alpha particle confinement in the european demo€¦ · alpha particle con nement in the european...
TRANSCRIPT
Alpha particle confinement in the European DEMO
D.Pfefferle1,2
W.A.Cooper1 J.P.Graves1 A.Fasoli1
R.Wenninger3 DEMO Physics Basis Development group3
1 Centre de Recherches en Physique des Plasmas (CRPP), 1015 Lausanne, Switzerland2 Princeton Plasma Physics Laboratory (PPPL), Princeton NJ, 08543-0451, USA
3 Max-Planck-Institut fur Plasmaphysik (IPP), D-85748 Garching, Germany
September 1st, 2015
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 0 / 22
Motivation
Motivation
In the refinement of the European DEMO design
integrate knowledge from existing machines (JT60-SA, etc.) + ITER
take into account wide range of tokamak related phenomena
compromise/trade-offs but also opportunity for optimisation
Fusion alpha particles
assess/verify confinement in current coil design
special focus on magnetic ripple created by the 18 TF coils
application of modelling capabilities:
Coil.Sphell (vacuum fields, Biot-Savart) [Cooper et al., 2004]
VMEC (3D MHD equilibrium) [Hirshman and Whitson, 1983]
VENUS-LEVIS (orbit solver, Monte-Carlo code) [Pfefferle et al., 2014]
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 1 / 22
Motivation
Modelling approach and work flow
description of TF and PF coils(current filaments)
Coil.Sphell
(Biot-Savart)3D vacuum fields
VMEC
(free-boundary MHD)
background profilesn(s), T (s), jφ(s)
2D or 3D equilibriumVENUS-LEVIS
(orbit-code)
saturated alpha particledistribution, losses, etc.
code input files intermediate result final result
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 2 / 22
Motivation
Outline
1 Coils, plasma and ripple: two contrasting models to represent 3Dstationary fields
Vacuum ripple field + 2D plasma model3D ideal MHD equilibrium model
2 Dynamics of ripple perturbed orbitsRipple well trapping and separatrix crossingStochastic diffusion of bounce tips
3 Fusion alpha confinementSlowing-down simulationsLost particles, loss rates
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 3 / 22
Coils, plasma and ripple
European DEMO with 18 TF coils
Single-null diverted plasma:R0 = 9.25m, a = 2.9m, B0 = 6T,Ip = 19.6MA, V = 2145m3, β = 2.2%
−15
−10
−5
0
5
10
15−15
−10−5
05
1015
−10
−5
0
5
y [m]x [m]
z [
m]
4 6 8 10 12 14 16
−10
−8
−6
−4
−2
0
2
4
6
8
CS3U
CS2
CS1
CS2L
CS3L
P1
P2
P3
P4
P5
P6
R [m]
Z[m
]
TF
~B, ~I
wall
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 4 / 22
Coils, plasma and ripple Vacuum ripple field + 2D plasma model
Coil.Sphell calculation of 3D vacuum field and ripple
0 0.2 0.4 0.6 0.8 1
−0.015
−0.01
−0.005
0
0.005
0.01
0.015
Nφ/2π
[T]
vacuum ripple field at (R,Z)=(11.5,0)
δB
φ
δBR
δBZ
δBφ ≈ δ(R,Z) cos(Nφ)Bφ[Yushmanov, 1990; McClements, 2005]
δ(R,Z) ∼ JN (αR) cosh(αZ) ∝ (αR)NR [m]
Z [
m]
Bφ/<B
φ>−1
6 8 10 12−6
−4
−2
0
2
4
%
0
1
2
3
4
5
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 5 / 22
Coils, plasma and ripple Vacuum ripple field + 2D plasma model
Coil.Sphell calculation of 3D vacuum field and ripple
8 10 12 14 16 1801
5
10
20max ripple within wall
N TF coils
δm
ax
8 10 12 14 16 181
5
10
20
∝ 0.76N
δBφ ≈ δ(R,Z) cos(Nφ)Bφ[Yushmanov, 1990; McClements, 2005]
δ(R,Z) ∼ JN (αR) cosh(αZ) ∝ (αR)NR [m]
Z [
m]
Bφ/<B
φ>−1
6 8 10 12−6
−4
−2
0
2
4
%
0
1
2
3
4
5
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 5 / 22
Coils, plasma and ripple Vacuum ripple field + 2D plasma model
Magnetic ripple from TF coils
permanent/fixed source of non-axisymmetric fields
can be reduced using ferritic inserts (FI)
no large magnetic islands nor stochasticity when added to 2D plasma(response neglected):minimal detachment of field-lines from flux-surfaces (high-n mode,small resonances at rational q, low shear)
Poincare plot of field-lines at 18φ/2π = 0.57
