PSFC/JA--9 Formation and stability of impurity snakes in tokamak plasmas L. Delgado-Aparicio,, L. Sugiyama, R. Granetz, J. Rice, Y. Podpaly, M. Reinke, D. Gates, P. Beirsdorfer 4, M. Bitter, S. Wolfe, E. Fredrickson, C. Gao, M. Greenwald, K. Hill, A. Hubbard, E. Marmar, N. Pablant, S. Scott, R. Wilson and S. Wukitch Princeton Plasma Physics Laboratory MIT - Plasma Science and Fusion Center MIT - Laboratory for Nuclear Science, 4 Lawrence Livermore National Laboratory July, Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge MA 9 USA This work was performed under US DoE contracts DE-FC-99ER545 at MIT and DE-AC-9CH466 at PPPL. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.
Formation and stability of impurity snakes in tokamak plasmas L. Delgado-Aparicio,, L. Sugiyama, R. Granetz, J. Rice, Y. Podpaly, M. Reinke, D. Gates, P. Beirsdorfer4, M. Bitter, S. Wolfe, E. Fredrickson, C. Gao, M. Greenwald, K. Hill, A. Hubbard, E. Marmar, N. Pablant, S. Scott, R. Wilson and S. Wukitch PPPL, Princeton, NJ, 854, USA MIT - PSFC, Cambridge, MA, 9, USA MIT - LNS, Cambridge, MA, 9, USA LLNL, Livermore, CA, 9455, USA (Dated: July, ) New observations of the formation and dynamics of long-lived impurity-induced helical snake modes in tokamak plasmas have recently been carried-out on Alcator C-Mod. The snakes form as an asymmetry in the impurity ion density that undergoes a seamless transition from a small helically displaced density to a large crescent-shaped helical structure inside q <, with a regularly sawtoothing core. The observations show that the conditions for the formation and persistence of a snake cannot be explained by plasma pressure alone. Instead, many features arise naturally from nonlinear interactions in a D MHD model that separately evolves the plasma density and temperature. MW/m MW/m.87 inboard.4.6..6 b).4 Chord # 5 5 r/a~ core sightline. nd a). st.8 outboard.5 C-Mod # 5.9. C-Mod # 56 One of the most interesting and cited examples of D magnetohydrodynamic (MHD) activity in the core of a magnetically confined fusion plasma is the long-lived helical mode found at the Joint European Torus []-[] more than 5 years ago. The typical snake-like helical patterns observed are characterized by a small region of localized and enhanced plasma density that rotates within the field of view of various diagnostics and is radially concentrated on, or inside the q = surface. The standard model [] to describe the snake formation is based on the physics of tearing modes and suggests that the localized cooling of the q = surface is responsible for an increase of the local plasma resistivity which in turn causes a drop in the current density that leads to the formation of a magnetic (m, n) = (, ) island. This island is assumed to trap the particles from the pellet and form the snake. Snakes have been a common feature in every major tokamak fusion experiment, as well as in spherical tori and reversed field pinches. A second type, produced by an accumulation of impurity ions rather than the deuterium ions from injected fueling pellets, is also observed; these impurity snakes probably appeared first in type O discharges in Doublet-III [4]. Both types of snakes possess surprisingly good MHD stability and particle confinement, since they can survive tens to hundreds of sawtooth cycles. This letter reports new experimental data on the heavy impurity snakes in the Alcator C-Mod experiment, which leads to a new picture of its formation and sustainment, as well as its complex relationship with the sawtooth instability. A suite of novel spectroscopic imaging diagnostics has facilitated the identification of the major impurity ion species and the determination of the perturbed radiated power inside the q region with unprecedented temporal and spatial resolution. For the first time, it is possible to infer the impurity density, electron temperature, Zef f, and resistivity of the n = helical structure. These results can also shed light on the formation and stability of pellet-induced snakes. Helical snake-modes like the ones depicted in Fig. Chord # 5 5 r/a~ core sightline FIG.. (Color online) SXR brightness profiles of two impurity snakes; the dotted lines indicate the time of their formation. have been observed at Alcator C-Mod [5] ohmic discharges during the plasma current ramp-up phase or early in the plasma current flattop, where the high edge temperature increases the high-z impurity (e.g. molybdenum) erosion from the inner wall, and the absence of sawtooth crashes allow on-axis impurity peaking. An example of the formation of such - apparently - spontaneous phenomena [] is depicted in Fig. -a) using the time-history of the soft x-rays (SXR) brightness profiles. The second snake shown in Fig -b) had nearly identical radiation profiles before the snake formation until an inadvertent high-z impurity injection - ms before the snake formation - nearly tripled its radiated power at mid-radius [compare Figs. -a) and -b)]. A common feature between snakes is thus the presence of a peak radiated power density and SXR emissivity which peaks slightly off-axis ( r cm, r/a /5 ) due a peaked-density pressure-driven Shafranov shift.
