adam stanier 1, p. browning 1, m. gordovskyy 1, k. mcclements 2, m. gryaznevich 2,3, v.s. lukin 4...
TRANSCRIPT
Adam Stanier1, P. Browning1, M. Gordovskyy1,K. McClements2, M. Gryaznevich2,3, V.S. Lukin4
Simulations of magnetic reconnection during merging start-up in the MAST Spherical Tokamak
EPS Conference, Espoo, July 2013
MAST
1Jodrell Bank Centre for Astrophysics, University of Manchester, UK2EURATOM/CCFE Fusion Association, Culham Science Centre, UK3Present affiliation: Imperial College of Science and Technology, London, UK4Space Science Division, Naval Research Laboratory, DC, USA
Why study reconnection in MAST?
▶ Reconnection important energy release mechanism in magnetotail, solar corona.
▶ Can degrade plasma confinement in magnetic fusion energy device.
▶ We can study reconnection in the laboratory under controlled conditions and with many diagnostics.
▶ Several experiments (mostly) dedicated to the study of reconnection:
▶ RSX (LANL), TS-3/4 (University of Tokyo), MRX (Princeton), VTF (MIT)
▶ Merging start-up in the Mega-Ampere Spherical Tokamak is not dedicated, but has stronger magnetic fields and reaches higher temperatures.
▶ High-resolution Thomson scattering system gives detailed profiles of electron temperature and density.
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▶ Merging start-up is an attractive alternative for start-up without central solenoid.
▶ Breakdown and current induction around in-vessel P3 coils.
▶ Flux-ropes merge via reconnection at mid-plane to form single Spherical Tokamak (ST) plasma.
▶ Up to 0.5 MA plasma current obtained.
▶ Up to Te = 1 keV achieved in on ms timescale
measured with Thomson Scattering (TS) laser.
Merging start-up
Th
om
son
Sca
tter
ing
las
ers
P3Plasma
P3
φφ
Magnetic: Bp = 0.1 T, BT = 0.5 T, IT = 0.2 - 0.5 MA
Thermal: Te = Ti = 10 eV, n = 5x1018 m-3, Deuterium
Typical start-up parameters:
0 1 2 3 4 5 6Time (ms)
200
150
100
50
0
250
Cu
rre
nt
(kA
.tu
rn)
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Merging start-up
Time resolution: 0.1 ms. Total time: ~ 7ms.
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Fluid model
βT = 4x10-5 βp = 10-3
▶ Initial Lundquist #: S = 2 x 104 → Collisional Current Sheet (CS) width: δSP ~ 1 cm.
▶ Kinetic scales become important when larger than collisional CS width.
▶ Ion skin depth: di = 15 cm, Electron: de = 0.25 cm, Larmor radius: ρi = ρis = 0.13 cm.
Hyper-resistivity(electron viscosity)
▶ Heat cond.: , ion-stress tensor:
▶ Will vary μ, η and ηH in simulations presented.
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φ
Toroidal(R,φ,Z)
Code and initial conditions
▶ Solved in 2D Cartesian and toroidal geometry with spectral-element code HiFi.
▶ 4th Order polynomial basis functions.
▶ Stretched grid: High resolution in current sheet.
▶ Crank-Nicolson (θ = 0.5) time advance.
(Glasser and Tang 2004, Lukin 2008).
▶ Currently no measurements of flux-rope structure – use idealised flux ropes, IT = 0.27 MA.
▶ Balanced against pinching by BT increase (βp ~ 10-3), individually force-free.
▶ Conducting walls with line-tied vertical flux B
v = -0.03 T.
▶ Radial dependence (1/R) of toroidal field.
Grid:∆Rmin = 0.5mm∆Zmin = 0.3mm
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Hall-MHD simulation in toroidal geometry
▶ Final nested flux-surfaces qualitatively similar for Hall-MHD (di=15 cm, shown) and resistive MHD (di=0, not shown).
▶ Resistive MHD runs exhibit flux-rope “sloshing” (eg. Biskamp and Welter 1980), for η ≤ 10-4 due to magnetic pressure pile-up.
