January, 2016

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 and others at MIT and DE-AC02-09CH11466 at PPPL. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

PSFC/JA-16-1

Locked-Mode Avoidance and Recovery without External Momentum Input

L. Delgado-Aparicio1, J. Rice2, E. Edlund2, I. Cziegler3,L. Sugiyama4, D. Gates1, J. Terry2, S. Wolfe2,C. Gao2,

T. Golfinopoulos2, J. Irby2, R. Granetz2, Y. Lin2, S. Wukitch2,M. Greenwald2, A. Hubbard2, J. W. Hughes2, M. Porkolab2,E. Marmar2, S. Houshmandyar5, P. Phillips5 and W. Rowan5

1PPPL, Princeton, NJ, 08540, USA 2MIT - PSFC, Cambridge, MA, 02139, USA 3UCSD, San Diego, CA, 92093, USA 4MIT - LNS, Cambridge, MA, 02139, USA 5The University of Texas at Austin, TX, 78712, USA

Locked-mode avoidance and recovery without external momentum input

L. Delgado-Aparicio1, J. Rice2, E. Edlund2, I. Cziegler3, L. Sugiyama4, D. Gates1, J. Terry2, S. Wolfe2,

C. Gao2, T. Golfinopoulos2, J. Irby2, R. Granetz2, Y. Lin2, S. Wukitch2, M. Greenwald2, A. Hubbard2,

J. W. Hughes2, M. Porkolab2, E. Marmar2, S. Houshmandyar5, P. Phillips5 and W. Rowan5

1PPPL, Princeton, NJ, 08540, USA2MIT - PSFC, Cambridge, MA, 02139, USA

3UCSD, San Diego, CA, 92093, USA4MIT - LNS, Cambridge, MA, 02139, USA

5The University of Texas at Austin, TX, 78712, USA(Dated: January 17, 2016)

New observations of the formation and dynamics of error-field-induced locked-modes at ITERtoroidal fields, without fueling and external momentum input have recently been carried out onAlcator C-Mod. Delay of the mode onset and recovery from pre-existing locked-modes has beensuccessfully obtained using Ion Cyclotron Resonance Heating (ICRH). The use of external heatingconcomitant with the n = 1 error-field ramp-up resulted in a delay of the mode-onset avoidingthe density pump-out and achieving high-confinement “H-modes”. Heating the low-density plasmaafter the mode-onset was not conducive to an L→H transition but resulted in unlocking the plasmawithout external torque and obtaining co/counter-current flows at the edge/core. This simple heat-ing technique could provide an important actuator to circumvent error-field-induced locked-modedisruptions in tokamak plasmas.

The objective of tokamak research is to demonstratethe scientific and technological feasibility of fusion powerfor world energy production. One fundamental advan-tage of the tokamak concept is its toroidal symmetry.However, magnetic field perturbations arise inevitablybecause of departures from axisymmetry due to imper-fections or misalignment of the poloidal and toroidal fieldcoils, current feeds to these coils, eddy currents and fer-ritic material in the vicinity of the plasma. These smalldeviations from toroidal axisymmetry are well known todestabilize non-rotating tearing modes (also known aslocked-modes), which can significantly impact plasma op-eration. Experimentally, it has been confirmed that a res-onant field component with (2, 1) poloidal and toroidalharmonics can induce a locked magnetic island in bothconventional and spherical tokamaks [1]-[8].

Controlled experiments with error-field-inducedlocked-modes are observed to result in a strong densitypump-out due to the effect of the resonant magneticperturbation, partial or complete braking of toroidalrotation, modification of pressure-driven ‘sawteeth’instabilities and a significant reduction in energy andparticle confinement, often leading to disruptions andassociated vertical displacements. The deleterious effectsfrom these 3D perturbations are more easily producedin low-density plasmas, and so are of most concernfor ITER, especially during the early heating phaseproposed for high-confinement “H-mode” access. Thisrestriction has placed design and operational constraintsusing error-field-correction by 3D coils and various formsof driving plasma rotation for mode stabilization.

The relative magnitude of the critical helically resonantfield obtained from torque balance considerations is often

parameterized as B(m,n)⊥ /BT ∝ ω0τA (τrec/τv)

1/2where,

ω0 is a function of the rotation frequency, τA is the Alfventime, and τrec/τv is the reconnection time normalized

to the viscous diffusion time (see [1]-[8] and referencestherein). For a given perturbation, locking is favored atlower density as the EM torque is applied in slowing lessmass with a weak dependence on magnetic field sinceτA ∝

√ni/B. In the absence of bulk rotation, the rota-

tion frequency for a tearing mode is of the order of theelectron diamagnetic frequency ωe,D = ∇pe/eneBr, sothe sensitivity to error fields is expected to be greater asthe device size and field increases.

