Abstract. Several interesting new results have come from studies of ICRF-heated, H-mode plasmas in Alcator C-Mod. Dimensionless scaling studies have found gyro-Bohm-like transport similar to that reported on other devices; however, the dependence on collisionality was surprisingly strong, with BE  −1. Despite high edge temperatures and strong edge pressure gradients, type I edge-localized modes (ELMs) are not observed in C-Mod. Instead we obtain a regime that we have dubbed enhanced D  (EDA) which is accompanied by high-frequency density fluctuations. For all H-modes, core gradients were found to increase linearly with edge temperature, suggesting the importance of critical gradient/marginal stability behaviour. Comparisons with the IFS-PPPL model have begun, showing quantitative agreement in some cases. Impurity particle transport was studied via the laser blow-off technique with impurity confinement found to be effectively infinite for ELM-free discharges but reduced into the range 0.1–0.2 s for the EDA plasmas. 1

Dorland, W.

Granetz, R.

Greenwald, M.

Hubbard, A.

Rice, J.

Schachter, J.

Snipes, J.A.

Stek, P.

Wolfe, S.

DSpace@MIT

 1  Transport Phenomena in Alcator C-Mod H-ModesM. Greenwald, J. Schachter, W. Dorland*, R. Granetz, A. Hubbard, J. Rice,J. A. Snipes, P. Stek, S. WolfeMIT - Plasma Science and Fusion Center, Cambridge, MA 02139, USA*U. Texas at Austin, Institute for Fusion Studies,  Austin, TX 78712, USAAbstractSeveral interesting new results have come from studies of ICRF heated, H-mode plasmasin Alcator C-Mod. Dimensionless scaling studies have found gyro-Bohm like transportsimilar to that reported on other devices however, dependence on collisionality was sur-prisingly strong, with BτE ~ ν*-1. Despite high edge temperatures and strong edge pres-sure gradients, type I ELM’s are not observed in C-Mod. Instead we obtain a regime thatwe have dubbed Enhanced Dα (EDA) which is accompanied by high frequency densityfluctuations. For all H-modes, core gradients were found to increase linearly with edgetemperature, suggesting the importance of critical gradient/marginal stability behavior. Comparisons with the IFS-PPPL model have begun, showing quantitative agreement insome cases. Impurity particle transport was studied via the laser blow-off technique withimpurity confinement found to be effectively infinite for ELMfree discharges but re-duced into the range 01.-0.2 seconds for the EDA plasmas.  Finally, strong toroidal rota-tion was observed, ~ 105 m/sec, despite the lack of a significant external torque. 2  1. IntroductionPrevious work [1,2] reported on heating and confinement experiments on C-Mod H-modes. The C-Mod device is somewhat unique in several respects. First, as a compacthigh-field device, it typically runs at high densities where Ti~Te and where fast-ion con-tent is minimal. Secondly, its only auxiliary heating scheme is ICRH, while most ma-chines report results with NBI.  Finally, all plasma facing components are made of therefractory metal molybdenum overcoated with boron. Energy confinement in H-mode istypically about 2 times that of L-mode and somewhat greater than that predicted by scal-ing laws derived using data from other devices [1].  Experiments described here werecarried out with BT from 2.6 - 8 T, IP from 0.4 - 1.2 MA, ne from 2 - 4 x 1020/m3, κfrom 1.5 - 1.8, and  input power from 1.7 to 3.5 MW.2. Dimensionless ScalingThe difficulties encountered with traditional empirical scaling methods have encouragedseveral groups to begin systematic investigations into the dimensionless scaling ofplasma transport [3,4]. This approach offers the possibility of straightforward extrapola-tion to reactor regimes and at least a tenuous connection with the underlying physics [5].On C-Mod, experiments were carried out to determine the scaling of the normalized con-finement time, BτE, and normalized thermal diffusivity, χ/χBohm, with ρ* and ν* [6]. With a fixed ICRH frequency of 80 MHz, these experiments compared deuterium dis-charges heated via first harmonic hydrogen minority at 5.3 T to those heated at secondharmonic hydrogen minority at 2.6 T. In the first set of experiments, heating power,plasma current and density were adjusted to match the profiles for q, β, and ν* whilevarying ρ* by a factor of about 1.6. Further experiments matched β and ρ* while varyingν* by almost an order of magnitudeThe results of the ρ* scans can be seen in figure 1. Global scaling was observed to be 3  gyroBohm like; that is, BτE was found to be proportional to ρ*-3.1 where Bohm scalingwould imply BτE ~ ρ*-2. The error in