Magnetic islands with complex structure NSTX Supported by Magnetic islands with complex structure in NSTX K. L. Wong PPPL and the NSTX Research Team College W&M Colorado Sch Mines Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics New York U Old Dominion U ORNL PPPL PSI Princeton U SNL Think Tank, Inc. UC Davis UC Irvine UCLA UCSD U Colorado U Maryland U Rochester U Washington U Wisconsin Culham Sci Ctr U St. Andrews York U Chubu U Fukui U Hiroshima U Hyogo U Kyoto U Kyushu U Kyushu Tokai U NIFS Niigata U U Tokyo JAEA Hebrew U Ioffe Inst RRC Kurchatov Inst TRINITI KBSI KAIST POSTECH ASIPP ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching ASCR, Czech Rep U Quebec 53rd APS-DPP annual meeting at Salt Lake City-UT November 14-18, 2011

NSTX plasmas are rich in MHD activities Alfvén Eigenmodes: 100 kHz – 2 MHz Kink, tearing and ballooning modes: 1 – 100 kHz Resistive wall modes < 1 kHz Locked modes (due to tearing or RW modes) f  0 Typical Mirnov signal

Low frequency multiple harmonic oscillations (MHO) #138326: Ip=0 Low frequency multiple harmonic oscillations (MHO) #138326: Ip=0.8MA H-mode, Pb=2MW, Prf=0.9MW turned on at 0.25s Mirnov signal: fn ~ n Δf ~ n f1 Island identified by a flat region in fΦ is rotating with fΦ ~ 20 kHz ~ Δf

Doppler shift: ω’ = ω + k.V = ω + kϕVϕ= ω + nVϕ/R This relation was used to determine the toroidal mode number n of TAEs in TFTR Ref: Wong et al, PPCF(1994) For low-n tearing modes, ω << ω’ ~ nVϕ/R Let B =m,n bmn exp[i(m+n)] If an island localized at q=m/n has multiple toroidal mode numbers, then the island observed in the lab should have multiple harmonic frequencies with fn = n fϕ Resonance condition: m/n=q Multiple n  multiple m Large m => corrugated island surface/ irregular boundary in Poincaré plot

Most likely scenario in #138326: Prf turned on at 0 Most likely scenario in #138326: Prf turned on at 0.25s & form 1/1 island enhanced transport (or sawtooth crash?) between 0.2817-0.2983s during MHO RF turned on at 0.25s, ELMy H-mode, Wmhd & neutron rate level off after 0.3s - enhanced transport due to MHO (no broadband noise in Mirnov signal) Te in core drops between 0.2817 – 0.2983s

Stochastic magnetic field near separatrix of an island Express the perturbed B in Fourier series: B =m,n bmn exp[i(m+n)]   Stochastic B during sawtooth crash due to the overlap for second order island chains (action-angle variables) Ref: Lichtenberg et al., Nucl. Fusion (1992) When the island has many m, n harmonics, we can also expect a larger region of multiple stochastic layers and separatrix.

Island at q = 2 near r~0 (from MSE) after RF turned off #130608: 1MA, Pb=2MW, Prf~1.8MW tripped off by an ELM –TRANSP130608Z10 RF tripped off by an ELM at 0.376s, Then Wmhd & neutron rate drop Δf~22kHz at 0.386s, droops to 12kHz at 0.4s

Island fΦ approx. corresponds to Δf in Mirnov signal

MHOs enhance plasma energy transport Grad.Te reduced in plasma core (r/a<0.6) after MHOs appear Grad.Ti reduced in plasma core (r/a<0.6) after MHOs appear

MHO during RF flat-top #138413@0.41s, Ip=1MA, Pb~2MW, Prf~1.9MW, At t=0.406s, only 1 island @ q~1, 30kHz At t=0.416s, another island @ q~2, 16 kHz  m/n = 2/1, 4/2, 6/3, 8/4 . . . . There was an ELM just before 0.4s that may triggered the MHO Prf & Pb remained constant in 0.4-0.44s

MHO with rising freq after Prf switched off (#138143) Prf turned off at 0.46s. An island appears at R>130cm & grows in size and rotation speed. Te(r) falls when island gets large (after 0.5s)

Combination of several sets of MHOs at different regions Several islands at different regions overlap – avalanche : severe deterioration of global plasma confinement – big drop in stored energy & neutron emission At 0.37s, several sets of MHOs appear at the same time with different Δf: fϕ slowing down in plasma core & spinning up at plasma edge

MHO near edge (q~4) developed into locked mode #129169: Ip=1MA, Pb=2MW, Prf=1.2MW, L-mode edge Rapid MHD growth at 0.27s, RF tripped off at 0.28s, Locked mode ( f ~ 0 ) at 0.293s

Change of fΦ(R) due to MHO (0. 27s - 0 Change of fΦ(R) due to MHO (0.27s - 0.29s) plasma core has reversed magnetic shear before 0.27s fΦ(R) from TRANSP: 0.2s< t <0.3s

fΦ pedestal outside region of reversed magnetic shear fΦ and q measured with 10ms resolution ΩΦ(R) changes slowly from .27-.29s : ΩΦ pedestal in region with positive magnetic shear  reversed magnetic shear improves momentum confinement Sudden change of q(R) at .27s : Appearance of MHOs coincides with q(0) collapse (from 3.0 to 1.2) - double tearing modes at 0.27s?

Enhanced momentum & edge electron energy transport due to locked mode Grad Te(r/a:.6-1) at .27s, .28s, .29s, .3s : falls with time at plasma edge (r/a>0.85) due to edge cooling at r/a>0.8 Grad ΩΦ(r/a:.4-.9) at .27s, .28s, .29s, .3s : falls with time after locked mode appears

Enhanced core impurity transport & edge cooling due to MHOs MHOs at edge have similar effect as EHOs in DIII-D QH-mode plasmas During MHO : Zeff increases at r/a>0.8 , and decreases at r/a<0.8 Te drops at r/a>0.8 during MHO

Relevance to conventional tokamak experiments Quiescent H-mode in D3D - edge harmonic oscillations - are these MHOs at plasma edge that work as ergodic divertor ? Current ribbon at q=4 in JET - Can be constructed by choosing bmn

Why no MHOs in the core of conventional tokamaks? Microtearing modes can exist in edge region of conventional tokamaks. Conjecture : When they appear at edge of DIIID at quasi steady state EHOs which reduce Zeff QH-mode. When they appear at edge of JET current ribbon. δB from unstable tearing modes resonate at q=m/n to form magnetic islands. Microtearing modes are unstable from core to edge in NSTX beam heated plasmas MHOs from core to edge. They are stable in core of conventional tokamaks No MHOs in core.

Multiple harmonics in high-k scattering data These data are rare : It requires a big island, and the scattering volume must be at the right place nth harmonic of island rotating at fϕ produces EM fields in plasma with fn = n fϕ and the plasma will respond at the same freq fn = n fϕ : Oscillations need not be normal mode - D(ω,k)~0

Summary Is this a special feature of ST? MHOs are common in NSTX It can happen under many different plasma conditions. It is associated with a rotating magnetic island with complex structure - multiple helicity. The island location varies from core to edge. They can produce stochastic B and enhance plasma transport. Can cause multiple peaks in high-k scattering signal. The cause for this behavior in NSTX may be due to microtearing modes. Microtearing modes in NSTX beam-heated plasmas can be unstable from core to edge, but only at the edge in conventional tokamaks. EHOs in DIII-D QH-mode may be a rotation island with multiple helicity at the plasma edge. Appropriate values of bmn at q=4 can lead to current ribbon in JET.