January, 2014

Plasma Science and Fusion Center Massachusetts Institute of Technology

Cambridge MA 02139 USA This work was performed under US DoE contracts including 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-14-1

Destabilization of Internal Kink by Suprathermal Electron Pressure

L. Delgado-Aparicio1, S. Shiraiwa2, L. Sugiyama3, R. Granetz2, J. Irby2, R. Parker2, S. G. Baek2, I. Faust2, G. Wallace2, R. Mumgaard2, S. Scott1, D. A. Gates1, N. Gorelenkov1, N. Bertelli1, C. Gao2, M. Greenwald2, A. Hubbard2, J. Hughes2, E. Marmar2, P. Phillips4, M. L. Reinke2, J. E. Rice2, W. Rowan4, R. Wilson1, S. Wolfe2 and S. Wukitch2

1Princeton Plasma Physics Laboratory, Princeton, NJ, 08540 2MIT - Plasma Science and Fusion Center, Cambridge, MA, 02139, USA 3MIT - Laboratory for Nuclear Science, Cambridge, MA, 02139, USA 4University of Texas - Austin, TX, 78759, USA

Destabilization of Internal Kink by Suprathermal Electron Pressure

L. Delgado-Aparicio1, S. Shiraiwa2, L. Sugiyama3, R. Granetz2, J. Irby2, R. Parker2, S. G. Baek2, I. Faust2,

G. Wallace2, R. Mumgaard2, S. Scott1, D. A. Gates1, N. Gorelenkov1, N. Bertelli1, C. Gao2,

M. Greenwald2, A. Hubbard2, J. Hughes2, E. Marmar2, P. Phillips5, M. L. Reinke2,

J. E. Rice2, W. Rowan5, R. Wilson1, S. Wolfe2 and S. Wukitch2

1PPPL, Princeton, NJ, 08540, USA2MIT - PSFC, Cambridge, MA, 02139, USA3MIT - LNS, Cambridge, MA, 02139, USA

5University of Texas - Austin, TX, 78759, USA(Dated: January 17, 2014)

New observations are reported on the structure and dynamics of short-lived periodic (1, 1)“fishbone”-like oscillations that appear during radio frequency current-drive experiments in toka-mak plasmas. For the first time, measurements directly relate the high energy electrons to themode onset, saturation, and damping. Suprathermal electron energies are measured directly usingthe downshift of electron gyrofrequency due to relativistic effects and correlate with the mode. Theinstability appears to be destabilized by the non-resonant suprathermal electron pressure and growsindependently of the (1, 1) sawtooth crash driven by the thermal plasma pressure.

The economic feasibility of a fusion reactor can bemeasured in terms of a non-dimensional pressure β ≡p/(B2/2µ0

), where p is the plasma pressure and B2/2µ0

is the magnetic field energy density. The presence of mag-netohydrodynamic (MHD) instabilities can distort theorbits of fast ions and electrons compared to the equilib-rium, causing an off-axis redistribution of the fusion heat-ing and current density to the detriment of the centralβ, reducing the fusion power and the production of fastneutrons for tritium breeding. Therefore, understandingthe stability and behavior of 3D helical modes in the coreof an axisymmetric toroidal configuration remains one ofthe challenges of fusion research [1]-[6]. It is doubly sig-nificant for burning plasma designs such as ITER, wherethe q = 1 radius that bounds these instabilities may reachhalf the minor radius.

A new type of helical internal kink-like mode [7, 8] withdominant poloidal and toroidal mode numbers m = 1,n = 1 has recently been observed in the Alcator C-Mod tokamak [9], during the development of advancedfusion scenarios using lower hybrid current drive (LHCD)[10, 12]. During LHCD operation, soft x-ray (SXR) de-tectors measure periodic bursts of oscillations, as shownin Fig. 1. Their structure is characterized by a small(1,1) helical region of enhanced plasma density and tem-perature that is radially concentrated on or inside thesurface with magnetic safety factor q = 1 and rotatestoroidally with the plasma.

The (1,1) oscillations are distinct from the sawtoothinstability. In Figure 1-a) the instability occurs duringthe sawtooth ramp and disappears before the subsequentsawtooth crash. In Figure 1-b), sawteeth are stable andthe mode appears as a successive train of bursts. Thegrowth and amplitude of the core internal kink (IK) arenearly identical in both cases; however, the amplitude ofthe off-axis re-distribution for the new mode is differentfrom that of the sawtooth precursor (SP) and crash (SC),suggesting a distinct (1,1) nature. Growth and dampingof the mode occur over approximately 1 ms intervals, sim-

IK

IKSP

IK

SX

R b

rig

htn

ess [A

rb.]

