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An accurate control of the magnetic boundary ofa thermonuclear plasma is an important issue in magnetic confinement research. The development of methods for the active control of magnetohydrodynamic instabilities and correction oferror fields is mandatory. A substantial modification of the layoutof the RFX-mod device is in progress: the aim of this paper isto assess the potential advantages of the proposed solution with advanced numerical techniques based on integral formulations.

This paper presents a model based procedure for in situ error compensation of spatially distributed magnetic sensors. The proposed approach is numerically validated on RFX-mod, a magnetically confined plasma experiment presently being upgraded with a new magnetic diagnostic system and a state-of-the-art real time control system. The numerical simulations are performed with the CAFE code; synthetic measurements are used to assess the reliability of the proposed method.

The dynamics of turbulent filaments in L and ELM-free H-mode in the RFX-mod device operating as a tokamak is discussed in the present work. L-H transition and sustained H-mode have been achieved in the RFX-mod with the aid of an external electrode biasing (Spolaore et al 2017 Nucl. Fusion 57 116039). Through advanced statistical techniques, turbulent filaments are detected and tracked from the edge to the scrape-off layer (SOL) in a two-dimension floating potential map (measured with a 2D array of Langmuir probes) related with extreme events of a fixed ion saturation current signal in the SOL. While in L-mode filaments travel almost freely, their motion becomes restricted to the near SOL during the induced biasing H-mode. In this region, the background shear decorrelation time becomes shorter than the convective filament time, favouring its suppression. However, the experimental observation of a nearly 'trapped' monopole potential points out the possible role of the vortex selection mechanism. The sign and magnitude of the turbulent parallel vorticity are consistent with the E × B background vorticity in the SOL in this regime, while in L-mode, the inferred turbulent vorticity is always above the background one. The sparse filamentary transport in the far SOL during H-mode is further confirmed from the measurements of a poloidally symmetric array of electrostatic sensors on the wall. Lastly, the radial velocity of filaments in both regimes was discussed in the framework of analytical scalings. Filaments in L-mode exhibit a reasonable agreement with the sheath-limited regime in the cold ion approximation, with a non-negligible associated parallel current density measured with a set of 3-axial pick-up coils installed in the probe head. In H-mode, the collisionality increases near the separatrix while filaments seem to follow the inertial regime before become trapped.

This paper reviews the research on the reversed field pinch (RFP) in the last three decades. Substantial experimental and theoretical progress and transformational changes have been achieved since the last review (Bodin 1990 Nucl. Fusion 30 1717–37). The experiments have been performed in devices with different sizes and capabilities. The largest are RFX-mod in Padova (Italy) and MST in Madison (USA). The experimental community includes also EXTRAP-T2R in Sweden, RELAX in Japan and KTX in China. Impressive improvements in the performance are the result of exploration of two lines: the high current operation (up to 2 MA) with the spontaneous occurrence of helical equilibria with good magnetic flux surfaces and the active control of the current profile. A crucial ingredient for the advancements obtained in the experiments has been the development of state-of-art active feedback control systems allowing the control of MHD instabilities in presence of a thin shell. The balance between achievements and still open issues leads us to the conclusion that the RFP can be a valuable and diverse contributor in the quest for fusion electricity.

A major refurbishment of the toroidal complex of the RFX-mod device is in progress and will include the removal of the Inconel vacuum vessel and a modification of the stainless steel supporting structure to be made vacuum tight. The plasma facing graphite tiles will be mounted onto the inner surface of the copper shell so as to increase the plasma proximity factor. New operation regimes are expected to provide a significant reduction of the amplitude of RFP tearing modes with magnetic chaos mitigation and confinement improvement. On the other hand, due to the shorter distance from the passive structures, the plasma is expected to be even more sensitive to magnetic field errors at the plasma boundary, produced by the induced currents near the cuts of the same structures. In preparation to the new RFX-mod2 experiments, a thorough revision of the conditions triggering the error fields due to the eddy currents was undertaken. An analysis of the static and dynamic equilibrium magnetic field has been carried out in RFX-mod and RFX-mod2 to estimate the magnetic field driving the shell eddy currents. A lower equilibrium magnetic field should be required in RFX-mod2. Analyses of different configurations of the poloidal gap were also carried out by a specialized computational tool. A solution with a spaced poloidal gap and a more extended overlapping was envisaged capable of maintaining the same error fields at the closer plasma boundary with the same forcing field and meeting the more stringent insulation and assembly requirements of RFX-mod2.

In this paper we validate the finite element code RAPLICASOL, which models radiofrequency wave propagation in edge plasmas near ICRF antennas, against calculations with the TOPICA code. We compare the output of both codes for the ASDEX Upgrade 2-strap antenna, and for a 4-strap WEST-like antenna. Although RAPLICASOL requires considerably fewer computational resources than TOPICA, we find that the predicted quantities of experimental interest (including reflection coefficients, coupling resistances, S- and Z-matrix entries, optimal matching settings, and even radiofrequency electric fields) are in good agreement provided we are careful to use the same geometry in both codes.