4 P rad [MW/m] CORE C-Mod # 56 t =.4 s t =.85 s -------------------------- Kink-snake: θ~, θ~π 65 7 75 8 85 9 C-Mod # 5 t =. s t =.4 s t =.4 s -------------------------- Kink-snake: θ~, θ~π a) MW/m b) ms 65 7 75 8 85 9 FIG.. (Color online) Radiated power density profiles before and during the formation of the two snakes shown in Fig...4.9..8 [MW/m ] Plasma height (cm) - a) Δt~.5 ms (kink-like, θ~) 6 7 8..6.9. b) Δt~5 ms (crescent, θ~) q= q= q= q= 6 7 8 FIG.. (Color online) Typical SXR emissivity contours during the nd and rd stages of the snake formation. The identification and localization of the main impurity species was possible using the High Resolution X- ray crystal imaging spectrometer with Spatial resolution (HiReX-Sr) [6]. Although this diagnostic was designed primarily for extracting temporally and spatiallyresolved spectra from argon, it is also possible to monitor intrinsic impurities such as molybdenum; the latter is the main intrinsic high-z impurity at C-Mod with an average ion charge of Z Mo = in the plasma core. A detailed comparison between the time-history of the SXR core brightness profiles and the intensity of the Mo + line has enabled the determination that the net core emission, during the impurity peaking and the snake formation, is mainly due to molybdenum charge states [6]; consequently, the snake-like pattern in the SXR data shown in Fig. is formed by a small region of localized and enhanced Mo density on or inside the q = surface. The C-Mod snake formation can be described by a multi-step process corresponding to the numbers in Fig.. The first condition - before the snake formation - is characterized by a plasma with peaked SXR and radiated power density (P rad ) profiles [see also grey profiles for t.85 s and t.4 s in Figures -a) and - 4 6 4 6 a) P rad, AXUV - Array A Frequency (khz) b) T e, FRC-ECE.8...4.6 AXUV [MW/m].7 Te [kev] R~.69 m dte/te~.% C-Mod # 56 c) Arrays A vs J C-Mod # 56 R~7. cm R~69. cm d) R~68.6 cm.58.89.9.9 FIG. 4. (Color online) P rad and T e, fluctuations during the formation of the snake shown in Fig. -a). In c), the AXUV signals are from two arrays displaced 8 o in toroidal angle. b), respectively]. For the snake shown in Fig. -a), the core electron density (n e ) before the impurity accumulation (t.4 s) is flat and. m, while before the snake formation (t.85 s) the density peaks to n e. m. A net core P rad of. MW/m will then correspond to a core Mo density n Mo.4 7 m and a peaked impurity concentration (c Mo = n Mo /n e ) of 6. 4 ; the latter calculation uses a Mo cooling factor L Mo 7 W m [7]. Such an impurity density can increase the core Z eff, as well as the collision frequency (ν e,i ) and resistivity (η), by more than 5% over the molybdenum-free state. Central P rad of up to.6 MW/m have been observed so stronger increments of Z eff, ν e,i and η would be possible. The snake then forms as a growing and rotating kinklike (m, n) = (, ) helical impurity density concentration with a nearly circular cross section [see Fig. -a)]. A common feature of these plasmas is that the sawtooth onset is preceded by this kink activity which is constrained to small minor radii. The peak SXR and P rad emissivity associated to the kinked-core increases by an additional 5 % (see Fig. ), since most of the impurity emission is confined to a smaller volume element. From the net radiated power density and assumed quasi-neutrality it is possible to infer the impurity density at the center of the snake (δn Mo δp rad /n e, L Mo ) and its associated electron density perturbation (δn e Zδn Mo ); a net.7 MW/m with a flat core n e.7 m will correspond to an increased snake density of δn Mo. 7 m with δn e 7 8 m. The perturbations in density and charge can be as high as δn e /n e, 4% and δz eff /Z eff, 6 7% (assuming Z eff, ), respectively. The δp rad ( δn Mo ) and temperature oscillations during the formation of the kink snake are depicted in Figs. 4-a) and -b). Typical δt e oscillations measured with an electron cyclotron emission (ECE) radiometer are shown in Fig. 4-d) and are of the order of %.
