Office of Science. Supported by. 21 st IAEA Fusion Energy Conference, Chengdu, China, 2006. MHD in the Spherical Tokamak. EX/7-2Ra. - PowerPoint PPT Presentation
MHD in the Spherical Tokamak MAST authors: SD Pinches , I Chapman, MP Gryaznevich, DF Howell, SE Sharapov, RJ Akers, LC Appel, RJ Buttery, NJ Conway, G Cunningham, TC Hender, GTA Huysmans, R Martin and the MAST and NBI Teams NSTX authors: A.C. Sontag, S.A. Sabbagh, W. Zhu, J.E. Menard, R.E. Bell, J.M. Bialek, M.G. Bell, D.A. Gates, A.H. Glasser, B.P. Leblanc, F.M. Levinton, K.C. Shaing, D. Stutman, K.L. Tritz, H. Yu, and the NSTX Research Team 21 st IAEA Fusion Energy Conference, Chengdu, China, 2006 This work was jointly funded by the UK Engineering & Physical Sciences Research Council and Euratom Supported by Office of Science EX/7-2Rb EX/7-2Ra
Transcript
MHD in theSpherical Tokamak
MAST authors: SD Pinches, I Chapman, MP Gryaznevich, DF Howell, SE Sharapov, RJ Akers, LC Appel, RJ Buttery,NJ Conway, G Cunningham, TC Hender, GTA Huysmans,
R Martin and the MAST and NBI Teams
NSTX authors: A.C. Sontag, S.A. Sabbagh, W. Zhu, J.E. Menard, R.E. Bell, J.M. Bialek, M.G. Bell, D.A. Gates, A.H.
Glasser, B.P. Leblanc, F.M. Levinton, K.C. Shaing, D. Stutman, K.L. Tritz, H. Yu, and the NSTX Research Team
21st IAEA Fusion Energy Conference, Chengdu, China, 2006
This work was jointly funded by the UK Engineering & Physical Sciences Research Council and Euratom
Supported byOffice ofScience
EX/7-2Rb
EX/7-2Ra
MHD physics understanding to reduceperformance risks in ITER and a CTF
– Error field studies
– RWM stability in high beta plasmas
– Effects of rotation upon sawteeth
– Alfvén cascades in reversed shear
EX/7-2RaEX/7-2Rb
Error field studies in MAST
Four ex-vessel (ITER-like)error field correction coils wired to produce odd-n spectrum,Imax = 15 kA·turns (3 turns)
[Howell et al. to be submitted Nucl. Fusion (2006)][Buttery et al., Nucl. Fusion (1999)]
B21 is the m = 2, n = 1 field component normal to q = 2 surface:
Error fields contribute to βN limit: n=1 kink
EX/7-2Ra
•Similar density scaling observed on NSTX
•Extrapolating to a Spherical Tokamak Power Plant / Component Test Facility gives locked mode thresholds ≈ intrinsic error prudent to include EFCCs
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
RWM active stabilization coils
RWM sensors (Bp)
Non-axisymmetric coil enables key physics studies on NSTX
• RWM active stabilization Midplane control coil similar to
ITER port plug designs n > 1 studied during n = 1
stabilization
• RWM passive stabilization Plasma rotation profile, ion
collisionality, ii, important for stability
• Plasma rotation control A tool to slow rotation, , by
resonant or non-resonant fields Plasma momentum dissipation
physics studied quantitatively
RWM sensors (Br)
Stabilizerplates
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
RWM actively stabilized at low, ITER-relevant rotation
• First such demonstration in low-A tokamak Long duration > 90/RWM
Exceeds DCON Nno-wall
for n = 1 and n = 2 n = 2 RWM amplitude
increases, remains stable while n = 1 stabilized
• n = 3 magnetic braking to reduce