Within the EUROfusion MST1 work package, a series of experiments has been conducted on AUG and TCV devices to disentangle the role of plasma fueling and plasma shape for the onset of small ELM regimes. On both devices, small ELM regimes with high confinement are achieved if and only if two conditions are fulfilled at the same time. Firstly, the plasma density at the separatrix must be large enough (), leading to a pressure profile flattening at the separatrix, which stabilizes type-I ELMs. Secondly, the magnetic configuration has to be close to a double null (DN), leading to a reduction of the magnetic shear in the extreme vicinity of the separatrix. As a consequence, its stabilizing effect on ballooning modes is weakened. Peer Reviewed Article escrit per 365 autors/autores: Labit, B.; Eich, T.; Harrer, G. F.; Wolfrum, E.; Bernert, M.; Dunne, M. G.; Frassinetti, L.; Hennequin, P.; Maurizio, R.; Merle, A.; Meyer, H.; Saarelma, S.; Sheikh, U.; Adamek, J.; Agostini, M.; Aguiam, D.; Akers, R.; Albanese, R.; Albert, C.; Alessi, E.; Ambrosino, R.; Andr be, Y.; Angioni, C.; Apruzzese, G.; Aradi, M.; Arnichand, H.; Auriemma, F.; Avdeeva, G.; Ayllon-Guerola, J. M.; Bagnato, F.; Bandaru, V. K.; Barnes, M.; Barrera-Orte, L.; Bettini, P.; Bilato, R.; Biletskyi, O.; Bilkova, P.; Bin, W.; Blanchard, P.; Blanken, T.; Bobkov, V.; Bock, A.; Boeyaert, D.; Bogar, K.; Bogar, O.; Bohm, P.; Bolzonella, T.; Bombarda, F.; Boncagni, L.; Bouquey, F.; Bowman, C.; Brezinsek, S.; Brida, D.; Brunetti, D.; Bucalossi, J.; Buchanan, J.; Buermans, J.; Bufferand, H.; Buller, S.; Buratti, P.; Burckhart, A.; Calabr, G.; Calacci, L.; Camenen, Y.; Cannas, B.; Cano Megías, P.; Carnevale, D.; Carpanese, F.; Carr, M.; Carralero, D.; Carraro, L.; Casolari, A.; Cathey, A.; Causa, F.; Cavedon, M.; Cecconello, M.; Ceccuzzi, S.; Cerovsky, J.; Chapman, S.; Chmielewski, P.; Choi, D.; Cianfarani, C.; Ciraolo, G.; Coda, S.; Coelho, R.; Colas, L.; Colette, D.; Cordaro, L.; Cordella, F.; Costea, S.; Coster, D.; Cruz Zabala, D. J.; Cseh, G.; Czarnecka, A.; Cziegler, I.; D’Arcangelo, O.; Dal Molin, A.; David, P.; De Carolis, G.; De Oliveira, H.; Decker, J.; Dejarnac, R.; Delogu, R.; Den Harder, N.; Dimitrova, M.; Dolizy, F.; Domínguez-Palacios Durán, J. J.; Douai, D.; Drenik, A.; Dreval, M.; Dudson, B.; Dunai, D.; Duval, B. P.; Dux, R.; Elmore, S.; Embréus, O.; Erds, B.; Fable, E.; Faitsch, M.; Fanni, A.; Farnik, M.; Faust, I.; Faustin, J.; Fedorczak, N.; Felici, F.; Feng, S.; Feng, X.; Ferreira, J.; Ferr, G.; Février, O.; Ficker, O.; Figini, L.; Figueiredo, A.; Fil, A.; Fontana, M.; Francesco, M.; Fuchs, C.; Futatani, S.; Gabellieri, L.; Gadariya, D.; Gahle, D.; Galassi, D.; Gałązka, K.; Galdon-Quiroga, J.; Galeani, S.; Gallart, D.; Gallo, A.; Galperti, C.; Garavaglia, S.; Garcia, J.; Garcia-Lopez, J.; Garcia-Mu oz, M.; Garzotti, L.; Gath, J.; Geiger, B.; Giacomelli, L.; Giannone, L.; Gibson, S.; Gil, L.; Giovannozzi, E.; Giruzzi, G.; Gobbin, M.; Gonzalez-Martin, J.; Goodman, T. P.; Gorini, G.; Gospodarczyk, M.; Granucci, G.; Grekov, D. 1; Grenfell, G.; Griener, M.; Groth, M.; Grover, O.; Gruca, M.; Gude, A.; Guimarais, L.; Gyergyek, T.; Hacek, P.; Hakola, A.; Ham, C.; Happel, T.; Harrison, J.; Havranek, A.; Hawke, J.; Henderson, S.; Hesslow, L.; Hitzler, F.; Hnat, B.; Hobirk, J.; Hoelzl, M.; Hogeweij, D.; Hopf, C.; Hoppe, M.; Horacek, J.; Hron, M.; Huang, Z.; Iantchenko, A.; Iglesias, D.; Igochine, V.; Innocente, P.; Ionita-Schrittwieser, C.; Isliker, H.; Ivanova-Stanik, I.; Jacobsen, A.; Jakubowski, M.; Janky, F.; Jardin, A.; Jaulmes, F.; Jensen, T.; Jonsson, T.; Kallenbach, A.; Kappatou, A.; Karpushov, A.; Kasilov, S.; Kazakov, Y.; Kazantzidis, P. V.; Keeling, D.; Kelemen, M.; Kendl, A.; Kernbichler, W.; Kirk, A.; Kocsis, G.; Komm, M.; Kong, M.; Korovin, V.; Koubiti, M.; Kovacic, J.; Krawczyk, N.; Krieger, K.; Kripner, L.; Křivská, A.; Kudlacek, O.; Kulyk, Y.; Kurki-Suonio, T.; Kwiatkowski, R.; Laggner, F.; Laguardia, L.; Lahtinen, A.; Lang, P.; Likonen, J.; Lipschultz, B.; Liu, F.; Lombroni, R.; Lorenzini, R.; Loschiavo, V. P.; Lunt, T.; MacUsova, E.; Madsen, J.; Maggiora, R.; Maljaars, B.; Manas, P.; Mantica, P.; Mantsinen, M. J.; Manz, P.; Maraschek, M.; Marchenko, V.; Marchetto, C.; Mariani, A.; Marini, C.; Markovic, T.; Marrelli, L.; Martin, P.; Martín Solís, J. R.; Martitsch, A.; Mastrostefano, S.; Matos, F.; Matthews, G.; Mayoral, M.-L.; Mazon, D.; Mazzotta, C.; Mc Carthy, P.; McClements, K.; McDermott, R.; McMillan, B.; Meineri, C.; Menkovski, V.; Meshcheriakov, D.; Messmer, M.; Micheletti, D.; Milanesio, D.; Militello, F.; Miron, I. G.; Mlynar, J.; Moiseenko, V.; Molina Cabrera, P. A.; Morales, J.; Moret, J.-M.; Moro, A.; Moulton, D.; Nabais, F.; Naulin, V.; Naydenkova, D.; Nem, R. D.; Nespoli, F.; Newton, S.; Nielsen, A. H.; Nielsen, S. K.; Nikolaeva, V.; Nocente, M.; Nowak, S.; Oberkofler, M.; Ochoukov, R.; Ollus, P.; Olsen, J.; Omotani, J.; Ongena, J.; Orain, F.; Orsitto, F. P.; Paccagnella, R.; Palha, A.; Panaccione, L.; Panek, R.; Panjan, M.; Papp, G.; Paradela Perez, I.; Parra, F.; Passeri, M.; Pau, A.; Pautasso, G.; Pavlichenko, R.; Perek, A.; Pericoli Radolfini, V.; Pesamosca, F.; Peterka, M.; Petrzilka, V.; Piergotti, V.; Pigatto, L.; Piovesan, P.; Piron, C.; Piron, L.; Plyusnin, V.; Pokol, G.; Poli, E.; Pölöskei, P.; Popov, T.; Popovic, Z.; Pór, G.; Porte, L.; Pucella, G.; Puiatti, M. E.; Pütterich, T.; Rabinski, M.; Juul Rasmussen, J.; Rasmussen, J.; Rattá, G. A.; Ratynskaia, S.; Ravensbergen, T.; Réfy, D.; Reich, M.; Reimerdes, H.; Reimold, F.; Reiser, D.; Reux, C.; Reznik, S.; Ricci, D.; Rispoli, N.; Rivero-Rodriguez, J. F.; Rocchi, G.; Rodriguez-Ramos, M.; Romano, A.; Rosato, J.; Rubinacci, G.; Rubino, G.; Ryan, D. A.; Salewski, M.; Salmi, A.; Samaddar, D.; Sanchis-Sanchez, L.; Santos, J.; Särkimäki, K.; Sassano, M.; Sauter, O.; Scannell, R.; Scheffer, M.; Schneider, B. S.; Schneider, P.; Schrittwieser, R.; Schubert, M.; Seidl, J.; Seliunin, E.; Sharapov, S.; Sheeba, R. R.; Sias, G.; Sieglin, B.; Silva, C.; Sipilä, S.; Smith, S.; Snicker, A.; Solano, E. R.; Hansen, S. K.; Soria-Hoyo, C.; Sorokovoy, E.; Sozzi, C.; Sperduti, A.; Spizzo, G.; Spolaore, M.; Stejner, M.; Stipani, L.; Stober, J.; Strand, P.; Sun, H.; Suttrop, W.; Sytnykov, D.; Szepesi, T.; Tál, B.; Tala, T.; Tardini, G.; Tardocchi, M.; Teplukhina, A.; Terranova, D.; Testa, D.; Theiler, C.; Thorén, E.; Thornton, A.; Tilia, B.; Tolias, P.; Tomes, M.; Toscano-Jimenez, M.; Tsironis, C.; Tsui, C.; Tudisco, O.; Urban, J.; Valisa, M.; Vallar, M.; Vallejos Olivares, P.; Valovic, M.; Van Vugt, D.; Vanovac, B.; Varje, J.; Varju, J.; Varoutis, S. 1; Vartanian, S.; Vasilovici, O.; Vega, J.; Verdoolaege, G.; Verhaegh, K.; Vermare, L.; Vianello, N.; Vicente, J.; Viezzer, E.; Villone, F.; Voitsekhovitch, I.; Voltolina, D.; Vondracek, P.; Vu, N. M. T.; Walkden, N.; Wauters, T.; Weiland, M.; Weinzettl, V.; Wensing, M.; Wiesen, S.; Wiesenberger, M.; Wilkie, G.; Willensdorfer, M.; Wischmeier, M.; Wu, K.; Xiang, L.; Zagorski, R.; Zaloga, D.; Zanca, P.; Zaplotnik, R.; Zebrowski, J.; Zhang, W.; Zisis, A.; Zoletnik, S.; Zuin, M.

