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The European power system faces two main challenges: first, the increasing share of fluctuating energy sources in the power generation sector challenges the balance of generation and demand. Second, the expected shift towards using more electricity in the heating and transportation sectors leads to rising demand. To ensure both sufficient energy supply and long-term power system stability of the power system, fusion power is expected to play an important role in the future. This paper provides a sensitivity analysis of fusion power plant parameters in a power system with a large fraction of renewable energies. The results depend strongly on the underlying scenario assumptions, especially on future technical and economic improvements. Finally, the amount of fusion power investments depends on both demand level and relative costs of competing technologies.

In preparation for extending the JOREK nonlinear MHD code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (arXiv:1907.12486) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present., Comment: 23 pages, 1 table, 7 figures. Submitted to Journal of Plasma Physics

Reduced magnetohydrodynamic (MHD) equations are used to study the nonlinear dynamics of external kinks in a quasi-axisymmetric (QA) stellarator with varying fractions of external rotational transform. The large bootstrap currents associated with high beta plasmas may make QA configurations susceptible to low n external modes, limiting their operational space. The violence of the nonlinear dynamics, and, in particular, when these modes lead to a disruption, is not yet understood. In this paper, the nonlinear phase of external kinks in an unstable QA configuration with an edge safety factor below two is simulated. An axisymmetric approximation of this stellarator is constructed in the nonlinear MHD code, JOREK, capturing the influence of the external rotational transform. The use of this approximation for the considered stellarator is validated by comparing the linear dynamics against the linear viscoresistive MHD code, CASTOR3D. The nonlinear dynamics of this stellarator approximation are compared with an equivalent tokamak to understand the influence of a relatively small external rotational transform. While the external rotational transform does have a stabilising influence on the MHD activity, it remains violent. To explore the first order influence of a larger external rotational transform, this equilibrium parameter is artificially increased for the considered stellarator, reducing the effective plasma current. The violence of the kink instability is quantified, and shown to reduce with the increasing external rotational transform. At the same time, the external kink triggers internal modes that exacerbate the loss in confinement during the nonlinear phase, such that it remains large over much of the parameter space. It is only with a significant fraction of external rotational transform that these subsequent modes are stabilised., Comment: This article has been submitted to Nuclear Fusion. This version includes revisions to take into account reviewer comments

The effect of externally applied resonant magnetic perturbations (RMPs) on the local equilibrium plasma current density profile is studied numerically based on two-fluid equations in simplified cylindrical geometry. It is found that a moderate RMP below its penetration threshold, via non-linear mode coupling, induces a parallel electric field around its rational surface that can significantly change the local flux-surface-averaged current density gradient. At a given RMP amplitude, the modification of the current density profile increases with increasing electron temperature, and it significantly depends on the bi-normal electron fluid velocity at the resonant surface. The effect of this modification on the magnetic island growth is demonstrated by the example of small m/n = 2/1 islands (m/n being the poloidal/toroidal mode numbers), driven by an unfavorable plasma current density profile and bootstrap current perturbation. The 2/1 mode growth is stabilized by moderate static 4/2 or 6/3 RMPs if the local electron fluid velocity is in the ion drift direction or sufficiently large in the electron drift direction. These results reveal that a weakly three-dimensional equilibrium, containing a moderate 4/2 RMP and the associated shielding current, can be more stable against the 2/1 mode, which often causes tokamak plasma major disruptions.

