Alpha particle confinement in the European DEMO€¦ · Alpha particle con nement in the European...

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]


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


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


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


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



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



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


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



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)



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


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




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




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





light rippleD.Pfefferle (CRPP-PPPL) DEMO alphas, 14th IAEA September 1st, 2015 10 / 22





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]


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


Dynamics of ripple perturbed orbits Stochastic diffusion of bounce tips

Resonant/stochastic motion of bounce tips in DEMO (low)

precession/bounce

resonances


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


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



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)



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 ?



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



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



Thank you for your attention

Questions?


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


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).


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).


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