The externally applied loop voltage, required to drive current carrying magnetic configurations, such as tokamaks or reversed field pinches (RFP), can induce currents between the plasma and the surrounding conducting components, such as limiters, divertor sections, stabilizing plates or enclosing stabilizing shells with insulated electrical gaps. An appropriate modeling of this problem can quantify these currents and give constraints for the design of new devices. In this paper a methodology based on lumped element circuit is used to evaluate this problem for the case of in vessel components of the RFX-mod2, which led to a redesign of the electrical connections of plasma facing components. In the new design some parts, having applied potential in the kV range, are still exposed to the weakly ionized scrape off plasma. The process of arc formation between them and their prevention had been experimentally investigated and possible arc suppression strategies identified.

The ASDEX Upgrade (AUG) programme, jointly run with the EUROfusion MST1 task force, continues to significantly enhance the physics base of ITER and DEMO. Here, the full tungsten wall is a key asset for extrapolating to future devices. The high overall heating power, flexible heating mix and comprehensive diagnostic set allows studies ranging from mimicking the scrape-off-layer and divertor conditions of ITER and DEMO at high density to fully non-inductive operation (q95 = 5.5, ) at low density. Higher installed electron cyclotron resonance heating power 6 MW, new diagnostics and improved analysis techniques have further enhanced the capabilities of AUG. Stable high-density H-modes with MW m−1 with fully detached strike-points have been demonstrated. The ballooning instability close to the separatrix has been identified as a potential cause leading to the H-mode density limit and is also found to play an important role for the access to small edge-localized modes (ELMs). Density limit disruptions have been successfully avoided using a path-oriented approach to disruption handling and progress has been made in understanding the dissipation and avoidance of runaway electron beams. ELM suppression with resonant magnetic perturbations is now routinely achieved reaching transiently . This gives new insight into the field penetration physics, in particular with respect to plasma flows. Modelling agrees well with plasma response measurements and a helically localised ballooning structure observed prior to the ELM is evidence for the changed edge stability due to the magnetic perturbations. The impact of 3D perturbations on heat load patterns and fast-ion losses have been further elaborated. Progress has also been made in understanding the ELM cycle itself. Here, new fast measurements of and Er allow for inter ELM transport analysis confirming that Er is dominated by the diamagnetic term even for fast timescales. New analysis techniques allow detailed comparison of the ELM crash and are in good agreement with nonlinear MHD modelling. The observation of accelerated ions during the ELM crash can be seen as evidence for the reconnection during the ELM. As type-I ELMs (even mitigated) are likely not a viable operational regime in DEMO studies of 'natural' no ELM regimes have been extended. Stable I-modes up to have been characterised using -feedback. Core physics has been advanced by more detailed characterisation of the turbulence with new measurements such as the eddy tilt angle—measured for the first time—or the cross-phase angle of and fluctuations. These new data put strong constraints on gyro-kinetic turbulence modelling. In addition, carefully executed studies in different main species (H, D and He) and with different heating mixes highlight the importance of the collisional energy exchange for interpreting energy confinement. A new regime with a hollow profile now gives access to regimes mimicking aspects of burning plasma conditions and lead to nonlinear interactions of energetic particle modes despite the sub-Alfvénic beam energy. This will help to validate the fast-ion codes for predicting ITER and DEMO. 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. "Article signat per més de 100 autors/es: H. Meyer, for the AUG Team: D. Aguiam, C. Angioni, C.G. Albert, N. Arden, R. Arredondo Parra, O. Asunta, M. de Baar, M. Balden, V. Bandaru, K. Behler, A. Bergmann, J. Bernardo, M. Bernert, A. Biancalani, R. Bilato, G. Birkenmeier, T.C. Blanken, V. Bobkov, A. Bock, T. Bolzonella, A. Bortolon, B. Böswirth, C. Bottereau, A. Bottino, H. van den Brand, S. Brezinsek, D. Brida, F. Brochard, C. Bruhn, J. Buchanan, A. Buhler, A. Burckhart, Y. Camenen, D. Carlton, M. Carr, D. Carralero, C. Castaldo, M. Cavedon, C. Cazzaniga, S. Ceccuzzi, C. Challis, A. Chankin, S. Chapman, C. Cianfarani, F. Clairet, S. Coda, R. Coelho, J.W. Coenen, L. Colas, G.D. Conway, S. Costea, D.P. Coster, T.B. Cote, A. Creely, G. Croci, G. Cseh, A. Czarnecka, I. Cziegler, O. D'Arcangelo, P. David, C. Day, R. Delogu, P. de Marné, S.S. Denk, P. Denner, M. Dibon, A. Di Siena, D. Douai, A. Drenik, R. Drube, M. Dunne, B.P. Duval, R. Dux, T. Eich, S. Elgeti, K. Engelhardt, B. Erdös, I. Erofeev, B. Esposito, E. Fable, M. Faitsch, U. Fantz, H. Faugel, I. Faust, F. Felici, J. Ferreira, S. Fietz, A. Figuereido, R. Fischer, O. Ford, L. Frassinetti, S. Freethy, M. Fröschle, G. Fuchert, J.C. Fuchs, H. Fünfgelder, K. Galazka, J. Galdon-Quiroga, A. Gallo, Y. Gao, S. Garavaglia, A. Garcia-Carrasco, M. Garcia-Muñoz, B. Geiger, L. Giannone, L. Gil, E. Giovannozzi, C. Gleason-González, S. Glöggler, M. Gobbin, T. Görler, I. Gomez Ortiz, J. Gonzalez Martin, T. Goodman, G. Gorini, D. Gradic, A. Gräter, G. Granucci, H. Greuner, M. Griener, M. Groth, A. Gude, S. Günter, L. Guimarais, G. Haas, A.H. Hakola, C. Ham, T. Happel, N. den Harder, G.F. Harrer, J. Harrison, V. Hauer, T. Hayward-Schneider, C.C. Hegna, B. Heinemann, S. Heinzel, T. Hellsten, S. Henderson, P. Hennequin, A. Herrmann, M.F. Heyn, E. Heyn, F. Hitzler, J. Hobirk, K. Höfler, M. Hölzl, T. Höschen, J.H. Holm, C. Hopf, W.A. Hornsby, L. Horvath, A. Houben, A. Huber, V. Igochine, T. Ilkei, I. Ivanova-Stanik, W. Jacob, A.S. Jacobsen, F. Janky, A. Jansen van Vuuren, A. Jardin, F. Jaulmes, F. Jenko, T. Jensen, E. Joffrin, C.-P. Käsemann, A. Kallenbach, S. Kálvin, M. Kantor, A. Kappatou, O. Kardaun, J. Karhunen, S. Kasilov,, Y. Kazakov, W. Kernbichler, A. Kirk, S. Kjer Hansen, V. Klevarova, G. Kocsis, A. Köhn, M. Koubiti, K. Krieger, A. Krivska, A. Krämer-Flecken, O. Kudlacek, T. Kurki-Suonio, B. Kurzan, B. Labit, K. Lackner, F. Laggner, P.T. Lang, P. Lauber, A. Lebschy, N. Leuthold, M. Li, O. Linder, B. Lipschultz, F. Liu, Y. Liu, A. Lohs, Z. Lu, T. Luda di Cortemiglia, N.C. Luhmann, R. Lunsford, T. Lunt, A. Lyssoivan, T. Maceina, J. Madsen, R. Maggiora, H. Maier, O. Maj, J. Mailloux, R. Maingi, E. Maljaars, P. Manas, A. Mancini, A. Manhard, M.-E. Manso, P. Mantica, M. Mantsinen, P. Manz, M. Maraschek, C. Martens, P. Martin, L. Marrelli, A. Martitsch, M. Mayer, D. Mazon, P.J. McCarthy, R. McDermott, H. Meister, A. Medvedeva, R. Merkel, A. Merle, V. Mertens, D. Meshcheriakov, O. Meyer, J. Miettunen, D. Milanesio, F. Mink, A. Mlynek, F. Monaco, C. Moon, F. Nabais, A. Nemes-Czopf, G. Neu, R. Neu, A.H. Nielsen, S.K. Nielsen, V. Nikolaeva, M. Nocente, J.-M. Noterdaeme, I. Novikau, S. Nowak, M. Oberkofler, M. Oberparleiter, R. Ochoukov, T. Odstrcil, J. Olsen, F. Orain, F. Palermo, O. Pan, G. Papp, I. Paradela Perez, A. Pau, G. Pautasso, F. Penzel, P. Petersson, J. Pinzón Acosta, P. Piovesan, C. Piron, R. Pitts, U. Plank, B. Plaum, B. Ploeckl, V. Plyusnin, G. Pokol, E. Poli, L. Porte, S. Potzel, D. Prisiazhniuk, T. Pütterich, M. Ramisch, J. Rasmussen, G.A. Rattá, S. Ratynskaia, G. Raupp, G.L. Ravera, D. Réfy, M. Reich, F. Reimold, D. Reiser, T. Ribeiro, J. Riesch, R. Riedl, D. Rittich, J.F. Rivero-Rodriguez, G. Rocchi, M. Rodriguez-Ramos, V. Rohde, A. Ross1, M. Rott, M. Rubel, D. Ryan, F. Ryter, S. Saarelma, M. Salewski, A. Salmi, L. Sanchis-Sanchez, J. Santos, O. Sauter, A. Scarabosio, G. Schall, K. Schmid, O. Schmitz, P.A. Schneider, R. Schrittwieser, M. Schubert, T. Schwarz-Selinger, J. Schweinzer, B. Scott, T. Semer, E. Seliunin, M. Sertoli, A. Shabbir, A. Shalpegin, L. Shao, S. Sharapov, G. Sias, M. Siccinio, B. Sieglin, A. Sigalov, A. Silva, C. Silva, D. Silvagni, P. Simon, J. Simpson, E. Smigelskis, A. Snicker, C. Sommariva, C. Sozzi, M. Spolaore, A. Stegmeir, M. Stejner, J. Stober, U. Stroth, E. Strumberger, G. Suarez, H.-J. Sun, W. Suttrop, E. Sytova, T. Szepesi, B. Tál, T. Tala, G. Tardini, M. Tardocchi, M. Teschke, D. Terranova, W. Tierens, E. Thorén, D. Told, P. Tolias, O. Tudisco, W. Treutterer, E. Trier, M. Tripský, M. Valisa, M. Valovic, B. Vanovac, D. van Vugt, S. Varoutis, G. Verdoolaege, N. Vianello, J. Vicente, T. Vierle, E. Viezzer, U. von Toussaint, D. Wagner, N. Wang, X. Wang, M. Weiland, A.E. White, S. Wiesen, M. Willensdorfer, B. Wiringer, M. Wischmeier, R. Wolf, E. Wolfrum, L. Xiang, Q. Yang, Z. Yang, Q. Yu, R. Zagórski, I. Zammuto, W. Zhang, M. van Zeeland, T. Zehetbauer, M. Zilker, S. Zoletnik, H. Zohm and the EUROfusion MST1 Team55