1.0C-Mod # 1120612015 C-Mod # 1120612007

1.10 1.11 1.12

Time (s)

1.03 1.04 1.05

Time (s)

SC

a) b)

IKSPSC

0.8

FIG. 1. (Color online) On-axis SXR signatures of a (1,1)internal kink-like (IK) mode in the a) presence or b) absenceof sawtooth precursors (SP) and crashes (SC).

ilar to the growth of the sawtooth precursor and muchlonger than the 20-40 µs of the sawtooth crash. On occa-sions, the mode can coalesce with the sawtooth precursoroscillations in a “hybrid” crash with larger amplitude,as in the third and fifth sawteeth depicted in the fre-quency spectrograms shown in Fig. 2-a). The integratedpower spectrum in Fig. 2-b) shows the smooth gaussian-shaped growth and damping of the mode compared tothe sharper sawtooth crash, and the wider double pulserepresenting the hybrid crash; in this case, the sawtoothprecursor appears to grow from the oscillations remainingfrom an incompletely damped mode. The three modeshave distinct amplitudes, but nearly identical frequen-cies; small differences may arise from the sawtooth re-covery. They propagate toroidally in the counter-currentor the electron diamagnetic drift direction, with the samedirection and speed as the background plasma rotation,as does the sawtooth precursor. The background toroidalrotation, measured with a high-resolution x-ray crystalimaging spectrometer [13, 14], was 50–75 km/s for themodes of Fig. 1.

These observations are from C-Mod plasmas which had

2

1.06 1.07 1.08 1.09 1.10 1.11

Time (s)

C-M

od

# 1

12

06

12

01

5, F

req

. ran

ge

: 10

:20

kH

zC

-Mo

d #

11

20

61

20

15

IK

SC

SC SC

SC

IKIK

20

Fre

qu

en

cy (

kH

z)

12

14

16

18

1

2

3

4

Inte

gra

ted

po

we

r sp

ectr

um

(x1

03)

IKhM hM

a)

b)

IK

SXR - core

FIG. 2. (Color online) a) Frequency spectrogram of SXR sig-nal from the core (raw intensity as a function of time is shownin white for reference). b) Integrated power spectrum between10-20 kHz. The internal kink-like bursts (IK, in black) andsawtooth crashes (SC, in red) can coexist in a (1,1) hybridmode (hM, in green).

R0 ' 68.5 cm, a = 22 cm, Ip ' 0.5 MA, Bt,0 ' 5.4 T, andcentral plasma densities and temperatures on the order ofne0 ∼ (1.35 → 1.75)× 1020 m−3 and Te,0 ∼ 2.80 → 2.35keV, with nearly identical central electron and ion pres-sures. Lower hybrid (LH) waves are quasi-electrostaticplasma waves with a frequency intermediate between theelectron and ion cyclotron frequencies which are absorbedby relatively fast background electrons (v‖ & 3vth par-allel to the magnetic field) via electron Landau damp-ing. The C-Mod LHCD system is capable of drivingup to 580 kA of current at zero loop voltage in mod-erate plasma densities (ne ∼ 5 × 1019 m−3). How-ever, at the high densities of these discharges, an LHCDpower of PLHCD ∼ 700 kW at parallel refractive indexn||,LHCD ' −1.6 drove a smaller reduction in the loopvoltage, ∆Vloop ' −0.3 V below the typical C-Mod ohmicVloop ∼ 1 V. The current density on axis typically reached14 MA/m2 with q0 ' 0.9; the broad LHCD current andpower deposition profiles extended well outside q = 1.