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 6 / 22
Coils, plasma and ripple 3D ideal MHD equilibrium model
Input profiles in VMEC
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
ρtor =√
ΦN
ne [10
19 m
−3]
ni [10
19 m
−3]
Te [keV]
Ti [keV]
0 0.2 0.4 0.6 0.8 10
0.5
1
0 0.2 0.4 0.6 0.8 10
1
2
3
4
ρtor =√
ΦN
P[MPa]jtor
q @ 19.6MAq @ 16.6MA
SOF profiles jtor, ne, ni, Te, Ti, P =∑njTj (ions: 50%D, 50%T )
1 at 19.6MA with qedge = 3.22 at 16.6MA with qedge = 4.9
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 7 / 22
Coils, plasma and ripple 3D ideal MHD equilibrium model
3D MHD equilibrium with free-boundary VMEC
3D MHD plasma response with nested flux-surfaces: no islands norstochasticityfine-tuning of PF coil currents, sensitive results to changes in currentprofile (q-profile)
ripple included in 3Dgeometry, deformations ofLCFS < 1cm
← enhanced displacement
200× (R3D −R2D)
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 8 / 22
Coils, plasma and ripple 3D ideal MHD equilibrium model
3D MHD ripple from VMEC is similar to vacuum field
high-n and non-resonantperturbation ⇒ identical ripplefield as vacuum model(unlike previous work on RMPs
[Pfefferle et al., 2015])
0 0.2 0.4 0.6 0.8 1
−0.015
−0.01
−0.005
0
0.005
0.01
0.015
Nφ/2π
[T]
B3D
−B2D
at (R,Z)=(11.5,0)
δBφ
δBR
δBZ
R[m]
Z[m
]
6 8 10 12
−6
−4
−2
0
2
4
|δ B
|/B
%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 9 / 22
Dynamics of ripple perturbed orbits
Effect of ripple on energetic ion orbits (collisionlessly)
Axisymmetry ⇒ GC motion is integrable by virtue of E, µ and Pφbeing CoM ⇒ drift-surfaces
Magnetic ripple spoils conservation of Pφpassing not important as long as no magnetic islands nor stochasticitytrapped significant effect on bounce tips (stochastisation)
axisymmetric
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 10 / 22
Dynamics of ripple perturbed orbits
Effect of ripple on energetic ion orbits (collisionlessly)
Axisymmetry ⇒ GC motion is integrable by virtue of E, µ and Pφbeing CoM ⇒ drift-surfaces
Magnetic ripple spoils conservation of Pφpassing not important as long as no magnetic islands nor stochasticitytrapped significant effect on bounce tips (stochastisation)
axisymmetric
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 10 / 22
Dynamics of ripple perturbed orbits
Effect of ripple on energetic ion orbits (collisionlessly)
Axisymmetry ⇒ GC motion is integrable by virtue of E, µ and Pφbeing CoM ⇒ drift-surfacesMagnetic ripple spoils conservation of Pφ
passing not important as long as no magnetic islands nor stochasticitytrapped significant effect on bounce tips (stochastisation)
axisymmetricD.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 10 / 22
Dynamics of ripple perturbed orbits
Effect of ripple on energetic ion orbits (collisionlessly)
Axisymmetry ⇒ GC motion is integrable by virtue of E, µ and Pφbeing CoM ⇒ drift-surfacesMagnetic ripple spoils conservation of Pφ
passing not important as long as no magnetic islands nor stochasticitytrapped significant effect on bounce tips (stochastisation)
light rippleD.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 10 / 22
Dynamics of ripple perturbed orbits
Effect of ripple on energetic ion orbits (collisionlessly)
Axisymmetry ⇒ GC motion is integrable by virtue of E, µ and Pφbeing CoM ⇒ drift-surfacesMagnetic ripple spoils conservation of Pφ
passing not important as long as no magnetic islands nor stochasticitytrapped significant effect on bounce tips (stochastisation)
larger rippleD.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 10 / 22
Dynamics of ripple perturbed orbits Ripple well trapping and separatrix crossing
Ripple wells and separatrix crossing in DEMOmodulus of |B| along field-line
−0.1 0 0.1 0.2 0.3 0.4 0.5−1
