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Fig.11_ctrlcoil [W7ASrev_11_ctrlcoil] Effect of control coils (B = 1.25 T, vac = 0.52, P NBI = 3.1 MW). (a) A significant increase of the stored energy can be achieved in the high- phase. This is attributed to the compensation of pressure induced edge islands as suggested by the flat region in the electron temperature profile at the plasma edge, which disappears with a proper coil current (b). At low the edge islands are overcompensated causing a deterioration of the confinement. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_iota [W7ASrev_11_iota] a) Comparison of volume-averaged (approximate values from diamagnetic energy) achieved before (shaded region) and after installation of divertor modules in W7-AS (before and after year 2000 ) as a function of the total rotational transform (including contributions from net-toroidal currents). Discharge #56403 with the so far highest value of (≈3.4% from a detailed equilibrium analysis) yields a maximum of ≈ 3.4% (#56403, marked in the plot). b) The time evolution of this shot (at B = 0.9 T and ext ≈ 0.5) exhibits a MHD-quiescent quasi-stationary discharge with a flat top at ≈ 3.2 % (peak value 3.4 %) corresponding to about 70 confinement times. The diamagnetic energy agrees with the energy derived from saddle coils which detect the magnetic flux of the vertical field generated by the Pfirsch-Schlüter currents (top traces). Below the line integrated electron density from the HCN interferometer, the central electron temperature obtained from an X ‑ ray two-foil analysis, the injected NBI power and the radiated power from bolometer measurements are given. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_flattop [W7ASrev_11_flattop] as a function of the flattop time normalized to the confinement time (a). The open symbols refer to the time in the discharge, where the VMEC analysis was performed. The solid symbols represent time averages during the flattop. In addition a typical dataset of Asdex Upgrade (AUG) is included [courtesy of H. Zohm], and the approximate range covered by large tokamaks is indicated. For the same dataset a comparison of measured energy confinement times with the ISS95 scaling is shown (b). The absorbed NBI power is calculated by the FAFNER code. The cases with highest beta-values are marked by solid symbols. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_greenw [W7ASrev_11_greenw] Operational diagrams obtained by substituting the edge rotational transform (a) by equivalent tokamak currents with. In the Hugill diagram (a) the normalized densities in W7 ‑ AS are far beyond the tokamak density limit imposed by q = 2 and the Greenwald limit. On the right, the normalized beta values are plotted versus the line averaged densities normalized to the Greenwald density. The shaded area marks the range accessible in tokamaks. The solid symbol represents again the AUG dataset (compare fig. 3). von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_equil [W7ASrev_11_equil] Dependency of the maximum plasma beta on the rotational transform (a). The lower data points fitted by the solid line to guide the eye are obtained with B = 1.25 T and full NBI heating Power (P NBI,abs ≈ 3.1 MW). In the optimum range of iota the plasma beta can be raised further by decreasing the magnetic field to B = 0.9 T (2 data points). The decrease of towards low iota is attributed to enhanced losses occurring as the equilibrium beta limit (upper solid line) is approached. The dashed lines represent estimates for the maximum beta, which can be achieved with the available power according to the W795 scaling at the density limit (for B = 1.25T and B =0.9 T). (b) Flux surfaces calculated with VMEC for and cases of = 0.57 (left) and = 0.30 (right). In the latter case the equilibrium limit is reached in the elongated cross section plane. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_pies [W7ASrev_11_pies] Effect of the control coils on the flux surface topology of high- equilibria calculated with the PIES code (B = 1.25 T, vac = 0.52, P NBI = 3.1 MW). The outermost thick contours represent the plasma boundary defined by the scrape-off due to in- vessel components, as calculated by the VMEC code. Without the control coils (a) significant flux surface degradation due to formation of island chains and ergodic regions at the edge is seen. By using the divertor control coils the fraction of good flux surfaces can be increased at comparable beta (b). Deteriorated flux surfaces are observed again with higher beta (c). von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_pies2 [W7ASrev_11_pies2] Pressure induced reduction of good flux surfaces by predicted by the PIES code (referring to fig. 2). The deterioration of the flux surface geometry can be mitigated by adjusting the field of the control coils. Lower data points: without control coils, upper data points: I cc /I m = 0.15 (Icc, Im : coil currents of control coils and modular field coils). von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_sx [W7ASrev_11_sx] (a) Tomographic reconstructions of X-ray emissivity distributions referring to a configuration with ext = At the maximum beta of (bottom) the pressure induced horizontal shift is large compared with the low- phase where. For comparison corresponding flux surfaces according to free boundary VMEC calculations are included in the plots. The dashed and solid lines mark the locations of the magnetic axis of the vacuum and of the finite-beta configurations, respectively. (b) The experimental data points represent the radial plasma axis positions as deduced from the peak position of the X-ray distributions for three configurations of different iota as a function of the volume averaged beta. The dashed lines give the positions of the corresponding VMEC calculations. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_bevolution [W7ASrev_11_evolution Evolution of beta as a function of the total edge transform in discharges with significant toroidal (OH) current. Current ramps in co-direction (a) provoke collapses of the plasma energy induced by tearing modes at = 1/2 and = 2/3. The counter- current cases (b) appear tearing stable, but fast MHD crashes, presumably caused by resistive ballooning modes, can take place at the equilibrium boundary. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_highb-OH [W7ASrev_11_oh] High- equilibria in the presence of significant toroidal (OH) current. The counter-current case (a) with, ext = 0.52 and I tor = +8.7 kA leads to low-iota and low-shear (lower dashed profile in (c)) and hence to a large axis shift as seen in the X-ray tomogram. The solid contours represent equilibrium flux surfaces calculated by VMEC. Co-current drive with, ext = 0.3 and I tor = kA (b) generates a large rotational transform in the center resulting in a reduced axis shift. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_mercier [W7ASrev_11_mercier] Stability analysis of equilibrium sequence in optimum high- configuration ( #51755, B = 0.9 T, ext = 0.52, ). The growth rates of unstable ideal free boundary MHD perturbations, as calculated by the CAS3D global stability code, decrease with increasing beta (a). The mode spectrum is dominated by (m,n) = (2,1) as indicated by the inset showing perturbed pressure contours. No unstable modes were found for. The peak in the n = 1 growth rate at is due to the appearance of the rational surface = 5/11 at the boundary. The local stability parameter according to the Mercier criterion (b) is shown as a function of 0 (central value of parabolic -profile) and normalized toroidal flux (radial coordinate). At low the configurations are Mercier unstable throughout the plasma radius. With increasing the resonant surface = 1/2 are generated and moves in radius. The stable region first expands and shrinks again beyond (0) ≈ 7 % reached in experiment. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_blowniota [W7ASrev_11_lowniota] Equilibrium fitting indicates that strong MHD modes occurs when edge iota ≈ 0.5 or 0.6 (m/n = 2/1 or 5/3). Confinement is degraded by strong MHD activity. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_tomo [W7ASrev_11_tomo] Large scale m = 2 pressure driven mode causing a transient collapse at intermediate beta ( = 1.7 %) following a complete locking of the mode rotation. The m = 2 structure is seen in the X-ray tomograms a-d). Perturbed and total emissivities are shown in a,b) and c,d), respectively. The data are consistent with mode islands, which are locked in the position where the (cold) o-point coincides with the o-point of the fixed island induced by the W7-AS error field. Just before the collapse, the large islands cause a splitting of the plasma column (d). In this configuration the iota-profile is flat and close to = 1/2 for a broad pressure profile (f). In this case the global ideal stability analysis with CAS3D yield an (m,n) = (2,1) unstable modes. The calculated perturbed pressure is shown in e). von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_sparam [W7ASrev_11_sparam] Partial thermal crashes induced by fast ( s) MHD events. The left part (a) shows discharges of a magnetic field scan ( T), in which a reverse ramp of the edge rotational transform was generated by inductive current drive during the density plateau. The crashes occur, when the parameter (bottom) has decreased to s ≈ 0.5 (in %, in keV). In the right part (b) volume averaged -values normalized to 2 from a database of 57 shots are plotted versus a conductivity parameter (~ T e 3/2 ). The parameters just prior to MHD crashes (solid triangles) are close to the value s = 0.5 represented by the dotted line. The solid lines are the trajectories of the discharges shown on the left. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_ripple [W7ASrev_11_ripple] Characteristics of high- discharges in configurations with different mirror ratio corresponding to I 5 /I m = 1.0 (standard case), 1.2 and 1.3. The plasma beta shows a bifurcation depending on the modular field ripple in correlation with strong MHD activity consisting of fast ELM-like bursts. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_ripple2 [W7ASrev_11_ripple2] Ideal ballooning stability predicted by the COBRA code for configurations with different modular field ripple adjusted by I 5 /I m. The bifurcations seen in the experimental data for I 5 /I m > 1 may be due to the wider unstable gap between the 1 st and 2 nd stability boundaries. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_secstab [W7ASrev_11_secstab] Marginal stability diagrams for infinite-n ballooning modes obtained by a 3-D equilibrium perturbation method (Hegna, Hudson). A sequence of five equilibria has been constructed with beta ranging from 0.5 % to 2.5 % based on a configuration with I 5 /I m = 1.4 s). The symbols indicate the measured values and the curves mark the stability boundaries for the flux surface with r/a = 0.7. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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Fig.11_idealstab [W7ASrev_11_idealstab] Ideal Stability diagrams of equilibrium sequence in optimum high- configuration (#51755, B = 0.9 T, ext = 0.52, ≤ 3.3%). The local stability boundary according to the Mercier (left) and resistive interchange criterion (right) is shown as a function of and normalized toroidal flux (radial coordinate). At low the configurations are Mercier unstable throughout the plasma radius. With increasing beta a stable region develops which first expands and shrinks again beyond ≈ 3% reached in experiment. von Weller: aus w7asRev_Kap12_highbeta_Weller_fig.doc

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