Changes in Core Electron Temperature Fluctuations Across...

March, 2012

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 Nos. DE-SC0006419, DE-FC02-99ER54512. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

PSFC/JA-13-10

Changes in Core Electron Temperature Fluctuations Across the Ohmic Energy

Confinement Transition in Alcator C-Mod Plasmas

C. Sung, A. E. White, N. T. Howard, C. Y. Oi, J. E. Rice, M. L. Reinke, C. Gao, P. Ennever, M. Porkolab, F. Parra, D. Mikkelsen*, D. Ernst, J. Walk, J. W. Hughes, J. Irby, C. Kasten, A. E. Hubbard, M. J. Greenwald and the Alcator C-Mod Team * Princeton Plasma Physics Laboratory.

Changes in Core Electron Temperature Fluctuations

Across the Ohmic Energy Confinement Transition

in Alcator C-Mod Plasmas

C. Sung1, A. E. White1, N. T. Howard1, C. Y. Oi1, J. E. Rice1,

C. Gao1, P. Ennever1, M. Porkolab1, F. Parra1, D. Mikkelsen2,

D. Ernst1, J. Walk1, J. W. Hughes1, J. Irby1, C. Kasten1, A. E.

Hubbard1, M. J. Greenwald1 and the Alcator C-Mod Team1 Plasma Science and Fusion Center, Massachusetts Institute of Technology,

Cambridge, Massachusetts 02139, USA2 Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA

E-mail: [email protected]

Abstract. The first measurements of long wavelength (kyρs < 0.3) electron

temperature fluctuations in Alcator C-Mod made with a new Correlation Electron

Cyclotron Emission (CECE) diagnostic support a long-standing hypothesis regarding

the confinement transition from Linear Ohmic Confinement (LOC) to Saturated Ohmic

Confinement (SOC). Electron temperature fluctuations decrease significantly (∼40%)

crossing from LOC to SOC, consistent with a change from Trapped Electron Mode

(TEM) turbulence domination to Ion Temperature Gradient (ITG) turbulence as the

density is increased. Linear stability analysis performed with the GYRO code [Candy

and Waltz 2003 J. Comput. Phys. 186 545] shows that TEMs are dominant for long

wavelength turbulence in the LOC regime and ITG modes are dominant in the SOC

regime at the radial location (ρ ∼ 0.8) where the changes in electron temperature

fluctuations are measured. In contrast, deeper in the core (ρ < 0.8), linear stability

analysis indicates that ITG modes remain dominant across the LOC/SOC transition.

This radial variation suggests that the robust global changes in confinement of energy

and momentum occurring across the LOC/SOC transition are correlated to local

changes in the dominant turbulent mode near the edge.

Changes in Core Te Fluctuations Across the Ohmic Energy Confinement Transition 2

1. Introduction

One of the oldest unsolved problems in tokamak transport research is the change of

confinement regime in ohmic plasmas. It has been observed in several tokamaks spanning

a wide range of parameters that energy confinement time increases linearly with the

average electron density, before saturating above a critical density value[1, 2, 3, 4, 5, 6,

7, 8, 9, 10, 11]. These confinement regimes are referred to as the Linear and Saturated

Ohmic Confinement (LOC and SOC) regimes, respectively. An example from Alcator

C-Mod is shown in Figure 1. One hypothesis that has long been considered is that a

change of the dominant type of turbulence, from TEM in the LOC to ITG in the SOC,

is related to the change of confinement regime [5, 6, 12].

Numerous investigations of the LOC to SOC transitions have been performed on

tokamaks around the world. In Alcator C, it was observed that the propagation of the

density fluctuations measured by the CO2 laser scattering and correlation techniques

changed from electron to ion diamagnetic direction across the LOC/SOC transition [13].

In ASDEX-U, it was found that density profiles in the LOC regime were flattened when

Electron Cyclotron Heating(ECH) is applied, consistent with quasi-linear predictions in

TEM dominated plasmas[12]. In FTU, power balance analysis indicates that electron

heat diffusivity decreases and ion heat diffusivity increases as density increases in ohmic

plasmas, implying the change of turbulence from TEM to ITG as density increases[7].

In DIII-D, using coherent Thomson scattering, it was observed that there is a sudden

increase of line integrated density fluctuations in the low frequency range near the

boundary between LOC and SOC. Linear gyrokinetic simulation with adiabatic electrons

suggests the observed turbulence in the SOC regime was consistent to ITG modes[6].

Using a similar scattering system, ion mode turbulence in the SOC regime was also

observed in TEXT, and found to be also consistent with ITG modes [14]. However, in

Tore-Supra, a decrease in the relative density fluctuation level was observed as density

increases in ohmic plasmas. Power balance analysis of these plasmas found that the

electron heat diffusivity was reduced as density increases without a significant change

of ion heat transport, opposing the hypothesis about ohmic confinement regime being

linked to a change in ITG/TEM dominance[3]. In Alcator C-Mod, using Phase Contrast

Imaging(PCI)[8, 15] ion mode turbulence was observed in the SOC regime, and through

gyrokinetic simulations, it was concluded that ITG modes are dominant in the SOC

regime in the past. However, in the LOC regime, electron and ion heat diffusivities

from experimental profiles were not consistent with the values from nonlinear gyrokinetic

simulations[16].

Despite extensive previous work, the cause of the different ohmic confinement

regimes is still not well understood, and experiments aimed at correlating the change

in ohmic confinement regime with changes in measured turbulence have been restricted

to line integrated density fluctuations. Local measurements of the turbulence, along

with measurements of different fluctuating fields(e.g. temperature), can help to test the

hypothesis that the ohmic confinement transition is related to changes in the dominant


turbulent mode.

In this paper, we present measurements of electron temperature fluctuations

obtained using a newly commissioned Correlation Electron Cyclotron Emission (CECE)

system on Alcator C-Mod. These measurements are both the first local turbulence

measurement and the first measurements of electron temperature fluctuations ever to

be performed in LOC and SOC regimes.

2. Experimental setup

This analysis presented here focuses primarily on the long stationary periods of two

ohmic plasma discharges in C-Mod (t=0.9-1.4 sec, i.e., ∆t=0.5sec, during the plasma

discharge); one in the LOC regime and one in the SOC regime. These discharges were

operated with toroidal magnetic field of Bt=5.4 T in co-current direction, Ip=0.9 MA

in Lower Single Null (LSN) configuration with R=0.67m, a=0.22m, elongation,κ=1.6,

lower triangularity, δl=0.54 and upper triangularity, δu=0.26. They differ only in

their densities (central chord line integrated density, ne = 0.5 × 1020m−2 for LOC

and ne = 0.8 × 1020m−2 for SOC). We also use a series of LOC and SOC shots to

observe the change of electron density and temperature fluctuations across LOC/SOC

transition. For both LOC/SOC plasmas, the toroidal magnetic field was set to 5.4T

on axis, and the direction of toroidal magnetic field was co-current direction. Plasma

current, Ip was in the range of 0.8-1.2 MA in lower/upper single null configuration with

R=0.67m, a=0.22m and κ=1.6-1.7. In LSN configuration, δl=0.50 and δu=0.28, and in

USN configuration, δl=0.34 and δu=0.62.

