halo current studies with self-consistent mhd simulations
TRANSCRIPT
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Disclaimer: The views and opinions expressed herein do not necessarily reflect those of the ITER Organization
Halo current studies with self-consistent
MHD simulations
for ITER 15 MA plasmas
F.J. Artola1, G.T.A. Huijsmans2, M. Lehnen1, I. Krebs3, A. Loarte1
1. ITER Organization, SCD, 13067 Saint Paul Lez Durance Cedex, France
2. CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
3. Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA
email: [email protected]
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Outline
β’ The JOREK-STARWALL code for halo current modelling
β’ 2D VDE benchmark with M3D-C1 and NIMROD
β’ Understanding the 2D halo currents at ITER (15 MA/5.3T)
β’ Prediction of the halo properties and B.C.s
β’ Conclusions and future work
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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The JOREK-STARWALL code
for halo current modelling
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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The JOREK-STARWALL code for halo current modelling
JOREK
β’ 3D non-linear MHD equationsβ’ Toroidal geometry
β’ C1 Finite elements in poloidal plane
β’ Fourier harmonics for π directionβ’ Fully implicit time evolution
[Huysmans, NF2007]
STARWALL
β’ Solves Maxwellβs equations and Ohmβs law
β’ Greenβs function method
β’ Thin wall approximation
[P. Merkel, 2015]
Implicit coupling through B.C.s for π΅
[Hoelzl, 2012]
π΅tan = Τ¦π π΅π, π
Tangential fieldNormal field Wall currents
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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The JOREK-STARWALL code for halo current modelling
EM boundary conditions
Reduced MHD, the E-field is
β« has resistive wall free-boundary conditions
β« Ideal wall BCs for poloidal E-field
β« Poloidal currents calculated from
force balance
Strong assumption. Poloidal
currents do not decay in the
wall (infinite conductivity in
the poloidal direction)
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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2D VDE benchmark with
M3D-C1 and NIMROD
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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2D VDE benchmark with M3D-C1 and NIMROD
VDE based on the NSTX #139536 discharge
[I. Krebs, F.J. Art ola, C. Sovinec 2019]
Phase 1: Hot VDE until wall contact
Phase 2: Artificially triggered TQ
when the plasma becomes limited
(increasing π β₯ )
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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2D VDE benchmark with M3D-C1 and NIMROD
VDE based on the NSTX #139536 discharge
[I. Krebs, F.J. Art ola, C. Sovinec 2019]
Phase 1: Hot VDE until wall contact
Phase 2: Artificially triggered TQ
when the plasma becomes limited
(increasing π β₯ )
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents
at ITER (15 MA / 5.3T)
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Halo current different regimes
β« Hot VDE regime
πΌπ ~ cte during VDE
β« Ideal wall regime
πππ₯ππ = π(πΌπ) [D. Kiramov 2017 PoP]
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Parametric scan in CQ time
Plasma resistivity is prescribed as a flux function
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Scan in CQ time (scaling plasma resistivity profile)
πΌ βπππ/πΌ π0(%
)
ππΆπ/ππ€ (Log-scale)
β’ Strong dependence on
CQ time to wall time ratio
(ππͺπΈ/ππ)
β’ Maximum at ππΆπ/ππ€ β β
Halo currents stabilize
VDE
β’ Minimum at ππΆπ/ππ€ β 0
Eddy currents stabilize
VDE
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Scan in CQ time (scaling plasma resistivity profile)
πΌ βπππ/πΌ π0(%
)
ππΆπ/ππ€ (Log-scale)
β’ Strong dependence on
CQ time to wall time ratio
(ππͺπΈ/ππ)
β’ Maximum at ππΆπ/ππ€ β β
Halo currents stabilize
VDE
β’ Minimum at ππΆπ/ππ€ β 0
Eddy currents stabilize
VDE
CAT I I EM loads(up to 300 events
at 15 MA)
CAT I EM loads
(up to 3000 events
at 15 MA)
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Halo current different regimes
β« Hot VDE regime
β’ Cold halo
β’ Hot halo
β« Ideal wall regime
β’ Cold halo
β’ Hot halo
also discussed in [Boozer PoP 2013]
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Hot VDE + cold halo
β« Currents are lost in wall and halo
faster than in plasma core
β« Currents are re-induced in plasma
edge (large current densities)
β« Big drop of edge safety factor
πΌπ is largely conserved (ππ β π2)
β« Potential destabilization of
external kink modes
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Hot VDE + hot halo
β« Toroidal current is transferred into
the halo region as the plasma
moves vertically
β« Halo currents stabilize vertical
motion
β« After stabilization, motion is given
by resistive decay of core + halos
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Hot VDE + hot halo
Halo resistivity scan
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Hot VDE + hot halo
Halo resistivity scanLarger πΌπ(faster halo
decay)
Smaller halos
Less vertical stabilization
Faster VDE
Larger halo drive
Increase in halos
Regulating
mechanism for
πΌβπππ,π
π°ππππ,π depends weakly on πΌπ
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Hot VDE + hot halo
Halo resistivity scan
But π°ππππ,πππ depends strongly
on πΌπ through ππ
Finally increasing the halo
resistivity gives larger poloidal
halo currents
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Hot VDE + hot halo
Halo width scan
π°ππππ,π also has a weak
dependence on the halo width
Weak dependence through
ππ β ππ/πΌπ
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Hot VDE + hot halo
Halo width scan
π°ππππ,π also has a weak
dependence on the halo width
Weak dependence through
ππ β ππ/πΌπ
But πΌβπππ,πππ has a much
stronger dependence
through ππ. More effective
at narrow halos.
