October 2014

Plasma Science and Fusion Center Massachusetts Institute of Technology

Cambridge MA 02139 USA This work was supported by the U.S. Department of Energy, Grant No. DE-FC02-99ER54512-CMOD. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

PSFC/JA-14-56

Study of Profile Shape Variations with Confinement Regimes in Alcator C-Mod Discharges

C. Sung, O. Sauter*, A. White, C. Gao, M. Greenwald, N.

Howard**, A. Hubbard, J. Hughes, M. Reinke, J. Rice and J. Walk

*EPFL-CRPP, Lausanne, Switzerland **ORISE Postdoctoral Fellowship

Study of profile shape variations with confinement regimes in

Alcator C-Mod discharges

C. Sung, O. Sauter, A. White, C. Gao, M. Greenwald, N. Howard,A. Hubbard, J. Hughes, M. Reinke, J. Rice and J. Walk

Abstract

The changes of self-similarity properties in ne and Te profiles with different confine-ment regimes in C-Mod discharges are investigated by applying the methodology usedin L-mode discharges in TCV [Sauter PoP 2014]. First, we probe the changes in theshape of ne and Te profiles across the ohmic confinement transition. Our observationsshow that the shapes of ne and Te profiles are almost constant in ρinv < ρ . 0.8, whereρinv is the sawtooth inversion radius, regardless of different ohmic confinement regimes.The radial variable is the square root of the normalized volume, ρ = (V/V (a))0.5. It isalso observed that the increase of the gradient in the edge ne profile (ρ & 0.8) and thene value at ρ ∼ 1.0 correlate with the linear increase of energy confinement with theaverage electron density in the linear ohmic confinement regime, consistent with thefindings in TCV. Similar analyses were performed on the discharges in the improvedconfinement regimes (H-mode and I-mode [Whyte NF 2010]) to explore the changesin the profile self-similarity with the improvement of energy/particle confinement. Itis found that improvements in energy and particle confinements correlate with the in-crease of the gradient in the edge Te and ne profiles (ρ & 0.95), respectively. In thecore region (ρ . 0.8), the gradient scale length of the Te profile does not change in theimproved energy confinement regimes, H-mode and I-mode. However, the self-similarregion, which can be fit by an exponential function and is usually defined as ρ . 0.8in L-mode, is extended to the top of the pedestal (ρ ∼ 0.95) in I/H-modes.

1 Introduction

Understanding transport phenomena and improved confinement of energy in fusion plasmasare important for the development of fusion energy. The shape and height of density andtemperature profiles indicate the quality of confinement and transport in the plasmas. Wetherefore need to investigate the change of the shape and height of profiles, if any, withdifferent discharge conditions. In this context, the so-called “stiffness” property has beenstudied, along with the related critical gradient model([1, 2] and references therein).

A recent study in TCV showed two interesting features in profile changes with differentdischarge conditions such as external heating power, plasma current, plasma shaping (tri-angularity) and average electron density in L-mode discharges[3]: the correlation between

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the change profiles in the edge region(ρ & 0.8, where ρ is the square root of normalizedplasma volume) and confinement improvement (or L-mode pedestal) and maintaining asimilar shape of core ne and Te profiles (ρinv < ρ . 0.8, where ρinv is the sawtooth inver-sion radius)[3]. The core Te profiles in TCV were represented by an exponential function,and the power of exponential function for core Te profiles keeps similar in spite of the changein the discharge conditions, maintaining a similar shape of the profiles. The same tendencywas also observed in the core ne profiles in the same study. Previous studies in C-Mod andother tokamaks also showed the similar shape of core Te profiles[4, 5, 6] and the importanceof the edge region in improvements of confinement in H-mode discharges[5, 6, 7, 8]. Studyin TCV[3] quantified the similar shape of core profiles by applying an exponential fit. Thisstudy also extends the importance of edge region to L-mode discharges, and the shape ofedge profiles is quantified by a linear fit. It is interesting to investigate whether the findingsin TCV, profile self-similarity quantified by an exponential fit and the importance of theedge region (ρ > 0.8) in L-mode discharges, are universal or not by analyzing profiles intokamaks other than TCV.

In this study, we will apply the same analysis method used in TCV [3] to the ne andTe profiles in the Alcator C-Mod tokamak[9]. That is, we will first apply the exponentialfit to the core ne and Te profiles, and apply the linear fit to the edge ne and Te profilesin C-Mod ohmic discharges in different ohmic confinement regions. Then, the change offitting parameters for the core and edge profiles across the ohmic confinement transitionwill be studied to see if the results in C-Mod are consistent with the findings in TCVor not. We will also extend these analyses to the high energy confinement regimes, i.e.,H-mode and I-mode. While both particle and energy confinement is improved in H-mode,only energy confinement is improved in I-mode. In other words, I-mode has H-mode likeTe profiles and L-mode like ne profiles[10, 11]. Comparing the fitting parameters for neand Te profiles with the changes of confinement regime (L/I/H-modes) will be not onlyinteresting for understanding I-mode and H-mode, but is also helpful to understand bothenergy and particle transport generally.

Last, we need to clarify the terms we use in this study. As pointed out in [1], thedefinition of “stiffness” is ambiguous. It sometimes refers to the resistance of the changein profile shape to external heating[1, 2, 3], while the degree of stiffness (or even stiffnessitself) is defined as the ratio of diffusivity (or heat flux) to the difference between thetemperature gradient scale length and its critical gradient scale length[1, 12, 13] or thechange of diffusivity of heat pulses compared to the value from power balance in powermodulation experiments[14, 15]. In other words, stiffness refers to the global change insome cases, while it refers to the local change in the other cases. Following critical gra-dient arguments, if the gradients of a profile are near the critical gradient value in theregion where a profile keeps its shape, then the profile in this region will be stiff and keepthe gradient scale length with the change of input heating power. In this case, stiffnessused for the local change will be connected to the global change. However, the similarshape of profiles with different discharge conditions is not a necessary condition for this

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assumption, but a sufficient condition. It is also noteworthy that the property of keepingthe shape of profiles with the change of experimental conditions is also called in severaldifferent terms such as self-similarity[5, 6], profile consistency[16], profile resilience[4, 17]and profile stiffness[1, 3, 2]. In order to prevent any confusion from using different terms,“self-similarity” will be used to refer to “the similar shape of core profiles with differentdischarge conditions” in this study and using the term “stiffness” will be avoided.

2 Profile analysis in C-Mod discharges

In order to analyze the self-similarity and the change of profile shapes in the edge in AlcatorC-Mod, the Thomson scattering diagnostic[18] (for ne and Te) and the ECE diagnostic[19](for Te) were used. In the same way as described in [3], a flat profile shape was used to fitinside the sawtooth inversion radius(ρ < ρinv), and exponential and linear fits were appliedin the core (ρinv < ρ ≤ ρped) and edge regions (ρ ≥ ρped), respectively. ρped is the outerboundary of the core region, where the exponential fit is valid. That is, the Te profile onoutboard side was fitted with the following three equations.

Te(ρ) = Te,o for ρ < ρinv

Te(ρ) = Te,oe−λTe (ρ−ρinv) for ρinv < ρ ≤ ρped,Te

Te(ρ) = Te,edge + µTe(1− ρ)for ρ ≥ ρped,Te

(1)

Here, Te,o is the averaged Te value in ρ < ρinv, and λTe is an exponential fittingparameter. This parameter is approximately a normalized gradient scale length, a/LTe inthe core region, where a/LX = a

X |dXdr |, and a is the minor radius. That is, λTe = 1

TedTedρ =

a/LTe | 1adrdρ |. It may be possible to resolve the variation of the gradient scale length in

the core region using another fitting method such as bspline fitting. Nevertheless, if anexponential fit works well within the uncertainty of the data, the variation of λTe in thefitting region will be small enough to consider λTe as a good parameter which can representa characteristic of the profile in the fitting region, which is the average gradient scale length.The fitting parameter in the edge region, µTe , is the slope of the linear fit, and Te,edge isthe Te value at ρ=1.0, determined by the linear fit. µTe and Te,edge have the same units asTe. In this analysis, we define the pedestal position of the Te profile, ρped,Te as the radiallocation which has a minimum value in difference between two fitting lines (exponentialfunction and linear function) at ρ > ρinv. The same equations and definitions are used forthe ne profile.