Experimental locked-mode threshold studies have con-sidered only engineering/global macroscopic parametersresulting in a scaling law of the form Blockr /BT ∝nαne BαB

T qαq

95RαR0 [1]-[8]. The determination of this depen-

dence is useful for extrapolating low-aspect and standard-aspect ratio tokamak results to ITER. However, theinfluence of drift-MHD as well as collisional and neo-classical flow-damping effects dependent on local kineticprofiles [9]-[12] can alter the predicted scaling. Includ-ing the effects of toroidal rotation (ωφ), the locked-

mode threshold can be modified to δB(2,1)(ωφ)/BT =(δB(2,1)/BT

)·(0.2ωφ/ωi,D)

3/2, where ωi,D is the ion dia-

magnetic frequency [12]. This scaling suggests that thereis a strong dependence on rotation frequency, offering awindow of opportunity for mode stabilization regardlessof the torque source (e.g. extrinsic or intrinsic).

An obvious actuator for raising the error field thresholdis thus spinning the plasma using the external torque im-parted by a tangential neural-beam-injection (NBI) sys-tem. An increase of up to a factor of two in thresholdwith NBI has been demonstrated experimentally on DIII-D in L-mode [13], TEXTOR [14] and JET experiments[6, 15]. Unfortunately, enough toroidal momentum den-sity might not be available from the beams to stabilizethe mode in ITER. Previous tests on COMPASS-D [6, 16]and new experiments DIII-D [17] have shown that localElectron Cyclotron Resonance Heating (ECRH) and Cur-

2

t=0.444 s

t=0.494 s

t=0.711 s

t=1.261 s

C-Mod # 1100909002CORE

De

nsity n

e [×

10

20 m

-3]

1.0

0.6

0.2

1.4

0.7 0.8 0.9

Radius (m)

Te

mp

era

ture

T

e [ke

V]

1.5

1.0

0.5

2.0

C-Mod # 1100909002

Icc/4

Te,0/4ne,LO4/2

Wp/100

ne [×

10

20m

-3], T

e [ke

V],

I CC [kA

], W

p [kJ]

0 0.5 1.0 1.5

Time (s)

0.8

0.6

0.4

0.2

τLM

a)

c)

d)q=2

r/a~0.65Co-

current (+)

Counter-

current (-)

Lyα-line

(H-like Ar)

w-line

(He-like Ar)

20

10

0

-10

CO

RE

Vto

roid

al,A

r [k

m/s

] b) τLM

CORE

Te [kev]

(FRC-ECE)

0.7 0.8 0.9

C-Mod # 1140815021

q=2

1

2

FIG. 1. (Color online) a)-b) Main plasma parameters fromerror-field-induced locked-mode discharge in C-Mod. The neand Te profiles during mode-locking are shown in c) and d),respectively. The location of the 2/1 surface has been deducedfrom the flattening of the Te profile shown in the inset.

rent Drive (ECCD) can also stabilize and even removelocked-modes. One ‘small’ caveat is that stabilizationbecomes impossible if the mode ‘locks’ to the error-fieldor to the vacuum vessel wall in a position not accessibleto the EC launcher. Recent experiments in DIII-D usedn = 1 magnetic perturbations to control the rotation andtoroidal phase of locked modes, positioning the mode infront of the launchers and thereby enabling their sup-pression. However, after ECCD is turned off, 2/1 locked-modes grow again. A dedicated system of n = 1 fieldsfor locked-mode suppression in ITER may not be feasiblesince RMP fields will be used for a wide variety of otherapplications such as error field correction, ELM pacingand suppression as well as RWM stabilization. There-fore, actuators based on global RF heating and currentdrive - which could also have an indirect effect modifyingthe underlying momentum transport and toroidal andpoloidal rotation - must also be considered for a simplerstabilization approach.

Error-field-induced locked-modes can be studied in C-Mod at ITER toroidal fields and without NBI fueling andexternal momentum input. The typical plasma dischargeparameters used were Ip ∼ 0.8 MA, Bφ,0 ∼ 5.4 T, q95 ∼4, with central electron temperature and densities of 2.0keV and (0.6− 1.3)× 1020 m−3 (see Fig. 1). The safetyfactor on axis was q0 ∼ 0.9 and as a result sawteethactivity was present; scenarios with other MHD activitylike long- [18, 19] and short-lived [20] modes were notconsidered. A small non-perturbative concentration ofargon was injected to asses the toroidal rotation and iontemperature with an x-ray crystal spectrometer [21, 22]without altering plasma fueling and momentum input.

