Results from Helical Axis Stellarators
Boyd Blackwell, H-1 National FacilityAustralian National University
Thanks to:Enrique Ascasibar and TJ-II GroupProf. Obiki and Heliotron-J GroupDavid Anderson and HSX Crewand the H-1 Team
Outline
Acknowledgements: TJ-II, Heliotron-J, HSX and H-1 groups for their contributions and access to their data, in particular C. Alejaldre, E. Ascasibar, C. Hidalgo, T. Obiki, K. Nagasaki, D.T. Anderson, J.H.Harris, M.G. Shats, J. Howard, Nyima Gyaltsin, S. M. Collis and D.L. Rudakov.
Brief history
Comparative parametersmagnetic surfaces
plasma formation and heating
diagnostic issues
Transport
Stabilityfluctuations
Spitzer 1951Spitzer 1951 - figure-8 stellarator “spatial axis” which produces rotational transform
magnetic hill unstable to interchange
Koenig 1955Koenig 1955 - helical winding/axis: = 1 one pair of helices
Spitzer 1956Spitzer 1956 possibility of shear stabilization for higher order windings = 2,3demonstrated theoretically (resistivity 0) Johnson et al 1958Johnson et al 1958
Furth, Killeen, Rosenbluth 1963Furth, Killeen, Rosenbluth 1963 found resistive interchange instability possible even at low resistivity for small scale lengths
1964-5 several configurations proposed with magnetic well (average minimum B) found including heliac (straight).
Exploitation of avg. min B regions of bad curvature possible ballooning instability
Development of Helical Axis Stellarators
-I
+I = 1
Nagao 1977Nagao 1977 Asperator NP: toroidal helical axis stellarator (+extra helical windings)
Yoshikawa... 1982-4Yoshikawa... 1982-4 - toroidal heliac HX-1 proposal
Blackwell, Hamberger... 1984Blackwell, Hamberger... 1984 - SHEILA prototype heliac (0.2M, 0.2T, 1019m3)
Harris.. 1985 Harris.. 1985 flexible heliac: = 1 winding varies iota, well over large range
19851985 - Tohoku, H-1 and TJ-II and heliacs proposed - and Ribe’sRibe’s linear heliac UW - Operation in 1987 (Tohoku, Sendai) 1992 (H-1) and 1996(TJ-II, Spain)
1988 Nuhrenberg and Zille - 1988 Nuhrenberg and Zille - quasi-helical symmetry - restore outstanding features of straight heliac. [transport, beta limit(Monticello et. al 1983)]
1996-91996-9 Heliotron-J - combine heliotron/torsatron with advances in transport (optimise bumpy cpt, quasi-isodynamic)
1999 1999 HHelicallyelically S Symmetricymmetric EEXXperimentperiment first quasi-symmetric experiment exploit high iota, N-m scaling
Development of Helical Axis Stellarators II
Canberra, Australia external vacuum vessel
CIEMAT, Madrid internal vessel, upgrade to NBI
IAE Kyoto “inverted heliac” bumpy field cpt
TSL, Madison controlled “spoiling” of symmetry
.
Device Type Aspect Iota
H-1 Heliac 3 period heliac, toroidal>helical 5 .15
TJ-II Heliac 4 period heliac, helical>toroidal 7 0.9-2.2
Heliotron J helical axis heliotron (TFC + =1) 7-11 0.2-0.8
HSX modular coils, helical symmetry 8 1.05-1.2
Helical Axis Stellarators 2000bn,m
Canberra, Australia external vacuum vessel
CIEMAT, Madrid internal vessel, upgrade to NBI
IAE Kyoto “inverted heliac” bumpy field cpt
TSL, Madison controlled “spoiling” of symmetry
.
Device Type Aspect Iota
H-1 Heliac 3 period heliac, toroidal>helical 5 .15
TJ-II Heliac 4 period heliac, helical>toroidal 7 0.9-2.2
Heliotron J helical axis heliotron (TFC + =1) 7-11 0.2-0.8
HSX modular coils, helical symmetry 8 1.05-1.2
Helical Axis Stellarators 2000bn,m
Brief history
Comparative parameters
magnetic surfacesHeliotron J and HSX
plasma formation and heating
diagnostic issues
Transport
Stabilityfluctuations
Device Parameters of Heliotron J
Coil SystemL=1/M=4 helical coil 0.96MATToroidal coil A 0.6MATToroidal coil B 0.218MATMain vertical coil 0.84MATInner vertical coil 0.48MAT
Major radius 1.2mMinor radius of helical coil 0.28mVacuum chamber 2.1m3
Aspect ratio 7Port 65Magnetic Field 1.5TPulse length 0.5secPitch modulation of helical coil
Inner Vertical Coil
Toroidal Coil A
Outer Vertical Coil
Toroidal Coil BHelical Coil
Plasma
Vacuum Chamber
sin( )
0.4
M M
L L
The Heliotron J Device
Main VFC
TFC-A
TFC-B
Aux.VFC
HFC
Magnetic Surface Mapping
Fig.3 The magnetic surfaces at = 67.5 in the standard configuration. (a) The experimental results (corrected) and (b) The calculated magnetic surfaces.