The tokamak scrape-off layer (SOL) plasma dynamics is investigated in a circular limiter configuration with a low edge safety factor. Focusing on the experimental parameters of two ohmic tokamak inner-wall limited plasma discharges in RFX-mod [Sonato et al., Fusion Eng. Des. 74, 97 (2005)], nonlinear SOL plasma simulations are performed with the GBS code [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. The numerical results are compared with the experimental measurements, assessing the reliability of the GBS model in describing the RFX-mod SOL plasma dynamics. It is found that the simulations are able to quantitatively reproduce the RFX-mod experimental measurements of the electron plasma density, electron temperature, and ion saturation current density (jsat) equilibrium profiles. Moreover, there are indications that the turbulent transport is driven by the same instability in the simulations and in the experiment, with coherent structures having similar statistical properties. On the other hand, it is found that the simulation results are not able to correctly reproduce the floating potential equilibrium profile and the jsat fluctuation level. It is likely that these discrepancies are, at least in part, related to simulating only the tokamak SOL region, without including the plasma dynamics inside the last close flux surface, and to the limits of applicability of the drift approximation. The turbulence drive is then identified from the nonlinear simulations and with the linear theory. It results that the inertial drift wave is the instability driving most of the turbulent transport in the considered discharges.

In several tokamaks, non-axisymmetric magnetic field studies show that applied magnetic fields with a toroidal harmonic n = 2 can lead to disruptive n = 1 locked modes. In Ohmic plasmas, n = 2 magnetic reconnection thresholds in otherwise stable discharges are readily accessed at edge safety factors q similar to 3, low density, and low rotation. Similar to previous studies with n = 1 fields, the thresholds are correlated with the "overlap" field computed with the IPEC code. The overlap field quantifies the plasma-mediated coupling of the external field to the resonant field. Remarkably, the "critical overlap fields" at which magnetic islands form are similar for applied n = 1 and 2 fields. The critical overlap field increases with plasma density and edge safety factor but is independent of the toroidal field. Poloidal harmonics m> nq dominate the drive for resonant fields while m < nq harmonics have a negligible impact. This contrasts with previous results in H-mode discharges at high plasma pressure in which the toroidal angular momentum is sensitive to low poloidal harmonics. Together, these results highlight unique requirements for n > 1 field control including the need for multiple rows of coils to control selected plasma parameters for specific functions (e.g., rotation control or ELM suppression).

RFX-mod is equipped with an advanced active control system of MHD instabilities, which consists of 48x4 saddle coils, housed inside a stainless steel Toroidal Support Structure, and 48x4 radial field sensor loops processed in real time to drive the currents in the control coils. Thanks to the high flexibility of this system [1], RFX-mod operations in the last years have allowed to reach the design plasma current of 2 MA in the RFP configuration and to investigate the very low q Tokamak regimes. In order to further extend the operational space of RFX-mod, a major upgrade of its magnetic front-end is now being studied. By removing the Inconel vacuum vessel, presently surrounding the plasma, the thin (3 mm) stabilizing copper shell will become the conductive surface closest to the plasma, thus decreasing the shell proximity and reducing the deformation of the Last Closed Magnetic Surface. The aim of this paper is the accurate calculation of the 3D magnetic field structure produced by the MHD active coils in RFX-mod Upgrade, in the presence of the new complex (geometrically an topologically) conducting structures surrounding the plasma, with particular emphasis on the evaluation of the toroidal coupling effects and the aliasing affecting the measured magnetic field harmonics. A 3D model has been developed, which includes the finest geometrical details of the conductive structures and two sets of non-axisymmetric field sources (48x4 saddle coils for MHD instabilities control and 2x11 saddle coils for local (poloidal gaps) error field control). A state of the art integral formulation [2] [3] is used to solve the eddy current problem in the frequency domain. [1] P. Zanca, et al., 2012 PPCF 54 (12) 124018-124027 [2] P. Bettini et al., 2015 IEEE TMAG 51 (3) 7203904 [3] P. Alotto et al., 2015 IEEE TMAG 10.1109/TMAG.2015.2488699

This work presents the first evidence of helical flow in RFX-mod q(a) < 2 tokamak plasmas. The flow pattern is characterized by the presence of convective cells with m = 1 and n = 1 periodicity in the poloidal and toroidal directions, respectively. A similar helical flow deformation has been observed in the same device when operated as a reversed field pinch (RFP). In RFP plasmas, the flow dynamic is tailored by the innermost resonant m = 1, n = 7 tearing mode, which sustains the magnetic field configuration through the dynamo mechanism (Bonomo et al 2011 Nucl. Fusion 51 123007). By contrast, in the tokamak experiments presented here, it is strongly correlated with the m = 1, n = 1 MHD activity. A helical deformation of the flow pattern, associated with the deformation of the magnetic flux surfaces, is predicted by several codes, such as Specyl (Bonfiglio et al 2005 Phys. Rev. Lett. 94 145001), PIXIE3D (Chacón et al 2008 Phys. Plasmas 15 056103), NIMROD (King et al 2012 Phys. Plasmas 19 055905) and M3D-C1 (Jardin et al 2015 Phys. Rev. Lett. 115 215001). Among them, the 3D fully non-linear PIXIE3D has been used to calculate synthetic flow measurements, using a 2D flow modelling code. Inputs to the code are the PIXIE3D flow maps, the ion emission profiles as calculated by a 1D collisional radiative impurity transport code (Carraro et al 2000 Plasma Phys. Control. Fusion 42 731) and a synthetic diagnostic with the same geometry installed in RFX-mod. Good agreement between the synthetic and the experimental flow behaviour has been obtained, confirming that the flow oscillations observed with the associated convective cells are a signature of helical flow.