Locked-mode excitation is achieved by ramping-up aset of external control “A-coils” capable of producingnon-axisymmetric, predominantly n = 1, fields with dif-

Fre

qu

en

cy (

kH

z)

40

60

20

τ0 τ1 τLM

0.4 0.6 0.8 1.0 1.2 1.4 1.6

Time (s)

C-Mod # 1100909003, BPO_GHK

FIG. 2. (Color online) 40-70 kHz magnetic signatures mea-sured at the vacuum wall appear during error field penetrationand last for the entire locked-mode.

ferent toroidal phase and a range of poloidal mode, m,spectra [7]. The time, τLM , which “marks” the change insawteeth amplitude and frequency as well as the locking-phase of the core plasma were reproducible to within ±65ms and showed to be sensitive to the density evolution(〈ne〉 ∼ 0.75 × 1020 m−3) in accordance with a stronglinear dependence of mode-locking thresholds (αn → 1).Additional features at τLM include significant braking ofthe core toroidal rotation [see Fig. 1-b)], a strong den-sity pump out due to interaction between the plasma andthe resonant magnetic perturbation at nearly the sametemperature [see Figs. 1-c) and -d)], and a flatteningof the temperature profiles which is measured using theECE diagnostic at the q = 2 rational surface [see inset inFig. 1-d)]; the saturated island is approximately 6% ofthe minor radius. The density pump-out can also be theroot for a reduction in the mode-locking thresholds, andis the main cause for a strong reduction in stored energy,confinement time and neutron production [23]-[25].

As a result of the strong pump-out there is also a con-comitant decrease in the density fluctuations measuredby reflectometers (not shown here) and the ubiquitousappearance, before τLM , of high-‘m’ coherent edge mag-netic fluctuations as shown in Fig. 2; τ0 and τ1 corre-spond to the rise-time of the control coils to their maxi-mum current of ICC = 3.5 kA as shown in Fig. 1-a). Al-though the mode begins with a frequency of 40-45 kHz,it quickly branches out to frequencies up to 70 kHz last-ing for the entire locked-mode period. These fluctuationsare not core-localized since they cannot be ‘observed’ byhigh-resolution SXR, ECE or TCI diagnostics but are de-tected at the outer plasma using magnetic probes and Hegas-puff-imaging (GPI) at the edge.

An interesting observation during the slowing-downlocking phase is a strong change of the propagation of thelocal turbulence near the last-closed flux surface (LCFS)measured also with GPI (see Fig. 3). At 7 mm insidethe nominal LCFS the data show a clear structure mov-ing poloidally in the electron diamagnetic drift direction(EDDD, kθ > 0) in contrast with the data near the out-

3

100

150

200

f (kHz)

-6 -4 -2 0 2 4 60

50

100

kθ [cm-1]

-6 -4 -2 0 2 4 6

kθ [cm-1]

GPI Col. # 7 (in) GPI Col. # 5 (out)

b) Before c) Before

d) After e) After

50

a)

EDDDIDDD

567

GPI

nozzle

LCFS

150

FIG. 3. (Color online) a) GPI edge viewing geometry in C-Mod. Conditional spectra b)-c) before and d)-e) after lock-mode onset indicates strong phase velocity changes in theEDDD (kθ > 0).

side of the LCFS [see Fig. 3-c)] which show activity onlyin the ion diamagnetic drift direction (IDDD, kθ < 0).The spectral features in the medium-frequency range (50-150 kHz) are fit well by a linear dispersion and a phasevelocity of vθ = 3.5 km/s, while the high-frequency com-ponent of the spectrum moves at vθ = 5.0 km/s. Thewavenumber - frequency-spectrum S(k, f) - or its condi-tional spectrum s(k|f) = S(k, f)/S(f) - changes dramat-ically in the process of locking: the entire EDDD prop-agating turbulence disappears [compare Figs. 3-b) and-d)] while the phase velocity in the IDDD slows down.However, this change represents no turbulence suppres-sion, as evidenced by the lack of any significant decreaseof the total observed fluctuation power (not shown here).Consequently, these results rather suggest that the prop-agation of the local turbulence at this depth changes di-rection in the lab frame which is consistent with a plasmaspin-down during the locking phase.