In order to mitigate a scatter in the data, we used the data within one standard devia-tion from time averaging in each confinement regime when the time length of the confine-ment regime is longer than 0.1sec. When the time length of the confinement regime is lessthan 0.1sec, all raw data were included in the analysis since there were less than 5 datapoints at each radial location, which is not enough to use any statistical techniques, whenthe time length is shorter than 0.1sec. Equilibrium reconstruction (EFIT)[20] constrained

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by magnetic diagnostics[21] was used to map the measurement locations of Thomson scat-tering and ECE diagnostics to the normalized axis, the square root of normalized plasmavolume, in this study. Although we use a square root of normalized plasma volume as thehorizontal axis to compare results between C-Mod and TCV, it is noteworthy that theanalysis results are not different when a square root of normalized toroidal flux is used asthe horizontal axis.

2.1 Change of profile shape with density scans in ohmic discharges

In ohmic plasmas, the energy confinement time increases linearly with averaged electrondensity in lower density plasmas, and then saturates when the plasma density is higher thana critical value[22, 23, 24, 25, 26, 27, 28, 29, 30]. The regime where energy confinement timeincreases linearly with the density is called the Linear Ohmic Confinement (LOC) regime,and the regime with the saturated confinement time with density is called the SaturatedOhmic Confinement (SOC) regime. This ohmic confinement transition (LOC/SOC transi-tion) is an unsolved problem in the transport research. In the Alcator C-Mod tokamak, weobserved several interesting phenomena across the LOC/SOC transition, such as toroidalrotation reversal, poloidal asymmetry of impurity density, non-local heat transport andlocal turbulence changes near the edge(ρtor ∼ 0.8, ρtor: square root of normalized toroidalflux)[31, 32, 33, 34, 35]. Negligible changes of a/Lne , a/LTe and a/LTi profiles across theLOC/SOC transition were observed in the core region (ρtor <0.7-0.8) in Alcator C-Mod[34]and TCV[3]. In this section, we will check that these observations are consistent with theprofile analysis results in [3].

We first analyze two ohmic discharges (shot : 1120620027, 112062028) which havesimilar discharge conditions, such as ohmic power (∼1.5MW), plasma current (∼1.1MA)and equilibrium parameters (Lower Single Null (LSN) configuration, elongation, κ,∼ 1.6,upper triangularity, δu,∼0.3 and lower triangularity, δl,∼0.5) except for the average elec-tron density as shown in the “1st set” column of Table 1. The average electron density,ne,avg was varied more than 40% between two ohmic discharges (from 0.9×1020m−3 to1.7×1020m−3) by intentionally changing the edge gas puff fueling. Toroidal magnetic fieldon axis is slightly different between these two discharges (Bt(0)=5.4 and 5.6T), but thislevel of difference (< 5%) is ignorable in the comparison. We determined the confinementregime of each discharge from the direction of core toroidal rotation, which is the mostsensitive indicator of ohmic confinement regime in C-Mod[31].

Figure 1 shows plasma parameters of these two discharges with time. One can see thatthe two discharges have the same plasma current and ohmic input power (∼1.5MW). It canalso be seen that the increase of average electron density between two discharges correlateswith the rotation reversal in the discharge with the higher density. According to the toroidalrotation direction, the lower density discharge (shot 1120620027) is in the LOC regime, andthe higher density discharge (shot 1120620028) is in the SOC regime. In addition, thesetwo discharges have similar discharge condition with the discharges in Fig. 13 in [35], and

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the energy confinement time in Fig. 13 in [35] was saturated near ne,avg ∼ 1.1×1020m−3.This result also support the lower density discharge in this study (ne,avg ∼0.9×1020m−3)is in the LOC regime, and the higher density discharge (ne,avg ∼1.7×1020m−3) is in theSOC regime. The data in the shaded area in Fig. 1, which indicates the stationary periodin these discharges, were used in the profile analysis.

As shown in Fig. 2(a), the exponential function in Eq. 1 matches well Te data in thecore region (ρ ≤ ρped,Te) for the two ohmic discharges. Self-similarity of core Te profilescan be also seen in Fig. 2(b) and (c). Te data and the fitting lines are normalized by theTe value at 0.8 calculated from the fitting line, Te(0.8), in Fig. 2(b). We can see that thenormalized data in these two discharges are well overlapped in the ρ . 0.8 region, whichindicates that Te(0.8) value may determine the Te profile for ρ ≤ ρped,Te . Figure 2(b) alsoshows that the normalized fitting lines by Te(0.8) are close to each other, implying thatthe exponential fitting parameter, λTe , values are similar, and Te profiles are self-similarin the core region. In Fig. 2(c), the same λTe value, which is the mean value between thetwo discharges, is applied to these discharges. As shown in Fig. 2(c), the fit with single λTevalue (=3.34) works well for both discharges. Figure 2(a)-(c) indicate that Te profiles insideρ ≤ ρped,Te are self-similar and this property can be quantified by the exponential function.Figure 2(d) shows the edge temperature profiles (ρ ≥ ρped,Te) of the two ohmic dischargeswith the lines fit by the linear function in Eq. 1. Although there is a scatter in the edge Tedata, we can see that the edge data are not well fitted by the exponential function used forthe core Te data, and a linear fit is more appropriate in the edge region. It is also shownthat the slope of linear fit, µTe , decreases with the increase of the average density. Thevariations of ne profiles between the two ohmic discharges were also investigated as shownin Fig. 3. Like the core Te profiles, exponential fitting works well for core ne data. We canalso see the self-similarity of core ne profiles from the fact that a single λne value (=0.87)can be used to fit ne data in the core region for both ohmic discharges, and the normalizeddata by ne(0.8) are well overlapped. Figure 3(d) shows that linear fitting works betterthan exponential fitting for the edge ne profiles(ρ ≥ ρped,ne) and both the slope of fittingline, µne , and the ne value at ρ = 1.0 in the linear fit, ne,edge, increase with the averageelectron density.

The “1st set” column of Table 2 shows the change of profile shape with the averagedensity more clearly. Both ne and Te profiles between LOC/SOC discharges have the similarexponential fitting parameters (λTe and λne) within 20% in the core region regardless ofthe change of average electron density, which indicates that both ne and Te profiles are self-similar. It is also worth noting that these fitting parameters can be considered as averagegradient scale lengths, which are important for driving turbulence. These parameters donot change with electron density, while the ohmic confinement regime changes with thedensity. However, we did observe changes of fitting parameters for the edge ne profiles(µne and ne,edge). µne increases about more than three times with the average density, andne,edge also increases by two times. We also note that ρped,ne increases from 0.82 to 0.93in the SOC discharge. The increase of both µne and ne,edge makes ne(0.8) higher. With

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the increase of the average electron density, the Te(0.8) value decreases. However, µTe andTe,edge decrease by about 40%, decreasing Te(0.8) by a relatively smaller values as comparedto the increase of ne(0.8) between the two discharges. A relatively larger increase of ne(0.8)results in a larger electron pressure at ρ=0.8, pe(0.8), in the higher density discharge, whichindicates higher plasma energy or pressure in the core region, where the profiles exhibitself-similarity. It follows that the changes in the edge ne profile, which are the increasesof gradient and edge values, are responsible for the increase of energy confinement in C-Mod ohmic discharges with average electron density. These results are consistent with thefindings in TCV[3] and the observations from C-Mod[34, 35].

