QTYUIOP319–00/EJS/ci
MHD STABILITY ISSUES IN A BURNING PLASMA
byE.J. STRAIT
Presented at theUniversity Fusion Association Workshop on
Burning Plasma ScienceAustin, Texas
December 11–13, 2000
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PRESENT UNDERSTANDING OF MHD STABILITY LIMITS ISSUFFICIENT TO DESIGN A BURNING PLASMA EXPERIMENT
Ideal MHD stability limits are well understood and predictable
— Upper limit to plasma stability
— Credible foundation for design of next-step devices
Non-ideal effects introduce greater uncertainty
— Resistivity, finite Larmor radius, energetic ions, …
Resistive instabilities are less predictable but may be avoidable
— Neoclassical tearing modes can be avoided transiently by profile modification
— Recent experiments have suppressed NTMs with localized current drive
Steady operation very near stability limits has been demonstrated
Burning plasma experiments go beyond present experience with MHD stability,and present new scientific challenges
FULL STABILIZATION OF NTM OBTAINED WITH MODEST ECH POWER
Resonance moved 2 cm outwardNo ECCDFull Stabilization
After reaching the seed size,the stabilization is rapid becausethe mode growth rate is negative
βN increases during stabilizedphase
Even in presence of largesawteeth the mode doesn’tgrow
319–00/EJS/ciS A N D I E G O
DIII–DNATIONAL FUSION FACILITY
2500 3000 3500 4000 4500Time (ms)
0.0
5.0
10.0104328 104324 104335
1.7
2.1
2.5
0.9
0.6
1.2Neutron Rate
(1015/s)
Central SXR
n = 2 Mirnov (G)
βN
80
125
170
1.1 MW ECH
STEADY STATE HIGH PERFORMANCE DISCHARGES CAN BE ACHIEVED USING UNDERSTANDING OF STABILITY LIMITS AND DISCHARGE CONTROL
319-00 jyS A N D I E G O
DIII–DNATIONAL FUSION FACILITY
0
1010 × IP (MA)
4li
n = 2 Mirnov Ampi. (G)
0
2
4
0
4
8
0
2
4
0 2000 4000 6000 8000Time (ms)
04
8
⟨PNB⟩ (MW)
⟨ne⟩
βNH89
βN
β controlled toremain ~20% belowpredicted RWM limit
— β also kept 5%below experimental2/1 NTM β limit
Discharge continued in steady state untilbeam termination
No sawteeth
— q0 > 1~
104276 4625.00
38 channelMSE
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D
MSE shows J(r) profile has reached resistive equilibrium with q0 ~1.05
q
MSEq-profile
0 2000 4000 6000 8000Time (ms)
10
5
0
–5
–10
–15
MSEPitchAnglevs.R
0
2
4
6
8
0 1.0ρ
319-00 jy
¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥
3 τR
q0 ~ 1.05
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WHAT DISTINGUISHES A BURNING PLASMA FROMEXISTING EXPERIMENTS?