δn Z [x 7 m - ].5..5. CORE δr C-Mod # 56 65 7 75 8 85 9.8.4. sawtooth free T e [kev]...5 SXR brightnes [kw/m ] 4 a) Δt~66 μs Δt~6 μs Δt~6 μs Δt~ μs b) S a w t o o t h c r a s h c).446.448.45.45.454 kw/m -9 85 798 65 b) t=τ sc - μs c) t=τ sc + μs C-Mod # 5 FIG. 5. (Color online) Evolution of the impurity density perturbation during the last phase of snake formation for the case of Fig. -a). The n = nature of the density perturbation has been measured for the first time using using two toroidally displaced AXUV arrays [8] as shown in Fig. 4-c). The phase between the two signals ( 5 o ) is the same as the geometric angle between the arrays. The broad, almost circular kink then makes a seamless transition to the third phase, a / helical crescent-like structure which resembles the magnetic island produced by a resistive / internal kink [see Fig. -b)]; this form endures for the life of the snake. Over 5 ms, the typical net radiated power density carried by the snake decreases by. MW/m due to the combined effect of the background transport and sawtooth crashes [6]. The peak snake density decreases by 5%, while the core electron temperature remains nearly constant at.65-.7 kev (see Fig. 5). The density perturbation narrows steadily and the location of the helical peak-emission moves radially outwards in minor radius by δr cm. The resultant enhanced resistivity at the center of the island in comparison to that of the background core is of the order of δη/η δz eff /Z eff, 45%. The snake is strongly resilient to sawtooth crashes. In the late third phase, the high-impurity-density crescent nearly surrounds a smaller circular core of lower impurity density. During a sawtooth crash, as shown in Fig. 6, the small core moves rapidly outwards to the edge of the crescent radius, where it coincides with an outgoing electron heat pulse, then returns more slowly to its original position. The location of the peak of the SXR and AXUV emission shrinks inward by - cm at the crash. The snake toroidal transit frequency slows by 5% at the crash, but later recovers, suggesting a transient change of the toroidal or poloidal flow velocities. The snake formation departs strongly from the nonlinear island model based on a modified Rutherford equation, proposed by Wesson [] and used by others [9, ]. Plasma height (cm) - q= q= q= q= 6 7 8 6 7 8 FIG. 6. (Color online) Typical SXR snake profiles before and after a sawtooth crash for the case of Fig. -b). The basic premise for the standard snake formation can be ruled out since - as demonstrated in Fig. - the unintentional or deliberate injection of impurities with the subsequent cooling of the flux surfaces, does not constitute a necessary condition for the impurity-snake formation. In addition, this model, based on m tearing mode reconnection, considers only local conditions at the q = rational surface that affect the current density layer there. It greatly over-emphasizes the local effects of the cooling of the island by line and continuum radiation and the change of Z eff []. The two contribute with large destabilizing terms, but then the saturation of the mode for a sustained snake requires that the equilibrium jump in the magnetic flux ψ, measured by, be large and negative (stabilizing), and remain so throughout the sawtooth oscillations. Moreover, using a formalism is unrealistic since the (, ) mode displaces the entire core and no thin layer matching conditions are feasible. The likely explanation for the persistence of the snake is that it embodies a quasi-steady-state magnetic structure. Its / helical configuration and close association with the q = surface and ongoing sawtooth crashes suggest that it is related to the / internal kink mode [] with magnetic reconnection. The new observations of the snake s initial formation from zero amplitude, its completely smooth transition from a broadly kinked core to a crescent shape with no evidence of a phase shift, and the