A detailed understanding of island seeding is crucial to avoid neoclassical tearing modes and their negative consequences like confinement degradation and disruptions. In the present work, we investigate the growth of 2/1 islands in response to magnetic perturbations. Although we use externally applied perturbations produced by resonant magnetic perturbation (RMP) coils for this study, the results are directly transferable to island seeding by other MHD instabilities creating a resonant magnetic field component at the rational surface. Experimental results for 2/1 island penetration from ASDEX Upgrade are presented extending previous studies. Simulations are based on an ASDEX Upgrade L-mode discharge with low collisionality and active RMP coils. Our numerical studies are performed with the 3D, two-fluid, nonlinear MHD code JOREK. All three phases of mode seeding observed in the experiment are also seen in the simulations: first, a weak response phase characterized by large perpendicular electron flow velocities followed by a fast growth of the magnetic island size accompanied by a reduction of the perpendicular electron velocity and finally the saturation to a fully formed island state with perpendicular electron velocity close to zero. Thresholds for mode penetration are observed in the plasma rotation as well as in the RMP coil current. A hysteresis of the island size and electron perpendicular velocity is observed between the ramping up and down of the RMP amplitude consistent with an analytically predicted bifurcation. The transition from dominant kink/bending to tearing parity during the penetration is investigated.

Eine wichtige Anwendung der Plasmaphysik ist die Fusionsforschung. In gewissem Sinn ist Kernfusion die direkteste Nutzung der „Sonnenenergie“, denn ein Fusionskraftwerk soll – ahnlich wie die Sonne – Energie aus der Verschmelzung von Wasserstoffkernen gewinnen. Um eine ausreichende Anzahl von Fusionsreaktionen zu erzielen, mussen in einem kunftigen Kraftwerk Temperaturen von mehr als 100 Millionen Grad vorherrschen. Bei solch hohen Temperaturen bildet sich ein Plasma, ein Gas aus geladenen Teilchen. Plasmen konnen in Kafigen aus Magnetfeldern eingeschlossen werden, die auch fur die notige Warmeisolierung sorgen. Im Laufe der Fusionsforschung haben sich zwei Konzepte fur solche Magnetfeldkonfigurationen herauskristallisiert: der Tokamak und der Stellarator.

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

Edge localized modes (ELMs) are magnetohydrodynamic (MHD) instabilities that cause fast periodic relaxations of the strong edge pressure gradient in tokamak fusion plasmas. A novel diagnostic method allows the extraction of toroidal mode numbers, rotation velocities and spatial information during the ELM cycle including the crash. While mode number branches n = 3-6 and n = 8-10 are dominant just before the ELM crash, during the ELM crash n = 2-5 are observed in typical discharges with type-I ELMs in the tokamak experiment. These findings are compared to results from nonlinear MHD simulations. Although n = 6 is linearly dominant, nonlinear coupling in which n = 1 is particularly important leads to the dominance of n = 3-5 during the ELM crash, in excellent agreement with experimental observations. The simultaneous occurrence of these modes over a wide radial region leads to high stochasticity and thus increased transport.

A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at $q\approx 1$, thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C$^1$ code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated $(m=1,n=1)$ quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if $\beta$ is sufficiently high to provide the necessary drive for the $(m=1,n=1)$ instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile., Comment: submitted to Physics of Plasmas (23 pages, 15 Figures)

The CASTOR3D code, which is currently under development, is able to perform linear stability studies for 2D and 3D, ideal and resistive tokamak equilibria in the presence of ideal and resistive wall structures and coils. For these computations ideal equilibria represented by concentric nested flux surfaces serve as input (e.g. computed with the NEMEC code). Solving an extended eigenvalue problem, the CASTOR3D code takes simultaneously plasma inertia and wall resistivity into account. The code is a hybrid of the CASTOR_3DW stability code and the STARWALL code. The former is an extended version of the CASTOR and CASTOR_FLOW code, respectively. The latter is a linear 3D code computing the growth rates of resistive wall modes in the presence of multiply-connected wall structures. The CASTOR_3DW code, and some parts of the STARWALL code have been reformulated in a general 3D flux coordinate representation that allows to choose between various types of flux coordinates. Furthermore, the implemented many-valued current potentials in the STARWALL part allow a correct treatment of the m = 0, n = 0 perturbation. In this paper, we outline the theoretical concept, and present some numerical results which illustrate the present status of the code and demonstrate its numerous application possibilities.

