Experimental Results From Stellarators
Rudolf Brakel
MaxPlanckInstitut für Plasmaphysik
EURATOM Association
Garching, Germany
Summer University, Garching, September 2001
Toroidal confinement
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v B = |
mv 2 |
B B |
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2q |
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B3 |
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vE B = |
E B |
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B |
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in a toroidal field the ExB drift causes rapid plasma loss
what is required?
arotational transform = 1/q = R/r (Bpol/Btor)
helical field structure
flux surfaces
tokamak: Bpol by plasma current
stellarator: Bpol by external coils
I / 2
why stellarators?
advantages of stellarators
external magnetic fields
confinement does not need a high plasma current
inherent steady state capability
no current driven instabilities
no recirculating power for CD
configurational flexibility
drawbacks of traditional stellarators
large neoclassical transport
moderate limit ( p/B2)
large aspect ratio
use the advantages and overcome the drawbacks by optimizing the magnetic field structure
I / 3
Topics
the stellarator family
the vacuum magnetic field
plasma equilibrium and high operation ( p/B2)
transport and confinement
long pulse operation and divertor concepts
summary
I / 4
shut down |
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STELLARATORS / HELICAL DEVICES |
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operating |
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under construction |
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Fig.8 |
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A, B |
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Stellarators |
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Torsatrons |
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Heliotrons |
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Heliacs |
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ATF, CAT, |
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HeE, HeJ |
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H1, TJII |
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classical |
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CHS, LHD |
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C, Cleo, W7A, L2, U3M |
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modular
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advanced |
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quasisymmetric |
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W7AS |
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Helias |
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qhelical |
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qaxial |
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q... |
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W7X |
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HSX |
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NCSX, |
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CHSqa |
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po itm azi ito w n tih inc
etno chts ciniar latn s
hp isy sc
po mit iaz oit n
I / 5
Stellarator coil systems
classical (W7A)
modular (W7AS)
B. Carreras, Nuclear Fusion, 28 1613 (1988)
Torsatron (ATF)
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R/m |
a/m |
B/T |
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W7A |
2.0 |
0.10 |
3 |
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W7AS |
2.0 |
0.18 |
3 |
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W7X |
5.5 |
0.53 |
2 |
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HSX |
1.2 |
0.15 |
1.4 |
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ATF |
2.1 |
0.27 |
2 |
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CHS |
1.0 |
0.20 |
2 |
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LHD |
3.9 |
0.60 |
3 |
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TJII |
1.5 |
0.20 |
1 |
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Heliac (TJII)
I / 6
Magnetic shear and magnetic well
magnetic shear = |
magnetic well |
= B increases with radius |
radial variation of |
magnetic hill |
= B decreases with radius |
the rotational transform |
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shear and well are favourable for plasma stability
I / 7
Vacuum field properties of stellarators
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rotational |
magn. |
magn. |
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transform |
shear |
well |
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Stellarator |
low |
low |
global |
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(W7AS, X) |
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magn. well |
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Heliac |
high |
low |
global }stabilization |
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(TJII) |
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Torsatron |
moderate |
moderate |
central |
magn. shear |
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(ATF, LHD) |
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}stabilization |
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Heliotron |
high |
high |
hill |
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(HeE) |
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the plasma modifies the vacuum field properties by plasma currents
I / 8
Magnetic island formation by field perturbation
H. Wobig, Z. Naturforsch. 42a, 1054 (1987)
radial perturbation field Bnm:
„resonant surfaces“ (r) = n/m will be perturbed
magnetic islands appear
example:
- toroidally localized perturbation - poloidal Fourier components:
Bm/B0 ~ 0.01/(R/a), m = 2, 3
small shear:
islands become large,
but can be excluded by choice of
large shear:
islands become small,
but their number increases, they cannot be excluded
I / 9
Vacuum flux surfaces measurements (TJII)
E. Ascasibar, J. Plasma Fus. Res., 1 183 (1998)
An electron beam following the field lines is detected by a moving fluorescing rod
calculated measured
I / 10