Left: Plan of experimental toroidal CXRS diagnostic view on TCV. The neutral beam is injected at in the toroidal plane with the low field toroidal observation chords shown. The arrow indicates the positive toroidal direction. Right: Poloidal cross section showing poloidal observation viewing chords from the vessel floor. For the arrangement used in these experiments the poloidal array extends to the last closed flux surface, whereas the toroidal array does not extend as far out.
Toroidal angular velocity profiles for a sequence of limited discharges for a range positive plasma currents at a plasma density (rotation always in the counter-current direction). The maximum rotation (from the inversion radius inwards), decreases with plasma current and three radial rotation zones are identified: (i) The core rotation profiles are slightly “bulged” in the co-current direction but relatively flat up to the sawtooth inversion radius (indicated by the vertical lines); (ii) the plasma edge where the rotation is near zero; and (iii) an intermediate linking region which encompasses most of the velocity gradient.
Dependence of the plasma current normalized maximum toroidal velocity on ion temperature. The database includes positive and negative plasma currents and a wide plasma density range. Discharges with are not included. For the discharges shown, the maximum toroidal velocity is relatively constant within the sawtooth inversion radius.
The peak ion temperatures for the limited configuration data in Fig. 3 as a function of the average plasma density. For these Ohmically heated plasmas, the ions are increasingly heated by collisions with the hotter electrons for increasing plasma density. The scaling with ion temperature, shown in Fig. 3 , produced a better fit than by using the plasma density.
(a) Electron density, (b) ion temperature, and (c) toroidal rotation profiles for diverted configurations for a range of plasma currents. (Note: The plasma density is not the same for these discharges.) The flattening of the profile within the sawteeth inversion radius is seen, as in Fig. 2 but, contrary to the limited discharges, the toroidal rotation is now in the co-current direction and the plasma edge region is not always close to zero.
Top: Toroidal plasma rotation profiles in diverted configurations for a range of plasma densities. The toroidal rotation profile reverses from a co- to counter-current direction for a central plasma density . The toroidal rotation profile rotation almost exactly inverts about a nearly constant value at . With increasing plasma density, the rotation profile, including the edge region, increasingly rotates in the counter-current direction. Bottom: Profiles of the plasma density, electron, and CVI ion temperatures and the toroidal rotation profile for a rotation profile reversal in a limited configuration. Here, the toroidal profile again almost exactly inverts at a central plasma density from the counter- to the co-current direction and the rotation at remains close to stationary.
Toroidal rotation profile in the core as a function of the average plasma density for discharges with a density ramp. Four discharges (Nos. 28924, 28355, 28976, and 30988), separated by over a year of TCV operation, show that the rotation reversal phenomenon occurs close to an average plasma density in spite of many intervening machine conditioning boronizations resulting in significantly different machine conditions. The central toroidal rotation of discharge No. 32458, where the plasma current was reversed, is also shown. The density ramp rates for these discharges were not the same. All the discharges exhibit a counter- to co-current velocity reversal at close to the same density indicating that this phenomenon is more related to the local plasma physics than any machine-specific effect.
The evolution of the core toroidal velocity in discharge No. 28988 where a density ramp results in a velocity reversal following which the density is reduced resulting in a return to the counter-current direction (velocity again in the counter-current direction). (a) The evolution of the core plasma density as a function of time together with the core toroidal rotation. (b) The locus of the core density as a function of the core plasma density through this discharge. Although some hysteresis in the plasma density is present (the first transition occurs at but the return only occurs at ), the bifurcation in the toroidal rotation profile is reversible.
(a) The toroidal rotation evolution across a velocity reversal event at , 0.5, 0.8, and 0.85. (The values for are halved to increase the figure’s contrast.) (b) The poloidal rotation profiles at the times indicated by the vertical lines in (a) i.e., before and after the reversal. (c) and (d) show the deduced electric field using the ion force balance equation calculated with the poloidal, toroidal, and ion pressure profiles. The core electric field, dominated by the toroidal rotation, reverses between the plots whereas the deduced electric field in the plasma edge, dominated by the poloidal rotation, remains negative and appears strengthened after the toroidal velocity reversal.
(a) Plot of the sawteeth frequency for a series of discharges with a range of triangularity from to 0.48. A density ramp takes all these discharges across the value associated with a toroidal velocity reversal at . (b) The low and high field side sawteeth inversion radii for these discharges over the same period. Although the position of the sawteeth radii is a function of triangularity, there is no evidence for a modification of the sawteeth period or inversion radius at the toroidal rotation reversal time.
Addition of off-axis second harmonic (X2) ECH heating at moves the sawtooth inversion radius inwards from to . The toroidal rotation profile now peaks, almost doubling its maximum value. The profile outside the sawteeth inversion radius is little changed implying that the core rotation profile, in the absence of sawteeth, would be considerably higher. The possible flattening of the toroidal plasma may, in part, be ascribed to uncertainties in the observation chord positions that are exacerbated by these observation chords being tangential to the magnetic flux surfaces. Put directly, these points do not exclude that the core rotation, in the absence of sawteeth, could be linearly extrapolated from the toroidal profile gradient outside the sawteeth inversion radius.