The effect of externally applied resonant magnetic perturbations (RMPs) on the growth of magnetic islands is investigated based on two-fluid equations. It is found that if the local bi-normal electron fluid velocity at the resonant surface is sufficiently large, static RMPs of the same helicity and of moderate amplitude can suppress the growth of magnetic islands in high-temperature plasmas. These islands will otherwise grow, driven by an unfavorable plasma current density profile and bootstrap current perturbation. These results indicate that the error field can stabilize island growth, if the error field amplitude is not too large and the local bi-normal electron fluid velocity is not too low. They also indicate that applied rotating RMPs with an appropriate frequency can be utilized to suppress island growth in high-temperature plasmas, even for a low bi-normal electron fluid velocity. A significant change in the local equilibrium plasma current density gradient by small amplitude RMPs is found for realistic plasma parameters, which are important for the island stability and are expected to be more important for fusion reactors with low plasma resistivity.

The radial structure of toroidal Alfven eigenmodes (TAEs) is of great importance for comparison with theoretical predictions. A dual-channel fast frequency hopping millimeter-wave reflectometer installed on the ASDEX Upgrade tokamak is capable of measuring density fluctuations from the plasma edge to core, allowing the radial eigenfunction of n = 4 TAE and edge MHD modes to be obtained using phase perturbation and coherence data analysis techniques. The two techniques reveal similar results, and in particular the radial structure of the n = 4 TAE is found to be in good agreement with numerical predictions from linear gyrokinetic simulations. The first results of the radial localization of Alfven cascades are also presented.

The interpretation of hydrogen Balmer spectra emitted from a high-pressure arc discharge (Radtke and Gunther, Contrib. Plasma Phys. 26, 143 (1986)) is re-examined. Assuming local thermodynamic equilibrium, synthetic Balmer spectra are calculated for given temperature and density conditions. Radiation transport is accounted for using a one-dimensional plasma layer model. The lineshape of bound-bound transitions is determined using a microscopic quantum-statistical approach. Free-free and free-bound contributions are added by taking expressions from literature. Comparing the synthetic spectra with experimental ones, plasma temperature and density conditions are inferred. The plasma parameters are confronted with theoretical results for the compositions of dense plasma. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Brilliance spectra of a carbon plasma generated by subpicosecond high intensity laser pulses are analysed (Wilhein et al 1998 J. Opt. Soc. Am. 15 1235). The plasma parameters such as electron density and temperature are determined using a plasma slab model. Synthetic carbon He-α and He-β line profiles are calculated for the inferred plasma parameters by using thermodynamic Green's function, based on a microscopic quantum statistical approach assuming local thermal equilibrium. Self-absorption is taken into account considering one-dimensional radiation transport equation. The comparison between the measured spectrum and our calculated synthetic profile is good for He-α line (C V 1s2–1s2p), while discrepancies are found in the case of He-β line (C V 1s2–1s3p).

We present discretisation schemes for the heat diffusion equation in strongly magnetised plasmas in 2-d Cartesian and 3-d cylindrical geometry. The algorithms described do not use field-aligned coordinates, but show, nevertheless, a strong reduction of the pollution of perpendicular heat flux caused by parallel heat conduction, compared to standard finite element or other finite difference formulations. Results for test examples show independence of the numerical error from @g"@? for values of @g"@?/@g"@? up to 10^9 in plane and 10^1^2 in periodic cylinder geometry (simulating toroidal connection). The algorithms appear particularly well suited for dynamic MHD calculations, where the effort of using exactly aligned coordinates becomes prohibitive.

Significant progress has been made on ASDEX Upgrade during the last two years in the basic understanding of transport, in the extension of the improved H-mode in parameter space and towards an integrated operating scenario and in the development of control methods for major performance limiting instabilities. The important features were the understanding of particle transport and the control of impurity accumulation based on it, the satisfactory operation with predominantly tungsten-clad walls, the improved H-mode operation over density ranges and for temperature ratios covering (non-simultaneously) the ITER requirements on ν*, n/nGW and Te/Ti, the ELM frequency control by pellet injection and the optimization of NTM suppression by DC-ECCD through variation of the launching angle. From these experiments an integrated scenario has emerged which extrapolates to a 50% improvement in n T τ or a 30% reduction of the required current when compared with the ITER base-line assumptions, with moderately peaked electron and controllable high-Z density profiles.

