjusted to match the global plasma performance. In TCV discharges with electron cyclotron heating (ECH), the behaviour of the electron temperature exhibits some characteristics which have been recently observed to be common to several tokamaks. In particular, with central heating the electron temperature profile is stiff outside the power deposition region, that is the gradient scale length is independent of the heating power and essentially constant along the minor radius. With off-axis heating, transport is strongly reduced in the central region of the plasma, whereas a steep increase of the heat conductivity is observed at the power deposition location. Although the semi-empirical Rebut-Lallia-Watkins (RLW) transport model does not involve a critical gradient scale length, as the experimental observations would suggest, rather a critical electron temperature gradient, we have shown that it allows simulations which reproduce the described experimental features with very good agreement. Due to the relatively low toroidal magnetic field of TCV, the experimental temperature gradient with ECH exceeds by far the threshold included in the model. It can thus be stated that the parametric dependence of the electron heat conductivity of this transport model is adequate to reproduce the electron transport for plasma parameters in the operation domain of TCV. PRETOR, interfaced with the experimental data and the code TORAY-GA for the computation of the ECH source, has hence been used as a reliable tool for transport analysis and planning of new experiments. This has contributed to the identification of an improved central electron confinement (ICEC) regime in TCV, characterized by a precise heating scheme (strong electron cyclotron current drive in the counter-direction in the plasma center, and localized off-axis heating), with a specific time sequence. Transport simulations and investigations of this regime, in particular dedicated to the reconstruction of the current density profile during the high performance phase, have motivated further experiments which have confirmed numerical predictions. As a consequence, the magnetic shear reversa1 has been identified as the crucial ingredient for ICEC. The powerful ECH system in TCV does not allow only strong global current profile modifications but also local tailoring which has significant effects on sawtooth activity. A model introduced for the prediction of the sawtooth period in the proposed International Thermonuclear Experimental Reactor (ITER) has been extended to be applicable to Ohmic and ECH discharges in TCV. The model has been found in agreement with the experimental observations and thereby we were able to identify the physical mechanisms which make ECH capable of controlling the sawtooth period. The parameter dependence of the relevant stability threshold has been found consistent with dedicated experiments demonstrating the effects of localized heating and current drive on the sawtooth period. The simulations have pointed out the effects of the magnetic shear and of the pressure gradient at the q = 1 surface. Moreover, the most efficient heating location to stabilize the sawtooth period has been identified as located outside the q = 1 surface before the sawtooth crash. The same period model has been used for the simulation of the sawtooth period in recent discharges with neutral beam injection (NBI) in the Joint European Torus (JET), performed to assess the role of beam ions on sawtooth stabilization. With the inclusion of an analytical expression for the fast ion contribution to the internal kink potential energy, validated by the hybrid kinetic/MHD code NOVA-K, the simulations have been found in remarkable good agreement with the experimental observations. This work has demontrated the role of beam ions in sawtooth stabilization and validated the stability threshold for the resistive internal kink which was predicted to be the sawtooth crash trigger relevant for ITER operation

Density profile peaking in JET H-mode plasmas: experiments versus linear gyrokinetic predictions

As an independent complement to previous studies (Weisen et al 2005 Nucl. Fusion 45 L1-4, Weisen et al 2006 Plasma Phys. Control. Fusion 48 A457-66, Angioni et al 2007 Nucl. Fusion 47 1326-35), density peaking in the JET tokamak was investigated on the dataset, comprising virtually all H-mode experiments performed in 2006-2007. Unlike previous studies, this work focuses on low collisionality data as most representative of reactor conditions. The study confirms that collisionality is the most important parameter governing density peaking in H-mode, followed by the NBI particle flux and/or the T-i/T-e temperature ratio. For the first time in JET a modest, albeit significant dependence of peaking on internal inductance, or magnetic shear is seen. The experimental behaviour is compared with an extensive database of linear gyrokinetic calculations using the GS2 code. The predictions from GS2 simulations based on the highest linear growth rate mode are in good agreement with experimental observations. They are also corroborated by initial results from the non-linear code GYRO

Progress from ASDEX Upgrade experiments in preparing the physics basis of ITER operation and DEMO scenario development