We also analyze ne and Te profiles in ohmic discharges in which the reduction of relativelevel, Te/Te, of long wavelength (kθρs < 0.3) electron temperature fluctuations near theedge was observed across ohmic confinement transition (LOC/SOC transition)[34]. Asshown in Fig. 4 and the “2nd set” column of Table 1, these three ohmic discharges also havethe same toroidal magnetic field (Bt(0)∼5.4T), plasma current (∼0.9MA), ohmic power(∼1.0MW) and equilibrium parameters (LSN, κ ∼ 1.6, δu ∼0.3 and δl ∼0.5). According tothe direction of core toroidal rotation, the discharge with the lowest density in Fig. 4, whichhas co-current toroidal rotation, is in the LOC regime, and the highest density dischargehere is in the SOC regime, since the plasma rotated toroidally in counter-current direction.The discharge which has rotation reversal will be near the boundary between LOC/SOC.The authors refer to this discharge as “intermediate” in this study. Data in the stationarytime period, which is shown as shaded area in Fig. 4, were used in the analysis.

We can see the self-similarity property in the core region for both Te and ne profilesin these discharges as observed in the first set of ohmic discharges. Figure 5(a) and (c)show that core Te data are fitted well by an exponential function, and a single λTe(=3.34)can be used for all three discharges. It is also shown that Te data normalized by Te(0.8)overlap each other in Fig. 5(b). Figure 5(d)-(f) show that core ne data have the sameself-similar property as the core Te data have. We can also notice that the exponentialfitting parameter in the core region varies within 20% with the average density or acrossthe LOC/SOC transition from the “2nd set” column of Table 2. Figure 6 shows the edgeTe and ne profiles for these three discharges. µTe decreases by about 30% with almost thesame Te,edge values, while µne and ne,edge increase by about 90% and 50%, respectively, inthe intermediate and SOC discharges compared to the LOC discharge. These observationsare consistent with the first set of ohmic discharges. It is shown that the ne(0.8) valueincreases by about 40%, while the Te(0.8) value decreases by about 20% from the LOCto the intermediate discharge, increasing the pe(0.8) value in the intermediate discharge.Considering self-similar core ne profiles, the 40% increase of ne(0.8) may come from theincrease µne and ne,edge. Between the intermediate and the SOC discharge, edge fittingparameters in both ne and Te profiles varies within 10%, and ne(0.8) increases by about15%, and Te(0.8) decreases by also about 15%, which makes pe(0.8) comparable within5%. Considering the same input power and self-similar core ne and Te profiles, it indicatesthe saturation of ohmic confinement time, expected in the SOC regime. We also note that

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there is a correlation between the improvement of ohmic confinement and the increase ofµne and ne,edge in other ohmic discharges, not shown in this paper.

Since the change of the direction of core toroidal rotation was used as an indicatorof ohmic confinement regime in this study, it is of interest to compare Te and ne profilesat three different phases of toroidal rotation (before/during/after core rotation reversalfrom co- to counter-current direction). Figure 7 shows the rotation profile measured by thehigh resolution x-ray spectroscopy[36, 37] in the “intermediate” discharge (rotation reversaldischarge) in the second set of ohmic discharges. It is known that the change of rotationreversal occurs in the region where safety factor, q, is less than 3/2[31]. For this reversaldischarge, q=3/2 at ρ ∼0.6, and the change in the rotation profile occurs ρ < 0.6 regionas shown in Fig. 7. However, Figure 8(a) and (b) show that ne and Te profiles in the coreregion (ρ . 0.8) barely change and are almost the same before/during/after the rotationreversal, while the core toroidal rotation changes from ∼25km/s to ∼-10km/s. Table 3also shows that the λTe and λne values are similar within 10% across the rotation reversal.Although the evident changes are not observed in the edge region as shown in Fig. 8(c)and (d), table 3 shows that Te,edge values decrease more than 40% and µne increases byabout two times in the reversal and counter-current direction phase (during/after rotationreversal) compared to the co-current direction phase (before rotation reversal), while µTeand ne,edge values keep similar level within 20% across the rotation reversal. Consideringthe scattered edge data, it is hard to conclude whether the changes in the edge fittingparameters shown in table 1 are meaningful or not. For example, we can obtain anotherpossible fitting line for the edge ne profile in the co-current phase (before reversal) by fixingthe ne,edge value, which was a free parameter for the linear fit before, in co-current phase tothe level in reversal phase, 0.53×1020m−3. The change of ne,edge is less than 20%, withinthe uncertainty, but this change results in the increase of µne about two times, from 0.94to 1.72. Although the consistent tendency, i.e., the increase of µne and the decrease ofTe,edge with similar levels of other fitting parameters (µTe , ne,edge, λTe and λne) were foundin another rotation reversal discharge, which is not shown here, the authors note that astudy using other rotation reversal discharges with smaller uncertainties in the edge datais required to draw a solid conclusion in the future.

It was found that sawtooth activity is related to the rotation reversal[38] and acrossthe ohmic confinement transition in [3] in TCV. Thus, it is of interest to observe the saw-tooth activity across the ohmic confinement transition and rotation reversal in C-Mod.Figure 9 shows Te near the magnetic axis measured by the ECE diagnostic. We can seethat the sawtooth period is longer and irregular with the increase of density, similar tothe observation in TCV. In order to see whether the sawtooth activity changes rapidlywith the rotation reversal or not, we observed the changes in sawtooth activity with thedifferent rotation phases (co-current/reversal/counter-current). As shown in Fig. 10, saw-tooth activity barely changes with the different rotation phases. This may indicate thatsawtooth activity does not change abruptly as the core rotation direction changes in thereversal discharge. This result is also consistent with the study in TCV as shown in Fig.

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1st set 2nd setLOC SOC LOC Intermediate SOC

magnetic configuration LSN LSN LSN LSN LSN

Bt(0) [T] 5.6 5.4 5.4 5.4 5.4

Ip [MA] 1.1 1.1 0.9 0.9 0.9

ne,avg [1020m−3] 0.9 1.7 0.8 1.1 1.3

κ 1.6 1.6 1.6 1.6 1.6

δu 0.3 0.3 0.3 0.3 0.3

δl 0.5 0.5 0.5 0.5 0.5

Table 1: Discharge conditions of the two sets of ohmic discharges (1st set : LOC andSOC, 2nd set : LOC, Intermediate and SOC). Discharge conditions shown in this table aremagnetic configuration (whether Lower Single Null (LSN) or Upper Single Null (USN) ordouble null configuration), magnetic field on the axis, Bt(0) in Tesla, plasma current, Ip,in MA, average electron density, ne,avg, in 1020m−3, elongation, κ, upper triangularity, δu,and lower triangularity, δl. All shaping parameters (κ,δu and δl) are the values estimatedat the separatrix.

10 in [38]. The relation between the changes in the core region, such as rotation reversalsand sawtooth activities, and the changes of ne and Te profiles in the edge region should beexplored in the future. We only note their correlation in this section.