The 3D mode structure and its effects on the back-ground plasma were measured using a suite of spectro-scopic imaging diagnostics [5]. These instruments werealso used to infer the mode harmonic numbers, since themagnetic measurements at the wall were insensitive tointerior modes [5]. The spatial time history of the tomo-

1.038 1.040 1.042 1.044

Time (s)

SX

R e

mis

sio

n [M

W/m

3]

0.1

0.2

0.3

0.4

0.5R=68 cm

(CORE)

+1 cm

+2 cm+3 cm

+7 cm

+6 cm

+5 cm

+4 cm

+8 cm

C-Mod # 1120612007

a)

0.65 0.7 0.75

Radius (m)

b)

rq=1

θ~π

θ~0

-1.0

1.0

Δε S

XR(t

)-[A

rb.]

t=1.041024, 1.041056 s

FIG. 3. (Color online) a) Time history of the peak SXR emis-sivities over the midplane, from the magnetic axis ∆R = 0 to∆R . +14 cm on the low-field-side. b) SXR perturbation(black diamonds) has the analytical form of the lowest order1/1 internal kink eigenfunction, Bessel function J1(κr) cos θwith κ = 3.8317/rq=1 (red line). Reconstructions at θ = 0and π are shown in the bottom and top insets, respectively.

graphically reconstructed SXR emissivity for a typicalkink-like burst from Fig. 1-b) is shown in Fig. 3-a).At the magnetic axis, the background emissivity in theplasma center builds nearly to a peak before the modeonset (see top black and blue traces at ∆R = +1 and 2cm). In contrast, at ∆R = 4–5 cm the background emis-sivity falls steadily before the mode onset, then duringthe mode rises by 10% (∆εSXRq∼1 ' 20 kW/m3). The oscil-lations appear and disappear almost simultaneously overthe plasma cross section, including well outside q = 1at ∆R ' 4 cm. There is no signal inversion with ra-dius that might correspond to a “crash” of the centralcore. During the mode, the core background emissivitydecreases by 20% (∆εSXR0 ' −100 kW/m3). 2D recon-structions of the SXR emissivity profiles show that themode forms and then grows like a small amplitude (1, 1)kink with a nearly circular cross section, as shown inFig. 3-b). Its radial profile has the characteristic Besselfunction form of the cylindrical or lowest order toroidal1/1 kink eigenfunction [15]. Combining this functionalform with data from the ten-chord two-color interferom-eter (TCI, see [16]) we infer an internal kink-like electrondensity perturbation as large as δne0/ne0 ' 4% (see Fig.4). The position of the q = 1 surface indicated in Figs.3 and 4 was obtained from an MSE-constrained EFITreconstruction.

3

64 66 68 70 72

R (m)

TC

I - δn

e. L

[x1

01

7 m

-2]

0

2

-2

Z (

m)

0.04

0

-0.04

C-Mod #1120612007, t~1.03599 s

TCI

θ=π

θ=0

r q=

1FIG. 4. (Color online) Line-integrated perturbed electrondensity measured by the two-color interferometer (TCI) dur-ing the sawtooth-free scenario shown in Fig. 1-b). The mea-sured TCI line-integrated densities and the simulated ones ap-pear in blue and green, respectively. The background shadingis the corresponding 2D Bessel-like eigenfunction.

For the first time, experimental measurements demon-strate a direct dynamic relation between LHCD gener-ated fast electrons and a fishbone-like mode. A timehistory of the central electron temperature inferred bythe slow electron cyclotron emission (ECE) grating poly-chromator (GPC) [17] shows that the mode growth be-gins at the maximum of the inferred core Te, which fallsto a minimum by the disappearance of the mode [seedotted lines in Fig. 5-a)]. The GPC-ECE Te is approx-imately 0.5 keV higher than the 2.8 ± 0.1 keV obtainedfrom Thomson scattering measurements averaged over10 spline profiles, which is relatively insensitive to fastelectron effects. During this sawtooth stabilized scenariothe amplitude of the kink-like mode is nearly “constant”with no obvious signs of frequency chirping which offersa first clue of its non-resonant nature. The high resolu-tion, fast-time-response FRC-ECE radiometer [18] pro-vides additional evidence that the central fast electronsare connected to the mode as shown in Fig. 5-b). Ra-diation at the second harmonic of the electron cyclotronfrequency 2Ωce produced by fast electrons in the centralregion is detected in an edge channel of the radiometerlocated nearly 20 cm away from the magnetic axis, onlywhile the mode is active. The cyclotron frequency of thefast electrons is strongly downshifted by relativistic ef-fects, Ωce,rel = eB/γme where γe ≡ (1 − (ve/c)