An overview of recent results obtained at the tokamak ASDEX Upgrade (AUG) is given. A work flow for predictive profile modelling of AUG discharges was established which is able to reproduce experimental H-mode plasma profiles based on engineering parameters only. In the plasma center, theoretical predictions on plasma current redistribution by a dynamo effect were confirmed experimentally. For core transport, the stabilizing effect of fast ion distributions on turbulent transport is shown to be important to explain the core isotope effect and improves the description of hollow low-Z impurity profiles. The L–H power threshold of hydrogen plasmas is not affected by small helium admixtures and it increases continuously from the deuterium to the hydrogen level when the hydrogen concentration is raised from 0 to 100%. One focus of recent campaigns was the search for a fusion relevant integrated plasma scenario without large edge localised modes (ELMs). Results from six different ELM-free confinement regimes are compared with respect to reactor relevance: ELM suppression by magnetic perturbation coils could be attributed to toroidally asymmetric turbulent fluctuations in the vicinity of the separatrix. Stable improved confinement mode plasma phases with a detached inner divertor were obtained using a feedback control of the plasma β. The enhanced Dα H-mode regime was extended to higher heating power by feedback controlled radiative cooling with argon. The quasi-coherent exhaust regime was developed into an integrated scenario at high heating power and energy confinement, with a detached divertor and without large ELMs. Small ELMs close to the separatrix lead to peeling-ballooning stability and quasi continuous power exhaust. Helium beam density fluctuation measurements confirm that transport close to the separatrix is important to achieve the different ELM-free regimes. Based on separatrix plasma parameters and interchange-drift-Alfvén turbulence, an analytic model was derived that reproduces the experimentally found important operational boundaries of the density limit and between L- and H-mode confinement. Feedback control for the X-point radiator (XPR) position was established as an important element for divertor detachment control. Stable and detached ELM-free phases with H-mode confinement quality were obtained when the XPR was moved 10 cm above the X-point. Investigations of the plasma in the future flexible snow-flake divertor of AUG by means of first SOLPS-ITER simulations with drifts activated predict beneficial detachment properties and the activation of an additional strike point by the drifts.This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.Peer Reviewed"Article signat per més de 50 autors/es: U. Stroth, D. Aguiam, E. Alessi, C. Angioni, N. Arden, R. Arredondo Parra, V. Artigues, O. Asunta, M. Balden, V. Bandaru, A. Banon-Navarro, K. Behler, A. Bergmann, M. Bergmann, J. Bernardo, M. Bernert, A. Biancalani, R. Bielajew, R. Bilato, G. Birkenmeier, T. Blanken, V. Bobkov, A. Bock, T. Body, T. Bolzonella, N. Bonanomi, A. Bortolon, B. Böswirth, C. Bottereau, A. Bottino, H. van den Brand, M. Brenzke, S. Brezinsek, D. Brida, F. Brochard, C. Bruhn, J. Buchanan, A. Buhler, A. Burckhart, Y. Camenen, B. Cannas, P. Cano Megias, D. Carlton, M. Carr, P. Carvalho, C. Castaldo, M. Cavedon, C. Cazzaniga, C. Challis, A. Chankin, C. Cianfarani, F. Clairet, S. Coda, R. Coelho, J.W. Coenen, L. Colas, G. Conway, S. Costea, D. Coster, T. Cote, A.J. Creely, G. Croci, D.J. Cruz Zabala, G. Cseh, A. Czarnecka, I. Cziegler, O. D'Arcangelo, A. Dal Molin, P. David, C. Day, M. de Baar, P. de Marné, R. Delogu, S. Denk, P. Denner, A. Di Siena, J.J. Dominguez Palacios Durán, D. Dunai, A. Drenik, M. Dreval, R. Drube, M. Dunne, B.P. Duval, R. Dux, T. Eich, S. Elgeti, A. Encheva, K. Engelhardt, B. Erdös, I. Erofeev, B. Esposito, E. Fable, M. Faitsch, U. Fantz, M. Farnik, H. Faugel, F. Felici, O. Ficker, S. Fietz, A. Figueredo, R. Fischer, O. Ford, L. Frassinetti, M. Fröschle, G. Fuchert, J.C. Fuchs, H. Fünfgelder, S. Futatani, K. Galazka, J. Galdon-Quiroga, D. Gallart