Since most observations in C-Mod ohmic discharges are consistent with the results inTCV, it will be interesting to compare the fitting parameters in C-Mod with the parametersin TCV. The parameters in the edge region change with the discharge conditions such asplasma current, total power or average electron density, as shown in Fig. 24, 25 and 26(a)in [3]. In contrast, Fig. 26(b) in [3] shows that the exponential fitting parameters (λTe andλne) in the core region do not vary with the discharge conditions. Thus, λTe and λne willbe appropriate for the comparison between two machines, which have different dischargeconditions. Table 2 shows that λTe ∼3.0-3.4 and λne ∼0.7-1.0 in two sets of C-Mod ohmicdischarges used in this study. From the appendix in [3], λTe for discharges used in [3] is∼3.0-3.5, and the values of λne are ∼2.0-2.5. It is noteworthy that the values of λTe aresimilar between C-Mod and TCV, while λne values in TCV are about two times higherthan C-Mod, indicating that the shape of the core ne profile is more sensitive to dischargeconditions than the shape of core Te profile.

2.2 Changes of profile self-similarity with the confinement phase in RF-heated discharges

In the previous section, we analyzed ne and Te profiles in C-Mod ohmic discharges. Inthis section, we will explore the change of profile self-similarity with different confinementphases: L/I/H-modes. In one discharge (shot 1120824006), three different confinementphases were obtained. Table 4 shows the discharge conditions. This discharge was run in

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1st set 2nd set

Parameters LOC SOC LOC Intermediate SOC

core Te λTe 3.44 3.24 3.33 3.29 3.39(ρ ≤ ρped,Te) Te(0.8) [keV] 0.70 0.47 0.59 0.47 0.41

edge Te µTe [keV] 3.02 1.88 2.61 1.95 1.77(ρ ≥ ρped,Te) Te,edge [keV] 0.08 0.05 0.03 0.03 0.03

ρped,Te 0.71 0.73 0.71 0.73 0.73

core ne λne 0.77 0.90 0.76 0.93 0.92(ρ ≤ ρped,ne) ne(0.8) [1020m−3] 0.70 1.27 0.60 0.85 0.95

edge ne µne [1020m−3] 2.41 8.51 1.27 2.48 2.59(ρ ≥ ρped,ne) ne,edge [1020m−3] 0.26 0.52 0.41 0.56 0.61

ρped,ne 0.82 0.93 0.87 0.92 0.90

Pe(0.8) [kPa] 7.84 9.55 5.66 6.39 6.23

Table 2: Parameters calculated from fitting with different ohmic confinement regimes inthe two sets of ohmic discharges (1st set : LOC and SOC, 2nd set : LOC, Intermediateand SOC). λTe is an exponential fitting parameter for the core Te profile, and µTe is theslope of the linear fitting line applied to the edge Te profile. Te,edge indicates the Te valueat ρ = 1.0 from the linear fitting line applied to the edge Te profile. ρped,Te is the radiallocation which has the minimum difference between the exponential and linear fitting line.The same definitions are applied to λne , µne , ne,edge and ρped,ne for ne profiles.

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Parameters Co-current Reversal Counter-current

core Te λTe 3.04 3.23 3.22(ρ ≤ ρped,Te) Te(0.8) [keV] 0.53 0.48 0.48

edge Te µTe [keV] 2.10 2.15 1.94(ρ ≥ ρped,Te) Te,edge [keV] 0.09 0.02 0.05

ρped,Te 0.71 0.72 0.73

core ne λne 0.94 0.95 0.92(ρ ≤ ρped,ne) ne(0.8) [1020m−3] 0.78 0.82 0.84

edge ne µne [1020m−3] 0.94 (1.72) 2.01 2.11(ρ ≥ ρped,ne) ne,edge [1020m−3] 0.62 (0.53) 0.53 0.57

ρped,ne 0.92 0.88 0.91

Pe(0.8) [kPa] 6.61 6.30 6.45

Table 3: Parameters calculated from fitting with different rotation phases in the ”inter-mediate” discharge in the second set of ohmic discharges. λTe is an exponential fittingparameter for the core Te profile, and µTe is the slope of the linear fitting line appliedto the edge Te profile. Te,edge indicates the Te value at ρ = 1.0 from the linear fittingline applied to the edge Te profile. ρped,Te is the radial location which has the minimumdifference between the exponential and linear fitting line. The same definitions are appliedto λne , µne , ne,edge and ρped,ne for ne profiles. The values in the parenthesis in the µne andne,edge rows in the co-current column are the values obtained when the ne,edge value is fixedto 0.53×1020m−3.

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the Lower Single Null (LSN) configuration with Bt(0)=5.5T, Ip=1.0MA and the followingshape parameters, κ=1.6, δu=0.3, δl=0.5. These parameters were constant regardless ofconfinement regime as shown in Table 4. We can also notice the increase of the averageelectron density by about 40% in the H-mode phase compared to L- and I-modes, whilethe difference of the average electron density between L-mode and I-mode is about 5%.Figure 11(a) shows the change of fluctuations measured by the reflectometry[39] channelnear the edge (r/a∼0.99) with the different confinement phase, and Fig. 11(b)-(d) showthe changes in RF heating power [MW], electron temperature on the magnetic axis, andelectron temperature near the edge (ρ ∼ 0.9). In this discharge, the plasma accessed theI-mode phase, which can be identified by the Weakly Coherent Mode (WCM)[10], betweent∼0.6-0.8s. From t∼0.8s, the WCM disappeared and fluctuations were suppressed, whichindicates the plasma went into the Edge Localized Mode (ELM)-free H-mode phase[5] untilt∼1.0s. At t∼1.0s, the RF power was tripped, and the plasma went into L-mode phase.After RF power was recovered to the level at t=0.8s, L/I transition and back transitionoccurred repeatedly. As a result, we can see the WCM and broadband fluctuations upto 200kHz repeatedly as well. We determined the time range for the analysis in eachconfinement phase as the region which has the steady on axis Te and Te near the edge(ρ ∼ 0.9), as represented by the shaded area in Fig. 11.

Figure 12(a) shows Te profiles with the fitting lines in the whole radial region. In allthree confinement phases, Te data in the core region, at least ρ > 0.5, are well fitted byexponential functions. In Fig. 12(b), we can see that Te data normalized by Te(0.8) areoverlapped in ρ <0.8 region for L/I/H-modes, which indicates that the exponential fittingparameter, λTe , does not change significantly across the L to I/H transition. Table 5 showsthat λTe varies about 10% among L/I/H-modes. These results indicate that Te profilesin the core region are self-similar across the L to I/H transition. At the same time, wenote differences of Te data in the edge region between the low energy confinement regime(L-mode) and the high energy confinement regimes (I/H-modes). In L-mode, edge Te dataare not on the exponential fit line as we observed in the ohmic discharges, while edge Tedata in I/H-modes are well fit by the exponential fit line up to the top of the pedestalregion. Thus, in this discharge, the radial region where self-similarity is valid extends tothe top of the pedestal region in high energy confinement regimes such as I/H-modes. Inother words, the value of ρped,Te increases in I- and H-modes compared to L-mode. Table 5shows ρped,Te increases from 0.75 to 0.96 and 0.97 in I- and H-modes, respectively. FromFig. 12(c) and Table 5, we can also see that the slope of the linear fit, µTe , increases morethan five times in I/H-modes compared to L-mode, while the Te value at ρ = 1.0 from thelinear fit, Te,edge, is similar in I-mode, and even smaller in H-mode compared to L-mode,These results may suggest that the increase of µTe associated with ρped,Te correlates withthe higher energy confinement.