the ρ* coefficient was estimated conservatively tobe +/- 0.6. Figure 1b shows the results of local analysis of a pair of shots from the samedata set. In this case, the ratio of normalized thermal diffusivity between a high field dis-charge and a low field discharge are plotted. Again, the results are consistent with gyro-Bohm scaling across most of the profile. Errors in this measurement are large and sepa-ration of the ion and electron channels is probably not statistically significant. These re-sults are similar to those reported in references 3 and 4. Surprisingly, even with all threeexperiments, C-Mod, DIII-D, and JET, showing gyro-Bohm scaling; scaling betweenthese machines gives a result closer to Bohm [1]. The results of the collisionality scans,shown in figure 2, showed a surprisingly strong dependence. Both global and localanalysis gave approximately a linear dependence on ν*.5 6 7 8 9 10ρ∗ x 10000.010.101.00Bτ E (T s)BτE ~ ρ∗-3.1 ± 0.62.5 T5.3 T0.2 0.3 0.4 0.5 0.6 0.7 0.8Normalized Radius0.00.51.01.5(χeff/χB) HI / (χ eff/χB) LOgyroBohmBohmGoldstonFigure 1. Results of normalized gyro-radius, ρ* scans with q95, β (normalized plasmapressure) and ν* (normalized collisionality) fixed (a) Global scaling, showing the nor-malized energy confinement btau vs gyro-radius, ρ*, (b) Local scaling showing the ratiosof normalized diffusivity, χ/χBohm between high field (low ρ*) and low field (high ρ*)plasmas.  Expectations of different types of scaling are shown by the dotted curves [5].Both local and global analysis show approximately gyro-Bohm like scaling. 4  3. ELM’s/EDAWe have observed a promising regime which evolves out of ELMfree discharges and ischaracterized by high levels of Dα light, good energy  confinement and moderate parti-cle confinement. [1,2] Because of uncertainty over the relationship of this mode to ELMbehavior, we use the term Enhanced Dα (EDA) to describe it. Edge temperature pedes-tals typically are slightly smaller than in ELMfree discharges resulting in slightly re-duced energy confinement. No type I ELMs have been observed so far on C-Mod thoughthe edge temperature can be high, 600-800 eV, and the pressure gradient in the transportbarrier would seem to challenge stability limits. Values of the edge β can reach 0.5% andrecent data suggest that the pressure gradient length can be as short as 3-4 mm. The EDAis characterized by increased density fluctuations in the barrier region [7,8]. These arebroadband, extending to at least 400 kHz with a quasi-coherent feature which can appearanywhere from 60 - 130 kHz.Figure 2. Results of ν* scans with q95, β, and ρ* fixed (a) Global scaling, showing btauvs ν* (b) Local scaling, showing the local exponent, γ, defined by χ ~ χBohmν*γ.  Ap-proximately linear dependence is seen in both cases.0.1 1.0ν∗e0.010.101.00BτE (T s)BτE ~ ν∗e-1.0 ± 0.22.5 T5.1 T0.2 0.3 0.4 0.5 0.6 0.7 0.8Normalized Radius0.00.51.01.5γ (r)γ for χeffγ for χeγ for χi 5  4. Critical Gradient/Marginal Stability BehaviorEdge temperature and core confinement are tightly correlated[1] for L and H-modes inC-Mod over a wide variety of regimes including ELMfree, and ELMy/EDA H-modes,ordinary L-modes, and "enhanced" L-modes which are achieved by strong heating of re-versed field plasmas. This result is summarized in figure 3 where the core electron tem-perature gradient is plotted against the pedestal temperature, demonstrating that the im-proved confinement is not merely the result of adding a temperature and density pedestalto an L-mode discharge. Here, the  core gradient is defined as an average over the regionoutside the sawteeth and inside the edge transport barrier. This behavior is qualitativelyconsistent with critical gradient transport models (for example, ITG turbulence). Figure 3. The average core Te gradient is plotted vs edge temperature (measured at the95% flux surface).  The core gradient is defined as the average gradient between theouter edge of the sawtoothing region and the top of the H-mode pedestal. 6  Figure 4 shows the result of a simulation from one such theory, the IFS-PPPL model [9]plotted against experimental data. The model gives fairly good agreement for ion tem-peratures in C-Mod H-modes (though it consistently underpredicts Ti in L-mode) [6].The electron temperature is often overpredicted as shown in the figure. There are a num-ber of possible reasons for this. First, Dorland’s nt code, which is used for the simula-tions, does not have a sawtooth model and sawteeth are very strong in C-Mod dis-charges. The result of adding an ad-hoc sawtooth mixing model to the simulation sub-stantially reduces the discrepancy as shown in the figure. Second, the model onlyincludes effects on the electrons from the ITG mode and additional sources for electronmay be present. Finally, it is worth noting that the C-Mod collisionality falls outside therange of validity assumed in reference 9. Figure 4. Comparison between experimental data and predictions of the IFS/PPPLmodel.  