Shift and broadening of isolated neutral helium lines 7281A (21P − 31S), 6678 A (21P − 31D), and 4713 A (23P − 43S) in a dense plasma are investigated. Based on a quantum statistical theory using thermodynamic Green's functions, where the electronic contributions to the shift and width are considered. Dynamical screening of the electron-atom interactions are included. Compared to the width, the electronic shift is more affected by dynamical screening. This effect is increased at high density. A cut-off procedure for strong collisions is used. The effect of the ions are taken into account in a quasi-static approximation, with both the quadratic Stark effect and the quadrapole interaction. The results for shift and width agree well with theoretical calculations and experimental data.

Writing the expression of the potential energy in terms of the perturbation of the flux function, and performing an Euler minimization, one obtains a system of ordinary differential equations in that perturbation. For a diverted configuration, the usual vanishing boundary conditions for the perturbed flux function at the magnetic axis and at infinity can no longer be used. An approach to fix “natural” boundary conditions for the perturbed flux function just at the plasma boundary has been developed; this replaces the vanishing boundary conditions at infinity. To obtain the necessary metric coefficients from an equilibrium solver, a function exhibiting the same singularity at the X point has been introduced, and thus the separatrix contour was described by a reduced number of moments.

Two families of exact analytical solutions of the Grad–Shafranov equation are presented by specifying the highest polynomial dependence of the plasma current density on the flux function Ψ in such a way that the Grad–Shafranov equation becomes a linear inhomogeneous differential equation. Both the pressure profile and the poloidal current profile each have two free parameters. X-points can be represented by superposition of solutions. Examples of the exact equilibrium solution are given for both a D-shaped plasma and a toroidally diverted plasma.

An MHD stability analysis of the edge plasma shows that in highly triangular plasmas, the increasing global βp has a stabilizing effect on the low-n instabilities that trigger edge localized modes (ELMs). The improved stability allows the access of higher edge pressure gradients before the ELM is triggered. At the same time, the edge plasma moves closer to the high-n ballooning mode stability boundary. The stability changes can explain why the high value of βp helps to access smaller ELMs.

Numerical modeling on the stabilization of neoclassical tearing modes by localized radio frequency (rf) current drive has been carried out to study the effects of various wave and plasma parameters on the stabilization and the associated physics. The change of the rf current profile due to the magnetic island has been taken into account by modeling the two-dimensional transport of the fast electrons induced by the rf wave. It is found that, when the rf deposition width is much larger than the island width, the modulated rf current drive to deposit the rf current around the island’s o point has a stronger stabilizing effect than a nonmodulated one. The slowing down time of the fast electrons and the initial island width when applying the rf wave are also found to be important in determining the stabilizing effect.

Numerical modeling results of the nonlinear growth and saturation of neoclassical tearing modes are presented and compared with analytical theories. The saturated magnetic island width obtained numerically in most cases approximately agrees with that derived from generalized Rutherford equation. For a high bootstrap current density fraction and/or a small magnetic shear at the rational surface, however, the change of the local magnetic shear due to the loss of the bootstrap current inside the island should be taken into account in calculating the saturated island width. At island saturation the tearing mode stability index, Δ′, is found to approximately agree with that found from the linear outer region equation of the tearing mode and to linearly decrease with the saturated island width. During the growth of the island, however, the value of Δ′ depends not only on the island width but also on other parameters which affect the plasma current density profile.