For these plasmas, we kept most plasma parameters fixed, changing electron density

on a shot by shot basis. The central chord line integrated density was scanned from

0.5− 0.9× 1020m−2. It has been observed robustly that a direction of toroidal rotation

is reversed at the LOC/SOC transition[9]. In C-Mod, LOC plasmas have core toroidal

rotation in co-current direction and it changes to counter-current direction in the SOC

regime. We used the change in the core toroidal rotation direction to distinguish between

ohmic confinement regimes since it is the most sensitive indicator[9, 10, 11].

The Thomson scattering diagnostic[17, 18] was used to measure the electron density

and temperature profiles, and the ECE grating polychrometer diagnostic[18, 19] is also

used to measure temperature profiles. The ion temperature and toroidal rotation

profiles were measured with high resolution imaging x-ray spectroscopy[20, 21]. A

two color interferometer was used to measure line averaged electron density [18, 22].

Line integrated electron density fluctuations were measured by PCI[8, 15], and electron

temperature fluctuations were measured by the CECE diagnostic[23].

The CECE diagnostic can measure electron temperature fluctuations associated

with long wavelength turbulence(kyρs < 0.3, where ky is the poloidal wave number of

the turbulence and ρs is the ion sound gyroradius, which is defined by ρs = cs/Ωci,

where cs =√Te/mi and Ωci = eB/mic). The measured fluctuation level is expected to

vary due to the relative position in the plasma [24] and also due to changes in poloidal


resolution along the beam path[23], thus we take care to compare electron temperature

fluctuation levels measured in several ohmic plasmas at the same radial position, near

ρ ∼0.8, where ρ is the normalized square root of toroidal flux.

CECE uses correlation techniques to reduce the uncorrelated thermal noise and

elucidate the time-averaged electron temperature fluctuations. The sensitivity of CECE

diagnostic is given by[25],

T 2e

T 2e

≥ 1√N

2Bvid

BIF

(1)

where N is the independent sample used in correlation, which is given by N =

2Bvid∆t[26]. BIF is IF bandwidth, which indicates the detection bandwidth determined

by the bandwidth of the intermediate frequency (IF) filter. Bvid is the video bandwidth,

which indicates the signal bandwidth determined by the bandwidth of video amplifier

or post processing such as digital filtering.

From Eq. 1, the sensitivity of CECE can be ∼0.3% through correlation over a long

enough time(∆t=0.5s) with BIF=200MHz, Bvid=500kHz. Since long time averaging is

required to measure small Te fluctuations(∼1%), the plasmas should be steady during

a long enough time interval so that the correlation technique can be used to suppress

thermal noise in the data and to obtain meaningful fluctuation data from CECE.

In order to verify stationary plasma conditions, we consider macroscopic plasma

parameters such as plasma current and central line averaged electron density. Figure 2

shows the time series data for a typical LOC plasma (shot 1120626023) and a

SOC plasma (shot 1120626028) in C-Mod during the measurement time (0.9-1.4s).

Figure 2(a) shows the plasma current of two plasmas. We can see that the plasma

current is almost constant in this time range. C-Mod also has a very steady toroidal

magnetic field (varies less than 1% of the mean value during measurement time), which

ensures the position of CECE channels will be also steady. Figure 2(b) shows the

central chord line averaged density. As shown in the figure, this quantity was steady,

and fluctuated less than 5% of the mean value during the averaging time range (0.9-1.4s).

We also checked electron density and temperature at the CECE measurement position

(ρ ∼ 0.8) in this time range, shown in Figure 2(c) and (d). The electron density and

temperature at the CECE measurement position did not vary outside the error of each

measurement. Figure 2(e) shows the electron temperature at the plasma center, where

the presence of sawtooth activity results in perturbations of the electron temperature.

However, the CECE measurement region is well outside of the sawtooth inversion radius,

and is unaffected by this perturbation. Other shots used in this study also had similar

time series data. These plasmas were steady and correlation techniques can be reliably

applied to these plasmas to obtain the time-averaged temperature fluctuations from

CECE. Figure 2(f) shows the core toroidal velocity. As expected, the LOC plasma (shot

1120626023) has toroidal rotation in the co-current direction, and the SOC plasma (shot

1120626028) rotates toroidally in the counter-current direction.


3. Fluctuation measurements

3.1. Determination of Temperature Fluctuation Levels from CECE measurements

Using CECE, we measured electron temperature fluctuations in ohmic plasmas just

across the ohmic confinement transition, and also deep into both the LOC and SOC

regimes. For this measurement, we calculate the cross-correlation of two signals from

the CECE radiometer, which are separated in frequency space. However, the separation

is smaller than the ECE linewidth. In this measurement, two channels are separated by

0.5GHz but the linewidth of the EC emission is about 2.5GHz. This means that emission

measured by the two adjacent channels comes from physically overlapped sampling

volumes in the plasma. Since two signals come from overlapped emission volumes, they

will have in common the electron temperature and fluctuation information. As long as

the frequency bands of the IF filters in the receiver do not overlap, the thermal noise

is decorrelated between the two channels as shown in Figure 8 in [27]. Thus, cross

correlation of the two CECE signals eliminates the thermal noise and we can obtain the

amplitude and spectrum of time averaged electron temperature fluctuations. Further

explanations about this decorrelation scheme can be found in [25, 26, 27].

The cross correlation coefficient(Cxy) is defined as[28],

Cxy(τ) =Rxy(τ)√

Rxx(0)Ryy(0)(2)

where τ is the lag time, the Rxx(0) and Ryy(0) are auto correlation functions of each

signal when lag time, τ , is equal to 0, and Rxy(τ) is a cross correlation function of the

two signals, and are written as follows[28].

Rxx(τ) =1

T

∫ T

0x(t)x(t+ τ)dt (3)

Ryy(τ) =1

T

∫ T

0y(t)y(t+ τ)dt (4)

Rxy(τ) =1

T

∫ T

0x(t)y(t+ τ)dt (5)

If two CECE signals have coherent temperature fluctuations and incoherent random

noise, Rxy(0) will be proportional to the amplitude of time-averaged electron

temperature fluctuations, and we can obtain the relative temperature fluctuation

level(Te/Te) from Cxy(0) value (see appendix A). We also can observe electron

temperature fluctuations using the cross spectral density function(Gxy(f)) or

coherence(γxy(f)) spectrum. The coherence(γxy) in this figure is defined as [28],

γxy(f) =

√√√√ |Gxy(f)|2Gxx(f)Gyy(f)

(6)

where the Gxx(f) and Gyy(f) are auto spectral density functions for signal x(t) and

y(t), and Gxy(f) is a cross spectral density function of the two signals. The meaningful

turbulence features will be coherent, and will be larger than the statistical limit of


coherence, which is taken to be the standard deviation of the coherence[28]. We can

determine the amplitude of the coherent fluctuations by integrating the cross spectral

density function(Gxy(f)) in the frequency range where we observe fluctuations above the

statistical limit. The relative electron temperature fluctuation level can be calculated

by Eq. 7.

TeTe

=

√√√√ 2BvidT∫ f2f1|Gxy(f)|df

2BIF [∫∞0 |XT (f)|2df

∫∞0 |YT (f)|2df ]0.5

(7)

with [f1, f2] are the frequency range for cross spectral density integration. The derivation

of Eq. 7 is given in the appendix.

