1. Magnetic islands with complex structure
NSTX
Supported by
Magnetic islands with complex structure
in NSTX
K. L. Wong
PPPL
and the NSTX Research Team
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53rd APS-DPP annual meeting at Salt Lake City-UT
November 14-18, 2011

2. 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

3. 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

4. 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

5. 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 s 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
– s

6. 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.

7. 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

8. Island fΦ approx. corresponds to Δf in Mirnov signal

9. 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

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

11. 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)

12. 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

13. 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

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

15. fΦ pedestal outside region of reversed magnetic shear fΦ and q measured with 10ms resolution
ΩΦ(R) changes slowly from s :
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?

16. 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

17. 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

18. 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

19. 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.

20. 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

21. 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.