In contrast to the Te profiles, the shape of the core ne profiles changes in H-mode.Figure 12(d) and Table 5 show that the exponential fitting parameter of core ne profile, λne ,decreases about 50% in H-mode compared to L/I-modes, while the change of λne between

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L- and I-modes is almost the same. Figure 12(e) shows that core ne data normalizedby ne(0.8) in L-mode overlap with the normalized core ne values in I-mode, while thenormalized data in H-mode are lower than L/I modes in the core region, which confirmsthe lower λne in H-mode compared to L/I-modes. The pedestal structure is shown clearlyin the H-mode ne profiles in Fig. 12(f). Figure 12(f) also shows that linear fit works wellon the pedestal. The pedestal in H-mode ne profile results in the remarkable increase ofthe slope of the linear fit, µne and the increase of ne(0.8) by 60-80% in H-mode comparedto L/I-modes as shown in both Fig. 12(f) and table 5. If we assume that edge ne profilesets the boundary condition for the core ne profile, the decrease of ne,edge by about 30%will not contribute to the increase of core ne profile in H-mode, but the significant increaseof µne in H-mode compared to L/I-modes will be the reason of the increase of the corene profile in H-mode. The increase of µne in high particle confinement regime (H-mode)is analogous to the change in the edge Te profile in high energy confinement regime (I/H-modes) compared to L-mode. In other words, as we observed in Te profiles, the increaseof µne value correlates with the increase of core ne profile and the improvement of particleconfinement in H-mode.

We can also notice the eightfold increase in µne in I-mode compared to L-mode fromFig. 12(f) and table 5. However, the ne(0.8) value increases about 10% in I-mode comparedto L-mode and the scattered ne data in L- and I-modes overlap each other in the wholeradial region. We also note that the increase of µne is not always observed across the L/Itransition in other discharges. These observations may indicate that the changes in the edgene profile in I-mode compared to L-mode are inconclusive in this study and not remarkablecompared to the change of both shape and amplitude of the ne profile in H-mode.

The changes in ne profile in H-mode are associated with not only higher slope of thelinear fitting line in the edge region, µne , but also the lower exponential fitting parameter inthe core region, λne . Studies in the past showed the density peaking with lower collisionality[40, 41]. Using the definition of collisionality, νeff = 0.1Zeff < ne > R/ < Te >

2 , where<> indicates the volume averaged quantity, major radius, R, is in m and < ne > and< Te > are measured in 1019m−3 and keV, respectively, Zeff was set to 2.0, in [41],νeff ∼0.81 and ne(0)/ < ne >∼ 1.2 at the H-mode phase in this discharge. These valuesare qualitatively consistent with Fig. 2 in [41], which implies that the decrease of theexponential fitting parameter, λne , may also correlate with collisionality. Other previousstudies also show that the shape of ne profile can be varied with collisionality, externalheating power or the dominant turbulence mode while the gradient scale length of Teprofile is less varied relatively[42, 43, 44]. Understanding the change of core ne profileshape (or density peaking) will require more sophisticated analysis and data sorting suchas comparison data with different collisionality or dominant turbulence mode obtained fromgyrokinetic analysis as well as different particle confinement regimes, which are beyond thescope of this paper.

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L-mode I-mode H-mode

magnetic configuration LSN LSN LSN

Bt(0) [T] 5.5 5.5 5.5

Ip [MA] 1.0 1.0 1.0

ne,avg [1020m−3] 1.4 1.4 2.0

κ 1.6 1.6 1.6

δu 0.3 0.3 0.3

δl 0.5 0.5 0.5

Table 4: Discharge conditions of the three confinement phases (L-mode, I-mode and H-mode) in one RF heated discharge. Discharge conditions shown in this table are magneticconfiguration (whether Lower Single Null (LSN) or Upper Single Null (USN) or doublenull configuration), magnetic field on the axis, Bt(0) in Tesla, plamsa current, Ip, in MA,average electron density, ne,avg, in 1020m−3, elongation, κ, upper triangularity, δu, andlower triangularity, δl. All shaping parameters (κ,δu and δl) are the values estimated atthe separatrix.

Parameters L-mode I-mode H-mode

core Te λTe 3.12 2.97 2.83(ρ ≤ ρped,Te) Te(0.8) [keV] 0.66 1.09 1.17

edge Te µTe [keV] 2.38 13.93 21.21(ρ ≥ ρped,Te) Te,edge [keV] 0.1 0.1 0.01

ρped,Te 0.75 0.96 0.97

core ne λne 0.92 0.90 0.46(ρ ≤ ρped,ne) ne(0.8) [1020m−3] 0.98 1.08 1.75

edge ne µne [1020m−3] 1.29 8.31 39.89(ρ ≥ ρped,ne) ne,edge [1020m−3] 0.77 0.68 0.46

ρped,ne 0.92 0.97 0.97

Pe(0.8) [kPa] 10.35 18.84 32.76

Table 5: Parameters calculated from fitting with the different confinement phases (L/I/H-modes) in one discharge. λTe is an exponential fitting parameter for the core Te profile,and µTe is the slope of the linear fitting line applied to the edge Te profile. Te,edge indicatesthe Te value at ρ = 1.0 from the linear fitting line applied to the edge Te profile. ρped,Te isthe radial location which has the minimum difference between the exponential and linearfitting line. The same definitions are applied to λne , µne , ne,edge and ρped,ne for ne profiles.

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3 Discussion

In this study, radial variations in ne and Te profile shapes with different ohmic confinementregimes, as recently observed in TCV[3], were investigated in Alcator C-Mod to studyself-similarity and related stiffness properties. With the increase of average density (col-lisionality) or the change of ohmic confinement regime from LOC to SOC in two sets ofohmic discharges, it was found that an exponential fit can be applied in the core region(ρinv < ρ ≤ ρped,Te) with a similar gradient scale length in both ne and Te profiles, re-gardless of the ohmic confinement regime. It follows that both ne and Te profiles in thisregion are self-similar across the ohmic confinement transition. However, the differencesbetween ne and Te profiles were found in the edge region, and changes in the linear fittingparameters for the edge ne profiles, the increase of the slope of the linear fitting line forthe edge ne profile, µne , and the ne value at ρ = 1.0 from the linear fit, ne,edge, values, inthe SOC regime compared to the LOC regime correlate with the improvement of energyconfinement. These observations are consistent with the findings in TCV.

We also study the change of profile shape with the change of core toroidal rotation. Itwas shown that both shape and amplitude of ne and Te profiles in the core region changelittle in the rotation reversal discharge, the “intermediate” discharge in the second set ofohmic discharges in Section 2.1. In the edge region, we observed the decrease of the Te valueat ρ = 1.0 from the linear fit, Te,edge, and the increase of µne across the rotation reversal.Considering the uncertainty of edge ne and Te data, we may need more investigation inthe future to resolve whether this observation is meaningful or not. At this point, we notethat we cannot eliminate the possible correlation between the edge profile changes and thecore rotation reversal.

It is noteworthy that the LOC discharges in both sets of ohmic discharges rotate in theco-current direction in the core region and that both SOC discharges rotate in the counter-current direction in the core region, and we observed the increase of µne and the decreaseof µTe between LOC/SOC discharges in both sets of ohmic discharges. If the observedchanges in the edge region across the rotation reversal in one discharge are meaningful,then, the increase of µne across the rotation reversal is consistent with the changes in twosets of ohmic discharges, but the similar level of µTe is not consistent with them. This maysuggest that changes in the edge ne profile are correlated with the rotation reversal in thecore region.