Thanks to its advanced system for the control of magnetohydrodynamic modes, the RFX-mod device run as a tokamak is particularly suited to the study of the possible impact on runaway electron (RE) de-confinement in response to applied magnetic perturbations. This paper shows that during the flat-top phase in RFX-mod discharges, with a plasma current of I p ∼ 150 kA and a low density ( n e < 10 19 m−3), the amount of REs scales with the m = 2,n = 1 perturbation both in q(a) q(a) > 2 plasmas. Similar results have also been obtained in post-disruption phases, but still with limited statistics. The mechanisms generating REs and the effect of magnetic perturbation (MP) on their confinement are interpreted by numerical simulations with the relativistic guiding center code ORBIT. The role played by different magnetic equilibria on the energy of REs and on their loss rates is investigated. ORBIT simulations indicate that RE-enhanced losses are associated with a raised level of stochasticity, the effect being more pronounced when the MP amplitude is higher and internally resonant.

The RFX-mod experiment is a fusion device designed to operate as a reversed field pinch (RFP), with a major radius R = 2 m and a minor radius a = 0.459 m. Its high versatility recently allowed operating it also as an ohmic tokamak, allowing comparative studies between the two configurations in the same device. The device is equipped with a state of the art MHD mode feedback control system providing a magnetic boundary effective control, by applying resonant or non-resonant magnetic perturbations (MP), both in RFP and in tokamak configurations. In the fusion community the application of MPs is widely studied as a promising tool to limit the impact of plasma filaments and ELMs (edge localized modes) on plasma facing components. An important new research line is the exploitation of the RFX-mod active control system for ELM mitigation studies. As a first step in this direction, this paper presents the most recent achievements in term of RFX-mod tokamak explored scenarios, which allowed the first investigation of the ohmic and edge biasing induced H-mode. The production of D-shaped tokamak discharges and the design and deployment of an insertable polarized electrode were accomplished. Reproducible H-mode phases were obtained with insertable electrode negative biasing in single null discharges, representing an unexplored scenario with this technique. Important modifications of the edge plasma density and flow properties are observed. During the achieved H-mode ELM-like electromagnetic composite filamentary structures are observed. They are characterized by clear vorticity and parallel current density patterns.

After 10 years of operation since its major modification, an upgrade of the RFX-mod experiment is presently under design. The scientific objective is the improvement of 3D physics studies through a more robust transition to higher confinement regimes in both Reversed Field Pinch (RFP) and Tokamak configuration obtained thanks to an advanced system for the active control of MHD instabilities. The main design driver requirements for this machine upgrade are the removal of the present resistive vacuum vessel and the enhancement of the ‘shell-plasma proximity’, to reduce the deformation of the last close magnetic surface and to improve the self-organized helical plasma regimes. The fulfillment of these requirements implies a major change of the internal components of the machine such as the replacement of the whole first wall, the change of the support system of the stabilizing shell and the modification of the present toroidal support structure to provide the function of vacuum barrier. In combination, other components of the machine will be upgraded, such as magnets and power supply, diagnostic systems and a NBI will be integrated. The paper presents an overview of the engineering design of the new components and highlights the critical aspects of the new torus assembly.

The RFX-mod system for the active control of MHD instabilities has been operating for more than 2 years contributing to improvements of the discharge quality and length. In the past years a dynamic black-box model of the active coils and saddle probes has been developed to analyze and simulate the system electromagnetic behaviour, which is strongly dependent on the frequency due to the presence of passive conductors. Satisfactory results were achieved in reproducing most of experimental responses and the model was used to select and test the gains of operating PID regulators. However, difficulties have emerged in reproducing some flux distributions such as those corresponding to m = 0, low n current patterns. In view of higher current operation a further increase in control system performance and model accuracy is desirable, if not mandatory. To this purpose, new measures have been recently acquired in order to reassess data of critical magnetic couplings and an activity has been started aimed at the verification and integration of data from a white-box model provided by the 3D finite element electromagnetic code Cariddi. The above verification is also a preliminary step for the validation of the CarMa computational tool adaptation to RFX-mod, which has been undertaken to study the plasma resistive wall modes. The paper describes the results of a comparative analysis carried out on experimental and simulation data obtained with the black-box and white-box models.

The modified RFX is a very flexible device used for a variety of control schemes for MHD instabilities and for advanced reverse field pinch scenarios. Relative to the previous machine, RFX-mod has a thin Cu shell with vertical field penetration time τS, lowered from 450 to 50 ms and shell/plasma proximity from b/a ≤ 1.24-1.1. Toroidal equilibrium is feedback-controlled and new power supplies provide better Bφ control. Newly designed graphite tiles protect the vessel from localized power deposition. A mesh of 192 external saddle coils, supervised by a digital feedback system, controls radial fields due to field errors and MHD modes. The paper presents an overview of the very encouraging results obtained using both new and 'standard' advanced operational modes in the current range 0.3-1 MA. A dramatic improvement of plasma performance was obtained by using the saddle coils to cancel all the radial field components, an operation mode dubbed virtual shell (VS). The toroidal voltage was lowered by more than 25% and the pulse length was tripled, up to 7 times the τS. Steady-state RFP pulses are now limited only by the applied volt-seconds. The improved magnetic boundary also has an effect on the tearing modes underlying the sustainment of the RFP, whose core amplitude is more than halved. The VS combined with new schemes for the active rotation of the MHD dynamo modes has allowed us to obtain reliable and well-controlled long RFP pulses in the MA current range. This results in a 100% increase in the particle and energy confinement time relative to the previous experiment and opens the possibility of exploring the machine performance in the 2 MA design range. © 2007 IAEA.

Confinement in the reversed field pinch (RFP) has been shown to increase strongly with current profile control. The MST RFP can operate in two regimes: the standard regime with a naturally occurring current density profile, robust reconnection and dynamo activity; and the improved confinement regime with strong reduction in reconnection, dynamo and transport. New results in standard plasmas include the observation of a strong two-fluid Hall effect in reconnection and dynamo, the determination that the m = 0 edge resonant mode is nonlinearly driven, and the determination that tearing modes can lock to the wall via eddy currents in the shell. New results in improved confinement plasmas include observations that such plasmas are essentially dynamo-free, contain several isolated magnetic islands (as opposed to a stochastic field) and contain reduced high frequency turbulence. Auxiliary current drive and heating is now critical to RFP research. In MST, a programme to apply auxiliary systems to the RFP is underway and progress has accrued in several techniques, including lower hybrid and electron Bernstein wave injection, ac helicity injection current drive, pellet injection and neutral beam injection.

This paper reports the main recent results of the RFX-mod fusion science activity. The RFX-mod device is characterized by a unique flexibility in terms of accessible magnetic configurations. Axisymmetric and helically shaped reversed-field pinch equilibria have been studied, along with tokamak plasmas in a wide range of q(a) regimes (spanning from 4 down to 1.2 values). The full range of magnetic configurations in between the two, the so-called ultra-low q ones, has been explored, with the aim of studying specific physical issues common to all equilibria, such as, for example, the density limit phenomenon. The powerful RFX-mod feedback control system has been exploited for MHD control, which allowed us to extend the range of experimental parameters, as well as to induce specific magnetic perturbations for the study of 3D effects. In particular, transport, edge and isotope effects in 3D equilibria have been investigated, along with runaway mitigations through induced magnetic perturbations. The first transitions to an improved confinement scenario in circular and D-shaped tokamak plasmas have been obtained thanks to an active modification of the edge electric field through a polarized electrode. The experiments are supported by intense modeling with 3D MHD, gyrokinetic, guiding center and transport codes. Proposed modifications to the RFX-mod device, which will enable further contributions to the solution of key issues in the roadmap to ITER and DEMO, are also briefly presented. © 2017 IAEA, Vienna.