Escolà, A. Gallo10, Y. Gao11, S. Garavaglia3, M. Garcia Muñoz16, B. Geiger21, L. Giannone1, S. Gibson32, L. Gil2, E. Giovannozzi18, S. Glöggler1, M. Gobbin8, J. Gonzalez Martin, T. Goodman, G. Gorini, T. Görler, D. Gradic, G. Granucci, A. Gräter, H. Greuner, M. Griener, M. Groth, A. Gude, L. Guimarais, S. Günter, G. Haas, A.H. Hakola, C. Ham, T. Happel, N. den Harder, G. Harrer, J. Harrison, V. Hauer, T. Hayward-Schneider, B. Heinemann, T. Hellsten, S. Henderson, P. Hennequin, A. Herrmann, E. Heyn, F. Hitzler, J. Hobirk, K. Höfler, J.H. Holm, M. Hölzl, C. Hopf, L. Horvath, T. Höschen, A. Houben, A. Hubbard, A. Huber, K. Hunger, V. Igochine, M. Iliasova, T. Ilkei, K. Insulander Björk, C. Ionita-Schrittwieser, I. Ivanova-Stanik, W. Jacob, N. Jaksic, F. Janky, A. Jansen van Vuuren, A. Jardin, F. Jaulmes, F. Jenko, T. Jensen, E. Joffrin, A. Kallenbach, S. Kálvin, M. Kantor, A. Kappatou, O. Kardaun, J. Karhunen4, C.-P. Käsemann, S. Kasilov, A. Kendl, W. Kernbichler, E. Khilkevitch, A. Kirk, S. Kjer Hansen, V. Klevarova, G. Kocsis, M. Koleva, M. Komm, M. Kong, A. Krämer-Flecken, K. Krieger, A. Krivska, O. Kudlacek, T. Kurki-Suonio, B. Kurzan, B. Labit, K. Lackner, F. Laggner, A. Lahtinen, P.T. Lang, P. Lauber, N. Leuthold, L. Li, J. Likonen, O. Linder, B. Lipschultz, Y. Liu, A. Lohs, Z. Lu, T. Luda di Cortemiglia, N.C. Luhmann, T. Lunt, A. Lyssoivan, T. Maceina, J. Madsen, A. Magnanimo, H. Maier, J. Mailloux, R. Maingi, O. Maj, E. Maljaars, P. Manas, A. Mancini, A. Manhard, P. Mantica, M. Mantsinen, P. Manz, M. Maraschek, C. Marchetto, L. Marrelli, P. Martin, A. Martitsch, F. Matos, M. Mayer, M.-L. Mayoral, D. Mazon, P.J. McCarthy, R. McDermott, R. Merkel, A. Merle, D. Meshcheriakov, H. Meyer, D. Milanesio, P. Molina Cabrera, F. Monaco, M. Muraca, F. Nabais, V. Naulin, R. Nazikian, R.D. Nem, A. Nemes-Czopf, G. Neu, R. Neu, A.H. Nielsen, S.K. Nielsen, T. Nishizawa, M. Nocente, J.-M. Noterdaeme, I. Novikau, S. Nowak, M. Oberkofler, R. Ochoukov, J. Olsen, F. Orain, F. Palermo, O. Pan, G. Papp, I. Paradela Perez, A. Pau, G. Pautasso, C. Paz-Soldan, P. Petersson, P. Piovesan, C. Piron, U. Plank, B. Plaum, B. Plöck, V. Plyusnin, G. Pokol, E. Poli, L. Porte, T. Pütterich, M. Ramisch, J. Rasmussen, G. Ratta, S. Ratynskaia, G. Raupp, D. Réfy, M. Reich1, F. Reimold, D. Reiser, M. Reisner, D. Reiter, T. Ribeiro, R. Riedl, J. Riesch, D. Rittich, J.F. Rivero Rodriguez, G. Rocchi, P. Rodriguez-Fernandez, M. Rodriguez-Ramos, V. Rohde, G. Ronchi, A. Ross, M. Rott, M. Rubel, D.A. Ryan, F. Ryter, S. Saarelma, M. Salewski, A. Salmi, O. Samoylov, L. Sanchis Sanchez, J. Santos, O. Sauter, G. Schall, K. Schlüter, K. Schmid, O. Schmitz, P.A. Schneider, R. Schrittwieser, M. Schubert, C. Schuster, T. Schwarz-Selinger, J. Schweinzer, E. Seliunin, A. Shabbir, A. Shalpegin, S. Sharapov, U. Sheikh, A. Shevelev, G. Sias, M. Siccinio, B. Sieglin, A. Sigalov, A. Silva, C. Silva, D. Silvagni, J. Simpson, S. Sipilä, E. Smigelskis, A. Snicker, E. Solano, C. Sommariva, C. Sozzi, G. Spizzo, M. Spolaore, A. Stegmeir, M. Stejner, J. Stober, E. Strumberge1, G. Suarez Lopez, H.-J. Sun, W. Suttrop, E. Sytova, T. Szepesi, B. Tál, T. Tala, G. Tardini, M. Tardocchi, D. Terranova, M. Teschke, E. Thorén, W. Tierens, D. Told, W. Treutterer, G. Trevisan, E. Trier, M. Tripský, M. Usoltceva, M. Valisa, M. Valovic, M. van Zeeland, F. Vannini, B. Vanovac, P. Varela, S. Varoutis, N. Vianello, J. Vicente, G. Verdoolaege, T. Vierle, E. Viezzer, I. Voitsekhovitch, U. von Toussaint, D. Wagner, X. Wang, M. Weiland, A.E. White, M. Willensdorfer, B. Wiringer, M. Wischmeier, R. Wolf, E. Wolfrum, Q. Yang, Q. Yu, R. Zagórski, I. Zammuto, T. Zehetbauer, W. Zhang, W. Zholobenko, M. Zilker, A. Zito, H. Zohm, S. Zoletnik and the EUROfusion MST1 Team "Postprint (published version

