Localization of the WCM and the QCM in the Er well

C. Theiler, J. Terry, R.M. Churchill, J. Hughes, B. LaBombard et al.

C-Mod ideas forum 2014

We know that in I-mode …

2  C. Theiler et al., C-Mod ideas forum, 2014

… low frequency fluctuations are suppressed and WCM (and GAM) appear:

the GAM activity to where the mean Er well is detected viaCXRS.

This observation has three important implications: (1)the fluctuations of the poloidal flow velocity have a non-zeromean flow background, (2) the poloidal speed of the WCMat its maximum can be measured in the frame co-movingwith the average E! B flow, and (3) the shared spatial loca-tion of the GAM and WCM open up the question of temporalcharacteristics and mode interaction in this increasinglycomplicated picture of edge turbulence.

The first one of these can be approached from the oppo-site perspective as well, namely, that it is the edge zonal flowthat is fluctuating. While the latter phrasing corresponds wellto the theoretical expectation of the collisionless GAMdamping which leaves behind the Rosenbluth–Hinton resid-ual, i.e., the zonal flow,1,10,39 it also highlights the need for aquantitative comparison between the two flows. The samplethat is analyzed for both steady state electric field and GAMprofiles in Fig. 6 was taken from a steady I-mode, with awell-developed temperature pedestal and Er-well, both ofwhich lie in the mid-range of values observed during C-ModI-mode discharges.21 It is worth mentioning here that thebackground flow and the turbulence driven component ofthis electric field are experimentally indistinguishable. Thegraphed GAM profile (mode amplitude, i.e., 1/2 peak-to-peak) shows a typical magnitude in the velocity fluctuationof ~vh " 2:2 km=s corresponding to ~Er " 10 kV=m, while thedepth of the time-average well is approximately!Er " 30 kV=m. Due to the considerable amount of noise inthe detection of velocities from the motion of turbulent struc-tures, the empirical GAM amplitude must be regarded as alower estimate. Even so the slowly evolving edge flow(including ZF) velocity and the GAM amplitude velocity areof comparable magnitude and, therefore, the radial shear isat least partially periodically destroyed in an I-mode.

For the second point, we here note that we are consideringthe “central” frequency of the WCM, the meaning of whichwill be elucidated in Sec. V. For now, we simply take it as thecentroid of the frequency range at which the WCM appears inthe shot plotted in Fig. 6, fWCM " 200 kHz. This leads to apropagation speed in the frame moving with the local E! Bvelocity at vh " 12:163:8 km=s in the electron diamagneticdrift direction (including an error of only 20kHz in the fre-quency, see Sec. V). The speed is still considerably smallerthan the electron diamagnetic velocity at v#e " 31610 km=s.

Finally, Fig. 7 shows the spectrograms of poloidal velocityand density fluctuations in a typical I-mode onset followed bya long, steady I-mode, which lasts longer than the 0.3 s dura-tion of the GPI data window. In the given example, the L-Itransition settles at 1.13 s, marked by the change of slope inthe decay of the edge electron temperature following the ar-rival of the heat-pulse due to the sawtooth crash shown in thetop two panels of the figure. The two “dithers” into I-modebefore this time are rather common at the onset of the regime,their “on”-phase always triggered by the temperature increaseat the arrival of sawtooth heat-pulses.40 As previously reported,the WCM is completely contemporaneous with the I-mode. Itis important to note, however, that the WCM only appears asthe distinguishable, broad feature at high frequencies, whenthe GAM (apparent as the narrow peak in the middle panel) ispresent. The GAM appears sensitive to local Te, as a drop of$100 eV %$ 20%& during the sawtooth cycle in this transientstage is enough to eliminate it, while in the case of the WCM,it is the lab frame frequency of the mode that is clearly modu-lated by the temperature fluctuations, perhaps indicating aDoppler-shift by a temporary increase of the diamagnetic com-ponent of Er. Nevertheless, the most obvious feature of theexperiment is that in the I-mode the GAM is not a transientmode that quickly dissipates and leaves behind the residualRosenbluth–Hinton-flow to saturate turbulence, but it exists

FIG. 6. Radial location of the edge turbulence features in I-mode; (top) ra-dial profile of the mode amplitude of the WCM (squares, right axis) and theGAM (full circles, left axis) exhibiting nearly identical distributions; (bot-tom) radial electric field profile in the same I-mode discharge as above in asample including the time of the velocity measurement. Profile is calculatedfrom CXRS measurements.

FIG. 7. Time history of a long lived I-mode discharge; (a) core electron tem-perature, (b) electron temperature at the GAM measurement location, i.e.,the top of the pedestal, (c) spectrogram of the TDE poloidal velocity ~vh, (d)spectrogram of density fluctuations ~n in the same spatial location restrictedto a wavenumber range 0:5 cm'1 < kh < 2:0 cm'1 to highlight the WCM.(a) and (b) are measured via ECE and (c) and (d) by GPI.

055904-5 Cziegler et al. Phys. Plasmas 20, 055904 (2013)… Er wells are relatively deep and asymmetric:

ρ

However, there is currently no reliable radial alignment of GPI and edge CXRS measurements

Ø  Location of WCM inside Er well unknown Ø  Phase velocity of WCM in plasma frame unknown Ø  Role of Er well in I-mode transport barrier not clear

0

500

1000

T B5+ [e

V]

0.92 0.94 0.96 0.98 1 1.02!80

!60

!40

!20

0

20

40

60

!

E r [kV/

m]

Shot

: 112

0921

026

Tim

e:0.

966s

!1.

145s

TpolTtor

Er

GPI-CXRS alignment based on recent in-vessel calibrations questionable

3  C. Theiler et al., C-Mod ideas forum, 2014

87 87.5 88 88.5 890

500

1000

r [cm]87 87.5 88 88.5 89

100

50

0

87.5 88 88.5

100

200

300

400

500

600

700

800

r [cm]87.5 88 88.5

100

80

60

40

20

0

20

40I-mode EDA H-mode

Er Er

Ti Ti

GPI views detecting WCM

GPI views detecting QCM

Contradicts measurements with MLP in ohmic, small R-gap EDA H-modes !

Plan: Radially align GPI and CXRS by connecting GPI detectors to CXRS views

4  

GPI views (tor)

CXRS views (pol)

CXRS views (tor)

C. Theiler et al., C-Mod ideas forum, 2014

C-Mod top view

GPI detectors

CXRS detectors

GPI detectors

•  Align views in EDA H-mode based on QCM location

•  Try to align views in I-mode based on WCM location or e.g. skewness profile

•  Compare with MLP whenever possible