2)−1/2 isthe Lorentz factor [12, 21–24]. Electron cyclotron wavesemitted in the core at these frequencies can travel to theoutboard plasma edge without being re-absorbed by thethermal electrons. Assuming a 1/R dependence for thetoroidal magnetic field, the relativistic factor is foundto be γe=1.21-1.28, corresponding to electron energiesEe = 108-144 keV. The innermost FRC-ECE channelthat detects the same coherent phenomena corresponds

1.02 1.03 1.04 1.05 1.06 1.07

Time (s)

GPC-ECE

3.1

3.2

3.3

3.4

GP

C-E

CE

Te

,0 [ke

V]

1

2

3

4

Inte

gr. p

ow

er

sp

ectr

um

(x1

03)

Mo

de

-on

se

t

Damped

C-M

od

# 1

12

06

12

00

7

12

14

16

18

SXR: core - 68.5 cm

FRC-ECE

Ch. #03, R~85.44 cm

Ee~126±18 keV

Fre

qu

en

cy (

kH

z)

a)

b)

FIG. 5. (Color online) a) Integrated power spectrum of theSXR signals (in black) for the fishbone-like mode observed in asawtooth-free discharge. The core temperature inferred fromthe slow GPC-ECE radiometer appears in red. b) FFT ofan edge channel of high resolution fast FRC-ECE radiometershowing activity that should correspond to core MHD.

to γe=1.15-1.22 or Ee=81-115 keV. The observed ener-gies fall within the range of peak energies expected foran LHCD scenario. Signals from lower energy electronsare lost, since the plasma is optically thick at the corre-sponding frequencies and the waves are re-absorbed be-fore reaching the detectors.

The mode appears to be a fishbone-like, (1,1) internal-kink disturbance that smoothly grows, saturates, and de-cays, without any sign of a “crash” or reconnection event.It is observed only with LHCD and appears to be drivenby a build-up of LH-generated fast electrons over q < 1and to saturate by causing their loss. This behavior couldbe consistent with an internal kink destabilized by thesuprathermal fast electron pressure (βhote ).

An estimate for the central fast electron pressure,based on the change in the loop-voltage, the centralcurrent density, an approximate density of fast elec-trons, and an average electron energy for parallel veloc-ities between 3vth,e and v‖,max = c/n‖, yields phote0 ≈1.52×1019 keV·m−3, or 4% of the thermal electron pres-sure pthe0. A slightly more accurate approach uses theGENRAY/CQL3D code [10–12, 19, 20] to calculate theanisotropic electron distribution function f(v‖, v⊥). Theelectron pressure is the moment of the velocity distribu-tion, pe =

∫∞0Ef(E)d3v. Writing it as pe =

∫∞0I(E)dE,

4

ΔI(r0)

ΔI(rq=1)

a)

b)

(×1010)

0 100 200 300 400

E (keV)

1010

1012

1014

2

4

6

8

10r/a = 0.025

r/a = 0.175

0 100 200 300 400 500

E (keV)

1010

1012

1014

108

c)

I(OH+LH,r0)

I(OH,r0)

I(OH+LH,rq=1)

I(OH,rq=1

)

FIG. 6. (Color online) a) Contour plot of electron distribu-tion function in velocity space. The integrands [I(E)] of thecentral electron pressure for Ohmic- vs. LHCD plasmas, andtheir difference are shown in b)-d), respectively.

the integrands I(E) can be calculated for ohmic andLHCD heated plasmas as shown in Figs. 6-a) and -b).The difference between the LH and ohmic distributions,plotted in Fig. 6-c) at two radii r ' 0 and q = 1, showsthat the LH fast electron pressure comes mainly from en-ergies between 30 and 200 keV, with a peak around 80keV. The ratio of the fast electron pressure to the thermalpressure is phote0 /p

the0 ' 2.5% at the magnetic axis, when

numerically integrated from 3vth,e to 2.5 MeV, similarto the q = 1 surface value of 2.8%. This is compara-ble to the drop in the thermal electron pressure due tothe mode, ∆pthe0/p

the0 & 2.75%, derived from before and

after measurements of the central radiated power den-sity and ECE Te. Such values are sufficient to destabilizea marginally stable internal kink mode, but are smallerthan the typical change over a sawtooth.