Performance-limiting magnetohydrodynamic (MHD) instabilities on ASDEX Upgrade are discussed. In the conventional H-mode scenario, the main MHD performance limitation is found to be the neoclassical tearing mode (NTM). The onset {beta} of NTMs in ASDEX Upgrade scales with the poloidal ion gyroradius, in agreement with theoretical expectations. At higher {beta} values, NTMs occur in a more benign form, the frequently-interrupted-regime NTMs, which lead to a smaller confinement degradation than normal NTMs. Active control of NTMs by electron cyclotron current drive in the island has been demonstrated on ASDEX Upgrade. In advanced tokamak regimes with reversed shear, a variety of performance-limiting instabilities has been observed. The shear reversal zone can be unstable to double tearing modes or to infernal modes; both have been identified in ASDEX Upgrade. Due to the broad current profile in advanced tokamak discharges, the ideal external kink mode can be unstable at relatively low {beta}{sub N} {

Numerical modeling results of the linear drift tearing modes are presented. The present model is based on the two-fluids equations, and the perturbed bootstrap current is also included. The electron temperature and the density perturbations are self-consistently calculated by solving the two-dimensional transport equations. It is found that, with the inclusion of the electron perpendicular heat transport, which is neglected in the previous theory, the behavior of the drift tearing mode becomes significantly different, and a new type of tearing mode instability appears. This mode is driven unstable by a sufficiently large electron temperature gradient in a certain range of the electron diamagnetic drift frequency ω*e. The stability of the drift tearing mode is found to be mainly determined by ω*e. The parallel ion flow driven by the parallel pressure gradient is found to be stabilizing for the drift tearing modes, while the perturbed bootstrap current is destabilizing for large or small ω*e but can be stabilizing for a certain range of ω*e.

In the theoretical description of the neoclassical tearing mode the bootstrap current is assumed to completely vanish inside the magnetic island if finite perpendicular transport can be neglected. In this paper, the effects due to both the finite-orbit width of the trapped ions and their toroidal precession (not included in the standard analytic theory) on the island current are investigated. The evolution of the ion distribution function in toroidal geometry in the presence of a perturbed magnetic equilibrium is computed numerically employing the δf method, collisions being implemented by means of a Monte Carlo procedure. It is shown that a significant fraction of the (ion) bootstrap current survives inside the island when the ion banana width wb approaches the island width W, and no loss is observed for wb/W≥1. This effect is reduced when the collision time becomes longer than the toroidal drift time. The value of the current is found to be inconsistent with the local gradients in the island region. The finite-banana-width effect leads to a linear scaling of the value of the poloidal β at the mode onset with the normalized ion poloidal gyroradius ρ*p, in agreement with the experimental results of ASDEX Upgrade.

The MFBE_2001 code computes the magnetic field in a form suitable for field line tracing inside and outside the plasma boundary of two- and three-dimensional finite-β equilibria. It is a modified version of the Magnetic Field Solver for Finite-β Equilibria (MFBE) code which was developed for the investigation of stellarator equilibria without net toroidal current. The numerical method used in MFBE_2001 is based on the `virtual casing' principle which also allows the computation of magnetic fields of equilibria with net toroidal current, such as quasi-axisymmetric and tokamak equilibria. The numerical accuracy of the code is tested for an axisymmetric tokamak equilibrium and the corresponding three-dimensional one including the toroidal field ripple. For this purpose, the results obtained with the code system VMEC/NEMEC+MFBE_2001+GOURDON are compared with those computed with the axisymmetric equilibrium code DIVA.

The development of techniques for neoclassical tearing mode (NTM) suppression or avoidance is crucial for successful high beta/high confinement tokamaks. Neoclassical tearing modes are islands destabilized and maintained by a helically perturbed bootstrap current and represent a significant limit to performance at higher poloidal beta. The confinement-degrading islands can be reduced or completely suppressed by precisely replacing the “missing” bootstrap current in the island O-point or by interfering with the fundamental helical harmonic of the pressure. Implementation of such techniques is being studied in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] in the presence of periodic q=1 sawtooth instabilities, a reactor relevant regime. Radially localized off-axis electron cyclotron current drive (ECCD) must be precisely located on the island. In DIII-D the plasma control system is put into a “search ...