The toroidal and poloidal flow velocities in the bound-ary (ρ > 0.9) during a locked-mode transition [shown inFig. 4-a)] were measured using a transient D2 gas puff.These CXRS measurements show a decrease from +20km/s (co-current) to zero over the course of about 70ms. This is approximately equivalent to the time it takesfor the density to pump out as the plasma locks. Mea-surements of the toroidal velocity at the magnetic axis(ρ ∼ 0) - using the high-resolution argon x-ray imag-ing spectrometer - indicates a much slower but similarslowing-down trend reducing the core velocity from −20km/s (counter-current) to zero [see velocity time historiesinferred from He- and H-like argon emission lines shownFig. 1-b). After several confinement times the edge andcore plasma are assumed therefore to be at rest.

The first experiments aiming at delaying the mode on-set using ion cyclotron resonance heating (ICRH) areshown in Figs. 5-a), -b) and -c); for these cases heat-

0

20

Sh

ot: 1

14

08

14

00

8

Tim

e:0

.62

76

5s −

0.6

59

62

s

Toroidal CXRS

Poloidal CXRS

vφ

vθ

b) During mode-locking

0.9 0.95 1

ρ

Sh

ot: 1

14

08

14

00

8

Tim

e:0

.66

60

5s −

0.7

17

22

svφ

vθ

a) Before mode-locking

0

20

ED

GE

po

loid

al &

to

roid

al ve

locity (

km

/s)

FIG. 4. (Color online) CXRS edge poloidal and toroidal ve-locities a) before and b) during mode-locking; green arrowsindicate tendency to ‘lock’ in time.

a) PICRH

1 MW

b) PICRH

2 MW

Fre

qu

en

cy (

kH

z)

40

60

Fre

qu

en

cy (

kH

z)

40

60

Fre

qu

en

cy (

kH

z)

40

60

C-M

od #

1100909009, B

PO

_G

HK

C-M

od #

1100909010, B

PO

_G

HK

C-M

od #

1100909

015, B

PO

_G

HK

τLM

τLM

τLM

d) PICRH

1 MW

e) PICRH

2 MW

f) PICRH

3 MW

C-M

od #

1100909018, B

PO

_G

HK

C-M

od #

1100909021, B

PO

_G

HK

C-M

od #

1100909

024, B

PO

_G

HK

τLM

τLM

τLM

c) PICRH

3 MW

ICRH LM-avoidance ICRH LM-recovery

0.4 0.6 0.8 1.0 1.2 1.4 1.6

Time (s)

0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

FIG. 5. (Color online) Magnetic signatures during ICRHpower-scan aimed at a)-c) delaying LM-onset and d)-f) at-tempting LM recovery.

ing was applied in-sync with the current ramp-up of theerror-field control coils. The use of 1 MW delayed themode-onset but was not sufficient to transition into an H-mode even when the stored energy was doubled from 25to 55 kJ. However, for the 2 and 3 MW cases the plasmaexperienced L → H transitions as the average density,core ion temperature, toroidal velocity and stored energyincreased up to 2 × 1020 m−3, 2-2.5 keV, 50-60 km/s inthe co-current direction (following the Rice’s scaling [26]-[28]) and 150 kJ, respectively. Nonetheless, when ICRHpower is turned off the core plasma ‘locks’ at later timesand its characteristic high-frequency magnetic signaturesreappear until the end of the discharge [see Figs. 5-a),-b) and -c)]. The locking times (τLM ) after the heatingpulse are similar for all these cases due to nearly identicaltime-histories of density, temperature and toroidal flowvelocity. H-mode access in the presence of an error-field

4

Locked-mode

recovery

phase - ICRH

(1.04<t<1.05 s)

L-mode

before τLM(0.67<t<0.68 s)

Locked-mode

before ICRH(0.98<t<0.99 s)

r/a~0.5F

RC

EC

E -

Te [ke

V]

1.4

1.0

0.6

0.8 0.82 0.84 0.86

Radius (m)

C-M

od

# 1

14

08

15

01

40.2

r/a~0.8

q=2

r/a~0.65

FIG. 6. (Color online) Electron temperature profiles beforethe mode onset (in black), during the LM phase showingdegradation outside r/a > 0.55 (R > 81 cm, in green), andduring the LM-recovery phase re-heating the entire plasmaboth recovering and enhancing the edge gradients (in red).

and ICRF heating appears therefore not be a challengeat the high densities after the plasma Ip ramp-up.