The temporal evolution of this instability and its in-teraction with sawteeth resembles the so-called “electronfishbones” and its hybrid “sawbone” modes observed dur-ing electron cyclotron resonance heating (ECRH) and/orLHCD. A number of wave-particle resonant interactionshave been proposed to explain the destabilization of fastelectron fishbone modes [25]-[31]. The C-Mod fishbone-like mode appears instead to be a nonresonant internalkink driven by the fast electron pressure contribution tothe central β. The local diamagnetic drift frequencyof the background plasma is smaller than the plasmatoroidal rotation mainly due to the weak density and tem-perature gradients. Thus, perpendicular resonances thatrely on ω∗e,i appear unlikely. Characteristic propertiesof the C-Mod LH fast electron distribution [10] are alsounfavorable to resonant modes. A very fast electron de-trapping rate means that few trapped electrons exist forperpendicular resonance, unlike in many ECRH plasmas.Parallel resonances are also unlikely. LH-driven parallelvelocities are distributed over a wide range 3-10vth, sothat there are relatively few particles at any given reso-

nant velocity. In contrast, ion fishbones driven by par-allel wave-particle resonance [32] in neutral beam heatedplasmas, have a high power source of fast parallel ionsconcentrated at the beam energy that provides a strongcandidate for resonance; LH powers are generally muchweaker than typical NBI heating powers. In addition,the lack of significant chirping in the C-Mod case alsosuggests that perpendicular resonance is not important.

Two main possibilities then exist for mode saturation.One is that the non-axisymmetric kink actively expelsfast electrons from q < 1 to larger radii faster than theircreation. Unlike ion and most ECH electron fishboneswith large gyro- or trapped particle orbits, there is noobvious mechanism for strong perpendicular expulsion offast particles without a core “crash,” which is not ob-served. Electron gyro-radii are very small and almostno trapped particles exist, due to the extremely rapidde-trapping rate, so fast electrons remain strongly tiedto the magnetic field lines. Alternatively, the kink non-axisymmetry could alter the LH wave propagation to ex-clude power and current drive deposition from the kinkregion. This scenario is consistent with experimental ob-servations. The loss time for LH fast electrons near theplasma center due to radial diffusion and other processesis 1 ms, similar to the mode growth and decay times andshorter than the collisional slowing down time of 4-5 ms.Since the total absorbed LH power remains fairly con-stant, extra power should be deposited outside q < 1,consistent with the observed background SXR changesthere. However, kink effects on the LH power depositionhave not been studied theoretically, since numerical cal-culations in realistic configurations have so far assumedtoroidal axisymmetric plasmas.

Electron cyclotron resonance heating (ECRH) andLHCD driven “electron fishbone” (1/1) modes have beenobserved in DIII-D [33], FTU [34], Tore Supra [35]-[37],HT-7 [38, 39], HL-1M [25], HL-2A [40] and recentlyEAST [41] and TCV [42]. In some cases, the wave-particle resonance appears clear, particularly for ECHor ECCD applied on the high field side [33]. In othercases the interpretation is inconclusive due to lack of suf-ficiently precise measurements; nonetheless, the conclu-sions are commonly framed within the formalism of reso-nant electron fishbone theory. In most of these cases,Doppler shift correction of the mode frequency (f) isoverlooked due to the complications in the measurementof core toroidal rotation profiles. In addition, inadequateestimates of the resonant electron energies (Ee) are madeusing changes of the hard x-ray spectrum. Therefore, us-ing the expression for the resonant precession drift fre-quency (f = qEegλ/2πR0Brs) [43] under such assump-tions will lead to an imprecise inference of the values ofgλ (function of pitch angle), which result in the need ofinvoking the role of various flavors of circulating and/ortrapped particles. Since most LH or LHCD experimentalconditions and electron distributions are similar to thosein C-Mod, the mode driving mechanism is also likely tobe the nonresonant suprathermal electron pressure.

5

In summary, a new type of periodic fishbone-like insta-bility with a (1, 1) internal kink-like structure has beenobserved on Alcator C-Mod with LHCD. For the firsttime, measurements at high spatial and temporal reso-lution directly connect changes in the fast LH-generatedelectrons to the mode. The results suggest that the modeis destabilized by the nonresonant suprathermal electron

pressure contribution to the central beta instead of thewave-particle resonance of traditional fishbones. The in-dependence of the fast electron pressure from the thermalpressure that drives the conventional internal kink alsoexplains its varied co-existence with the sawtooth crashand precursor oscillations. This work was performed un-der US DoE contracts including DE-FC02-99ER54512and others at MIT and DE-AC02-09CH11466 at PPPL.