The response of the edge plasma to a magnetic perturbation (MP) is studied in the RFX-mod device, in both reversed field pinch (RFP) and tokamak discharges. The use of spatially distributed diagnostics, in particular along the poloidal direction, allows a direct 3D characterization of the plasma. It is shown that there is a difference between the spectrum of the MP and that of different properties of the edge plasma, such as the floating potential, the electron pressure and the flow, for both RFP and tokamak plasmas. In particular, for RFP cases, even if the magnetic perturbation is mainly m = 1, with the amplitude of the m = 0 and m = 2 sidebands negligible, the connection length to the wall of the magnetic field L cw has a more complex structure. The ergodic regions, with L cw larger than the Kolmogorov length, are due to the interaction of both m = 1 and m = 0 modes, showing a complex and non-monochromatic behaviour along the poloidal angle. This structure of L cw is responsible for the impure m = 1 behaviour of the plasma wall interaction, floating potential and electron pressure. Thus the helicity of the edge plasma is quite different from that of the dominant MP.

This paper describes the soft X-ray (SXR) cross-sectional distributions measured in the European Reversed Field Pinch (RFP) experiment RFX by means of a tomographic diagnostic. Due to the non-invasive character of this diagnostic, the plasma radiation emissivity pattern can be reconstructed. The emissivity depends on various crucial parameters and can be used to study several plasma properties. To reconstruct SXR emissivity in RFX, three different inversion schemes have been compared: the Cormack technique, based on the Bessel-Fourier series expansion, a maximum entropy algorithm and a hybrid method where the previous techniques have been merged together. In this paper the first survey of the SXR emissivity properties in the RFP configuration have been presented. Measurements have been taken in a variety of plasma conditions. The measured SXR data has been compared with the results of a one dimensional impurity diffusion model, which predicts the absolute SXR emissivity, with good agreement. In particular the effect of mode locking on plasma equilibrium in the standard Multiple Helicity (MH) states has been studied. This has given a significant contribute to the description of the plasma MHD structure, both in MH regime and in the Quasi Single Helicity (QSH) state, whose signature is the growth of a sizable m=1 structure in the emissivity distributions, and which has been experimentally discovered thanks to the tomography. A good correlation between SXR tomographic reconstruction and magnetic measurements has been found.

An accurate control of the magnetic boundary of a thermonuclear plasma is an important issue in magnetic confinement research. The development of methods for the active control of magnetohydrodynamic instabilities and correction of error fields is mandatory in view of fusion reactors or experimental test reactors under design. Recently, a very effective control scheme, named clean mode control (CMC), has been proposed in a reversed field pinch experiment (RFX-mod). The CMC is based on the real-time correction (cleaning), under simplifying hypothesis, of the sideband harmonics in the magnetic field produced by the discrete local active coils. In this paper, we focus on the problem of carefully computing the penetration of sidebands through a realistic load assembly, but still with a simplified cylindrical geometry, to allow for a detailed comparison with the crude CMC algorithm without the additional complication of the coupling between the poloidal harmonics due to the toroidal geometry.

The first wall and the vessel of the Reversed Field Pinch RFX has been in situ coated with a B/C:H film by glow discharge cleaning with a mixture of 12.5% of trimethylboron ((CH3)(3)B) in He. The film has been analysed and the effects on the plasma discharges of the boronized wall are reported for a plasma current of 520 kA. The main effects on the plasma are a reduction in the oxygen content by a factor of 5 to 10 and a decrease in the carbon content by a factor of two. The Z(eff) has been reduced from 2-2.5 to 1.4-1.5. A slight reduction of the loop voltage is observed. The radiation power decreases by a factor of 2, enhancing the high density operation limit with a consequent increase of the poloidal beta beta(theta) and of the energy confinement time tau(E).

In the last years, the RFX-mod experiment has given important insights into the physical mechanisms that rule the tearing mode dynamics in p resence of magnetic feedback control. The RFX-mod device is suitable for the study of this to pic: it is equipped with 192 active coils and a corresponding grid of radial, toroidal and poloidal field sensors, which allow a good detection of unstable modes. Several feedback schemes for tearin g mode control on RFX have been modelled through the RFXlocking code [1,2] and tested in rev ersed field pinch experiments: from the intelligent shell concept to the clean mode control [1,3,4,5]. The experience acquired on tearing mode control recently has been exported in tokamak plasmas. Common features between such magnetic configurations have been observed on teari ng mode control. The most important common denominator is the importance of the removal from t he feedback variable of sideband harmonics, induced by the discrete nature of the active coils, in order to have an effective action on such instabilities. In both RFP and tokamak experiments , the magnetic feedback system reduces tearing mode amplitude at the plasma edge and maintains the mode into rotation in the slow frequency branch, of about 10-100Hz. The magnetic feedback va riable can also be set to maintain the mode amplitude at a finite value, by means of helical bo undary conditions, either rotating or static. On th e other hand the feedback action can not fully suppre ss a tearing mode, but it can at its best replicate the effect of an ideal shell located at the resisti ve shell radius. RFXlocking outcomes suggest that i f certain physics players are neglected in the moment um balance equation, such as the electro- magnetic torque due to the conductive structures an d the feedback, as well as the viscous torque related to the plasma flow, as proposed in [6], tea ring modes can indeed be stabilized against the RFX-mod experimental evidences. References [1] Zanca P. et al 2007 Nucl. Fusion 47 1425 [2] Zanca P. 2009 Plasma Phys. Control. Fusion 51 015006 [3] Martini S. et al 2007 Nucl. Fusion 47 783 [4] Marrelli L. et al 2007 Plasma Phys. Control. Fu sion 49 B359 [5] Piron L. et al 2010 Nucl. Fusion 50 115011 [6] Richardson A.S. et al 2010 Phys. Plasmas 17 112511

The study of electron temperature profiles of quasi-single helical states (QSH) in RFX-Mod (and, in general, in other RFP machines) was carried out in the past mainly using Thomson scattering, thus being limited to a time resolution of the order of some milliseconds and to the collection of single, isolated cases, which displayed clear transport barriers. A new multichord double filter SXR spectrometer was developed and installed. Temperature profiles are now measured up to a frequency of some kHz, allowing one to determine the entire time evolution of electron temperature during a QSH cycle. A mapping technique, originally developed for Thomson temperature profiles, is adapted to deal with the line-integrated nature of the SXR diagnostic. In particular, temperature gradients related to the presence of transport barriers are reconstructed and analysed in a helical reference system, coherently with the underlying plasma equilibrium. The method is discussed in its capabilities and limits and then applied to a wide QSH database. As a result, a clear difference in temperature gradient behaviour between the rising phase of QSH and the saturated (or flattop) phase is observed. In the rising phase the expected correlation of temperature gradient with magnetic spectrum is confirmed, showing a positive trend between dominant mode amplitude and thermal structure dimension, as well as a negative correlation of secondary mode amplitudes and temperature gradient. On the other hand, in the flattop phase the presence of a thermal structure is intermittent, and much less influenced by the magnetic dynamics. This suggests the simultaneous presence of different mechanisms that enhance energy transport.

Electron temperature profiles in RFX-mod 3D helical plasmas are characterized by a complex dynamics recently investigated thanks to the high time resolution \textit{Te} measurements obtained by double filter technique with a multichord soft-x-ray diagnostic.\footnote{P.Franz et al., Nucl. Fusion 53 (2013) 053011} This study is focused in particular on the characterization of the intermittent behaviour of thermal structures developing in helical states and on the loss of helical topology. A statistical approach reveals that the increase of the magnetic chaos and the partial break of the 3D magnetic configuration usually occur in a phase where the electron temperature gradient is already decreasing. For a deeper understanding of this phenomenology the microtearing perturbations and the pressure driven instabilities, the latter investigated by using the stability COBRA code,\footnote{R. Sanchez et al., Computer Physics Communications 141 (2001) 55--65} are considered in the analysis.