A reduction in turbulent density fluctuations is observed in internal transport barrier (ITB) discharges in the ASDEX Upgrade tokamak with an L-mode edge and reversed magnetic shear. The turbulence reduction is localized spatially to around the ITB gradient and the ITB foot-point region, coincident with strong shearing in the toroidal rotation velocity. The radial extent and degree of reduction is related to the strength of the ITB. Strong (narrow and steep) ITBs are well localized and display greater turbulence reduction. Weaker ITBs are less localized with less reduction. The formation of a subsequent H-mode edge barrier moves the velocity shearing region to the edge and weakens the ITB to the point of extinction. During the ITB the turbulence is reduced across a broad frequency range, however a residual level of low-frequency fluctuations (f

Neoclassical tearing modes (NTMs) are studied in the ASDEX Upgrade tokamak [O. Gruber, H.-S. Bosch, S. Gunter et al., Nucl. Fusion 39, 1321 (1999)]. The onset βN for NTMs scales with the normalized ion gyroradius ρ*, independent of the normalized collisionality ν* for a wide range of ν*. This scaling is in accordance with both polarization current and χ⊥/χ∥ model, if for the latter, the heat flux limit on parallel heat conductivity is taken into account. Analysis of NTM stabilization experiments indicates that the typical seed island size is 1–1.5 cm, again in agreement with both models. Mode coupling to the q=1 surface is a crucial element in determining the impact of the NTM on the discharge performance. Complete stabilization using electron cyclotron current drive (ECCD) has been demonstrated at βN=2.5 and with about 10% of the total heating power. The results are in good qualitative agreement with modeling using the Rutherford equation and in quantitative agreement with a two-dimensional nonlinear cyl...

The 7th EFPW took place in December 1999 at Kloster Seeon in Germany. It was hosted by the Association IPP-Euratom, Garching and sponsored by the European Commission. Within an overall theme of plasma heating and current drive systems, four topics of importance to the future development of magnetically confined fusion were discussed in detail: the injection of heating, current and momentum; the interplay between heating systems and transport barriers; MHD control issues for heating and current drive systems; and energetic particle physics. In addition, a review of recent JET experiments, the organization of the JET scientific programme under EFDA and the new ITER design were presented. The main issues discussed in each session and the areas identified as requiring further study are summarized here.

In addition to the Greenwald density limit and the threshold conditions for H-mode access, neoclassical tearing modes (NTMs) pose the most severe constraint to tokamak operation in discharges with conventional (monotonic) current density profiles. We show, at hand of the example of ASDEX Upgrade the resulting constraints on density and useful heating power. At high densities, collisionality effects can lead to the appearance of a second stable regime for NTMs. A further limitation can arise from the appearance of fishbone instabilities which, depending on the orientation of the injected beams, can also lead to a clamping of the total plasma energy content. The resulting diagram is also useful as a guide for a strategy to expand the operating range by feedback stabilisation of the neoclassical tearing modes and for the orientation of the beamlines.

Modulated Electron Cyclotron Resonance Heating was applied in ASDEX Upgrade to study the electron heat diffusivity χ e . Its dependence on the isotope mass was found to be opposite to that one known from the power balance analysis. Off-axis ECRH deposition leads to a reduced electron heat transport in the centre which cannot be explained by an inward heat pinch. Electron Cyclotron Current Drive was applied to completely stabilise a (3/2)-neoclassical tearing mode with a consequent recovery of the plasma energy. High electron and ion temperatures have been simultaneously achieved by application of central counter ECCD in a discharge with an internal ion transport barrier.

Confinement improvement beyond the usual L-mode proceeds in most cases through the formation of localized transport barriers in the edge (H-mode) or in the interior regions of the plasma (ITBs). The standard interpretation of this is the quenching of the usually prevailing turbulence by the formation of layers of sheared E×B rotation. Regarding interior transport barriers, this phenomenon has been observed in two distinctively different situations, with predominant ion or electron heating, and Te either significantly smaller or larger than Ti. The reactor relevant regime is, however, one with approximately equal Te and Ti. The availability of ECRH (and, to a lesser degree, also that of LH or FW heating) has allowed the study of the effect of the Te/Ti ratio in a controlled way. The standard transport model of ion-temperature-gradient and trapped-electron-mode-driven turbulence predicts (for situations with significant ion heating) a negative effect of an increase in this ratio. Experimental results show, however, that this confinement deterioration can be avoided in certain situations. These observations can be reconciled with theoretical expectations, if the simultaneous increase in Shafranov shift, which can reverse the theoretical predictions, is taken into account.