If we show that the edge ne and Te profiles changes barely across the rotation reversal inthe rotation reversal discharge in the future, there will be an inconsistency in the relationbetween core rotation directions and edge profile changes. This is because the changes ofedge ne and Te profile shapes between LOC and SOC discharges, which have the oppositecore rotation directions, will not be consistent with negligible change in ne and Te profilesin the rotation reversal discharge. In this case, two possibilities can be considered toexplain this inconsistency. First, if we consider the direct relation between the change ofedge profiles and the direction of core toroidal rotation, these results will indicate that

14

the change of edge profiles requires longer time scale than the change in the core toroidalrotation. Second, if we assume that the average electron density affects directly both coretoroidal rotation and edge profiles and that core toroidal rotation and edge profiles haveno direct relation, the results in this study will imply that toroidal rotation in the coreregion is more sensitive to the change of average density than edge profiles. This is becausethe difference of the average density between the LOC and SOC discharges in both setsof ohmic discharges, which have the opposite rotation direction, is much larger than thedifference of the average density of the different rotation direction phases (co-/counter-current directions) in the rotation reversal discharge. Considering the edge profile changesacross L to I/H transition in a single discharge shown in Section 2.2, the latter assumptionwill be more plausible. However, we need to check it experimentally. We may proveor disprove the second possibility from one discharge which has step-wise or two stepsof average density values while keeping other discharge conditions constant. Last, it isnoteworthy that the shape of ne and Te profiles in the core region are similar regardless ofthe direction of core toroidal rotation (either co- or counter-current direction) in both setsof ohmic discharges, consistent with the previous studies in C-Mod[34, 45].

The changes in sawtooth activity across the ohmic confinement transition were alsoinvestigated. We observed that the sawtooth signals have a longer period and becomemore irregular in the SOC discharge than the LOC discharge, consistent with the findingsin TCV[3]. However, negligible change in sawtooth activity was found across the rotationreversal in the rotation reversal discharge. It is worth noting that the relation of rotationwith edge profile changes could be consistent with a related change of the sawtooth activityand a lower Te profile due to a lower Te(0.8), leading to a flatter q profile with increasingqo[3, 38]. Although the decrease of Te,edge was observed across the rotation reversal in thesame discharge, with the similar slope of the linear fitting line for the edge Te profiles,µTe , this decrease does not change the core Te profile significantly. Table 1 shows Te(0.8)decreases within 10% across the rotation reversal, while we observed 20-30% decrease acrossthe LOC/SOC transition in two sets of ohmic discharges.

We compared ne and Te profiles in different energy confinement regimes (L/I/H-modes)for one discharge. We show that an exponential fit is valid and similar λTe values are used incore Te profiles regardless of different confinement regimes. However, the core region of theTe profile, where an exponential fit is valid, extends outward radially towards the top of thepedestal region in I/H-modes in this discharge. Considering a pedestal as the region wherethe transport property starts to change from the core region, this observation supports theuse of the term “pedestal” in L-mode discharges in [3]. This is because the core gradientscale length, one of the parameters related to transport behavior in the core region, startsto change near ρ ∼0.8 in the L-mode Te profile as it changes from the top of the pedestalin I/H-mode Te profiles. It is noteworthy that the extension of the self-similarity regionwas also observed in the L-mode discharges with different RF powers in ASDEX-U[17]. In[17], the self-similarity region extends radially outward as RF power increases. This mayindicate that the extension of the self-similarity region can occur with different discharge

15

conditions as well as the changes in the global energy confinement. Figure 26(a) in [3] alsoshows that the outer boundary of the self-similarity region, ρped, varies from 0.65 to 0.9in both Te and ne profiles. It will be of interest to investigate the extension of the self-similarity region with the different discharge conditions in each confinement regime in thefuture. An exponential fit is also valid for core ne profiles in all L/I/H-modes. However, theexponential fitting parameter for the core ne profile, λne , decreases in H-mode comparedto L/I-modes, it is inconclusive whether the self-similarity region in ne profiles extendsradially outward in H-mode compared to L/I-modes.

It was observed that the slope of linear fitting for core Te profiles, µTe , increases morethan five times with the comparable or lower Te,edge values in I/H-modes compared to L-mode, while λTe in the core region varies around 10% in all confinement regimes, implyingthat µTe correlates with the improvement of energy confinement. We also observed thatthe remarkable increase of µne in H-mode compared to L/I-modes. Although λne decreasesin H-mode compared to L/I-modes, this decrease will cause lower particle confinement,indicating that the increase of µne correlates with the improvement of particle confinementas the increase of µTe does with the improvement of energy confinement. This finding isconsistent with the previous studies which show the correlation between the edge profileand global confinement[5, 6, 8].

However, this study also shows that the extension of the self-similar region in Te profilesfrom ρ ∼ 0.8 to the top of the pedestal is related to the improvement of global energyconfinement. Then, the next question will be about the relation between extension ofthe self-similarity region and the increase of µTe . Assuming the critical gradient modeland causality between stiffness (in terms of local heat flux change with the gradient scalelength) and self-similarity, it is possible to explain the extension of the self-similarity regionas the result of the increase of Te at 0.8< ρ <0.95 with the higher value of µTe . The lowTe in the edge region makes a/LTe higher than the critical gradient scale length, makingthe edge region non-stiff[1]. We can also see the non-stiffness with low Te as the decreaseof gyro-Bohm power level, the saturated level of the conducted heat flux by turbulent

transport. Since gyro-Bohm power is proportional to T5/2e [46], the lower Te in the edge

region compared to the core region will result in the gyro-Bohm power being lower thanthe total conduction heat power in the edge region. Thus, the gradient will not be keptby turbulent transport, but will be varied with the total conducted heat flux, making theprofile non-stiff. Figure 4 and 6 in [17] show that a gradient scale length of Te increasesabruptly as the value of Te decreases below a certain value and electron heat transportbecomes non-stiff when a gradient scale length of Te is above a certain point. Figure 1in [46] also shows that experimental temperature gradient scale length tends to separatefrom the critical gradient scale length, as experimental diffusivity is larger than gyro-Bohmdiffusivity. Assuming electron heat transport at 0.8< ρ <0.95 is non-stiff in L-mode, thenthe increase of µTe will increase Te and decrease a/LTe and increase gyro-Bohm heat flux,moving this region (0.8< ρ <0.95) from non-stiff to stiff. If the total conducted heat poweris lower than the gyro-Bohm heat flux and the critical gradient scale length at 0.8< ρ <0.95

16

is close to the critical gradient scale length at ρ >0.8, then the profile at 0.8< ρ <0.95 willalso show self-similarity.

It is noteworthy that several assumptions are made in this explanation, and theseassumptions should be proved in the future. We should note that it is also possible thatthe extension of the self-similarity region up to ρ ∼ 0.95 with the fixed Te,edge results inthe increase of µTe or that these two changes do not have a cause-effect relationship. Assuggested in [47], localized edge heating may elucidate the relation between the extensionof self-similarity and the increase of µTe across the L to I/H transition. It is also worthnoting that the reduction of turbulence in the high energy confinement regimes (I/H-modes) compared to the low energy confinement regime (L-mode) occurs not only in theedge region but also in the core region, where Te profiles are self-similar[48, 47]. Thesestudies indicate that the global confinement change is associated with the change not onlyin the edge region but also in the core region. We may need to consider the relation amongthe change of core turbulence, profile self-similarity in the core region and its extension,the change of edge turbulence and edge profiles to understand the physics related to thechange of global confinement.

We need to note that the analyses in this paper have caveats, which should be resolvedin the future. First, the authors note that the linear fit for the edge profiles shown in thisstudy do not prove or disprove that the edge region has the constant gradient since it ishard to resolve the gradient values accurately in the edge region due to the uncertainty ofthe measurements and the scattered data. Nevertheless, the results in this study show thatthe linear fit can be applied to the edge region within the uncertainties and the changesin the edge region with the different confinement regimes can be quantified by the linearfit. Second, the exponential fitting parameters for Te and ne profiles, λTe and λne , haveuncertainties around 20-25% due to the uncertainty of core Te and ne data. Thus, self-similar core profiles observed in this study do not refer to the profiles with the exact sameshape, but refer to the profiles which have similar shape and their differences cannot beresolved within the uncertainty of the data. More stationary discharges than the dischargestudied in this paper may help to reduce the uncertainty of the ne and Te data. We mayneed to consider shifting the plasma slightly to obtain better spatial resolution and moreaccurate gradients of ne and Te profiles as tried in [3, 17]. Dedicated experiments to removethe ambiguities in this study should be planned in the future.