Energy Confinement in Shaped TCV Plasmas with Electron Cyclotron Heating

The effects of plasma shape on confinement and sawtooth stability are studied for positive and negative discharge triangularity and for different elongations with 1.5 MW centrally deposited ECH powe

Exploring fusion-reactor physics with high-power electron cyclotron resonance heating on ASDEX Upgrade

The electron cyclotron resonance heating (ECRH) system of the ASDEX Upgrade tokomak has been upgraded over the last 15 years from a 2MW, 2 s, 140 GHz system to an 8MW, 10 s, dual frequency system (105/140 GHz). The power exceeds the L/H power threshold by at least a factor of two, even for high densities, and roughly equals the installed ion cyclotron range of frequencies power. The power of both wave heating systems together (>10MW in the plasma) is about half of the available neutral beam injection (NBI) power, allowing significant variations of torque input, of the shape of the heating profile and of Qe/Qi, even at high heating power. For applications at a low magnetic field an X3-heating scheme is routinely in use. Such a scenario is now also forseen for ITER to study the first H-modes at one third of the full field. This versatile system allows one to address important issues fundamental to a fusion reactor: H-mode operation with dominant electron heating, accessing low collisionalities in full metal devices (also related to suppression of edge localized modes with resonant magnetic perturbations), influence of Te/Ti and rotational shear on transport, and dependence of impurity accumulation on heating profiles. Experiments on all these subjects have been carried out over the last few years and will be presented in this contribution. The adjustable localized current drive capability of ECRH allows dedicated variations of the shape of the q-profile and the study of their influence on non-inductive tokamak operation (so far at q$_{95}$>5.3). The ultimate goal of these experiments is to use the experimental findings to refine theoretical models such that they allow a reliable design of operational schemes for reactor size devices. In this respect, recent studies comparing a quasi-linear approach (TGLF) with fully non-linear modeling (GENE) of non-inductive high-beta plasmas will be reported

Confinement in electron heated plasmas in Wendelstein 7-X and ASDEX Upgrade; the necessity to control turbulent transport

In electron (cyclotron) heated plasmas, in both ASDEX Upgrade (L-mode) and Wendelstein 7-X, clamping of the ion temperature occurs at Ti ∼ 1.5 keV independent of magnetic configuration. The ions in such plasmas are heated through the energy exchange power as ${n}_{\mathrm{e}}^{2}({T}_{\mathrm{e}}-{T}_{\mathrm{i}})/{T}_{\mathrm{e}}^{3/2}$, which offers a broad ion heating profile, similar to that offered by alpha heating in future thermonuclear fusion reactors. However, the predominant electron heating may put an additional constraint on the ion heat transport, as the ratio Te/Ti > 1 can exacerbates ITG/TEM core turbulence. Therefore, in practical terms the strongly 'stiff' core transport translates into Ti-clamping in electron heated plasmas. Due to this clamping, electron heated L-mode scenarios, with standard gas fueling, in either tokamaks or stellarators may struggle to reach high normalized ion temperature gradients required in a compact fusion reactor. The comparison shows that core heat transport in neoclassically optimized stellarators is driven by the same mechanisms as in tokamaks. The absence of a strong H-mode temperature edge pedestal in stellarators, sofar (which, like in tokamaks, could lift the clamped temperature-gradients in the core), puts a strong requirement on reliable and sustainable core turbulence suppression techniques in stellarators.EC/H2020/633053/EU/Implementation of activities described in the Roadmap to Fusion during Horizon 2020 through a Joint programme of the members of the EUROfusion consortium/Eurato

Gyrokinetic calculations of diffusive and convective transport of alpha particles with a slowing-down distribution function

Quasilinear gyrokinetic calculations of the transport of fast alpha particles with a slowing-down equilibrium distribution function in the trace limit are presented. Diffusive and convective contributions to the total flux are separated and their dependence on the ratio of the fast particle energy to the background plasma temperature is investigated. The results are compared with those obtained in the case an equivalent Maxwellian distribution function is assumed for the fast particles. On the basis of the gyrokinetic results, simple models for alpha particle transport are proposed for transport modeling purposes. (c) 2008 American Institute of Physics

Experimental investigation of the tilt angle of turbulent structures in the core of fusion plasmas

International audienceThe tilt angle of turbulent structures stands for the anisotropy of turbulence which is essential for understanding the dynamics of magnetized plasmas. It is a quantity predicted by theory and simulations, that provides information on the interplay between turbulence, micro-instabilities and plasma flows. A new method for measuring the tilt angle of turbulent structures in the core region of fusion plasmas using Doppler reflectometry is presented. First measurements of this type on the ASDEX Upgrade tokamak have shown a significant difference of tilt angle for different plasma conditions. The dominance of sheared flows in determining the structure tilt is experimentally demonstrated for different turbulence regimes