Since parasitic noise can also lead to coherent fluctuations above the statistical

limit, we need another tool to determine whether coherent fluctuations are real turbulent

fluctuations or not. The cross phase angle(θxy) can be a tool for this. The cross phase

angle(θxy) is defined as[28],

θxy(f) = tan−1Qxy(f)

Cxy(f)(8)

where Gxy(f) = Cxy(f) − jQxy(f). Since two CECE signals come from overlapped

emission volume, real turbulent fluctuations from two signals are likely to be in phase and

will not have random phase relation. In contrast, parasitic noise from two signals does

not necessarily have a fixed phase relation. Thus, we can distinguish the real physical

fluctuations from noise with more confidence by using both the coherence and cross phase

spectrum. In this study, we calculate the relative electron temperature fluctuation level

from coherence and cross phase spectrum rather than from cross correlation coefficient.

This is because we can minimize the effect of the noise in the calculation of electron

temperature fluctuations from coherence and cross phase spectrum. However, it is hard

to exclude the effect of parasitic noise when the fluctuation level is calculated from

Cxy(0).

Figure 3 shows the coherence(γxy) and cross phase angle(θxy) of two adjacent CECE

channels, which are separated radially about 2mm along CECE beam path and located

at ρ ∼ 0.8 for typical LOC (shot 1120626023) and SOC (shot 1120626028) plasmas. The

dotted line in the coherence spectrum indicates the statistical limit of coherence. The

spectrum in Figure 3 was averaged over 0.5sec (0.9-1.4sec) to reveal electron temperature

fluctuations and reduce random thermal noise. Figure 3(a) shows the spectrum in the

LOC (shot 1120626023) regime. We can see broadband fluctuations above the statistical

limit up to ∼170kHz in this spectrum. Figure 3(b) shows the coherence of two CECE

signals in a SOC plasma. We can see that fluctuations up to 170kHz were reduced in

the SOC regime compared to the LOC regime. We can also see that the cross phase

spectra in Figure 3(c) and (d) are correlated with the broadband fluctuations, indicating

that the observed fluctuations in Figure 3 (a) and (b) are real physical fluctuations. The

reduction of fluctuations can be also observed in Figure 4. Figure 4(a) and (b) shows the

cross correlation coefficient(Cxy) curve of the same LOC and SOC plasmas during 0.5sec


(0.9-1.4sec) respectively. As shown in Figure 4, we can see that the correlation peak

at lag time=0 decreases in the SOC regime compared to the LOC regime, implying

the reduction of the relative electron temperature fluctuation level across LOC/SOC

transition.

Using Eq. 7, the relative fluctuation level(Te/Te) was calculated. The proper

frequency range for cross spectral density integration was determined from coherence

and cross phase spectrum, and it was 10-170kHz and 70-170kHz for the LOC/SOC

plasma, respectively. The low frequency up to 10kHz was excluded due to electronics

noise in all CECE signals. Using Eq. 7, the calculated electron temperature fluctuation

level was reduced from 1.0% in the LOC regime to 0.6% in the SOC regime, a 40%

reduction.

Since the CECE measurement position in this study is near the edge, the optical

depth is not high enough to ignore the effect of the density fluctuations. The optical

depth range of plasmas used in this study is 1.6-3.3. It is known that fluctuation signals

in CECE diagnostic can be contaminated from density fluctuations when optical depth,

τ , is low(τ < 2)[29]. For second harmonic X-mode case like CECE measurements in

this study, the contribution of density fluctuations to the fluctuations in CECE signals

can be estimated from the given equations as[29],

< I1I∗2 >

I2= (1 + A)2

T 2e

T 2e

+ A2 n2e

n2e

+ 2A(1 + A)Re < Tene >

Tene(9)

where A = τ exp(−τ)1−exp(−τ)(1− χ

1−exp(−τ)1−χ exp(−τ)), I1,2 is the intensity of each CECE signal used in

correlation technique, and χ is the wall reflectivity with typical value of ∼ 0.8 for metal

wall facility like C-Mod in this estimation.

From Eq. 9, it is required to know the relative density fluctuation level and phase

between density fluctuation and temperature fluctuation to estimate the contribution of

density fluctuation to the measured radiation fluctuations. When density fluctuations

and temperature fluctuations are in phase or out of phase, the contribution of density

fluctuations is maximum. In Section 4, linear gyrokinetic analysis is used to predict the

phase angle between density fluctuations and temperature fluctuations, and we find that

it falls between 0 and π/2. Thus, assuming in phase relation between two fluctuations

will maximize the effect of electron density fluctuations. Although we do not measure

local density fluctuation level, it has been observed that the density fluctuation level

can be comparable to the temperature fluctuation level in the tokamak plasmas [24].

We use this information to estimate the maximum contribution of density fluctuations.

Since the maximum electron temperature fluctuation level observed in the 2012 C-

Mod campaign was ∼1.5%, it is reasonable to assume the density fluctuation level is

2% to estimate the contributions of density fluctuations to the CECE measurements.

Assuming a 2% density fluctuation level with an in phase relation to the electron

temperature fluctuations gives the upper bound on the density fluctuation contribution

to the measured temperature fluctuations.


3.2. Determination of relative density fluctuations with Phase Contrast Imaging(PCI)

Using the PCI system on Alcator C-Mod, the line integrated density fluctuations

are measured in the same LOC and SOC plasmas where CECE measurements are

made. Figure 5(a) and (b) shows the normalized frequency/wavenumber spectra of

PCI measurements, which is defined as the frequency/wavenumber spectra, S(kR, f)

divided by the square of the line averaged density in LOC and SOC plasma respectively.

Thus, the relative line integrated density fluctuation level, |∫nedl|/nel can be calculated

by integrating this spectrum. The positive wave number in this spectrum indicates

that the turbulence moves radially to the lower field side, and the negative wave

number represents turbulence that propagates to the higher field side radially in

PCI measurements. From these figures, we can observe that the SOC plasma has

larger fluctuations than the LOC plasma. The relative line integrated fluctuation

level(|∫nedl|/nel) was increased ∼20% in the SOC plasma compared to the LOC plasma

from 0.046% to 0.057% when whole kR values are included and the frequency range is

set to 50kHz<f<1000kHz.

In the past, there has been an observed “wing” structure in the fre-

quency/wavenumber spectra, S(kR, f) of PCI measurements of electron density fluc-

tuations in LOC plasmas. This structure disappears after the transition from LOC

to the SOC regime, as shown in Figure 22 in [9]. However, we could not observe in

our experiments any distinct structure in the PCI S(kR, f) spectrum for LOC plasmas

compared to SOC plasmas as shown in Figure 5. Since the rotation reversal at the

LOC/SOC transition occurs inside in a q=3/2 surface[9], the plasma current may be

related to whether this feature in the PCI spectra appears or not. Moreover, it was

only in a high plasma current LOC discharge (Ip ≥1 MA) that the wing structure was

observed in the past and the plasma in Figure 5 has lower plasma current (Ip ∼0.9

MA). Thus, low plasma current might be responsible for the lack of wing structure in

Figure 5. However, it is unclear whether the plasma current is directly related to the

wing structure or other relevant parameters that scaled with plasma current. The rela-

tion between the wing structure to the LOC/SOC transition is still inconclusive and is

being investigated. It is noteworthy that this feature in PCI spectra has been localized

by past analysis to a radial region farther inside of the plasma[9, 10] than the CECE

measurement position (ρ ∼0.8) in this work. In addition, one discharge used in Figure 6

has the wing structure. However, the contribution of the wing structure to the relative

line integrated fluctuation level (|∫nedl|/nel) is negligible.

