Overview of magnetic configuration properties of Wendelstein 7-X
J. Geiger, C. D. Beidler, M. Drevlak, P. Helander, H. Maaßberg, Yu. Turkin
Max-Planck-Institut for Plasma Physics, IPP-EURATOM Assoc., Greifswald, Germany
Problem and task:
● steady-state divertor operation => vanishing bootstrap current
● high- nTτ => low neoclassical transport, full-field (B=2.5T)
● fast-particle confinement => high-β, full-field
● high-β at full-field => high-nTτ (good confinement) + stability
Motivation
Wendelstein 7-X optimized with respect to
●
equilibrium & stability
●
neoclassical transport & small bootstrap current
●
α-particle confinement
Excursion to leading Fourier-coef. of |B| (Boozer-coord.)
in the configuration space of Wendelstein 7-X
Neoclassical confinement (εeff) and minimization of bootstrap current in highmirror configuration demands a compromise.
Wendelstein 7-X coil system and flux surface
modular coils
B 4 3 2 A 1
5
& planar coils
φ=0°
What can be gained by exploiting the flexibility of the coil system?
● Extend investigations of ε
to iota- and position-variations.
eff
● Investigate influence of toroidal mirror form on ε
and Ibs .
eff
Variation of toroidal mirror form
contour plot |B| (Boozer angles)
narrow mirror field
high-mirror configuration
broad mirror field
cent'd → only modular coils for mirror field, planar coils for iota
in/out-sh → planar coils for positioning (affects also mirror field,
readjusted with modular coils)
● range of variation limited and not independent
● for centered configurations b
and b10/b11 show linear dependence
01
● offsets for high-iota (larger b
) and low-iota (lower b01 )
01
● in/out-sh changes b
with minor effect on b10/b11 (gray dashed line).
01
● only for extreme mirror fields : nonlinear interaction of b
& b11 can
01
compete with b10 and suppress dipole-part of the PS-currents
φ=36°
Configurations defined by
6 coil current ratios ik = Ik/I1, k=2,...,5,A,B; normalizing current I1.
Reference configurations around the standard conf. show flexibility:
● toroidal mirror field
● rotational transform
B (φ=0 °)−B(φ=36°)
mirror-ratio mr=
● horiz. position
B (φ=0 °)+B(φ=36°)
● magnetic shear
Neoclassical transport
D
1/ ν
11
3/ 2
eff
∝ ϵ ⋅T
7/ 2
2
2
/( n⋅R ⋅B )
εeff important for neoclassical confinement
Previous results th
(see J.Geiger et al, 35 EPS Conf. 2008, Hersonissos, Crete, Greece
http://epsppd.epfl.ch/Hersonissos/pdf/P2_062.pdf )
●
●
viewed by figures of merit for collisionless trapped particles:
Γv = bounce averaged GradB-drift velocity
Γw = Γs·Γv2 ~ integral effect of square of GradB-drift
=> transport by trapped particles
( Γs – phase volume of trapped particles)
narrow mirror
Interchange stability degrades with higher mr / outward-shift / lower Iota
●
vacuum magnetic well => hill & less shear
PS-current suppression improves with higher mr / outward-shift / higher Iota
Basic configuration variations
- MHD and transport-properties IA=IB < 0
Decreasing
● PS-currents
high­iota
Decreasing
● vac.magn.well
● shear
● PS-currents
IA=-IB < 0
outward­
shifted
I1< I2< I3< I4< I5
low­mirror
Decreasing number
of trapped particles;
Beyond trapped
particles in strong
curvature region
broad mirror
inward­
shifted
IA=-IB > 0
standard
I1= I2= I3= I4= I5
high­mirror
Decreasing
● vac.magn.well
● shear
● PS-currents
I1> I2> I3> I4> I5
low­iota
Increasing number
of trapped particles
Increase of εeff
IA=IB > 0
→ V.V. Nemov et al., Phys. Plasmas 12, 112507 (2005)
l-io = low-iota
= 5/6
s-io = standard-iota
= 5/5
h-io = high-iota
= 5/4
cent'd = centered
i-sh
= inward-shifted
o-sh
= outward-shifted
●
εeff minimum around mr=2%, increases with mr, strong increase for mr<0
bootstrap current coefficient D31 small for high-mirror configuration (mr=10%)
●
bootstrap current Ibs > 0 for mr<10%, Ibs < 0 for mr > 10%
●
plasma-β increases Ibs (reduces mr)
●
D31 (r, Er , ν*) : net current may vanish, current density does not.