X-point at t = 0
Current Sheet(CS) width: δ = 2.4 cm
Grid:∆Zmin = 0.03cm
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Nd:
YA
G T
S la
ser
▶ Simulated density profile has double peak. Outer peak disappears after merging.
▶ What causes the double peak in density?
Density profiles: Comparison with experiment
Experiment: Nd:Yag ne
Hall-MHD Simulation: Density
5.4 ms5.5 ms5.6 ms5.7 ms
▶ Density measured at R = [0.2, 1.2 m], Z = 0.015 m.
▶ Typically has double peak at beginning of merging.
20 t040 t060 t080 t0
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What causes the double peak in density?
▶ Density “quadrupole” in Cartesian Hall-MHD simulation.
▶ High (low) density regions correspond to negative (positive) parallel electron velocity gradients. (see also Kleva et al. 1995).
Cartesian Hall-MHD simulation
▶ Resistive MHD simulation in toroidal geometry has inboard (outboard) density peak (cavity).
▶ Both two-fluid effects and toroidal geometry are needed for double peaked profiles in simulation.
Toroidal resistive MHD simulation
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Cartesian Hall-MHD: Effect of collisions
Scan in hyper-resistivity (collisions)W
eake
r co
llisi
onal
ity
▶ ηH = 10-6
▶ Stable.
▶ ηH = 10-8
▶ Island (ejected in toroidal geometry).
▶ ηH = 10-10
▶ Localised CS:
δ = 4.5 mm
ρis
= 2.9 cm
Grid: ∆Rmin = 4x10-4 m, ∆Zmin = 2x10-4 m
Grid: ∆Rmin = 1x10-4 m, ∆Zmin = 4x10-5 m
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Summary
▶ We use merging start-up in MAST as a magnetic reconnection experiment.
▶ Resistive and Hall-MHD simulations were run in Cartesian and toroidal axisymmetric geometry.
▶ We find MAST-like nested flux-surfaces after merging completion in toroidal geometry.
▶ Simulated Thomson Scattering density profiles evolve as in experiment.
▶ Three regimes in Hall-MHD simulations: collisional (δ >> ρis), open X-point (δ < ρ
is)
and an intermediate regime that is unstable to island formation (δ ≥ ρis).
Future work: Simulations and M9 Campaign (with H. Tanabe and the MAST team)
▶ Measure 2D Ion Temperature profiles, compare with simulations evolving separate ion and electron pressures.
▶ Look for density “quadrupole” with 2D Thomson scattering image.
▶ Compare q-profiles between experiment and simulation.
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Resistive MHD
▶ Several studies have shown length-scale ρis = (Te/m
i)1/2/Ωci important for fast reconnection
with strong BT.
▶ Peak reconnection rate in Hall-MHD for CS width > ρis have (weak) dependence on ηH.
▶ ηH = 10-10 is slow during CS formation, but explosive when width drops below ρis (t=7 t0).
Additional: Reconnection rates
(eg. Kleva et al. 1995., Simakov et al. 2010)
t=7 t0
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25 cells across CS width
Additional: Numerical grid and convergence
NR=360, N
Z=540, N
P=4
NR=180, N
Z=270, N
P=4
▶ Convergence test for simulation with ηH = 10-10 (lowest dissipation scale).
▶ Coarsening by factor of 2 changes peak reconnection rate by only 0.2 %.
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Additional slide: q-profile
▶ Paramagnetic equilibrium (just after merging).
▶ q-profile > 1: Sensible. Should be stable to m=n=1 kink-mode.
▶ Final state current profile qualitatively similar for resistive and Hall-MHD.
Vacuum field
t=60 midplane
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Additional: Resistive MHD sloshing
▶ Increase in BT between flux-ropes slows approach.
▶ Large aspect ratio current-sheet: L >> δ (Sweet-Parker).
▶ Initial low-β sheet: c.f. force-free Harris sheet.
▶ Pile-up of BR on sheet edge, and reconnection stalls.
▶ Sloshing of flux-ropes, c.f. coalescence instability.(Biskamp & Welter 1980, Knoll and Chacon 2005)