3.3. Variation of electron temperature fluctuations and density fluctuations across the

LOC/SOC transition

In order to explore possible causes for the observed differences in how electron

temperature and density fluctuations change in ohmic plasmas across the LOC/SOC

transition, we studied the dependence of the electron temperature and density

fluctuation levels on the normalized average electron density (ne/ncrit) where ncrit =


2.8Ip/B0.6 with ncrit in 1020m−3, on axis toroidal magnetic field, B, in T and Ip in MA,

and, is indicative of the transition from the LOC/SOC according to [9]. Since this

critical density comes from an empirical scaling, it is hard to say that the plasma with

average density value near the critical density is in the LOC or SOC regime. However,

considering errors in the scaling, we can robustly say that if this normalized density

value is less than 1(ne/ncrit < 0.85), the plasma is in the LOC regime, and for the

opposite case(ne/ncrit > 1.15), plasma is in the SOC regime. Figure 6 shows the changes

in electron temperature fluctuations and density fluctuations across the LOC/SOC

transition, plotted as a function of ne/ncrit. The black points in Figure 6(a) show

the relative electron temperature fluctuation level at ρ ∼ 0.8 in ohmic plasmas without

considering the contribution of density fluctuations. Two error sources are considered

to estimate the error bar of black points in Figure 6(a), the random error from CECE

radiometer’s signal and the uncertainty of IF bandwidth. The random error is evaluated

through random noise modeling, and the uncertainty of IF bandwidth is set to 20%.

The total error is calculated from error propagation of two errors. The red points in this

figure indicate minimum values of relative electron temperature fluctuation level when

relative density fluctuation level is 2%. As shown in the figure, the fluctuation levels from

both black and red points tend to decrease as the normalized density increases. Thus,

even when assuming large (2%) value for the density fluctuation level in the model,

it does not eliminate the trend that temperature fluctuations decrease in amplitude

with increases in density. Furthermore, since electron temperature decreases as density

increases, there must also be a reduction in absolute temperature fluctuation levels,

given the measured decrease in relative temperature fluctuation level.

Figure 6(b) shows the relative line integrated electron density fluctuation level for

the same plasmas. The error bar in Figure 6(b) was estimated from time averaging.

It is known that the low frequency fluctuations from PCI measurements propagate in

both the ion and electron diamagnetic directions. This indicates that low frequency PCI

signals come from the edge[16], and therefore to estimate the core density fluctuation

level, we only consider the higher frequency fluctuations. However, it is not clear what

the proper cutoff frequency should be to isolate the core density fluctuations, so we varied

the cutoff frequency. Unlike electron temperature fluctuations, for which there is a clear

correlation between decreasing fluctuation amplitude(Te/Te) and increasing density, it

does not appear that the line integrated density fluctuation level(|∫nedl|/nel) depends

on ne/ncrit, Fig. 6(b). This is true regardless of the chosen cutoff frequency used to

discriminate core fluctuations from edge fluctuations.

4. Linear stability analysis

We observed robust changes in electron temperature fluctuations across the LOC/SOC

transition: reduction of fluctuation amplitude in the SOC regime. This suggests that

the broadband electron temperature fluctuations in the LOC regime may be linked to

TEM driven turbulence. If this were the case, the reduction of the fluctuations may


Table 1. Input profile values for linear GYRO runs at the CECE measurement

position. The values are time averaged over 0.5s (0.9-1.4s). Quoted errors are the

standard deviation of the time averaged signal values

LOC SOC

(1120626023) (1120626028)

ρCECE 0.8 0.8

ne[1020m−3] 0.59 (±0.023) 0.96 (±0.030)

a/Lne1.13 (±0.49) 1.17 (±0.62)

Te [keV] 0.44 (±0.050) 0.36 (±0.039)

a/LTe7.99 (±1.40) 6.06 (±1.54)

Ti [keV] 0.33 (±0.010) 0.28 (±0.009)

a/LTi5.13 (±0.26) 5.21 (±0.32)

ν∗e 0.69 (±0.11) 1.08 (±0.17)

Zeff 2.6 1.6

q, safety factor 2.48 2.47

s, shear 2.93 2.84

be explained by the stabilization of TEMs resulting from the increase of density and

collisionality in the SOC regime.

In order to explore this, linear gyrokinetic simulations are performed using the

GYRO code [30]. Since the measured fluctuations were time-averaged (t=0.9-1.4s), we

used time-averaged profiles in the same time range as input to GYRO for this analysis.

Figure 7 shows the time-averaged profiles for LOC/SOC plasmas. The dotted line in

this figure represents the error in the measured profiles. This error was estimated from

the standard deviation of time-averaged profiles. The linear stability calculations use

the experimental profiles as input. Also in the simulations, one impurity species was

used to set the proper dilution fraction of impurity. The main ion density gradient was

not changed by including impurities in the simulations.

In Figure 7, a/LTe indicates the normalized scale length of Te by minor radius,

a, and defined as a/LTe = a|d(lnTe)/dr|. In the same manner, a/Lne and a/LTi are

normalized scale lengths of ne and Ti, respectively. Table 1 shows the profile data at the

CECE measurement position. At the CECE measurement position (ρ ∼ 0.8), we find

that the LOC plasma has a higher mean value of electron temperature and a/LTe value

than the SOC plasma while displaying a lower electron density. Both plasmas have

similar a/Lne , a/LTi and Te/Ti values. The LOC plasma has lower collisionality, ν∗e ,

than the SOC plasma due to smaller electron density and higher electron temperature.

Collisionality, ν∗e , is defined as ν∗e = νeωb,e

, where νe is the electron ion collision frequency

and ωb,e is the electron bounce frequency. The collisionality in the table 1 was calculated

from TRANSP‡.While it is not possible to measure the heat fluxes directly, we perform power

balance analysis using the TRANSP code to obtain experimental values for Qe and Qi,

‡ http://w3.pppl.gov/transp/


the electron and ion heat fluxes, and χe and χi, the diffusivities, χ = −Q/ndTdr

. Figure 8

shows the electron and ion heat diffusivities and heat fluxes for LOC and SOC plasmas.

The error in this figure was estimated from time averaging of the TRANSP calculated

heat fluxes and diffusivities over the steady periods of interest. As shown the figure, the

LOC plasma has higher electron heat diffusivity and heat flux than the SOC plasma,

although their difference is within the error. This result is consistent with the similar

analysis performed in the past in FTU[7] and C-Mod[16], but inconsistent with the

result in Tore Supra[3].

The lower collisionality in the LOC plasmas will increase the effect of trapped

particles, enhancing the TEM. Moreover, the LOC plasma has higher mean a/LTe .