Self-heating
— Less external control over profiles (p, j, Ω)
Energetic particle effects
— Large isotropic population of fast ions
New ranges of dimensionless parameters
— ρi* = ρi/a ~ T1/2/aB
— S = τA/τR ~ aBT3/2/n1/2Zeff
— ν* = νi/εωbi ~ nqRZeff/ε3/2T2
DIII–D C-MOD JT-60U JET FIRE IGNITOR ARIES-RS ITER-FEAT ITER-FDR
aB (m-T) 1.3 1.7 3.5 4.3 5.3 6.1 10 11 16
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EXISTING EXPERIMENTS ARE SUFFICIENT TO INVESTIGATE MANYISSUES OF MHD STABILITY
Ideal MHD stability limits
— Profile dependence
— Shape dependence
— Aspect ratio dependence
Feedback stabilization of RWM
ECCD stabilization of NTM
Edge-driven instabilities
— Identification of instability
— Dependence on bootstrap current
Stability with non-inductively driven current profiles
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BURNING PLASMA-SIZE EXPERIMENTS (WITHOUT ALPHA HEATING) AREREQUIRED TO INVESTIGATE SCALING OF MHD STABILITY PHYSICS
NTM beta limit scaling— Threshold island size decreases with decreasing ρi
∗
— Seed island size decreases with increasing S
Edge-driven instabilities— Edge gradients determine stability limit— Pedestal width determines coupling to core— Scaling of edge parameters is not well understood
Resistive wall mode stability— Rotation frequency required for stabilization may increase with S ( Ω τA ~ 0.05)
Runaway avalanche during disruption— Number of e-foldings increases with plasma current— Runaway electron current multiplication
>~ 102 at Ip = 2 MA
>~ 106 at Ip = 5 MA
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D
Sawtooth-induced 3/2 NTM, ELMing H–mode
βN ∝ ρi* f(ν) is consistent with polarization/inertial model of Wilson et al.
But scaling of βN/ρi* with collisionality is not consistent between machines
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ν ≡ (νi/ε)/ωe* ρi* (10–2)
JET
AUG
DIII–D
f(ν)/3βN
ρi* (10–2)βN
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0 0.05 0.10 0.150.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 0.2 0.4 0.6 0.8 1.0 1.2
B
B B
B
B
B
B
B
B
BB
B
B
B
B
B
B
BB
B
B
B
BB
B
B
B
B
B
B
B
B
B
J
JJJJ
J
JJ
J
J
J
JJ
J
HHH
H
H
H
H
H
H
H
H
H
H
H
H
BB
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
BBB
B
B
B
B
B
B
B
B
BBB
J
J
J
J
J
J
JJ
JJ
J
JJ
J
H
HH
HH
H
H
H
HH
H
H
HH
H
Best fit f(ν)is different foreach device
— Possible additional dependence on ρi* or S
NTM THRESHOLD SCALES LINEARLYWITH NORMALIZED ION LARMOR RADIUS
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NATIONAL FUSION FACILITYS A N D I E G O
DIII–D
SAWTOOTH INDUCED SEED ISLANDS SCALEINVERSELY WITH MAGNETIC REYNOLD'S NUMBER
Seed islands estimated from m/n = 3/2 Mirnov level upon excitation
Best fit has wseed/r
ws ≈ withBr≈ Bθ
Bθn = 2 (T)
1/2 416rRBr3s BT( ) 1
2 wall( )b
r~~~
2000
S (107)
0.0
6.0 (ST)2,2
3/2
Seed levelELM ELM ELM
×10–4
2100 2200 2300 2400 2500Time (ms)
~
∝ S–0.46±0.05, correl r = –0.74 consistent with
B JET
J AUG
H DIII–D
dynamical coupling model of Hegna et al.
B
B
B
B
B
B
B
B
BB
B
BBB
B
J
J
J J
J
J
JJ
J
J
J
J
J
J
H
HH
H
HH
H
H
H
H
HH
H
HH
HHH
0
5
10
15
20
25
0 2 4 6 8 10 12
wse
ed/r
(%)
EDGE STABILITY AND ELM CHARACTER DEPENDCRITICALLY ON COLLISIONALITY
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ELM SIZE CORRELATES WITH RADIAL WIDTH OF PREDICTED UNSTABLE INTERMEDIATE n KINK MODE
Predicted instability computed from GATO code penetrates into core⇒ High performance is lost
δTe ~400 eV
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Highly localized instability computed from GATO
⇒ Type I ELM has little effect
δTe ~300 eV
0.0 0.2 0.4 0.6 0.8 1.0ρ
1.0
0.0
0.5
xm
High p'Region
m = 6
2q = 6/5
m = 7
Discharge #92001H Mode
n = 5
0.0 0.2 0.4 0.6 0.8 1.0ρ
1.0
0.0
0.5
xm
m = 11m = 12
Discharge #87099NCS H Mode
High p'Region
n = 5
m = 13m = 14
m = 15
q = 11/5q = 11/5 11/5 12/5
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A BURNING PLASMA (STRONG ALPHA HEATING) IS NEEDED TOINVESTIGATE KEY ISSUES OF MHD STABILITY
Energetic particle interactions with MHD modes (sawteeth, fishbones, TAE,ballooning modes, etc.)