Mirror scan (cent'd, iota=1) for
norm. transport coeff. D*31
(DKES, vacuum conf.):
● strong mr-dependence
● minimum for mr~10%
● mr>10% iota-decreasing
component dominates
● mr <10% iota-increasing
component strong
● collisionality-dependence
● dependence on E (much less for electrons)
r
Strong dependence of bootstrap current on profiles (reff, Er, ν*) needs transport analysis
For comparison of configuration effects use
20
-3
● standard density profiles for n
=10
m
e,0
(X2) and for ne,0=1.5∙1020m-3 (O2)
● standard temperature profiles from transp.
simulations : 5MW ECRH in stand. config.
with ‹β›=2% (X2 or O2 according to density)
● simplification for bootstrap current calc.:
● neglect E in transport coefficients
r
(ion-root approximation)
(X2)
(O2)
(i.e. transport coef.s from different configurations)
Config.s at iota=1
(vacuum, ‹β›=2%,
‹β›=4%)
● I
 for mr 
bs
●
●
●
εeff dependence on mr generally persists
● increase of ε
with mr and Iota for mr > 3%
eff
new:
● reduction of ε
with
eff
● outward-shift,
● higher Iota at minimum (limited no of cases?)
● broad mirror configurations can reduce ε
significantly
eff
● narrow mirror configurations increase ε
eff
● β-dependence not strictly decreasing for broad mirror
→ consider finite-β for
best high-β confinement
Ibs  for β 
(configuration effect)
Further dependencies:
● I
 for iota 
bs
●
Ibs  for outward-shifted configurations
Ibs  for broader mirror configurations
Ibs from O2-scenario smaller than for X2
(temperature - collisionality)
low-iota configurations need unrealistically
large values of mr to make Ibs vanish!
Configurations with inherently small bootstrap current
●
Neoclassical transport:
●
Steady-state divertor operation without transformer crucially depends on a vanishing
or at least small bootstrap current (ECCD-capabilities good for n e,0≤1020m-3(140GHz,
X2-mode) but insufficient for higher densities (140GHz, O2-mode).
Estimation: Δι ≈0.00176·Itor [in kA] => 10-20kA will influence island position
Mirror and β-scan:
Fast particle confinement
MHD-properties:
Bootstrap current
at iota=1:
● high-mirror config.
● broad mirror needs larger mr
●
at high-iota (iota=5/4)
● stand. high-iota config.
● mirror may be adjusted
Examples for small to almost vanishing bootstrap current at high-iota:
vacuum, r/a=0.5
vacuum, r/a=0.5
stand. high-iota, ‹β›=2%
X2-scenario => Ibs ≈ -8.5kA
●
‹β›=4.2%, r/a=0.5
‹β›=4.2%, r/a=0.5
stand. high-iota, ‹β›=4%
O2-scenario => Ibs ≈ -13.7kA
stand.-iota, mr=11%, ‹β›=4%
O2-scenario => Ibs ≈ -2.0kA
min(Γv) almost independent of mr
min(Γw) increases with mr ( Γs  number of tr. part. increases!)
● fast particle confinement seems not to improve with increasing β
● lowest values of Γ in high-mirror configurations for (hi-io, o-sh)-case
v
Note: mr(vac.) > mr(β)
●
Color-coding for jb :
ions
electrons