4 Summary

This study shows that C-Mod L-mode discharges (both ohmic and RF) have self-similarne and Te profiles in the core region (ρ ≤ ρped) as observed in TCV L-mode discharges. Inthe ohmic discharges, the increase of the slope of linear fitting for the edge ne profile, µne ,and the ne value at ρ = 1.0 from the linear fit, ne,edge, correlate with the improvementof confinement with average density, consistent with [3]. We also observed the correlation

17

between the direction of core toroidal rotation and ne and Te profiles in the edge, butchange of ne and Te profiles across rotation reversal was inconclusive in a rotation reversaldischarge. The relation between toroidal rotation and edge profiles should be clarified inthe future.

When energy confinement is improved (I/H-modes), Te profiles keep the self-similarityproperty (or has the similar exponential fitting parameter for core Te profiles, λTe , within10%) as L-mode Te profiles have in the core region, but the self-similar region extendsfrom the core region up to the top of the pedestal region in improved energy confinementregime (I/H-modes). We also observed self-similar ne profiles in the core region, butthe exponential fitting parameter for core ne profiles, λne , is reduced in high particleconfinement regimes (H-mode). We also observed that the changes in the edge region arerelated to the improvement of confinement in both particle and energy, consistent withfindings in [3], but the extension of self-similar region with the improvement of energyconfinement was also observed in this study.

Although we observed similar variations in ne and Te profile shapes in other ohmicand RF heated discharges in Alcator C-Mod, not shown here, we should note that thisstudy is still preliminary. The changes in the shape of ne and Te profiles studied in [3] andthis paper should be investigated more in various plasmas conditions in C-Mod and othermachines to confirm the universality of these properties, and the physics related to theseobservations also should be studied in the future.

Acknowledgments

The authors thank S. Wolfe for EFIT analysis in C-Mod and C-Mod team for dischargesused in this study. This work is supported by the U.S. Department of Energy under GrantNos. DE-SC0006419 and DE-FC02-99ER54512.

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[29] B Esposito, M. Marinucci, G. Bracco, C. Castaldo, V. Cocilovo, E. Giovannozzi,M. Leigheb, G. Monari, S. Nowak, C. Sozzi, O. Tudisco, R. Cesario, D. Frigione,C. Gormezano, G. Granucci, L. Panaccione, V. Pericoli-Ridolfini, L. Pieroni, FTU,and ECRH teams. Transport analysis of ohmic, l-mode and improved confinementdischarges in ftu. Plasma Physics and Controlled Fusion, 46:1793, 2004.

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[31] J. E. Rice, B. P. Duval, M. L. Reinke, Y. A. Podpaly, A. Bortolon, R. M. Churchill,I. Cziegler, P. H. Diamond, A. Dominguez, P. C. Ennever, C. L. Fiore, R. S. Granetz,M. J. Greenwald, A. E. Hubbard, J. W. Hughes, J. H. Irby, Y. Ma, E. S. Marmar,R. M. McDermott, M. Porkolab, N. Tsujii, and S. M. Wolfe. Observation of coretoroidal rotation reversals in alcator c-mod ohmic l-mode plasmas. Nuclear Fusion,51:083005, 2011.

[32] ML Reinke, JE Rice, IH Hutchinson, M Greenwald, NT Howard, JW Hughes, J Irby,Y Podpaly, JL Terry, and A White. Non-neoclassical up/down asymmetry of impurityemission on alcator c-mod. Nuclear Fusion, 53(4):043006, 2013.

[33] C Gao, JE Rice, HJ Sun, ML Reinke, NT Howard, D. Mikkelson, A.E. Hubbard,MA Chilenski, J Walk, et al. Non-local heat transport in alcator c-mod ohmic l-modeplasmas. Nuclear Fusion, 54(8):083025, 2014.

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[34] C. Sung, A. E. White, N. T. Howard, C. Y. Oi, J. E. Rice, C. Gao, P. Ennever,M. Porkolab, F. Parra, D. Mikkelsen, et al. Changes in core electron temperaturefluctuations across the ohmic energy confinement transition in alcator c-mod plasmas.Nuclear Fusion, 53(8):083010, 2013.

[35] J. E. Rice, C. Gao, M. L. Reinke, P. H. Diamond, N. T. Howard, H. J. Sun, I. Cziegler,A. E. Hubbard, Y. A. Podpaly, W. L. Rowan, J. L. Terry, M. A. Chilenski, L. Delgado-Aparicio, P. C. Ennever, D. Ernst, M. J. Greenwald, J. W. Hughes, Y. Ma, E. S.Marmar, M. Porkolab, A. E. White, and S. M. Wolfe. Non-local heat transport,rotation reversals and up/down impurity density asymmetries in alcator c-mod ohmicl-mode plasmas. Nuclear Fusion, 53:033004, 2013.

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[41] M Greenwald, C Angioni, JW Hughes, J Terry, and H Weisen. Density profile peakingin low collisionality h-modes: comparison of alcator c-mod data to asdex upgrade/jetscalings. Nuclear Fusion, 47(9):L26, 2007.

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[43] Catherine L Fiore, Darin Richard Ernst, John E Rice, Kirill Zhurovich, N Basse,PT Bonoli, MJ Greenwald, Earl S Marmar, and Stephen J Wukitch. Internal transportbarriers in alcator c-mod. Fusion science and technology, 51(3):303–316, 2007.

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Figures

23

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

<ne> [1020m-3]

Ip [MA]

0.0

0.5

1.0

1.5

2.0

0.9 1.0 1.1 1.2 1.3

time [sec]

-40

-20

0

20

40

POH [MW]

Vtor (0) [km/s]

> [1020m-3]

A]

[MW]

(0) [km/s]

Red : LOC, Blue : SOC

Figure 1: Plasma parameters with time for two ohmic discharges with different averageelectron density, so different confinement regimes. Red : LOC, blue : SOC. The shadedregion is the stationary period used in profile analysis.

24

ρ

ρ

ρ

ρ

: LOC : SOC

(a) (c)

(b) (d)

λTe=3.34

0.0 0.2 0.4 0.6 0.8 1.0

1

2

3

4

Te

[k

eV

]

0.0 0.2 0.4 0.6 0.8 1.0

0.01

0.10

1.00

10.00

Te

[k

eV

]

0.0 0.2 0.4 0.6 0.8 1.0

0.1

1.0

10.0

Te

/ T

e a

t 0

.8

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

1.2

Te

[k

eV

]

Figure 2: Te profiles in two ohmic discharges (red : LOC, blue : SOC) with the fittlinglines (solid line : exponential fitting line for the core profile, dashed line : linear fitting linefor the edge profile) (a) Te Profiles with the fitting lines in linear scale (b) The normalizedTe profiles by Te(0.8) with the exponential fitting line, which is also normalized, in logscale (c) Te profile with the fitting line with the fixed λTe(=3.34) in log scale. (d) Edge Teprofiles with the fitting lines.

25

: LOC : SOC

ρ ρ

ρρ

(a) (c)

(d)(b)

λne=0.84

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

ne

[1

02

0

m-3

]

0.0 0.2 0.4 0.6 0.8 1.0

0.1

1.0

ne

[1

02

0

m-3

]

0.0 0.2 0.4 0.6 0.8 1.0

0.1

1.0

ne

/ n

e (

0.8

)

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.5

1.0

1.5

ne

[1

02

0

m-3

]

Figure 3: ne profiles in two ohmic discharges (red : LOC, blue : SOC) with the fittlinglines (solid line : exponential fitting line for the core profile, dashed line : linear fitting linefor the edge profile) (a) ne Profiles with the fitting lines in linear scale (b) The normalizedne profiles by ne(0.8) with the fitting line, which is also normalized, in log scale (c) neprofile with the fitting line with the fixed λne(=0.84) in log scale. (d) Edge ne profiles withthe fitting lines.