Deduced core toroidal rotation for the data in Fig. 2 (constant plasma density) linearly extrapolated from the toroidal profile gradient outside the sawtooth inversion radius (to be compared with Fig. 3 ). Most of the plasma current scaling of Fig. 3 is no longer present. If the toroidal velocity transport mirrors the ion power transport (the ion temperature profile is often relatively flat in the core region), this extrapolation will overestimate the core rotation in the absence of sawteeth.
Comparison of the toroidal rotation reversal with toroidal magnetic field. (a) The plasma is kept constant, (b) the plasma current is adjusted to keep the same edge safety factor . The toroidal rotation reversal occurs at the same density for the same magnetic configuration. No rotation reversal was obtained at the lower toroidal field. For constant , the plasma current is possibly below the current threshold observed for toroidal velocity reversal. At and , the position of the rational surface is extremely close to the plasma edge where the plasma rotation behavior changes strongly (see Fig. 2 ).
Two discharges where a toroidal velocity reversal is observed with a strong difference in the plasma carbon content. In spite of this, there is no change in the density at which the reversal occurs. The carbon content scaling, measured by the CXRS diagnostic are shown in the central frame. This data calculated as an effective plasma ion charge, , in the lower frame.
The outermost rotation values ( symptomatic of the edge region’s rotation) are shown for the stationary rotation profiles of diverted discharges for both favorable (FAV—circles) and unfavorable (UNFAV—triangles) ion drift directions. At lower densities, the toroidal rotation at the center saturates at . Both rotation values decrease with plasma density with the favorable discharges rotating faster in the counter-current direction than the unfavorable configurations, for a given plasma density. It is interesting to note that the edge rotation does not appear to mirror the core rotation before and after velocity reversal, indicated by the filled/red and hollow/blue symbols, respectively. With increasing plasma density, the edge region rotation is more strongly in the counter-current direction.
The difference between the core and edge region velocities for the discharges in Fig. 15 as a function of the average plasma density. Although the toroidal rotation profile peaks more strongly with plasma density, this scaling is less strong than that of the edge region rotation with plasma density. For these diverted discharges, the toroidal rotation profile is relatively constant with the absolute value determined by the rotation in the edge region that behaves as a boundary condition.
Evolution of the low frequency MHD spectrograms (a)-(d) across the density scan of the quiescent diverted discharges of Fig. 6(a) . A [2,1] mode at increases intensity with plasma density and a sawteeth precursor [1,1] mode, appearing at a slightly lower density, become apparent. (e) A MHD spectrogram during a limited discharge with a density ramp is shown together with the plasma rotation deduced from the passive CVI light of the innermost CXRS observation chord that is a parametric measurement of the core rotation. The [2,1] mode clearly commences before the toroidal velocity inverts, i.e., during the early density ramp phase where the plasma rotates increasingly strongly in the counter-current direction.
Toroidal rotation profile as a function of plasma elongation at constant plasma triangularity. To permit comparison, the plot times and discharges were selected to have similar ion temperature profiles and plasma densities shown in (a). The higher elongations result in an increase in the edge safety factor that was previously seen to result in an increased counter-current plasma rotation. (b) Here, however, increasing elongation results reduces the toroidal rotation so a decrease of spontaneous rotation with elongation is concluded. TCV’s unique plasma elongation possibilities will be used in the future to further investigate this observation.
Résumé of the toroidal rotation profiles as function of plasma triangularity . (a) The core toroidal rotation and (b) the toroidal rotation profiles, are shown for positive . The toroidal velocity reversal phenomenon becomes less pronounced with decreasing with the core toroidal rotation shown as a function of average plasma density. The profiles for and 0 (elliptical shape) are shown for average plasma densities of and , i.e., across the density associated with a toroidal rotation reversal. At , the rotation profile, for these diverted discharges, is small in the plasma core and now there is a strong counter-current rotation in the plasma edge at both densities. The trend with negative is summarized with a data from discharges with a triangularity of , , and . (c) The core as a function of plasma density and (d) toroidal velocity profiles for , i.e., above the density associated with the velocity reversal. The whole plasma rotates more strongly in the counter-current direction with decreasing and the profile with strongly negative appears to saturate in the plasma edge region at values .
(a) CVI ion temperature profiles shown for , 0, and at . The excellent agreement between the poloidal and toroidal diagnostic is a comforting demonstration of a good system alignment. With these Ohmically heated discharges, the ion temperature increase with decreasing results from collisions with the increasing hot electrons resulting from a concurrent improvement in the energy confinement. (b) The near linear increase in the carbon concentration for the same discharges, over this small shot range, may only be ascribed to a confinement improvement.
Poloidal rotation profiles for plasma triangularity , 0, and . Despite the strong change in the ion temperature with (Fig. 20 ), the poloidal rotation profiles are remarkably similar.
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