[1] J. Menard, et al., Phys. Rev. Letters, 97, 095002, (2006).[2] I. T. Chapman, et al., Nucl. Fusion, 50, 045007, (2010).[3] D. P. Brennan, et al., Nucl. Fusion, 52, 033004, (2012).[4] L. Delgado-Aparicio, et al., Phys. Rev. Letters, 110,

065006, (2013).[5] L. Delgado-Aparicio, et al., Nucl. Fusion, 53, 043019,

(2013).[6] D. Pfefferle, et al., Nucl. Fusion, in-print, (2014).[7] L. Delgado-Aparicio, et al., Proceedings of the 40th Euro-

pean Physical Society, P1.159, Helsinki, Finland, (2013).[8] L. Delgado-Aparicio, et al., Proceedings of the 55th An-

nual Meeting of the APS Division of Plasma Physics,(2013).

[9] Alcator C-Mod Team, Fusion Sci. Technol., 51, 3, (2007).[10] P. T. Bonoli, et al., Phys. Plasmas, 15, 056117, (2008).[11] R. Wilson, et al., Nucl. Fusion, textbf49, 115015, (2009).[12] G. Wallace, et al., Nucl. Fusion, 51, 083032, (2011).[13] M. L. Reinke, et al., Rev. Sci. Instrum., 83, 113504,

(2012)[14] L. Delgado-Aparicio, et al., Plasma Phys. Control. Fu-

sion, 55, 125011, (2013).[15] R. White, The Theory of Toroidally Confined Plasmas,

Imperial College Press, (2006).[16] C. P. Kasten, et al., Rev. Sci. Instrum., 83, 10E301,

(2012).[17] J. W. Heard, et al., Rev. Sci. Instrum., 70, 1010, (1999).[18] R. Chatterjee, et al., Fusion Engineering and Design, 53,

113, (2001).[19] K. Hizanidis, et al., Phys. Fluids, 27, 2669, (1984).[20] R. W. Harvey and M. McCoy, Proc. IAEA Technical

Committee Meeting on Simulation and Modeling of Ther-monuclear Plasmas (Montreal, Canada) pp 489, (1992).

[21] T. C. Luce, et al., Rev. Sci. Instrum., 59, 1593, (1988).[22] R. W. Harvey, et al., Phys. Fluids B, 5, 446, (1993).[23] S. Preische, et al., Phys. Plasmas, 3, 4065, (1996).[24] S. Coda, et al., Rev. Sci. Intrum., 79, 10F501, (2008).[25] L. Yan, et al., Chinese Phys. Lett., 18, 1227, (2001).[26] Y. Sun, et al., Phys. Plasmas, 12, 092507, (2005).[27] Z. Wang, et al., Chinese Phys. Lett., 23, 158, (2006).[28] F. Zonca, et al., Nucl. Fusion, 47 , 1588, (2007).[29] A. Merle, et al., Phys. Plasmas, 19, 072504, (2012).[30] S. Chen, et al., Chinese Phys. Lett., 29, 025203, (2012).[31] G. Vlad, et al., Nucl. Fusion, 53, 083008, (2013).[32] R. Betti, et al., Phys. Rev. Letters, 70, 3428, (1993).[33] K. L. Wong, et al., Phys. Rev. Letters, 85, 996 (2000).[34] R. Cesario, et al., Nucl. Fusion, 49, 075034, (2009).[35] P. Maget, et al., Nucl. Fusion, 46, 797, (2006).[36] A. Macor, et al., Phys. Rev. Letters, 102, 155005, (2009).[37] Z. Guimaraes-Filho, et al., Plasma Phys. Control. Fusion,

53, 074012, (2011); Nucl. Fusion, 52, 094009, (2012).[38] Y. Sun, et al., Plasma Phys. Control. Fusion, 47, 745,

(2005).[39] L. Xu, et al., Phys. Scr., 86, 039502, (2012).[40] W. Chen, et al., Nucl. Fusion, 49, 075022, (2009); Nucl.

Fusion, 50, 084008, (2010).[41] L. Xu, et al., Chinese Phys. Lett., 30, 075201, (2013).[42] J. Kamleitner, et al., Proceedings of the 40th European

Physical Society, P5.127, Helsinki, Finland, (2013).[43] J. C. Connor, et al., Nucl. Fusion, 23, 1702, (1983).