NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05 S. A. Sabbagh 1 , A.C. Sontag 1 , R. E. Bell 2 , J. Bialek 1 , A. Garofalo 1 , D.A. Gates 2 , A. H. Glasser 3 , B.P. LeBlanc 2 , F.M. Levinton 4 , J.E. Menard 2 , H. Reimerdes 1 , W. Zhu 1 , M.G. Bell 2 , T.M. Biewer 2 , C.E. Bush 5 , J.D. Callen 6 , M.S. Chu 7 , C. Hegna 6 , S. M. Kaye 2 , L. L. Lao 7 , R. Maingi 5 , D. Mueller 2 , K.C. Shaing 6 , D. Stutman 8 , K. Tritz 8 , C. Zhang 9 Aspect Ratio Considerations for Resistive Wall Mode Stabilization Supported by Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics NYU ORNL PPPL PSI SNL UC Davis UC Irvine UCLA UCSD U Maryland U New Mexico U Rochester U Washington U Wisconsin Culham Sci Ctr Hiroshima U HIST Kyushu Tokai U Niigata U Tsukuba U U Tokyo JAERI Ioffe Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching U Quebec IEA Workshop 59: Shape and Aspect Ratio Optimization for High Beta, Steady-State Tokamak February 14 – 15, 2005 General Atomics, San Diego, CA 1 Department of Applied Physics, Columbia University, New York, NY, USA 2 Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA 3 Los Alamos National Laboratory, Los Alamos, NM, USA 4 Nova Photonics, Princeton, NJ, USA 5 Oak Ridge National Laboratory, Oak Ridge, TN, USA 6 University of Wisconsin, Madison, WI, USA 7 General Atomics, San Diego, CA, USA 8 Johns Hopkins University, Baltimore, MD, USA 9 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China
19
Embed
Supported by Aspect Ratio Considerations for Resistive Wall ...NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05 Wall stabilization physics understanding is key to sustained plasma
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
S. A. Sabbagh1, A.C. Sontag1, R. E. Bell2, J. Bialek1, A. Garofalo1, D.A. Gates2,A. H. Glasser3, B.P. LeBlanc2, F.M. Levinton4, J.E. Menard2, H. Reimerdes1,W. Zhu1, M.G. Bell2, T.M. Biewer2, C.E. Bush5, J.D. Callen6, M.S. Chu7,C. Hegna6, S. M. Kaye2, L. L. Lao7, R. Maingi5, D. Mueller2, K.C. Shaing6,D. Stutman8, K. Tritz8, C. Zhang9
Aspect Ratio Considerations for Resistive Wall Mode Stabilization
Supported by
Columbia UComp-X
General AtomicsINEL
Johns Hopkins ULANLLLNL
LodestarMIT
Nova PhotonicsNYU
ORNLPPPL
PSISNL
UC DavisUC Irvine
UCLAUCSD
U MarylandU New Mexico
U RochesterU Washington
U WisconsinCulham Sci Ctr
Hiroshima UHIST
Kyushu Tokai UNiigata U
Tsukuba UU Tokyo
JAERIIoffe Inst
TRINITIKBSI
KAISTENEA, Frascati
CEA, CadaracheIPP, Jülich
IPP, GarchingU Quebec
IEA Workshop 59: Shape and Aspect Ratio Optimization for High Beta, Steady-State Tokamak
February 14 – 15, 2005General Atomics, San Diego, CA
1Department of Applied Physics, Columbia University, New York, NY, USA2Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA
3Los Alamos National Laboratory, Los Alamos, NM, USA4Nova Photonics, Princeton, NJ, USA5Oak Ridge National Laboratory, Oak Ridge, TN, USA6University of Wisconsin, Madison, WI, USA7General Atomics, San Diego, CA, USA8Johns Hopkins University, Baltimore, MD, USA9Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
Physics study of global MHD mode stabilization at low A provides understanding for all A, including ITER
• MotivationStudy / optimize high β stability of low A, spherical tokamakLow A, high q challenges theory and code benchmarkingCompare data from various A devices to test theory
• Key TopicsKink and RWM stabilization at low A; mode characteristicsToroidal rotation damping physicsCritical plasma rotation frequency for stabilization, Ωcrit
Resonant field amplification (RFA)Rotation effects on equilibrium at low A
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
Low A kink mode amenable to stabilization at high βN
θ/2π0.0 0.2 0.4 0.6 0.8 1.0
1
0
-1
δBψ
(arb
)
θ/2π(equal arc poloidal angle)
βN = 5.0114024
βN = 2.4104403
δBψ
(arb
) 1
0
-1
0 0 0 2 0 4 0 6 0 8 1 0
DIII-D 92544βN = 2.2
δBψ
(arb
) 2
0
-2
4
0.0 0.2 0.4 0.6 0.8 1.0
Higher A ~ 3.1 (DIII-D); βN = 2.2 (above βNno-wall)
Maximum amplitude on outboard side; relatively long poloidal wavelengthStrong wall coupling; effective wall stabilization
Lower A ~ 1.4 (NSTX)• βN = 2.4:
Minimum amplitude on outboard side; short poloidalwavelength inboard sideWeak wall coupling; ineffective wall stabilization
• βN = 5.0 (above βNno-wall)
Mode balloons out and can be effectively stabilized
R
Z θ
R0+ aR0- a
DCON
R0+ a R0+ aR0- a
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
Wall stabilization physics understanding is key to sustained plasma operation at maximum β
• High βt = 39%, βN = 6.8 reached
βN
li
βN/li = 12 68
4
10
wall stabilized
• Global MHD modes can lead to rotation damping, β collapse• Physics of sustained stabilization is applicable to ITER
• Operation with βN/βNno-wall > 1.3 at
highest βN for pulse >> τwall
βN
01234567
DCON
δW0
10
20
0.6 0.70.50.40.30.20.10.0t(s)
n=1 (no-wall)n=1 (wall)
112402
wall stabilized
0
1
2
3
4
5
6
7
8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
EFIT
core plasma rotation(x10 kHz)
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
Unstable n = 1-3 RWM observed
• n > 1 theoretically more prominent at low A
• Fitzpatrick-Aydemir (F-A) theory / experiment show
mode rotation can occur during growthgrowth rate, rotation frequency ~ 1/τwall
• << edge Ωφ > 1 kHz
RWM phase velocity follows plasma flown=1 phase velocity not constant due to error field
• Low frequency tearing modes absent
growth w/o mode rotation mode rotation during growth
βN
|δBp|(n=1)
(G)
(G)
(G)
|δBp|(n=2)
|δBp|(n=3)
φBp(n=1)(deg
)B
z(G) (f<40 kHz, odd-n)
n=2,3n=1 no-wall unstable
n=1-3 no-wall unstable
0.22 0.24 0.26 0.28t(s)
-20-10
010200
100200300
01020300
102030400
2040600246
0.18 0.20 0.22 0.24 0.26 0.28t(s)
-20-10
010200
100200300
0
10
200
1020300
1020300246
114147 114452
moderotation
mode growth
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
• Visible light emission is toroidally asymmetric during RWM
• DCON theory computation displays mode uses experimental equilibrium reconstructionincludes n = 1 – 3 mode spectrumuses relative amplitude / phase of n spectrum measured by RWM sensors
Camera shows scale/asymmetry of theoretical RWMRWM with ∆Bp = 92 G
Before RWM activity
114147t = 0.250s
114147t = 0.268s
Theoretical ∆Bψ (x10) with n=1-3 (DCON)
114147 114147
(interior view)(exterior view)
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
Plasma rotation damping described by NTV theory
• Evolution detail differs for other modesno momentum transfer across rational surfacesno rigid rotor plasma core (internal 1/1 mode)
t=0.265576
t=0.275576
113924
1.0 1.2 1.4 1.6R(m)
Ωφ/2
π(k
Hz) 2520
1015
5
T d(N
m-2
)
0.40.30.20.10.0
-0.1-0.2
0
t = 0.276s
TNTV
t=0.225729t=0.235729t=0.255729
40
30
20
10114452
Ωφ/2
π(k
Hz) t(s)
0.2260.2360.256
theory
• Neoclassical toroidal viscosity (NTV)
• Rapid, global damping observed during RWMEdge rotation ~ 2kHz maintainedLow frequency tearing modes absent
full rotation evolution
1.0 1.2 1.4 1.6R(m)
0.8
t(s)0.2660.276
initial rotation evolution
measured-ρR2(dΩφ/dt)
axis edge
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
NTV Torque depends on aspect ratio, n, q
Neoclassical toroidal viscosity (NTV) theory (K.C. Shaing et al., Phys. Fluids 29 (1986) 521)
( )21 2 2
2mode
, 0
1.3651.182 1.365
i
mni r
NTVm nt
p B n qT Rv B m nqφ
φ
π δε≠
= Ω − Ω + −
∑
dominant m:
( )21 2
2 2mode
i
i rNTV
t
p BT R n qv Bφ
φ
π δε
= Ω − Ω
• n, q (profile) variation can be considered in a single machine
• ε = 1/A variation can be made between machinesmeasured rotation profile
measured Ti0.5 profile
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
q1 2 3 4 5
ωφ/ω
A
0.5
0.4
0.3
0.2
0.1
0.0
stabilized1/(4q2)not stabilized
Experimental Ωcrit follows Bondeson-Chu theory
• Experimental Ωcritstabilized profiles: β >βN
no-wall (DCON)profiles not stabilized cannot maintain β > βN
no-wall
regions separated by ωφ/ωA =1/(4q2)
• Drift Kinetic TheoryTrapped particle effects significantly weaken stabilizing ion Landau damping Toroidal inertia enhancement more yields Ωcrit = ωA/(4q2)
• Neoclassical effect: Is there an ε0.5 scaling?
ωφ/ωA(q,t) profiles
Phys. Plasmas 8 (1996) 3013
NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05
ωφ/ω
AΩcrit follows F-A theory with neoclassical viscosity