A different set of experiments using transient ICRHpower pulses onto the low density, non-rotating phase ofthe locked-mode aimed at restoring the degraded plasmaprofiles and its gradients, as well as attempting to unlockthe core plasma. These L-mode plasmas did not expe-rience transitions to H-mode due to their lower-density(∼ 1/2 of the core density before locked-mode onset),even though PICRH was raised up to 3 MW. During theserecovery experiments, the core electron and ion temper-ature increased by 400, 600, 1000 eV when heated withPICRH=1, 2 and 3 MW, respectively. The density aug-ments were small and the stored energy increased by 20,35, 55 kJ, respectively. The high-frequency magnetic sig-natures remained when 1 MW was applied [see Fig. 5-d)]but were suppressed for the cases with PICRH=2 and 3MW [compare with Figs. 5-e) and -f)]. A noticeablechange in the electron temperature profile before and af-ter the ICRH pulse was recorded using the ECE diag-nostic and is shown in Fig. 6. The electron tempera-ture around the 2/1 surface was raised ∼ 400 eV, notonly restoring but increasing the temperature gradients.Similar trends have been observed heating the ‘electronchannel’ with Lower Hybrid Current Drive (LHCD) andwill be subject of a future contribution.

During the ICRH recovery phase a clear accelerationin the ion-diamagnetic-drift direction was observed at theedge (ρ ∼ 1) with the GPI diagnostic. Although the tem-porally Fourier-resolved signal, S(f), shows an increaseafter RF hits the plasma, we find that the conditionalspectrum s(k|f) does not show evidence of a feature inthe EDDD propagating at the critical 7 mm depth in ei-

200

300

400

500

600

700

-14

-13

-12

-11

-10

-9

-8

-7

-6

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

TA

r,0 -

Z-lin

e [e

V]

V,0

- Z

-lin

e [km

/s]

WMHD/Ip [J/A]

Counter-current

ICRH heating

0.5 MW

1.0 MW

2.0 MW

3.0 MW

FIG. 7. (Color online) Changes of the core toroidal velocityand ion temperature during the ICRH locked-mode recoveryexperiments. Power scan was in the range from 0.5 to 3 MW.

ther of these plasmas. Instead, the growth of fluctuationpower in the high frequency components with RF is dueto an acceleration in the IDDD (not shown here). Fur-thermore, this acceleration increases with the amount ofapplied heating power. The CXRS measurements at theedge (0.9 < ρ < 1.0) also indicate that the edge plasmaspins rapidly in the (+) co-current direction up to about20 km/sec, much faster than the braking phase and re-covering the toroidal velocity before the mode onset asshown in Fig. 4-a). Strong changes in the radial electricfield, E × B drifts and flow velocities are commonly ob-served when using ICRH [29, 30]. The observed velocitiesare consistent with the presence of changes in the electricpotential arising as a consequence of sheath rectificationof the parallel component of the launched waves.

A comparison of the change in core (ρ ∼ 0) toroidalflow velocity and ion temperature between an Ohmicand ICRH-heated locked-mode measured with the high-resolution x-ray crystal spectrometer is shown in Fig. 7.One interesting detail is that for every increase in the iontemperature due to heating, the change in core toroidalrotation ‘points’ always in the (−) counter-current direc-tion, unlocking the plasma and recovering the directionand magnitude of the toroidal flow before the formationof the locked-mode [see early phase in Fig. 4-b)], but op-posite to the Rice-scaling in the (+) co-current direction.

Exploring the connection between typical gradients(∇Te,i) and toroidal rotation (vφ) through the residualstress (e.g. by changing the underlying turbulence fromITG to TEM affecting anomalous momentum transport[26–28, 31, 32]) and the effects of neoclassical toroidal vis-cosity (NTV) can also provide a useful tool to indirectlyunlock the edge and core plasma. As mentioned above,the generation of poloidal or toroidal flow velocities is

5

a very attractive parameter for scaling the locked-modethresholds by its direct relation with the viscous torque.This simple heating technique could provide an impor-tant actuator to avoid or circumvent error-field-inducedlocked-mode disruptions in tokamak plasmas.

In summary, error-field-induced locked-modes at ITERtoroidal fields have been studied at C-Mod without theinfluence of external fueling and momentum input. Delayof the locked-mode onset and recovery from pre-existinglocked-modes has been successfully obtained using ICRH.The use of external heating in-sync with the error-fieldramp-up resulted in delay of the mode-onset. OncePICRH is turned off, the core plasma “locks” at later

times depending on the density and toroidal velocity evo-lution. In the presence of an error field, an L-mode dis-charge can transition into H-mode after the current rampup and still at high densities. For the mitigation exper-iments, applying ICRF heating to low-density plasmaswhich have already locked causes the edge/core plasmato spin in the co/counter-current direction, recovering therotation direction and magnitude that was present beforethe mode onset, conserving momentum density in the ab-sence of external NBI torques. This work was performedunder US DoE contracts including DE-FC02-99ER54512and others at MIT and DE-AC02-09CH11466 at PPPL.

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