4 FIG. 7. (Color online) Nonlinear MD simulation shows the n = non-axisymmetric density perturbation (red/blue) on top of the kink-like non-axisymmetric ψ contours []. details of the periodic sawtooth crashes rule out a purely pressure-driven process. Models of the snake based on pressure balance have a fundamental difficulty in explaining its co-existence with periodic sawtooth crashes []. The internal kink-type mode is driven by the axisymmetric pressure gradient over the q < region [] and it eventually displaces and destroys the high pressure central core. Previous MHD studies of non-axisymmetric equilibrium states, with / magnetic islands [4, 5] or without [6], generally equate the higher snake density with higher pressure. This puts the impurity snake on the same side of the kink structure as the hot core. Additional heating would then destabilize the kink and the resulting crash would remove both higher pressure core and the snake density. On the other hand, higher pressure on the island side would tend to stabilize the sawtooth crash [4]. In addition, the C-Mod observations clearly show that the snake grows smoothly from a broad / density kink into an island-shaped helical distribution, without the high density switching sides from the core to the island-like side of the magnetic structure. Nonlinear MHD simulations of the early snake phase in C-Mod-like plasmas with separate temperature and density evolution [], suggest that / helical density perturbations near q = are compatible with the observed snake formation and also with ongoing sawteeth. For a C-Mod shaped plasma with a small q < region and a small background toroidal rotation, similar to the early stages of the impurity snake, results from the MD initial value code show that a positive helical density (δn/n) of a few percent in an annulus peaked around or just outside the q = radius drives an internal kink-like mode inside q <, in such a fashion as to minimize the perturbed / pressure gradient. The n = temperature perturbation becomes positive where the n = perturbed density is negative and vice versa (see Fig. 7). As in the internal kink, the perturbed pressure and poloidal magnetic flux are closely aligned. The total density perturbation has a broad helically kinked shape, extending beyond q =, like the early C-Mod snake. It forms a long-lived quasisteady-state structure linked to the very slowly growing kink inside q <. The decoupled pressure and density would allow sawteeth driven by pressure that do not disrupt the density snake. The configuration is also consistent with an eventual transition to a crescent-shaped snake trapped in the / island, when the q = radius grows steadily and axisymmetrically due to the resistive current equilibration. For a more unstable and larger q < region a similar helical density perturbation can trigger a sawtooth crash as in the case of the typical pellet-induced snakes []. In conclusion, a suite of novel imaging diagnostics enables estimates of the n = helical structure of P rad, n Z, n e, T e, Z eff, and η inside the q region with adequate temporal and spatial resolution. These new high-resolution observations of heavy-impurity / snakes show details of their evolution and the accompanying sawtooth oscillations that suggest important differences between the density and temperature dynamics, ruling out a purely pressure-driven process. The observed differences are consistent with the results of nonlinear D MHD simulations that evolve plasma density and temperature separately. This work was performed under US DoE contracts including DE-FC-99ER545 and others at MIT and DE-AC-9CH466 at PPPL. Computational support was provided by the National Energy Research Scientific Computing Center under DE-AC- 5CH. [] A. Weller, et al., Phys. Rev. Lett., 59,, (987). [] R. D. Gill, et al., Nucl. Fusion,, 7, (99). [] J. Wesson, Nucl. Fusion, 7, A7, (995). [4] G.L. Jahns, et al., Nucl. Fusion, 49, (98). [5] Alcator C-Mod Team. Fusion Sci. Technol., 5,, (7). [6] L. Delgado-Aparicio, et. al., MIT-PSFC/JA--8 report. Rev. Sci. Instrum., 8,????, (). [7] K. Fournier, et. al., Nucl. Fusion, 7, 85, (997). [8] M. L. Reinke, Rev. Sci. Instrum., 79, E6, (8). [9] A.-L. Pecquet, et. al., Nucl. Fusion, 7, 45, (997). [] Y. Liu., et al., Proc. of the th IAEA Fusion Energy Conference, Vilamoura, Portugal, EX/P5-, (4). [] L. Delgado-Aparicio, et. al., Nucl. Fusion, 5, 847, (). [] L. Sugiyama and L. Delgado-Aparicio, et al., submitted to Phys. Plasmas, (). [] M. N. Bussac, et al., Phys. Rev. Lett., 5, 68, (975). [4] W. Park, et al., Phys.Fluids,, 85, (987). [5] A.Thyagaraja, et al., Phys.Fluids, B(), 58, (99). [6] W. A. Cooper, et al., Nucl. Fusion, 5, 7, ().