Neoclassical tearing modes are one of the most serious concerns for operation on a next-step tokamak device. The modes occur on present tokamaks at normalized pressure (beta (N)) values comparable to those envisaged For baseline scenarios in future devices, such as ITER-FEAT. Further, empirical scalings based on data from many of the present machines point to much lower thresholds on a larger device. However, physics-based models indicate an important role for the seed island mechanisms, which may in fact give rise to increased stability on larger devices-i.e. if the seed island width (required to trigger the NTM) falls below the critical levels required. Fits based on these models suggest this is the case, bur are too badly constrained at present to make reliable predictions, and the physics is complex, making quantitative theoretical calculation difficult. Further experiments are required to examine the scaling of the seed, as well as to identify the role and relative sizes of the stabilizing terms that set the critical size for mode growth. In the event that the modes are unavoidable, promising feedback stabilization techniques are being developed with the use of localized RF current drive to change the stability properties of the plasma. Further work is needed to demonstrate sustained access to higher beta (N) and provide data to refine models. This paper reviews the underlying physics and key issues, commenting on the present status of understanding and further work required.

Neoclassical tearing modes (NTMs) with different mode numbers have been observed in tokamak plasmas. These NTMs, however, never occur simultaneously in ASDEX Upgrade. As a mode with a different helicity starts to grow, this usually leads to suppression of the first NTM. Both analytical and numerical modelling have been carried out to investigate the interaction between NTMs of different helicities. It is found that once the two magnetic islands are close, the more unstable magnetic island survives and suppresses the less unstable one, in agreement with the experimental results. The mechanism responsible for this suppression is the decreased fundamental harmonic pressure perturbations of the NTM in the presence of magnetic perturbations of different helicities.

The effect of a static helical magnetic field on the nonlinear growth of the neoclassical tearing mode (NTM) is investigated. The NTM is found to be stabilized by an externally applied helical field of a different helicity if the field magnitude is sufficiently large, suggesting a very simple method for stabilizing the NTM. The mechanism responsible for this stabilization is the decreased fundamental harmonic pressure perturbation of the NTM in the presence of the helical field.

A theoretical approach to spectral line shapes of hydrogen-like emitters in plasmas has been developed. Within this approach, the line core as well as the line wings are well described. Besides the ion dynamics, shift and asymmetry are also included. The time evolution of the ionic microfield is taken into account by means of a simulation technique. Shift and asymmetry of the lines result from the inclusion of the electronic contributions to the line shift as well as from the inhomogeneities of the ionic microfield and the quadratic Stark effect. Calculated line profiles according to the presented formalism are given for the Lyman- line and the Lyman- line of atomic hydrogen in an argon plasma, and compared with results of other theories and corresponding experiments.

A stationary advanced tokamak scenario with an internal transport barrier (ITB) for ions and electrons, particles and momentum in combination with an H-mode barrier and flat shear (q0≈1) was maintained for 40 confinement times and several internal skin times with HITERL-89P βN≈5. Raising the density by edge gas fuelling close to 50% of the Greenwald density to integrate proper exhaust conditions causes an increase of the threshold power to sustain an ITB and a decrease of Zeff below 2. In contrast, a density increase caused by improved core particle confinement at more triangular plasma shapes does not change the ITB onset conditions. No temporal impurity accumulation even with high-Z Ar puffing was observed despite of peaked impurity density profiles. MHD modes contribute to the stationarity of the shear profile. In the ITB/H-mode scenario (1,1) fishbones with a large reconnection area `clamp' the q-value in the vicinity of one and avoid sawteeth during the whole high-performance phase. In ITB scenarios with reversed shear (qmin ≥2) fishbones can clamp the current profile development near the q = 2 surface without deteriorating energy confinement, whereas double-tearing modes, acting in a similar form, lead to substantial confinement losses. Applying central ECRF heating and current drive to beam heated reversed-shear ITB discharges shows an substantial effect on MHD stability, affecting the passage of the q-profile through qmin = 2, and degrading or prolonging the reversed-shear phase depending on the CD direction. Moreover, reactor relevant Te≥Ti operation with temperatures in excess of 10 keV was achieved with internal transport barriers for both electrons and ions simultaneously.