— Stabilization or destabilization of MHD modes by alphas
— Enhanced transport of alphas by MHD modes
Self-heating (Pα >> Pexternal ⇒ Q ≥ 10)
— Stability limits with pressure profiles determined by alpha heating
— Plasma rotation with little or no external momentum input (RWM stability,mode locking, error field sensitivity)
Ω ~ ω* ~ T/a2B ?
Steady-state operation (τ > τCR ~ a2T3/2/Zeff)
— Stability limits with self-consistent current density and pressure profiles
319-00 jyNATIONAL FUSION FACILITYS A N D I E G O
DIII–D
STABILITY LIMIT DEPENDS STRONGLY ONTHE FORM OF THE PRESSURE PROFILE
TFTR high po/⟨p⟩ ~ 6.0 (ERS–mode):βN < 2
— Limited by fast n = 1 disruption~
DIII–D high po/⟨p⟩ ~ 6.0 (L–mode):βN < 2.5
— Limited by fast n = 1 disruption~
DIII–D low po/⟨p⟩ ~ 2.5 (H–mode):βN < 4
— No disruptionlimited by ELM-like activity fromfinite edge pressure gradients
~
0 2 4 6 8 10
Resistive
Ideal
Unstable
H–modeL–mode
P(O) / ⟨P⟩
β N (%
-m-T
/MA)
Pressure (105 Pa)
0.0 0.4 0.8ρ0
1
2
ROTATION DECELERATES ABOVE THE NO-WALL β LIMIT(EVEN WITH LARGE TORQUE)
Two competing models are beinginvestigated
— Gimblett and Hastie torque balancemodel with marginally unstableRWM predicts qualitative behavior
— New data is consistent with resonantamplification of static error fieldsby marginally stable RWM
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DIII–DNATIONAL FUSION FACILITY
9256196519
ELMing
H–mode
H–mode
ELM-ing
0.5Ew = βN/βN
1.0 1.5
200
–200
0
8011192544
ELMing
H–mode
H–mode
dΩdt
(kHz/s)
(ρ~0.5)
no-wall
Acceleration
Deceleration
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CONCLUSIONS
Some issues of MHD stability require burning-plasma parameters to investigate
— NTM beta limit scaling
— Edge-driven instabilities
— Resistive wall stabilization
— Disruption scaling (runaway avalanche)
Some key issues of MHD stability can only be addressed with strong alpha heating
— Energetic alpha interactions with MHD modes
— Stability with profiles determined by self-heating (t >> τE)
— Stability with self-heating and relaxed current density profile (t >> τCR)
Many of the issues requiring a burning plasma are not purely MHD stability issuesbut issues of integration (transport, profile control, burn control, etc.)
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INTEGRATION OF SEPARATE ELEMENTS MAY BE THE MOSTIMPORTANT MISSION FOR A BURNING PLASMA EXPERIMENT
Strong coupling of transport, heating, and stability leads to a more “self-organized” plasma than in a short-pulse, externally heated tokamak
— Pressure → Fusion → Alpha heat → Thermal → Pressureprofile rate deposition transport profile
— Pressure → Bootstrap → Current → Thermal → Pressureprofile current profile transport profile
MHD instabilities can intervene in these loops:
— Pressure, current density, and fast ion → Instabilities → Modificationprofiles of profiles
Investigation of such a complex, non-linear system represents a scientificchallenge, and may yield some surprises
RECOMMENDATION: A “next step” burning plasma experiment is needed as the onlyway to address this challenge