(a) (b)
STD config, 0.03 Tesla, corrected for earth’s field
Configuration “A” is designed to create a helical divertor region shown in red and yellow.
The position of the plasma is shown relative to the helical conductor and the vacuum vessel
Other configurations
• island divertor
• standard
from T. Mizuuchi, M. Nakasuga et al. Stellararor Workshop 1999
Heliotron-J surfaces: cfg “A” - helical divertor
Helically Symmetric Experiment
UW, Madison
R = 1.2 a=0.15B0=1.3T 4 periodsiota 1.05-1.12 well ~1% essentially 1 term in B0 spect
28GHz@200kWne~3e12 for [email protected]
HSX Parameters
HSX Magnetic surfacesGood magnetic surfaces, iota ~ 1% accurateDrift surfaces coincide well with magnetic surfaces
- low toroidal effects, high effective iota (eff = N-m)
HSX Magnetic surfacesGood magnetic surfaces, iota ~ 1% accurateDrift surfaces coincide well with magnetic surfaces
- low toroidal effects, high effective iota (eff = N-m)
Measured drift surfaces mapped to Boozer coordinates
Expected drift if fully toroidal
Canberra, Australia external vacuum vessel
CIEMAT, Madrid internal vessel, upgrade to NBI
IAE Kyoto “inverted heliac” bumpy field cpt
TSL, Madison controlled “spoiling” of symmetry
.
Device Type Aspect Iota
H-1 Heliac 3 period heliac, toroidal>helical 5 .15
TJ-II Heliac 4 period heliac, helical>toroidal 7 0.9-2.2
Heliotron J helical axis heliotron (TFC + =1) 7-11 0.2-0.8
HSX modular coils, helical symmetry 8 1.05-1.2
Helical Axis Stellarators 2000bn,m
Comparative parameters
magnetic surfaces
plasma formation and heating (H-1, HSX)
diagnostic issuesTransport
H-1 Heliac: Parameters3 period heliac: 1992Major radius 1mMinor radius 0.1-0.2mVacuum chamber 33m2 excellent access
Aspect ratio 5+ toroidal
Magnetic Field 1 Tesla (0.2 DC)Heating Power 0.2(0.4)MW GHz ECH
0.3MW 6-25MHz ICH
Parameters: achieved / expected n 3e18/1e19
T ~100eV(Ti)/0.5-1keV(Te)
0.1/0.5%
H-1 Heliac: Parameters3 period heliac: 1992Major radius 1mMinor radius 0.1-0.2mVacuum chamber 33m2
Aspect ratio 5+Magnetic Field 1 Tesla (0.2 DC)Heating Power 0.2(0.4)MW GHz ECH
0.3MW 6-25MHz ICH
Parameters: achieved / expected n 3e18/1e19
T ~100eV(Ti)/0.5-1keV(Te)
0.1/0.5%
Complex geometry requires minimum 2D diagnostic
Cross-section of the magnet structure showing a 3x11 channel tomographic diagnostic
2D electron density tomography
coherent drift mode in argon, 0.08TH density profile evolution (0.5T rf)
Helical axis non-circular need true 2D
Movie Clip (AVI)
Raw chordal data Tomographically inverted data
HSX ECH Plasma
Utilize 2nd harmonic ECH at 28GHz to examine confinement of deeply-trapped electrons
Plasma production and heating: resonant and non-
resonant RF
<ne> 1018m-3
• Non-resonant heating is flexible in B0, works better at low fields.
• Resonant heating is much more successful at high fields. helicon/frame antenna
= Chon axisMagnetic Field (T)
radi
us
Ion Temperature Camera
Hollow Ti at low B0
0 10 20 30 time (ms)
Inte
nsity
te
mpe
ratu
re
rot
atio
n
Canberra, Australia external vacuum vessel
CIEMAT, Madrid internal vessel, upgrade to NBI
IAE Kyoto “inverted heliac” bumpy field cpt
TSL, Madison controlled “spoiling” of symmetry
.
Device Type Aspect Iota
H-1 Heliac 3 period heliac, toroidal>helical 5 .15
TJ-II Heliac 4 period heliac, helical>toroidal 7 0.9-2.2
Heliotron J helical axis heliotron (TFC + =1) 7-11 0.2-0.8
HSX modular coils, helical symmetry 8 1.05-1.2
Helical Axis Stellarators 2000bn,m
diagnostic issues
Transport
confinement (Heliotron-J, TJ-II, H-1)Stability/Fluctuations
Heliotron-J: Confinement during ECH
• ECH 400kW 53GHZ 50ms
• <> ~ 0.2%, <20% radiated
• some Fe Ti C O impurities
Plans:
• will upgrade to 70GHz, 500kW
• ultimately 4MW ~20kJ?