Non-resonant braking to accurately determine critical plasma rotation for RWM stability, crit
Sabbagh, et al., PRL 97 (2006) 045004.0.40 0.50 0.60 0.70 0.80 0.90t(s)
0.00.51.01.52.0
05
10152005
1015200.00.51.01.5
02468
Shot 120047
0
2
4
6
N
IA (kA)
Bpun=1 (G)
Bpun=2 (G)
/2 (kHz)
N > N (n=1)no-wall
120047
120712
< crit
92 x (1/RWM )
6420840
1.51.00.50.02010
02010
0
t(s)0.4 0.5 0.6 0.7 0.8 0.9Post-deadline paper
at this conference, PD/P6-2
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
measured
theory
t = 0.360s
116931
axis
n = 3field
TN
TV (
N m
) 3
4
2
1
00.9 1.1 1.3 1.5
R (m)
TN
TV (
N m
)
3
4
2
1
0
Observed plasma rotation braking follows NTV theory
• First quantitative agreement using full neoclassical toroidal viscosity theory (NTV) Due to plasma flow through
non-axisymmetric field Trapped particle effects, 3-D
field spectrum important
• Resonant field amplification (RFA) increases damping at high beta Computation based on applied
field, or DCON computed mode spectrum
• Non-negligible physics for simulations of in future devices (ITER, CTF)
appliedfieldonly
axis
t = 0.370s
116939With RFA
With RFA(DCON)
n = 1field
Zhu, et al., PRL 96 (2006) 225002.
RFA =Bplasma
Bapplied
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
Rotation profile shape important for RWM stability
• Benchmark profile for stabilization is c = A/4q2 *
predicted by Bondeson-Chu semi-kinetic theory**
theory consistent with radially distributed dissipation
• Rotation outside q = 2.5 not required for stability Applied n = 3 fields used to alter stable
profiles below c
• Scalar crit/A at q = 2 , > 2 not a reliable criterion for stability variation of crit/A at q = 2 greater than
measured in one time step consistent with distributed dissipation
*A.C. Sontag, et al., Phys. Plasmas 12 (2005) 056112.**A. Bondeson, M.S. Chu, Phys. Plasmas 3 (1996) 3013.
0.25
0.20
0.15
0.10
0.05
0.00
cr
it/
A
4.03.53.02.52.01.5q
no applied field n = 3 n = 3 max. braking tcrit - 10 ms
1/(4q2
)
0.4
0.3
0.2
0.1
0.0
crit/
A
4.03.02.01.0q
no applied field n = 3 DC n = 1 DC n = 1 traveling n = 1 & n = 3
1/4q2
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
crit not correlated with Electromagnetic Torque Model
• Rapid drop in when RWM unstable may seem similar to ‘forbidden bands’ theory model: drag from
electromagnetic torque on tearing mode*
Rotation bifurcation at 0/2 predicted
• No bifurcation at 0/2 observed no correlation at q = 2 or
further into core at q = 1.5 Same result for n = 1 and 3
applied field configuration
NSTX crit Database
*R. Fitzpatrick, Nucl. Fusion 33 (1993) 1061.
(0 steady-state plasma rotation)
1.0
0.8
0.6
0.4
0.2
0.0
crit/
02.42.01.61.2
q
n = 1 n = 3
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
Increased Ion Collisionality Leads to Decreased crit
(R. Fitzpatrick, et al., Phys. Plasmas 13 (2006) 072512.)
• Plasmas with similar vA
• Consistent with neoclassical viscous dissipation model at low , increased ii leads to
lower crit
modification of Fitzpatrick “simple” model
• Similar result for neoclassical flow damping model at high collisionality (ii > vtransit)
(K. C. Shaing, Phys. Plasmas 11 (2004) 5525.)