Predictions both with and without an ad-hoc sawtooth model are shown.  Agree-ment is fairly good for H-modes in C-Mod.0.00 0.05 0.10 0.15 0.20r (m)02468keVTe measuredTi measuredTi, No sawteethTi With sawteethTe No sawteethTe With sawteeth 7  5. Impurity transportImpurity particle confinement, τI, in ELMy/EDA plasmas is in the range 0.15-0.2 sec-onds, roughly 2-3 x τE, unlike ELMfree plasmas where τI > 0.5 seconds. Analysis ofimpurity profile evolution following injection of trace amounts of scandium by the laserblow-off technique can yield estimates of the transport coefficients. Compared to L-mode plasmas, in H-mode these are characterized by lower diffusivity in the core, and atransport barrier with very low diffusivity and a strong inward pinch in the plasma edge.Barrier diffusivity is higher and the pinch weaker for ELMy/EDA discharges than forELMfree.  This difference may be the result of additional turbulence which is observedas density fluctuations seen during EDA as described above.6. Plasma RotationAnother interesting new result on C-Mod is the observation of strong central toroidal ro-tation in H-mode discharges with only ICRF heating [10]. For the majority ions, veloci-ties up to 1.5 x 105 m/sec and Mach numbers on the order of 0.3 were measured andwere correlated with good core confinement and high stored energy rather than with highinput power alone, rotation being much stronger in H-mode than in L-mode or ohmicplasmas. While full rotation profiles are not yet available, strong shear is seen in the cen-tral rotation and Er’ may be large enough to affect transport. Though the origin of rota-tion of this magnitude in the absence of appreciable external torques is unclear, earlyspeculation has centered on turbulent Reynold’s stress.AcknowledgementsThe authors wish to thank the rest of the Alcator team, the technical staff, engineers, stu-dents, and scientists. This work was supported by DOE contract No. DE-AC02-78ET51013. 8  References[1] M. Greenwald, et al., 1997, Nucl. Fus., 37, 793.[2] Y. Takase, et al., 1997, (Proceedings of 16th Int. Conf., Montreal 1996), Vol 1,IAEA, Vienna (1997) 475.[3] C.C. Petty, et al., 1995, Phys. Rev. Lett., 74, 1763.[4] J. G Cordey, and JET team, 1997, Fusion Energy 1996 (Proc. 16th Int. Conf. Mont-real, 1996), Vol. 1, IAEA, Vienna (1997) 603[5] R.E. Waltz, J.C. DeBoo, M.N. Rosenbluth, 1990, Phys. Rev Lett., 65, 2390.[6] J. Schachter, 1997, "Local Transport Analysis for the Alcator C-Mod Tokamak",PhD thesis, PSFC/RR-97-12.[7] P. Stek, 1997, "Reflectometry Measurements on Alcator C-Mod" PhD thesis,PSFC/RR-97-5.[8]  J.  Snipes, et al., 1997, "ELMs and Fast Edge Fluctutaions in Alcator C-Mod", thisconference[9] M. Kotschenreuther, W. Dorland, M. A. Beer, and G.W. Hammett, 1995, Phys. Plas-mas, 2, 2381.[10] J. Rice, et al, 1997, "Observation of Central Toroidal Rotation in ICRF HeatedAlcator C-Mod Plasmas", to be published in Nuclear Fusion. 9  Figure CaptionsFigure 1. Results of normalized gyro-radius, ρ* scans with q95, β (normalized plasmapressure) and ν* (normalized collisionality) fixed (a) Global scaling, showing the nor-malized energy confinement btau vs gyro-radius, ρ*, (b) Local scaling showing the ra-tios of normalized diffusivity, χ/χBohm between high field (low ρ*) and low field (highρ*) plasmas.  Expectations of different types of scaling are shown by the dotted curves[5]. Both local and global analysis show approximately gyro-Bohm like scaling.Figure 2. Results of ν* scans with q95, β, and ρ* fixed (a) Global scaling, showing btauvs ν* (b) Local scaling, showing the local exponent, γ, defined by χ ~ χBohmν*γ.  Ap-proximately linear dependence is seen in both cases.Figure 3. The average core Te gradient is plotted vs edge temperature (measured at the95% flux surface).  The core gradient is defined as the average gradient between theouter edge of the sawtoothing region and the top of the H-mode pedestal.Figure 4. Comparison between experimental data and predictions of the IFS/PPPLmodel.  Predictions both with and without an ad-hoc sawtooth model are shown.  Agree-ment is fairly good for H-modes in C-Mod.

Transport Phenomena in Alcator C-Mod H-Modes

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