Internal transport barriers with the central electron temperature as large as the central ion temperature both in excess of 10 keV have been achieved in the Axi-symmetric divertor experiment (ASDEX Upgrade) [H. Vernickel et al., J. Nucl. Mater. 128, 71 (1984)]. By applying central electron cyclotron heating and current drive to negative central shear discharges, established by neutral beam heating in the current ramp, the core electron temperatures could be raised by more than a factor of 2. Despite the fivefold increase of the central electron heat flux, the ion and electron energy and also angular momentum transport did not deteriorate. For neutral beam injection alone and also with additional central electron cyclotron counter-current drive, a double tearing mode and the associated detrimental effect on the plasma confinement is destabilized only transiently, when the minimum of the safety factor (qmin) passes through 2. For co-current drive, however, the confinement does not recover after qmin has dro...

An ELMy ASDEX Upgrade plasma equilibrium is reconstructed taking into account the bootstrap current. The peeling mode stability of the equilibrium is numerically analysed using the GATO [1] code, and it is found that the bootstrap current can drive the plasma peeling mode unstable. A high-n ballooning mode stability analysis of the equilibria revealed that, while destabilizing the peeling modes, the bootstrap current has a stabilizing effect on the ballooning modes. A combination of these two instabilities is a possible explanation for the type I ELM phenomenon. A triangularity scan showed that increasing triangularity stabilizes the peeling modes and can produce ELM-free periods observed in the experiments.

Fast particle driven m=1/n=1 modes in the form of fishbones frequently initiate neoclassical tearing modes (NTMs) on Axisymmetric Divertor Experiment Upgrade [W. Koppendorfer et al., 14th International Conference on Plasma Physics and Controlled Fusion (International Atomic Energy Agency, Vienna, 1993), Vol. I, p. 127] and other neutral-beam-injection heated tokamaks, but disappear after the NTMs have reached a quasistationary state. A burst of other magnetohydrodynamic phenomena, described in this paper, appear instead, similar in repetition rate and time signature of frequency and amplitude. They are associated with the growth of the m=2/n=2 satellite of the m=3/n=2 neoclassical tearing mode, and a transient increase (termed FJ=frequency jump event) in the rotation frequency of the coupled mode system. They lead to a thermal crash, originating at q=3/2, propagating inwards up to the q=1 surface. With a lower repetition rate (more characteristic of sawteeth) similar events occur, where a large 1/1 component also appears and the fast crash propagates to the plasma center frequency jump with sawtooth character (FJST). The analogies to the fishbone case suggest that this phenomenon is caused by the interaction with fast particles, which transiently impress their precession frequency on the pre-existing magnetic perturbation of the NTM.

Numerical modeling of the stabilization of neoclassical tearing modes by localized radio frequency (rf) current drive is presented. The bootstrap current is self-consistently calculated from the pressure evolution equation, the rf current source is obtained from the ray-tracing code and the Fokker–Planck code, and the change of the driven current profile due to the change of the magnetic island width has also been taken into account by modeling the two-dimensional transport of the fast electrons induced by the rf wave. It is found that both parallel and the perpendicular transport of the fast electrons play important roles in the stabilization, and modulated and nonmodulated rf current drive have approximately the same stabilizing effect. The neoclassical tearing modes is shown to be stabilized by a continuous rf current drive. The simulation results essentially agree with experimental observations.