−0.5
0
0.5
1
along field−line
eff
ective
po
ten
tia
l µB
2D
2D+vac
ripple
local well
no well
criterion for existence of local wells:δ > |∂θB|/BNq ≈ ε| sin θb|/Nq
particles with v|| <√δ can
become trapped
∇B-drift leads to rapid verticalmotion (downward)
de-trapping, separatrix crossing[Yushmanov, 1990; Cary et al., 1988]
geometry, elongation, tear-dropshape and up-down asymmetryhelps
collisions ⇒ enhanced diffusivetransport (superbanana)[Yushmanov, 1983; Mynick, 1986]
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 11 / 22
Dynamics of ripple perturbed orbits Ripple well trapping and separatrix crossing
DEMO ripple well domain such thatδ > δw = |∂θB|/BNq
R [m]
Z [m
]
7 8 9 10 11
−4
−3
−2
−1
0
1
2
3
4
numerical evaluation (VENUS-LEVIS)of bounce tip displacement
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 12 / 22
Dynamics of ripple perturbed orbits Stochastic diffusion of bounce tips
Resonant/stochastic motion of bounce tips in DEMO (low)
precession/bounce
resonances
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 13 / 22
Dynamics of ripple perturbed orbits Stochastic diffusion of bounce tips
Resonant/stochastic motion of bounce tips in DEMO (low)
approximate criterion of stochasticthreshold [Goldston et al., 1981]
δ > δGWB =
(ε
Nπq
)3/2 1
ρLq′
but δGWB too low [White et al., 1996]
resonances are bound by KAMlayers ⇒ limited vertical motion
collisions ⇒ resonance regime[Yushmanov, 1983]
difficult to evaluate, depends ongeometry and orbit effects ⇒accurate orbit solver
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 14 / 22
Fusion alpha confinement Slowing-down simulations
Slowing-down simulations with VENUS-LEVIS
initial distribution of 3.5MeV 42He, isotropic in v/v,
R(x) = nDnT < σv >M [Bosch and Hale, 1992]
non-canonical guiding-centre equations [Littlejohn, 1983]
slowing-down and pitch MC operators [Boozer and Kuo-Petravic, 1981]
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
ρtor =√
ΦN
Pα
[M
W/m
3]
fusion yield
SD 2D
SD 3D
SD 2D+vac
fusion alpha densityD.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 15 / 22
Fusion alpha confinement Slowing-down simulations
Confined versus lost fusion alphas
prompt and ripple loss regions are faraway from core fusion power ⇒ goodconfinement
ripple causes losses at specific toroidallocations
lost particles at LCFS in 2D+vac ripple model
19.6MA plasma
fusion density and birth regions of
lost particlesD.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 16 / 22
Fusion alpha confinement Lost particles, loss rates
Phenomenology of losses
0 1000 2000 300010
14
1015
1016
1017
KeV
loss r
ate
[A
U]
loss spectrum
2D
2D+vac
3D
−5 −4 −3 −2 −1 0
1013
1014
1015
1016
log10
(t)
∝ lo
ss r
ate
flight time
2D
2D+vac
3D
quantitative match between 2D+vacuum and 3D ripple models
losses are enhanced by ripple, order of magnitude larger(resonance/stochastic regime)
losses peak at energy range 100− 200 KeV (superbanana regime),pitch-angle scattering increases well trapping ⇒ Helium ash removal
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 17 / 22
Fusion alpha confinement Lost particles, loss rates
Lost particle velocity-space
axisymmetric case 3D equilibrium
lost population in axisymmetric case consists of barely trappedparticles
ripple significantly enhances deeply-trapped particles losses (v|| ∼ 0,superbanana transport)
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 18 / 22
Fusion alpha confinement Lost particles, loss rates
0.2 0.4 0.6 0.80
2
4
6
8
10x 10
16
Nφ/2π
AU
2D
2D+vac
3D
Disagreement between ripple modelsof toroidal position of losses throughLCFS
field-lines have different nature
2D+vac separation from flux-surfacesequilibrium 3D deformation of nested
field-lines
behaviour outside plasma up towall ?