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F.J. Artola, 7th annual Theory and Simulation of Disruptions Workshop
Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Ideal wall regime
Halo resistivity scan
Halo currents also slow
down vertical motion
π°ππππ,π is also not
linear in πΌπ(self-regulating
mechanism)
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Β© 2019, ITER Organization
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Understanding 2D halo currents at ITER (15 MA / 5.3T)
Ideal wall regime
Halo resistivity scan
ππ and π°ππππ,πππdepend strongly on πΌπ
The poloidal halo fraction (HF) is a factor 5-10 smaller than in the
hot VDE regime
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Prediction of the halo properties
and B.C.s
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Prediction of the halo properties and B.C.s
β« Temperature dependence for resistivity and
parallel conductivity
β« Ohmic heating term in energy equation
β« Bohmβs boundary condition
β« Sheath heat flux B.C.
Currently working VDE model
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Prediction of the halo properties and B.C.s
β« Neutrals, recycling and atomic processes (key for
density evolution, now ππ(π))
β« Impurity evolution and radiation
β« Limit on ion saturation current (π½ β€ π½π ππ‘ ), (in progress)
Missing ingredients of VDE model
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Prediction of the halo properties and B.C.s
β« Upward ITER VDE, 15 MA / 5.3 T
β« Post-disruption equilibrium (π½π = 0.05)
β« Flat J-profile after helicity mixing (from DINA)
β« No radiation (ohmic heating re-heats the plasma)
β« Realistic Spitzer and Braginskii values for π0 and π β₯0
β« π β₯ = 4 m2/s, πΎπ βπππ‘β = 8, ππ = ππ, ππ€ = 0.5 s
Simulation setup
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Prediction of the halo width and B.C.s
Ξπ‘sim~0.48 s
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Prediction of the halo width and B.C.s
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Prediction of the halo width and B.C.s
Density scan (Zaxis=2.0 m)
Poloidal angle along the wall
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Conclusions and future work
JOREK / M3D-C1/ NIMROD benchmark: good agreement for 2D halo currents
2D VDEs ITER studies
β’ Hot VDE limit (ππ€ βͺ ππ) largest halo fractions (HFmax~50 %)
β’ Ideal wall limit (ππ βͺ ππ€) smallest halo fractions (HFmax < 10 %)
β’ ITER mitigated disruptions (HFmax ~ 10 β 25 %)
β’ Self-regulating mechanism for πΌhalo,π , weak dependence on πβ β π€β/πβ
β’ Poloidal halo currents depend strongly on ππ (πΌhalo,pol = πΌhalo,π /ππ), which
decreases at shorter πβ
β’ Maximum HF at (ππ€ βͺ πβ < ππ) with small halo widths
β’ Influence of initial ππ and core resistivity profile?
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Conclusions and future work
Prediction of halo width and temperature
β’ Current VDE model including
βͺ Realistic resistivities and conductivitiesβͺ Energy balance in the halo: sheath losses and ohmic heating
βͺ Sheath B.C.s
βͺ Imposed density π π
β’ Still missing
βͺ Density evolution with neutrals and atomic physics
βͺ Impurity radiation
βͺ Limit on current density (ion saturation current)
β’ Results for hot VDEs show
βͺ Large halo widths (for Jphi) at low temperature (on going density scans)