Since TEMs are driven by electron pressure gradient scale length[31, 32], higher a/LTevalue could destabilize TEMs. Thus, we can expect that TEMs are more unstable

in the LOC plasma at the CECE measurement position. On the other hand, ITG

modes are driven by the parameter, ηi, which is defined by the ratio of density gradient

length to ITG length. Assuming the ion density gradient is similar to the electron

density gradient, ηi value will be similar in both plasmas since the two plasmas have

similar a/Lne and a/LTi . Thus, we expect a similar level of ITG turbulence at CECE

measurement position. Unfortunately for these plasmas, we do not have a reliable

profile of the radial electric field from which to extract the ExB shearing rate at the

CECE measurement position. However, we expect ExB shearing rate at the CECE

measurement position is very similar for these two plasmas since the radial electric

field can be approximated as VtorBpol for these ohmic plasmas, and the rotation profile

outside q=3/2 surface is not changed across LOC/SOC transition[9]. Quantitative ExB

shearing rates will be obtained in the future to allow for comparisons with linear growth

rates.

The results of linear GYRO simulations at the CECE measurement position are

shown in Figure 9. From the linear GYRO simulation, we can obtain the information

about the dominant mode (fastest growing mode) which has the largest growth rate. In

order to obtain more information about the turbulence, including sub-dominant modes

and interaction between modes, a nonlinear simulation is required, and this is left for

future work. In Fig. 9, the real frequency(ωr) and growth rate(γ) of the dominant

turbulence mode is shown as a function of kyρs. Figure 9(a) and (b) show the results in

LOC and SOC plasma, respectively. The frequency and growth rate are normalized by

cs/a, where cs is the ion sound speed, and a is the minor radius of the plasma. In the

GYRO simulation, a positive real frequency indicates modes rotating in the electron

diamagnetic drift direction and a negative frequency indicates modes rotating in the

ion diamagnetic drift direction. The real frequency has a positive value over the whole

kyρs range in the simulation from Figure 9(a), indicating electron mode turbulence

is dominant in the LOC plasma at the CECE measurement position. However, from

Figure 9(b), it is hard to say what the dominant turbulence mode in the SOC plasma is

because ion modes are dominant in the low kyρs range (long wavelength turbulence) and

the dominant mode changed in kyρs larger than 0.6 in the SOC plasma. It is noteworthy


that CECE can only measure long wavelength fluctuations, which have kyρs < 0.3. In

Figure 9, the shaded region indicates the values of kyρs to which CECE is most sensitive.

In this long wavelength region, it is possible that electron modes are connected to TEMs,

and ion modes are connected to ITG modes. The linear stability analysis indicates that

the larger broadband TeTe

fluctuations that CECE measures in LOC plasmas come from

TEM driven turbulence, which is diminished as ITG modes became dominant in the

SOC plasma.

In order to consider errors of input profiles in Figure 7 and to determine the driving

gradients for the ion and electron modes identified in Figure 9, we performed a scan of

the gradients a/LTi and a/LTe . Figure 10 shows the result of this analysis where the

contours of the growth rate of the most unstable linear mode in the kyρs range[0.1-0.3]

are plotted. This kyρs range was chosen to best evaluate changes in the long wavelength

turbulence measured by CECE. However, we note that the qualitative results are not

changed when kyρs range is extended to higher value(∼ 0.6). The x and y axes indicate

the values of a/LTi and a/LTe used in each simulation, respectively, and the thick black

line in the contour indicates the boundary between electron and ion modes. The location

of the a/LTi and a/LTe value from the experiment is marked by + sign, and shaded

region indicates the experimental region within the errors. We can see that the growth

rate in the upper left region is sensitive to the a/LTe value. Consequently, the dominant

turbulence mode in this region is driven by the electron temperature gradient, indicating

TEM-type turbulence. In contrast, the growth rate of lower right region of the contour

is sensitive to the a/LTi value, so that the dominant mode in this region is driven by

the ion temperature gradient, indicating the ITG mode. From Figure 10(a), it can be

seen that the LOC plasma is in the electron mode dominant region in most of the input

data range, including errors. We can note that the SOC plasma is near the boundary

between TEM and ITG mode, Figure 10(b). The error for a/LTi in Figure 7 came from

the photon statistics. There will be also instrumental error. In order to include errors

from both photon statistics and instrumental error, the error of a/LTi was set to 20%

in this contour.

The linear analysis of these plasmas indicates a change from TEM to ITG across

the LOC/SOC transition only in the edge region where CECE measurements are made.

This is interesting since it is the rotation reversal across the LOC/SOC transition occurs

further inside, near the q=3/2 surface, and ITG/TEM stability only changes outside

of this region. The linear analysis at r/a∼0.5 is shown in Figure 11. Both LOC and

SOC plasmas are ion mode dominant at this radial location. This result is consistent to

the previous non-linear GYRO analyses for LOC/SOC plasmas in C-Mod[16], and also

consistent with another C-Mod study that showed the LOC/SOC plasmas straddled the

linear ITG/TEM boundary at r/a∼0.6[11]. In order to explore the ITG/TEM transition

deeper in the core, we need to measure local electron temperature fluctuations farther

inside. However, the present CECE optics limit the CECE measurement position up to

ρ ∼0.7, and CECE measurements deeper inside LOC and SOC plasmas is left for future

work.


Although the linear stability analysis results suggest that the measured reduction in

electron temperature fluctuations at ρ ∼0.8 across the LOC/SOC transition is consistent

with a change from TEM to ITG turbulence, we need more information to understand

the change in global ohmic energy confinement. From linear stability analysis alone

we do not obtain information about the heat flux or fluctuation levels, and in the

experiment we cannot measure phase angles for fluxes directly. However, we can combine

experimental data with theoretical predictions to estimate the differences in turbulent

heat fluxes for the C-Mod plasmas of interest. To do this, we calculate the linear

cross phase angle between two fluctuating quantities from GYRO, which is a function of

poloidal wave number, ky. We then calculate the phase angle between the two fluctuating

fields by averaging over CECE relevant values of ky. Using this calculated phase

angle and the measured fluctuation levels, we estimate the heat flux due to turbulence.

Since we cannot know the change of potential fluctuation level and the change of the

average wave number of the fluctuations from either the linear GYRO simulation or the

measurements in this study, there are still limitations in the following analysis. However,

tracking the change of calculated linear phase angle between two fluctuating quantities

will help elucidate the physics of LOC/SOC transition. We emphasize that only linear

phase angles are used in our analysis here. In past simulation studies, it was found that

the phase angles from linear analysis agree well with the phase angles from non-linear

gyrokinetic simulations for experimentally relevant values of normalized gradient scale

lengths[33, 34].

The energy flux due to electrostatic turbulent transport, Q, is given by < 32pvr >,

where p is the fluctuation in the pressure, vr is the radial ExB velocity. In addition, <>

indicates that this is an averaged quantity. This can be expressed as,

Q =3

2

pkyBt

[<|n||φ|n

sinαn,φ > + <|T ||φ|T

sinαT,φ >] (10)

From Eq. 10, we can see that turbulent energy transport is a function of phase angle,

as well as the fluctuating amplitude. If the phase angle between n and φ, αn,φ = 0, then

there will be no contribution from density fluctuations to turbulent heat transport. We

can expect the same relation for the phase angle between T and φ, αT,φ. Thus, not

only the fluctuating amplitude but also the cross phase angle can be a good indicator

of which fluctuating quantity can significantly affect the transport. Since energy flux

is approximately proportional to γ/k2y, long wavelength (low ky) turbulence dominates

the energy transport[35].

We evaluate the mean phase angles αn,φ and αT,φ for small kyρs, up to ∼ 0.3,

roughly the range to which CECE is sensitive. Table 2 shows αn,φ and αT,φ for both

electrons and ions at the CECE measurement position in the LOC and the SOC plasmas.