(a)
(b)
(c)
crit (km/s)
vA (km/s)
ii (kHz)
121083121071
Effects of rotation on sawtooth
• Increasing co-NBI sawtooth period increases• Increasing counter-NBI sawtooth period decreases
to a minimum, then increases
Ip = [680,740] kA, BT = [0.35,0.45] Tne = [1.6,2.2] 1020 m-3
[Chapman, submitted to Nucl. Fusion (2006)][Koslowski et al., Fusion Sci. Technol. 47 (2005) 260][Nave et al., 31st EPS (2004) P1.162]
MAST #13369
1.61 MW (co)
MAST #13575
1.56 MW (counter)
Co-NBICounter-NBI
EX/7-2Ra
Sawtooth Stability Modelling
The resistive, compressional linear MHD stability code MISHKA that includes ion diamagnetic effects (*i) has been extended to include toroidal and poloidal flow profiles (MISHKA-F)
In the case, vΦ << vA ands = (r/q)dq/dr ~ 1, (as in MAST) theory predicts that Doppler shifted mode frequency:
In MAST, rotation at q = 1 is key parameter, not rotational shear
Marginal q=1 position with flowAs sawtooth period, st, increases, radial location of q = 1 increases
Marginally stable q = 1 radius expected to correlate with st
Toroidal velocity at whichq = 1 radius for marginal stability is minimised agrees with when sawtooth period is minimised
Co-vΦ profile usedCounter-vΦ profile used
Experimental data MISHKA-F modelling
q
r
1
r(q=1)
t
Mar
gina
lly s
tabl
e q=
1 ra
dius
Ongoing extension to this work to include fast ion kinetic effects to study fast ion stabilisation of sawteeth and NTM triggering
EX/7-2Ra
MAST #15806
Log
(δB
)
Fre
quen
cy [
kHz]
Time [s]0.115 0.120 0.125 0.130 0.135
-2.0
-3.0
-4.0
-5.0
170
160
150
140
130
120
Alfvén Cascades and qmin(t) evolution
• Global shear Alfvén
waves driven by fast
beam ions
– Lowered beam
power to avoid
nonlinear effects
• ACs occur when
magnetic shear is
reversed
• Characteristic
frequency sweep
determined by qmin
– Determine qmin(t)
Single Alfvén cascade
eigenmode
Transistion to TAE and frequency
sweeping
EX/7-2Ra
Time [s]0.09 0.10 0.11 0.130.12 0.14 T
oroi
dal m
ode
num
ber,
n
5
4
3
2
1
MAST #16149F
requ
ency
[kH
z]140
120
100
80
60
qmin(t)
qmin=7/2 5/28/3 7/3
3
2
3/1
0.08
Summary & Conclusions• Error field studies highlight need for error field correction
coils on Spherical Tokamak Power Plant or Component Test Facility
• Inverse dependence of crit on ii indicates that lower collisionality on ITER may require a higher degree of RWM active stabilisation in advanced scenarios
• Similar inverse dependence of plasma momentum dissipation on ii in NTV theory indicates ITER plasmas will be subject to higher viscosity and greater reduction
• Strong B2 dependence of quantitatively verified NTV theory shows that error fields and RFA need be minimized to maximize
• Detailed sawtooth modelling agrees with experimental results and clarifies rôle of rotation in sawtooth stability
• Alfvén cascades have confirmed the sustainment of reversed magnetic shear and revealed the evolution of qmin
See posters EX/7-2Ra/b for more details
The End
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
Non-axisymmetric fields amplified by stable RWM at high N
• Toroidally rotating n = 1 fields used to examine resonant field amplification (RFA) when N N
no-wall
propagation frequency and direction scanned
RFA increases when applied field rotates with plasma flow
consistent with DIII-D results and theoretical expectations
• Single mode model of RWM fit to measured RFA data peak in fit at 45 Hz in direction
of plasma flow 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
-120 -90 -60 -30 0 30 60 90 120
RF
A m
ag
nitu
de
(n
= 1
)
Applied frequency (Hz)
Direction ofplasma flow
Counterplasma flow
Single modemodel fit
RFA =Bplasma
Bapplied
(H. Reimerdes, et al. PRL 93 (2004) 135002.)