Real-time feedback control of MHD instabilities is a topic of major interest in magnetic thermonuclear fusion, since it allows to optimize a device performance even beyond its stability bounds. The stability properties of different magnetic configurations are important test benches for real-time control systems. RFX-mod, a Reversed Field Pinch experiment that can also operate as a tokamak, is a well suited device to investigate this topic. It is equipped with a sophisticated magnetic feedback system that controls MHD instabilities and error fields by means of 192 active coils and a corresponding grid of sensors. In addition, the RFX-mod control system has recently gained new potentialities thanks to the introduction of the MARTe framework and of a new CPU architecture. These capabilities allow to study new feedback algorithms relevant to both RFP and tokamak operation and to contribute to the debate on the optimal feedback strategy. This work focuses on the design of new feedback schemes. For this purpose new magnetic sensors have been explored, together with new algorithms that refine the de-aliasing computation of the radial sideband harmonics. The comparison of different sensor and feedback strategy performance is described in both RFP and tokamak experiments.

In the reversed field pinch RFX-mod at the highest plasma current of 2 MA, when error fields are not effectively feedback controlled, localized thermal loads up to tens of MW m-2 can be produced. The graphite tiles withstand such high power loads, but the high hydrogen retention makes density control extremely difficult. Several wall conditioning techniques have been optimized in the last campaigns, including helium glow discharge cleaning and wall boronization by diborane glow discharges. More recently, lithium conditioning has been applied for the first time in a reversed field pinch by the evaporation technique. The main results are discussed in this paper. Lithization leads to important operational advantages: a significant improvement of the density control is obtained. Densities up to n/nG ≈ 0.5 can be produced in a controlled way. At the same value of input power, plasmas at higher densities can be sustained. However, due to the short particle confinement time, such densities are reached with high rates of gas puffing and the resulting profiles at high density are edge peaked. A lithium multipellet injector, to be applied in order to obtain a more uniform deposition, has been tested. © 2013 IAEA, Vienna.

The RFX-mod experiment is equipped with a sophisticated magnetic feedback system that controls simultaneously different types of MHD instabilities. Thanks to the recent introduction of the MARTe real-time framework [1], the RFX-mod control systemhas gained new potentialities allowing a flexible and efficient implementation of more complex and computation-demanding control schemes. These upgraded capabilities of RFX-mod make possible to study new MHD feedback algorithms relevant to both Reversed Field Pinch (RFP) and tokamak operation and, thus, to contribute to the scientific debate on the optimal feedback control strategies by a systematic experimental investigation on the problem. Recently, two new feedback schemes have been developed in RFX-mod for the radial magnetic field sensors: the Plasma Response and the Improved CleanMode Control (CMC). The Plasma Response algorithm uses as feedback variable the component of the radial magnetic field that is obtained by subtracting the field produced by the active coils from the measurements. Even if this control scheme is considered not very effective with radial sensors at least for the RWM control, as predicted by some models developed at RFX-mod [2-3], the actual radial sensor inefficiency has never been experimentally tested in RFX-mod and, thus, the aimof this new control option will be to validate the model predictions. As regards the second feedback scheme, the capabilities of the new control system have allowed to refine the sidebands computation inthe original CMC algorithm [4], where only the copper shell is considered and a fixed set of sideband harmonics are subtracted. The new model takes into account both the copper shell and the mechanical structure and subtracts a wider set of sideband harmonics in the computation. These new algorithms are planned to be tested in RFX-mod in both RFP and tokamak operation. In the latter configuration,the results will be compared to the ones obtained using the poloidal magnetic field as feedback variable in order to investigate the effectiveness of the different feedback schemes. References [1] Netò A. et al 2010 IEEE Trans. Nucl. Sci. 57 [2] Zanca P. et al 2012 Plasma Phys. Control. Fusion 54 [3] Marchiori G. et al 2012 Nucl. Fusion 52 [4] Zanca P. et al 2007 Nucl. Fusion 47

Disruptions caused by tearing modes (TMs) are considered to be one of the most critical roadblocks to achieving reliable, steady-state operation of tokamak fusion reactors. Here we have demonstrated a promising scheme to avoid mode locking by utilizing the electromagnetic (EM) torque produced with 3D coils that are available in many tokamaks. In this scheme, the EM torque is delivered to the modes by a toroidal phase shift between the externally applied field and the excited TM fields, compensating for the mode momentum loss through the interaction with the resistive wall and uncorrected error fields. Fine control of torque balance is provided by a feedback scheme. We have explored this approach in two widely different devices and plasma conditions: DIII-D and RFX-mod operated in tokamak mode. In DIII-D, the plasma target was high beta N in a non-circular divertor tokamak. Here beta N is defined as beta N = beta/(I-p/aB(t)) (% Tm/MA), where beta, I-p, a, B-t are the total stored plasma pressure normalized by the magnetic pressure, plasma current, plasma minor radius and toroidal magnetic field at the plasma center, respectively. The RFX-mod plasma was ohmicallyheated with ultra-low safety factor in a circular limiter discharge with active feedback coils outside the thick resistive shell. The DIII-D and RFX-mod experiments showed remarkable consistency with theoretical predictions of torque balance. The application to ignition-oriented devices such as the International Thermonuclear Experimental Reactor (ITER) would expand the horizon of its operational regime. The internal 3D coil set currently under consideration for edge localized mode suppression in ITER would be well suited for this purpose.

RFX-mod self-organized single helical axis (SHAx) states provide a unique opportunity to advance 3D fusion physics and establish a common knowledge basis in a parameter region not covered by stellarators and tokamaks. The VMEC code has been adapted to the reversed-field pinch (RFP) to model SHAx equilibria in fixed boundary mode with experimental measurements as constraint. The averaged particle diffusivity over the helical volume, estimated with the Monte Carlo code ORBIT, has a neoclassical-like dependence on collisionality and does not show the 1/ trend of un-optimized stellarators. In particular, the helical region boundary, corresponding to an electron transport barrier with zero magnetic shear and improved confinement, has been investigated using numerical codes common to the stellarator community. In fact, the DKES/PENTA codes have been applied to RFP for local neoclassical transport computations, including radial electric field, to estimate thermal diffusion coefficients in the barrier region for typical RFX-mod temperature and density profiles. A comparison with power balance estimates shows that residual chaos due to secondary tearing modes and small-scale turbulence still contribute to drive anomalous transport in the barrier region. © 2011 American Institute of Physics.

The wall of any magnetic fusion device is characterized by the presence of several 3D structures, such as portholes for diagnostics and for heating and current drive systems, coil feeds and other features. Time-varying magnetic fields induce eddy currents in the wall, whose pattern is modified by these structures, giving rise to magnetic field errors that can be amplified or shielded by the plasma. Two examples will be given on how the dynamic response of a 3D wall to external magnetic fields can be identified and used to optimize magnetic feedback. In the RFX-mod reversed-field pinch, a dynamic decoupler algorithm has been developed, which allows for the production of pure radial magnetic field harmonics inside the wall, reducing the harmonic distortion due to the 3D wall structures. This is applied here to the problem of producing helical boundary conditions to control helical RFP equilibria. In the DIII-D tokamak, a frequency-dependent scheme for the compensation of the magnetic sensors from spurious n = 1 fields due to the coupling with the feedback and axisymmetric coils has been recently implemented in real time and tested with plasma. The possible relevance of these 3D effects for high performance scenarios is discussed. © 2011 IOP Publishing Ltd.

This paper summarizes the main achievements of the RFX fusion science program in the period between the 2008 and 2010 IAEA Fusion Energy Conferences. RFX-mod is the largest reversed field pinch in the world, equipped with a system of 192 coils for active control of MHD stability. The discovery and understanding of helical states with electron internal transport barriers and core electron temperature >1.5 keV significantly advances the perspectives of the configuration. Optimized experiments with plasma current up to 1.8 MA have been realized, confirming positive scaling. The first evidence of edge transport barriers is presented. Progress has been made also in the control of first-wall properties and of density profiles, with initial first-wall lithization experiments. Micro-turbulence mechanisms such as ion temperature gradient and micro-tearing are discussed in the framework of understanding gradient-driven transport in low magnetic chaos helical regimes. Both tearing mode and resistive wall mode active control have been optimized and experimental data have been used to benchmark numerical codes. The RFX programme also provides important results for the fusion community and in particular for tokamaks and stellarators on feedback control of MHD stability and on three-dimensional physics. On the latter topic, the result of the application of stellarator codes to describe three-dimensional reversed field pinch physics will be presented. © 2011 IAEA, Vienna.