For phase angles between n and φ, both electron and ion phase angles (αne,φ, αni,φ) are

changed from ∼ 100 to ∼ 40 after the LOC/SOC transition. This implies that the

contribution of density fluctuations to heat flux will be decreased for both the ion and

electron channels if the amplitude of density fluctuations stays the same. In contrast,

the phase angle between Te and φ, αTe,φ is near 90 in both LOC and SOC regimes, and


Table 2. The phase angles between density and potential fluctuations (αn,φ) and

the angle between temperature and potential fluctuations (αT,φ) depending on species

(ion, electron) and ohmic confinement regime (LOC, SOC). These angles are the mean

values in the low kyρs region up to ∼ 0.3.

LOC SOC

(1120626023) (1120626028)

αne,φ [degree] 96.9 41.2

(sinα) (0.99) (0.66)

αTe,φ [degree] 84.6 103.1

(sinα) (1.00) (0.97)

αni,φ [degree] 108.6 40.3

(sinα) (0.95) (0.65)

αTi,φ [degree] 45.5 76.5

(sinα) (0.71) (0.97)

the phase angle between Ti and φ, αTi,φ, changes from ∼ 46 to ∼ 77, which indicates

that in the SOC regime, even if the Ti amplitude stays the same, the change in phase

angle means that the Ti contribution to the ion heat flux, Qi is increased.

Since we measure lower electron temperature fluctuations in the SOC regime,

and the calculated sinαTe,φ is almost the same in both regimes, we can expect that

contribution to the electron heat flux, Qe, from Te will decrease in the SOC regime. From

the measured line-integrated density fluctuations, we find that the relative fluctuation

amplitude stays roughly the same across the LOC/SOC transition, but the calculated

sinαne,φ is reduced in the SOC regime, which indicates that due to the change in phase

angle (rather than amplitude), the contribution to Qe from ne is reduced in the SOC

regime. Based on linear phase angle calculations and the measurements of the two-field

fluctuations, we conclude that the electron heat flux should actually be reduced in the

SOC regime but the ion heat flux should increase compared to LOC regime.

The difference in experimental heat diffusivities between the LOC and SOC plasmas

are consistent with the estimates of turbulence-driven heat fluxes calculated changes in

the linear phase angle and measured fluctuation levels, Te/Te and |∫nedl|/nel. For ions,

we find that the SOC plasma has higher ion heat diffusivity and heat flux than the LOC

plasma. It is noteworthy that our analysis shows that Ti changed to in phase with φ

in the SOC regime, which implies that ion heat transport can be enhanced due to the

increase of the contribution of Ti in the SOC regime even if the amplitude of Ti stays

the same. By “in phase” we mean the phase angle that gives the maximum contribution

to heat transport, i.e., α = π/2. Consequently, “out of phase” indicates α = 0, with

minimum contribution to heat transport. Our analysis indicates the saturation of energy

confinement in ohmic plasmas is due to the increase of the ion heat flux, which can be

attributed to phase angle changes (rather than fluctuation level changes). Since ITG

turbulence has long been considered to be the reason for the saturation of confinement in

ohmic plasmas, it is possible that this phase change is related to the change from TEM


to ITG turbulence in ohmic plasmas as density is increased. To explore this further,

nonlinear gyrokinetic analysis and expanded measurement capabilities are required.

5. Summary and Conclusion

In this study, we have examined for the first time changes in both electron temperature

fluctuations and density fluctuations measured simultaneously across the ohmic

confinement transition (LOC / SOC). Local electron temperature fluctuations (ρ ∼ 0.8)

were measured by the newly commissioned CECE diagnostic, and the PCI diagnostic

was used to measure line integrated electron density fluctuations. We could not find

any clear trend from PCI measurements across the LOC/SOC transition. Density

fluctuation levels(|∫nedl|/nel) change very little despite an increase in the fluctuation

intensity(|∫nedl|2) as the average density is increased (as shown in Figure 11 in [16]).

However, from CECE measurements, we observed a robust reduction of relative electron

temperature fluctuation level, Te/Te in the SOC regime compared to the LOC. From

linear stability analysis, for the long wavelength turbulence where the CECE diagnostic

is most sensitive, kyρs < 0.3, the LOC plasma is electron mode dominant at the CECE

measurement position and the SOC plasma is ion mode dominant. These linear stability

results and the CECE measurements support the conventional interpretation of LOC

and SOC regimes: LOC is TEM dominant, and SOC is ITG mode dominant.

In order to explore this further, the phase angle between n and φ and the phase

angle between T and φ were calculated from linear analysis and were combined with

measurements of fluctuation amplitudes to estimate heat flux due to turbulence using

a simple mixing length argument. It was found that both electron and ion density

fluctuations become more out of phase with the potential as the plasma transitions

from LOC to SOC while the phase between electron/ion temperature fluctuations and

the electrostatic potential is unchanged/more in phase, respectively. Considering both

experimental results and calculated phase angles, we would expect a decrease of electron

heat transport in the SOC regime compared to the LOC regime. This is in qualitative

agreement with the experimental trend in electron heat diffusivity. We also observed

higher ion heat diffusivity in the SOC plasma, which may be consistent with the change

of ion temperature phase angle in the SOC regime, but there are no measurements of

ion temperature fluctuations available to constrain this result.

We find that the measurements of density and electron temperature fluctuations,

the experimentally inferred changes in ion and electron heat transport, and the linear

gyrokinetic analysis results presented in this paper are consistent with the conventional

interpretation or hypothesis about the LOC/SOC transition. However, we also realize

that this ansatz is a crude statement. We have also shown that the dominant linear

instability varies across the plasma profile in LOC and SOC plasmas and it is therefore

hard to say which mode, in which region, may be responsible for the global transition of

confinement regime. Thus, additional measurements full profiles of local fluctuations, as

well as global (line integrated) fluctuations are required to further investigate the physics


of the LOC/SOC transition. Future analysis using non-linear gyrokinetic simulations

and CECE measurements deeper in the core will help elucidate the physics of the

LOC/SOC transition.

Acknowledgments

The authors thank S. Wolfe for EFIT analysis in C-Mod, and thank J. Wright and

T. Baker for maintaining the LOKI computer cluster, used to perform the GYRO

simulations. The authors are also very grateful to M. L. Reinke for rotation profile and

ion temperature profile analysis and for extensive discussions of error analysis. This

work is supported by the U.S. Department of Energy under Grant Nos. DE-SC0006419

and DE-FC02-99ER54512.

Appendix A. Derivation of Te fluctuation level calculation using cross

correlation coefficient

We can think of the CECE signal as having two parts, which are mean or steady part,x

and fluctuation part,x. If two signals have common electron temperature fluctuations

and do not have any correlated noise, the fluctuation part will consist of two parts, which

are thermal noise, Nth, and common electron temperature fluctuations, Te. Removing

the steady part of each signal, the fluctuation part of each signal will be,

x = Nth,x + Te/cx (A.1)

y = Nth,y + Te/cy (A.2)

where cx and cy are calibration factor of each signal.