• impurity control
• explore bumpiness and hel. divertorsFig. 2 Dependence of the diamagnetic stored energy on the magnetic field strength.
B*=0 (T)
Wp (kJ)
#1595 ~ #241653.2GHz ECH
0/
0.80 1.00 1.20 1.400
0.2
0.4
0.6
0.8
1
0.4 0.5 0.6 0.7
W-Diamagnetic vs B is peaked, 700J max
Initial Plasma: 700J stored energy
TJ-II Heliac, CIEMAT, Spain
• R = 1.5 m, a < 0.22 m, 4 periods
• B0 < 1.2 T
• PECRH < 600 kW from 2 ECH systems
• PNBI < 3 MW under installation
• helium and hydrogen plasma
• Te ~ 2keV, low radiated powers (<20%)
• wall desorption rate limits operation in He at P< 600 kW
Helical/central conductor
• Helium plasmas with injected power of 300 kW• Neoclassical Monte-Carlo agrees well
Inferred positive ambipolar Er, confinement time ~ 5ms ~ ISS95
yet no serious accumulation of impurities
0
0.5
1
1.5
-15 -10 -5 0 5 10 15
n e(1
019
m-3
)
reff
(cm)
Thomson scattering
0
0.5
1
1.5
-15 -10 -5 0 5 10 15
T e
(keV
)
reff
(cm)
• iota ~ 1.28 – 2.24, up to 1.2 x 1019 m-3 and 2.0 keV
0.0
0.5
1.0
1.5
2.0
1.2 1.4 1.6 1.8 2 2.2
Pinj
=300 kWP
inj=100 kW
Pinj
=200 kWP
inj=400 kW
Pinj
=500 kWP
inj=600 kW
W (
kJ)
Iota(0)
Helium
1.2 1.4 1.6 1.8 2 2.2Iota(0)
Hydrogen
Iota = 2
• When corrected for volume changes, a positive dependence on iota is revealed in helium, (less in H) (tendency sim. to ISS95)
Configuration Scan (iota)
Confinement transitions in H-1
6
5
4
3
2
1
00
0 . 5
1r / a
01 0
2 03 0
t ( m s )
I s i ( )m A( a )
M o d u l a t i o ni n v e r s i o n
“Pressure” (Is) profile evolution during transition
transition
PRF (kW)
B0(T)
•many features in common with large machines
•associated with edge shear in Er
•easily reproduced and investigated
Parameter space map, ~ 1.4
ExB and ion bulk rotation velocity in high confinement mode: magnetic structure causes
viscous damping of rotation
-6E+6
-4E+6
-2E+6
0E+0
2E+6
15 20 25
V_pol(cm/s)
(x10)
VExB
r(cm) (cm)
LCFS (cm)
pttpir BVBVPzen
E 1
0 0
Vp, Vt << VExB ~ 1/(neB) dPi/dr
Radial force balance
Mass (ion) flow velocities much smaller than corresponding VExB
Bulk Rotation Damped in Heliac
diagnostic issues
Transport
Stability fluctuations
Issues: Interchange and Ballooning Modes (DTEM low )
Tools: Configuration Flexibility e.g. transform andmagnetic well (even hill!)
First Impression: No unworkable instabilties or disruptions
“Drift-like” instability in H-1 at low field
–Triple-Mach-Triple probe
–disappears as B increases
Helical axis high iota short connection length
All devices need > 0.5-1% to test ballooning stability%30/
~/
~/~ iiee TTTTnn
TJ-II Turbulence/Fluctuation studies
• ExB sheared flows observed near edge rational surfaces (8/5, 4/2)
• Spectra mainly <200kHz, 10-40% (edge?), correlation time 10ms
• MHD (ELM-like) events (for W~1kJ) - magnetic activity - spike in the H signal.
• Fluctuations increase with magnetic hill near edge• resistive ballooning?
Summary - Future• Confinement in heliacs ~ISS95 or better (2keV, ~5ms). Ion beam
probe to elucidate role of Eradial in improved confinement
• New configurations with improved neoclassical transport initial results promising, await mature data, analysis
• HSX/H-J can compare similar configurations with vastly different neoclassical transport predictions.
• Confinement transitions possible at low power, many similarities with large devices/powers. Investigate effect of E-field imposed by localised ECH.
• No serious impurity accumulation problems yet. Real test when the ions are strongly heated
• No fatal instabilities observed yet. Several devices should have the heating capacity to test ballooning limits, at least in degraded configurations (consequence of flexibility).