26

<ne> [1020m-3]

POH [MW]

Ip [MA]

Vtor (0) [km/s]

Red : LOC, Green : Intermediate, Blue : SOC

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0

0.5

1.0

1.5

2.0

0.6 0.8 1.0 1.2 1.4 1.6

time [sec]

-40

-20

0

20

40

Figure 4: Plasma parameters with time for three ohmic discharges with different averageelectron density, so different confinement regimes. Red : LOC, green : Intermediate, blue: SOC. The shaded region is the stationary period used in profile analysis.

27

(a)

(b)

(c)

λTe=3.34

: LOC : Intermediate : SOC

ρ ρ

λne=0.87

(e)

ρ

(f )

ρ

(d)

ρ

ρ

0.0 0.2 0.4 0.6 0.8 1.0

1

2

3

4T

e [

ke

V]

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

ne

[1

02

0m

-3]

0.0 0.2 0.4 0.6 0.8 1.0

0.01

0.10

1.00

Te

[k

eV

]

0.0 0.2 0.4 0.6 0.8 1.0

1n

e /

ne

(0.8

)

0.0 0.2 0.4 0.6 0.8 1.0

0.1

1.0

ne

[1

02

0m

-3]

0.0 0.2 0.4 0.6 0.8 1.0

0.1

1.0

Te

/ T

e(0

.8)

Figure 5: Core Te and ne profiles of three ohmic discharges (red : LOC, green : Interme-diate, blue : SOC) with the exponential fitting line for the core profile (solid line). (a) Teprofiles with the fitting lines in linear scale (b) The normalized Te profiles by Te(0.8) withthe fitting line, which is also normalized, in log scale (c) Te profile with the fitting line withthe fixed λTe(=3.34) in log scale. (d) Te profiles with the fitting lines in linear scale (e)The normalized ne profiles by ne(0.8) with the fitting line, which is also normalized, in logscale (f) ne profile with the fitting line with the fixed λTe(=0.87) in log scale.

28

LOC

Intermediate

SOC

(a)

(b)

(c)

ρ

ρ

ρ

: LOC : Intermediate : SOC

(d)

(e)

(f )

ρ

ρ

ρ0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

Te

[k

eV

]

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

Te

[k

eV

]

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

Te

[k

eV

]

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

1.2

1.4

ne

[1

02

0m

-3]

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

1.2

1.4

ne

[1

02

0m

-3]

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

1.2

1.4

ne

[1

02

0m

-3]

Figure 6: Edge Te and ne profiles of three ohmic discharges (red : LOC, green : Inter-mediate, blue : SOC) with the exponential fitting lines (solid line : exponential fittingline for the core profile, dashed line : linear fitting line for the edge profile) (a) Edge Teprofile in the LOC regime, (b) Edge Te profile in the “intermediate” regime, (c) Edge Teprofile in the SOC regime, (d) Edge ne profile in the LOC regime, (e) Edge ne profile inthe “intermediate” regime, (f) Edge ne profile in the SOC regime

29

-40

-20

0

20

40

60

Vto

r [k

m/s

]

: Co-current : Reversal : Counter-current

0.0 0.2 0.4 0.6 0.8 1.0ρ

Figure 7: Core toroidal rotation profile measured by high resolution x-ray spectroscopy.The shaded regions indicate the time ranges used for the analysis at each rotation phase,red : co-current (before rotation reversal), green : reversal (during rotation reversal), blue: counter-current (after rotation reversal) in the rotation reversal discharge in the secondset of ohmic discharges.

30

ρ

ρ

(a)

(b)

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Te

[k

eV

]

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

ne

[1

02

0

m-3

]

: Co-current : Reversal : Counter-current

0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

(c)

ρ

0.75 0.80 0.85 0.90 0.95 1.00

0.2

0.4

0.6

0.8

1.0

ρ

(d)

ne

[1

02

0

m-3

]T

e [

ke

V]

Figure 8: Te and ne profiles with different toroidal phases (red : co-current (before rotationreversal), green : reversal (during rotation reversal), blue : counter-current (after rotationreversal) in the rotation reversal discharge in the second set of ohmic discharges) with thefittling lines (solid line : exponential fitting line for the core profile, dashed line : linearfitting line for the edge profile) (a) Te profiles with the exponential fitting line (b) ne profileswith the exponential fitting line (c) Edge Te profiles with fitting lines (d) Edge ne profileswith fitting lines

31

Red : LOC, Green : Intermediate, Blue : SOC

1.20 1.21 1.22 1.23 1.24 1.25time [sec]

0

1

2

3

4

Te,0

[keV] (b)

Red : LOC, Blue : SOC

Te,0

[keV] (a)

1.10 1.11 1.12 1.13 1.14 1.15time [sec]

0

1

2

3

4

Figure 9: Te near the magnetic axis measurd by the ECE diagnostic for (a) the first set ofohmic discharges (b) the second set of ohmic discharges.

32

2.6

2.4

2.2

2.0

1.8

1.6

1.40.76 0.78 0.80 0.82 0.84

Time [sec]

2.6

2.4

2.2

2.0

1.8

1.6

1.41.00 1.02 1.04 1.06 1.08

Time [sec]1.10

2.6

2.4

2.2

2.0

1.8

1.6

1.41.16 1.18 1.20 1.22 1.24

Time [sec]

Te,0

[keV]

Te,0

[keV]

Te,0

[keV]

(b)

(a)

(c)

Co-current

Reversal

Counter-Current

Figure 10: Te near the magnetic axis measurd by the ECE diagnostic in the rotation rever-sal discharge in the second set of ohmic discharges (a) Co-current phase (before rotationreversal) (b) Reversal phase (during rotation reversal) (c) Counter-current (after rotationreversal). 33

time [sec]

(a)

(b)

(c)

(d)

Figure 11: (a) Edge fluctautions of a L/I/H transtion discharge measured by reflectometry(b) RF heating power (c) Te on the magnetic axis (d) Te near the edge (ρ ∼0.9). Theshaded regions indicate the different confinement phases used in the analysis (Blue : L-mode, Green : I-mode, Red : H-mode)

34

: L-mode : I-mode : H-mode

ρ

ρ ρ

(a) (d)

(e)(b)

ρ ρ

ρ

(c) (f )

0.0 0.2 0.4 0.6 0.8 1.0

1

2

3

4

5

6

7

Te

[k

eV

]

0.75 0.80 0.85 0.90 0.95 1.00

0.5

1.0

1.5

2.0

Te

[k

eV

]

0.0 0.2 0.4 0.6 0.8 1.0

0.1

1.0

Te

/ T

e(0

.8)

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

ne

[1

02

0m

-3]

0.0 0.2 0.4 0.6 0.8 1.0

1

ne

/ n

e(0

.8)

0.75 0.80 0.85 0.90 0.95 1.00

0.5

1.0

1.5

2.0

2.5

ne

[1

02

0m

-3]

Figure 12: Te profiles in L/I/H-modes (blue : L-mode, green : I-mode, red : H-mode) withthe fitting lines (solid line : exponential fitting line for the core profile, dashed line : linearfitting line for the edge profile). (a) Te profiles with the exponential fitting line in linearscale (b) The normalized Te profiles by Te(0.8) with the exponential fitting line in log scale(c) Edge Te profiles with the fitting lines (d) ne profiles with the fitting lines in linear scale(e) The normalized ne profiles by ne(0.8) with the exponential fitting line in log scale (f)Edge ne profiles with the fitting lines

35