Assuming thermal noise is not correlated, from Eq. 3 and 4, Rxx, Ryy at τ = 0 are,

Rxx(0) = N2th,x + T 2

e /c2x (A.3)

Ryy(0) = N2th,y + T 2

e /c2y (A.4)

Thermal noise can be uncorrelated each other if two signals have the disjoint

frequency bands. Through cross correlation, thermal noise can be eliminated and

common electron temperature fluctuations will be revealed. Then, from Eq. 5, Rxy

is,

Rxy(0) = T 2e /(cxcy) (A.5)

Using Eq. A.3-A.5, the cross correlation coefficient when lag time is 0, Cxy(0) will be,

Cxy(0) =T 2e /(cxcy)√

(N2th,x + T 2

e /c2x)(N

2th,y + T 2

e /c2y)

(A.6)

Thermal noise level of the radiometry is given by[36],

N2th,x =

2Bvid

BIF

x2 =2Bvid

BIF

T 2e /c

2x (A.7)


N2th,y =

2Bvid

BIF

y2 =2Bvid

BIF

T 2e /c

2y (A.8)

For the CECE diagnostic in this study(Bvid=0.5MHz,BIF=200MHz), the thermal noise

level is ∼ 7% of mean value of the signal. Considering temperature fluctuations are

∼ 1%, we can ignore the contribution of electron temperature fluctuations in auto

correlation functions(Rxx, Ryy).

Rxx(0) = N2th,x + T 2

e /c2x ' N2

th,x =2Bvid

BIF

T 2e /c

2x (A.9)

Ryy(0) = N2th,y + T 2

e /c2y ' N2

th,y =2Bvid

BIF

T 2e /c

2y (A.10)

Using Eq. A.9 and A.10, Cxy(0) will be,

Cxy(0) =T 2e /(cxcy)√

(2Bvid

BIFT 2e /c

2x)(

2Bvid

BIFT 2e /c

2y)

=BIF T

2e

2BvidT 2e

(A.11)

Thus, relative fluctuation level(Te/Te) is,

TeTe

=

√2Bvid

BIF

Cxy(0) (A.12)

Appendix B. Derivation of Te fluctuation level calculation using cross

spectral density function

We can also obtain the relative fluctuation level(Te/Te) by integrating the cross spectral

power density, Gxy(f). The root mean square(RMS) fluctuation amplitude of the CECE

signal can be obtained by integrating the cross spectral power density in the frequency

range in which broadband fluctuations are observed[26]. For uncalibrated signals, the

RMS fluctuation amplitude will be proportional to the integration of the cross spectral

power density.

T 2e = cxcy

∫ f2

f1|Gxy(f)|df (B.1)

where cx and cy are calibration factors for x(t) and y(t) respectively, and [f1, f2] is the

frequency range in which the fluctuations are observed.

In order to obtain the relative fluctuation level, Te/Te for the uncalibrated signal,

we should find the mean temperature, Te from this signal. From appendix A, it was

shown that the auto correlation when lag time is equal to 0 or variance of the signal is

mostly given by thermal noise. Thus, using Eq. A.7, we can reasonably approximate

the variance of the signal is,

V ar[x(t)] =2Bvid

BIF

x(t)2 (B.2)

As appendix A, x(t) is represented as x(t) = x(t) + x(t).

According to Parseval’s theorem, the sum of the square of time series data is the

same as the sum of the square of Fourier transformed data. When the measured time


range is from t1 to t2 and total measuring time is T, Parseval’s theorem can be written

as, ∫ t2

t1|x(t)|2dt =

∫ ∞−∞|XT (f)|2df (B.3)

where XT (f) is the Fourier transformed quantity during time length, T. The variance

for the data is defined as,

V ar[x(t)] =1

T

∫ t2

t1|x(t)− x(t)|2dt =

1

T

∫ t2

t1|x(t)|2dt (B.4)

Using Eq. B.4 and Parseval’s theorem, we can obtain the information of the mean

value from the Fourier transformed quantity. Assuming we treat only the fluctuating

component for the Fourier transform, i.e., x(t) = 0, variance can be represented as,

V ar[x(t)] =1

T

∫ t2

t1|x(t)|2dt =

2

T

∫ ∞0|XT (f)|2df (B.5)

Then, the average value, x(t), can be obtained:

x(t)2 =BIF

2Bvid

2

T

∫ ∞0|XT (f)|2df (B.6)

The mean temperature in CECE measurements can be obtained using a calibration

factor in Eq. B.1.

Te2 = c2x

BIF

2Bvid

2

T

∫ ∞0|XT (f)|2df (B.7)

In CECE measurements, two data sets are required. Assuming that the temperatures

from two adjacent channels are the same, the mean temperature and the relative

fluctuation level(Te/Te) will be represented as,

Te2 = cxcy

BIF

2Bvid

2

T[∫ ∞0|XT (f)|2df

∫ ∞0|YT (f)|2df ]0.5 (B.8)

TeTe

=

√√√√ 2BvidT∫ f2f1|Gxy(f)|df

2BIF [∫∞0 |XT (f)|2df

∫∞0 |YT (f)|2df ]0.5

(B.9)

Using Eq. B.9, the relative Te fluctuation level can be determined.

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Figures

0.0 0.5 1.0 1.5 2.00

10

20

30

40

50

τE (

ms)

5.2 T 0.81 MA

89-P

LOC SOC

ne (1020m3)

Figure 1. An example of the ohmic confinement transition in Alcator C-Mod

discharges (Bt = 5.2T, Ip = 0.81MA). The vertical axis is the energy confinement

time [ms] and the horizontal axis is the line averaged electron density [1020m−3]. The

energy confinement time saturates as density increases above shaded transition region.

The solid green line is fit to the data in the LOC regime, and the purple dash-dot line

is the ITER 89P L-mode scaling. Adapted from ‘Ohmic energy confinement saturation

and core toroidal rotation reversal in Alcator C-Mod plasmas’ by J. E. Rice et al, 2012,

Physics of Plasmas, 19, 056106, copyright 2013 American Institute of Physics.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

Ip [MA]

0.0

0.5

1.0

1.5

<ne,line> [1020m-2]

0.0

0.5

1.0

1.5

2.0

ne,CECE [1020m-3]

0.9 1.0 1.1 1.2 1.3 1.4

time [sec]

0.0

0.5

1.0

1.5

2.0

Te,CECE [keV]

-30

-20

-10

0

10

20

30

Vtor (0) [km/s]

(a) (b)

(c) (d)

(f )

0.9 1.0 1.1 1.2 1.3 1.4

time [sec]

0.0

1.0

2.0

3.0

4.0

Te (0) [keV](e)

Figure 2. Time series data during CECE measurement time for LOC

(shot:1120626023, red solid line) and SOC (shot:1120626028, blue dotted line) plasma.

(a) Plasma current [MA], (b) central chord line integrated density [1020m−2], (c)

electron density [1020m−3] at CECE measurement position (ρ ∼ 0.8), (d) electron

temperature [keV] at CECE measurement position (ρ ∼ 0.8), (e) electron temperature

[keV] at plasma center, (f) central toroidal velocity [km/s].