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 19 / 22
Fusion alpha confinement Lost particles, loss rates
Conclusions
numerical simulation and theoretical considerations indicate thatfusion alpha confinement in the European DEMO is good
ripple does enhance losses via known diffusive and non-diffusivemechanisms, superbanana transport being dominant
stochastic ripple diffusion is difficult to predict, but threshold is higherthan expected
Coils, plasma and ripple
δmax ∝ 0.76N implies that increasing N = 18→ 20 will not make asignificant difference (having N odd would reduce resonances)
re-positioning of wall or adding ferritic inserts should be consideredinstead
unlike RMPs, minimal difference between 2D+vacuum and 3D plasmaresponse model ⇒ reliability of analytic calculations and scaling laws
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 20 / 22
Fusion alpha confinement Lost particles, loss rates
Conclusions (2)
Numerical results
integrated modelling exercise: realistic vacuum fields, consistentMHD equilibrium and accurate fusion alpha orbits
benchmarks against ASCOT are underway (2D+vacuum model)
Limitations and questions for future work
losses evaluated at LCFS, re-entry orbits neglected, not exact wallloads (toroidal position) ⇒ extension in progress
results sensitive to input profiles, plasma shape and position relativeto ripple field (control and scenario problem)
NBI fast ions may have wider radial distribution
toroidal flow is neglected (no radial electric field)
cyclotron resonance with ripple not considered: in principle negligibleeffect (mostly passing-particles), full-orbit simulations envisaged
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 21 / 22
Fusion alpha confinement Lost particles, loss rates
Thank you for your attention
Questions?
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 22 / 22
Appendix
Comparison between 19MA and 16MA case (qedge)
Same density, temperature, pressure and current profiles / varying totalplasma current and PF coils.
R [m]
Z [
m]
6 8 10 12−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
19.6MA, 16.6MAflux-surfaces
orbit width ∆ ∝ ε1/2v/Ωθ ∼ qρLε−1/2⇒ more prompt losses in 16MA case
lower ratio between ripple and 2D losses
0 1000 2000 30000
10
20
30
40
50
602D+vac
energy KeV
rip
ple
/axis
ym
lo
ss r
ate
19.6MA
16.6MA
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 23 / 22
Appendix
Bibliography I
W. A. Cooper, S. F. i Margalet, S. J. Allfrey, J. Kißlinger, H. F. G. Wobig,Y. Narushima, S. Okamura, C. Suzuki, K. Y. Watanabe, K. Yamazaki,et al., Fusion Science and Technology 46, 365 (2004).
S. P. Hirshman and J. C. Whitson, Physics of Fluids 26, 3553 (1983).
D. Pfefferle, W. Cooper, J. Graves, and C. Misev, Computer PhysicsCommunications 185, 3127 (2014).
P. N. Yushmanov, Rev. Plasma Phys. 16, 117 (1990).
K. G. McClements, Physics of Plasmas 12, 072510 (2005).
J. R. Cary, C. L. Hedrick, and J. S. Tolliver, Physics of Fluids 31, 1586(1988).
P. Yushmanov, Nuclear Fusion 23, 1599 (1983).
H. Mynick, Nuclear Fusion 26, 491 (1986).
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 24 / 22
Appendix
Bibliography II
R. J. Goldston, R. B. White, and A. H. Boozer, Phys. Rev. Lett. 47, 647(1981).
R. B. White, R. J. Goldston, M. H. Redi, and R. V. Budny, Physics ofPlasmas 3, 3043 (1996).
H.-S. Bosch and G. Hale, Nuclear Fusion 32, 611 (1992).
R. G. Littlejohn, Journal of Plasma Physics 29, 111 (1983).
A. H. Boozer and G. Kuo-Petravic, Physics of Fluids (1958-1988) 24, 851(1981).
D. Pfefferle, C. Misev, W. A. Cooper, and J. P. Graves, Nuclear Fusion 55,012001 (2015).
D.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 25 / 22