In this work the MHD stability of RFX mode tokamak discharges with q$_{edge}

A spontaneous transition to a helical equilibrium with an electron internal transport barrier is observed in RFX-mod as the plasma current is raised above 1 MA (Lorenzini R et al 2009 Nature Phys. 5 570). The helical magnetic equilibrium can be controlled with external three-dimensional (3D) magnetic fields applied by 192 active coils, providing proper helical boundary conditions either rotating or static. The persistence of the helical equilibrium is strongly increased in this way. A slight reduction in the energy confinement time of about 15% is observed, likely due to the increased plasma-wall interaction associated with the finite radial magnetic field imposed at the edge. A global helical flow develops in these states and is expected to play a role in the helical self-organization. In particular, its shear may contribute to the ITB formation and is observed to increase with the externally applied radial field. The possible origins of this flow, from nonlinear visco-resistive magnetohydrodynamic (MHD) and/or ambipolar electric fields, will be discussed. © 2011 IOP Publishing Ltd.

RFP states characterized by the presence of an hot helical structure in the plasma core have shown a significative improvement in the plasma performances. In this work we focused on DAX (Double AXis) states, in which the hot island is surrounded by a separatrix and does not cross the plasma centroid. These states, with respect to SHAx --or Single Helical Axis, [1]- , show smaller thermal structures, but the $\nabla $T$_{e}$ strength suggests a drastic local reduction of energy transport. The analysis relies on data obtained by the Main Thomson Scattering [2] and by the multichord double filter SXR spectrometer [3]. The general scaling properties of local $\nabla $T$_{e}$ are presented and the results are compared with SHAx datasets; overall confinement changing is analyzed relying both on T$_{e}$ and n$_{e}$ data. Finally, being data remapping on helical coordinates a widely used tool in SHAx analysis, limits and possibilities of this technique for DAX states are discussed. \\[4pt] [1] Lorenzini R. et al$.$, Nature Physics \textbf{5}, 570 - 574 (2009)\\[0pt] [2] Alfier A., Pasqualotto R., Rev. Sci. Instrum. \textbf{78}, 1 (2007)\\[0pt] [3] Bonomo F. , Rev. Sci. Instrum. \textbf{77, }10F313 (2006)

We define the safety factor q for the helical plasmas of the experiment RFX-mod by accounting for the actual three-dimensional nature of the magnetic flux surfaces. Such a profile is not monotonic but goes through a maximum located in the vicinity of the electron transport barriers measured by a high resolution Thomson scattering diagnostic. Helical states with a single axis obtained in viscoresistive magnetohydrodynamic numerical simulations exhibit similar nonmonotonic q profiles provided that the final states are preceded by a magnetic island phase, like in the experiment. © 2011 The American Physical Society.

With the exploration of the MA plasma current regime in up to 0.5 s long discharges, RFX-mod has opened new and very promising perspectives for the reversed field pinch (RFP) magnetic configuration, and has made significant progress in understanding and improving confinement and in controlling plasma stability. A big leap with respect to previous knowledge and expectations on RFP physics and performance has been made by RFX-mod since the last 2006 IAEA Fusion Energy Conference. A new self-organized helical equilibrium has been experimentally achieved (the Single Helical Axis - SHAx - state), which is the preferred state at high current. Strong core electron transport barriers characterize this regime, with electron temperature gradients comparable to those achieved in tokamaks, and by a factor of 4 improvement in confinement time with respect to the standard RFP. RFX-mod is also providing leading edge results on real-time feedback control of MHD instabilities, of general interest for the fusion community. © 2009 IAEA, Vienna.

A detailed knowledge of the interplay between MHD instabilities and energetic particles has been gained from direct measurements of fast-ion losses (FILs). Time-resolved energy and pitch angle measurements of FIL caused by neoclassical tearing modes (NTMs) and toroidicity-induced Alfven eigenmodes (TAEs) have been obtained using a scintillator based FIL detector. The study of FIL due to TAEs has revealed the existence of a new core-localized MHD fluctuation, the Sierpes mode. The Sierpes mode is a non-pure Alfvenic fluctuation which appears in the acoustic branch, dominating the transport of fast-ions in ICRF heated discharges. The internal structure of both TAEs and Sierpes mode has been reconstructed by means of highly resolved multichord soft x-ray measurements. A spatial overlapping of their eigenfunctions leads to a FIL coupling, showing the strong influence that a core-localized fast-ion driven MHD instability may have on the fast-ion transport. We have identified the FIL mechanisms due to NTMs as well as due to TAEs. Drift islands formed by fast-ions in particle phase space are responsible for the loss of NBI fast-ions due to NTMs. In ICRF heated plasmas, a resonance condition fulfilled by the characteristic trapped fast-ion orbit frequencies leads to a phase matching between fast-ion orbit and NTM or TAE magnetic fluctuation. The banana tips of a resonant trapped fast-ion bounce radially due to an E × B drift in the TAE case. The NTM radial bounce of the fast-ion banana tips is caused by the radial component of the perturbed magnetic field lines.

Several heuristic models for nonlocal transport in plasmas have been developed, but they have had a limited possibility of detailed comparison with experimental data. Nonlocal aspects introduced by the existence of a known spectrum of relatively stable saturated tearing modes in a low current reversed field pinch (RFP) offers a unique possibility for such a study. A numerical modeling of the magnetic structure and associated particle transport is carried out for the RFP experiment at the Consorzio RFX, Padova, Italy. A reproduction of the tearing mode spectrum with a guiding center code (White and Chance 1984 Phys. Fluids 27 2455) reliably reproduces the observed soft x-ray tomography. Following particle trajectories in the stochastic magnetic field shows the transport across the unperturbed flux surfaces to be due to a spectrum of Levy flights, with the details of the spectrum position dependent. The resulting transport is subdiffusive, and cannot be described by Rechester–Rosenbluth diffusion, which depends on a random phase approximation. If one attempts to fit the local transport phenomenologically, the subdiffusion can be fit with a combination of diffusion and inward pinch (Spizzo et al 2007 Phys. Plasmas 14 102310). It is found that whereas passing particles explore the stochastic field and hence participate in Levy flights, the trapped particles experience normal neoclassical diffusion.A two fluid nonlocal Montroll equation is used to model this transport, with a Levy flight defined as the motion of an ion during the period that the pitch has one sign. The necessary input to the Montroll equation consists of a time distribution for the Levy flights, given by the pitch angle scattering operator, and a distribution of the flight distances, determined numerically using a guiding center code. Results are compared with the experiment. The relation of this formulation to fractional kinetics is also described.

The magnetic topology of quasi-single helicity (QSH) regimes, in the reversed field pinch experiment RFX-mod, is characterized by a helical magnetic structure surrounded by partially chaotic field lines. In this paper we investigate the transport mechanisms within these helical structures, in particular, the particle diffusion due to the residual magnetic chaos. The diffusion coefficients have been estimated for different plasma temperatures, collisionality and magnetic perturbation amplitudes. In the typical high temperature QSH regimes of RFX-mod, ambipolar transport between ions and electrons is found to be ensured by the non-zero but very low level of secondary modes and by the reduced collisionality. Trapped ions give the largest contribution to particles diffusion, while those passing are almost well confined within the helical structure. In the best QSH experimental performances, ion diffusion coefficients computed by numerical simulations are not affected significantly by the residual magnetic chaos and are very close to those expected in a regime with only helical conserved surfaces.

The reversed field pinch configuration is characterized by the presence of magnetic structures both in the core and at the edge: in the core, at high plasma current the spontaneous development of a helical structure is accompanied by the appearance of internal electron transport barriers; at the edge strong pressure gradients, identifying an edge transport barrier, are observed too, related to the position of the field reversal surface. The aim of this paper is the experimental characterization of both the internal and edge transport barriers in relation to the magnetic topology, discussing possible analogies and differences with other confinement schemes. © 2009 IOP Publishing Ltd.