Co

he

ren

ce(γ

) o

f T

e

uct

ua

tio

n

0.02

0.04

0.06

0.10

100 200 300 400 500

f (kHz)

0.00

0.08

0

0.12

statistical limit

Co

he

ren

ce(γ

) o

f T

e

uct

ua

tio

n

0.02

0.04

0.06

0.10

100 200 300 400 500f (kHz)

0.00

0.08

0

0.12

statistical limit

(a) (b)

Cro

ss p

ha

se a

ng

le [

de

gre

e]

0

100

-100

100 200 300 400 500

f (kHz)

0

(C)

Cro

ss p

ha

se a

ng

le [

de

gre

e]

0

100

-100

100 200 300 400 500

f (kHz)

0

(d)

LOC (1120626023) SOC (1120626028)

Figure 3. (a) Coherence(γ) of two CECE signals in the LOC plasma

(shot:1120626023), horizontal dotted line indicates the statistical limit of coherence

(b) Coherence(γ) of two CECE signals in the SOC plasma (shot:1120626028) (c) the

cross phase spectrum of two CECE signals in the LOC plasma (d) the cross phase

spectrum of two CECE signals in the SOC plasma.


Cro

ss-c

orr

ela

tio

n c

oe

ci

en

t

0.00

0.01

0.02

-20 0 20 40lag time (μs)

-0.01-40

Cro

ss-c

orr

ela

tio

n c

oe

ci

en

t

0.00

0.01

0.02

-20 0 20 40lag time (μs)

-0.01-40

(a)

(b)

LOC (1120626023)

SOC (1120626028)

Figure 4. (a) Cross correlation coefficient(Cxy) depending on lag time(µs) of two

CECE signals in LOC plasma (shot:1120626023) (b) Cxy depending on lag time of two

CECE signals in SOC plasma (shot:1120626028).


-15 -10 -5 0 5 10 15

100

200

300

400

500

600

Fre

qu

en

cy [kH

z]

(n/n

)2/c

m-1/k

Hz

LOC PCI Spectrum

-15 -10 -5 0 5 10 15

100

200

300

400

500

600

Fre

qu

en

cy [kH

z]

SOC PCI Spectrum

(a)

(b)

Wavenumber [cm-1]

Wavenumber [cm-1](n

tild

e/n

)2/c

m-1/k

Hz

10-8

10-9

10-10

tild

e

10-11

10-12

10-13

10-8

10-9

10-10

10-11

10-12

10-13

Figure 5. Normalized frequency/wavenumber spectra (S(kR, f)/ne) of PCI

measurements (a) in LOC (shot:1120626023) and (b) in SOC (shot:1120626028)

plasmas.


(a)

(b)

Figure 6. Time averaged relative fluctuation level depending on average electron

density normalized to the critical density for rotation reversal due to the LOC/SOC

transition (a) electron temperature fluctuation level at ρ ∼ 0.8, black points are relative

electron temperature fluctuation levels without considering density fluctuations, and

red points are minimum values of the relative electron temperature fluctuation level

when relative density fluctuation level is 2% (b) line integrated density fluctuation

level.


0.5

1.0

1.5

0.0

2.0

0.5

1.0

1.5

0.0

2.0

5

10

15

0

20

1

2

0

3

0.5

1.0

1.5

0.0

2

0

4

6

8

0.0 0.2 0.4 0.6 0.8 1.0

(c) Te (keV)

(e) Ti (keV)

(a) ne (1020m-3) (b) a/Lne

(d) a/LTe

(f ) a/LTi

0.0 0.2 0.4 0.6 0.8 1.0

(g) Te/Ti

0.5

1.0

1.5

0.0

2.0

2.5

LOC (1120626023) SOC (1120626028), t=0.9-1.4s

40

30

20

10

0

-10

-20

(h) Vtor (km/s)

(i) νe*

1.0

2.0

3.0

0.0

4.0

5.0

1

0

2

3

4

(j) q

Figure 7. Time averaged profiles during 0.5s (t:0.9-1.4s). The red line indicates LOC

plasma (shot:1120626023) and the blue line indicates SOC plasma (shot:1120626028).

The solid lines show time averaged values and the dotted lines are the error in the

profiles. The green vertical line indicates the CECE measurement position for these

plasmas.


LOC (1120626023) SOC (1120626028)

(a) χe [m2/s]

(c) χi [m2/s]

0.2 0.4 0.6 0.8 1.00.2 0.4 0.6 0.8 1.00.00

0.05

0.10

0.15

0.20

0.00

0.10

0.20

0.30

0.40

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

3.0

2.5

(b) Qe [MW/m2]

(d) Qi [MW/m2]

, t=0.9-1.4s

Figure 8. Experimental electron and ion heat diffusivities(χe, χi) and

heat fluxes(Qe, Qi) from TRANSP. The red line indicates the LOC plasma

(shot:1120626023) and the blue line indicates the SOC plasma (shot:1120626028). The

solid lines show the time averaged values and the dotted lines are the errors from time

averaging.


0.0

0.2

0.4

0.8

0.6

0.0

1.0

-0.5

0.5

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

ωr [

cs/a

]

γ [c

s/a

]

1.5

0.0

0.2

0.4

0.8

0.6

0.0

1.0

-0.5

0.5

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

ωr [

cs/a

]

γ [c

s/a

]

1.5

(a)

(b)

electron direction

ion direction

electron direction

ion direction

LOC (1120626023)

SOC (1120626028)

Figure 9. Linear stability analysis from GYRO simulation at CECE measurement

position(ρ ∼ 0.8) for (a) LOC plasma (shot:1120626023) and (b) SOC plasma

(shot:1120626028). The left figures show real frequency(ωr), and the right figures

show the growth rate(γ) of the dominant turbulence mode. The unit is cs/a, where a

is the minor radius of the plasma, and cs is the ion sound speed. cs/a = 6.38× 105s−1

for (a), and cs/a = 5.78× 105s−1 for (b).


Growth Rate of Most Unstable Mode (c_s/a)

3 4 5 6 7

a/LTi

6

8

10

12

a/L

Te

0.136

0.181

0.226

0.226

0.272

0.272

0.3

17

0.317

0.362

0.407

0.2260.226

3 4 5 6 7

a/LTi

4

5

6

7

8

9

a/L

Te

0.0

83

0.1

24

0.1

65

0.2

07

0.207

0.2

48

0.248

0.2

89

0.289

0.3

31

0.331

0.3

72

0.2070.207

TEM

ITG

TEM

ITG

(a)

(b)

Figure 10. The maximum growth rate contours of the dominant mode in the range

kyρs=[0.1-0.3] depending on a/LTeand a/LTi

for (a) LOC (shot:1120626023) and (b)

SOC (shot:1120626028) plasmas. The shaded region indicates the measurement range

including errors.


0.02

0.04

0.06

0.00

0.10

-0.02

-0.3

0.0

-0.4

-0.20.08

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

ωr [

cs/a

]

γ [c

s/a

]

-0.1

-0.5

-0.6

0.12

0.02

0.04

0.06

0.00

0.10

-0.02

-0.3

0.0

-0.4

-0.20.08

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

kyρs0.4 0.6 0.8 1.00.0 0.2 1.2

ωr [

cs/a

]

γ [c

s/a

]

-0.1

-0.5

-0.6

0.12

(a)

(b)

LOC (1120626023)

SOC (1120626028)

Figure 11. The result of linear stability analysis at r/a = 0.5. (a) is the

result for the LOC plasma(shot:1120626023) and (b) is the result for the SOC

plasma(shot:1120626028). cs/a = 1.32 × 106s−1 for (a), and cs/a = 1.10 × 106s−1

for (b).

Changes in Core Electron Temperature Fluctuations Across...

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