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
RWM stabilized upon growth of other MHD modes
• n = 1 internal mode grows following unstable growth phase of n = 1 RWM
6
4
2
0
N
0.420.400.380.36
time (s)
20
15
10
5
0
Bp
(Gau
ss)
-10-505
10
B (
Gau
ss)
-2
-1
0
1
2
w (a.u
.)121100
odd-n, f < 40kHz
n = 1, RWM sensors
(b)
(a)
(c)
w < 0 is unstable
0.430.420.410.400.390.380.37
time (s)
EDGE
CORE
RWM growth
Inset Area
(a)
0.4300.4250.4200.4150.4100.405
time (s)
(b)
Chordal USXR Data
0.41 0.42 0.43t (s)
0.37 0.39 0.41 0.43t (s)
Edge
Core
RWM
0.36 0.38 0.40 0.42D
CO
N
W
N
64
20
Bp (
G)
B (
G)
1510
50
10
-10
0
t (s)
N > Nno-wall
vNBI
v*i (co)
v*i (counter)
Sawtooth studies in MAST
High power NBI into small (low moment of inertia) plasma volume fast rotation Important to understand for
future Component Test Facility (very high NBI power)
Studying effects of flow on sawtooth stability important for understanding slowly rotating ITER plasmas Decoupling rotation from
present-day results
Combination of experimental studies and numerical modelling
EX/7-2Ra
Reversed shear and Alfvén Cascades
• Alfvén Cascades observed on MAST showing duration of reversed shear• Also seen on interferometry signals
Plasma Current
NBI Power
#16095
#16149
Onset of AC with qmin~3
Onset of AC with qmin~2
Time (s)0.00 0.05 0.10 0.15 0.20 0.25
MW
0.0
0.5
1.0
1.5
kA
800
600
200
400
0
ACs indicate shear reversal
EX/7-2Ra
MAST #15806
Log
(δB
)
Fre
quen
cy [
kHz]
Time [s]0.115 0.120 0.125 0.130 0.135
-2.0
-3.0
-4.0
-5.0
170
160
150
140
130
120
Alfvén Cascades in MAST
• Global shear Alfvén
waves driven by super-
Alfvénic beam ions
– Lowered beam power
to avoid nonlinear
effects from strong
drive
• ACs occur when
magnetic shear is
reversed
• Characteristic frequency
sweep determined by
qmin
– Enables determination
of qmin(t)
Single Alfvén cascade
eigenmode
Transistion to TAE and frequency
sweeping
EX/7-2Ra
Alfvén cascades and qmin evolution
Time [s]0.09 0.10 0.11 0.130.12 0.14
Tor
oida
l mod
e nu
mbe
r, n
5
4
3
2
1MAST #16149
Fre
quen
cy [
kHz]
140
120
100
80
60
qmin(t)
qmin=7/2 5/28/3 7/3
3
2
3/1
0.08
EX/7-2Ra
New Sensors Reveal High Frequency MHD
[Appel et al., 31st EPS (2004) P4.195][Gorelenkov et al, Nucl. Fusion 42 (2002) 977]
New TAE antenna currently being installed leaves MAST well-placed to probe fast particle stability at tight aspect ratio
New high frequency sensors (<5 MHz) reveal modes similar to observations on NSTX
MAST #16106
Log
(δB
)
0.0
-3.0
-4.0
-5.0
-1.0
-2.0
-6.0
Fre
quen
cy [k
Hz]
1000
800
600
400
200
Time [s]0.228 0.230 0.232 0.2360.234 0.238 0.240 0.242
TAE modes
EAE modes
NAE modes
High frequency modes
NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb
NSTX supports ITPA / ITER locked mode threshold and disruption studies
(1) Locked mode threshold (2) Disruption studies
• NSTX contributing low-A, low B data density scaling nearly linear, similar
to higher-A
Will contribute B, q scaling data for ITER size scaling
(GA reportA25385)
• NSTX data contributes dependence of current quench time, CQ on A Important test of theory for ITER, CTF CQ independent of plasma current
density when A dependence of plasma inductance is included
ne [1019m-3]
Ap
pli
ed 2
/1 B
a
t lo
ck (
Gau
ss)
ne0.93
ne1.0 ITER Operating Range
9 MA 15 MA
J. Menard, PPPL
Access to new regime
Error field correction enables operation at previously inaccessible low densities to study current drive physics
