Simulations of magnetic reconnection during merging start-up in the MAST Spherical
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Simulations of magnetic reconnection during merging start-up in the MAST Spherical Tokamak. Adam Stanier 1 , P. Browning 1 , M. Gordovskyy 1 , K. McClements 2 , M. Gryaznevich 2,3 , V.S. Lukin 4. 1 Jodrell Bank Centre for Astrophysics, University of Manchester, UK

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Simulations of magnetic reconnection during merging start-up in the MAST Spherical Tokamak

Adam Stanier1, P. Browning1, M. Gordovskyy1,

K. McClements2, M. Gryaznevich2,3, V.S. Lukin4

1Jodrell Bank Centre for Astrophysics, University of Manchester, UK

2EURATOM/CCFE Fusion Association, Culham Science Centre, UK

3Present affiliation:Imperial College of Science and Technology, London, UK

4Space Science Division, Naval Research Laboratory, DC, USA

MAST

EPS Conference, Espoo, July 2013


Why study reconnection in MAST? in the MAST Spherical

  • 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.

Understanding of reconnection in parameter regime relevant to tokamak disruptions.

Solar flare: lifetime of active region ~ 1 week, release ~ 1025 J over 100 sec.

Tokamak Sawtooth crash: Build up (sawtooth period) ~ 100 ms, crash ~ 100 μs.


Merging start-up in the MAST Spherical

  • 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.

250

Current (kA.turn)

P3

200

Plasma

150

100

50

0

0

1

2

3

4

5

6

Time (ms)

Thomson Scattering lasers

Pick-up Coil (CCMV20)

P3

Typical start-up parameters:

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

φ

φ


Merging start-up in the MAST Spherical

Time resolution: 0.1 ms. Total time: ~ 7ms.


Fluid model in the MAST Spherical

  • 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.

βT = 4x10-5

βp = 10-3

Hyper-resistivity

(electron viscosity)

  • Heat cond.: , ion-stress tensor:

  • Will vary μ, η and ηH in simulations presented.

  • Hyper-resistivity is used to set dissipation scale for Whistler waves.

  • Can (and does) set diffusion scale here by breaking frozen-in condition.

  • Physically related to an electron viscosity:

Anisotropic heat conduction:

Hyper-resistivity (anomalous electron viscosity).

for

  • Solved with the HiFi framework (eg. Lukin and Linton) with 4th Order polynomial basis.

  • Crank-Nicholson time advance (to avoid CFL condition).


Code and initial conditions in the MAST Spherical

  • 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).

Toroidal

(R,φ,Z)

  • 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 Bv = -0.03 T.

  • Radial dependence (1/R) of toroidal field.

Grid:

∆Rmin = 0.5mm

∆Zmin = 0.3mm

φ

  • Currently no q-profiles of pre-merged flux-ropes (plan for M9 campaign).

  • Idealised initial conditions using


Hall-MHD simulation in toroidal geometry in the MAST Spherical

Current Sheet

(CS) width: δ = 2.4 cm

Grid:

∆Zmin = 0.03cm

X-point at t = 0

  • 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.


Density profiles: Comparison with experiment in the MAST Spherical

Experiment: Nd:Yag ne

5.4 ms

5.5 ms

5.6 ms

5.7 ms

  • Density measured at R = [0.2, 1.2 m], Z = 0.015 m.

  • Typically has double peak at beginning of merging.

Nd:YAG TS laser

Hall-MHD Simulation: Density

20 t0

40 t0

60 t0

80 t0

  • Simulated density profile has double peak. Outer peak disappears after merging.

  • What causes the double peak in density?


What causes the double peak in density? in the MAST Spherical

  • Density “quadrupole” in Cartesian Hall-MHD simulation.

  • High (low) density regions correspond to negative (positive) parallel electron velocity gradients.

Toroidal resistive MHD simulation

(see also Kleva et al. 1995).

Cartesian Hall-MHD simulation

  • Resistive MHD simulation in toroidal geometry has inboard (outboard) density peak (cavity).

  • Bothtwo-fluid effects and toroidal geometry are needed for double peaked profiles in simulation.

  • MHD: Density peak on inner side, cavitation on outer edge.

  • Two-fluid: Additional density asymmetry, disappears after merging completion.

di = 0.145 m

ηH = 10-8

MHD di = 0

High density seperator


Cartesian Hall-MHD: Effect of collisions in the MAST Spherical

Scan in hyper-resistivity (collisions)

  • ηH = 10-6

  • Stable.

Weaker collisionality

  • ηH = 10-8

  • Island (ejected in toroidal geometry).

Grid: ∆Rmin = 4x10-4 m, ∆Zmin = 2x10-4 m

  • ηH = 10-10

  • Localised CS:

    δ = 4.5 mm

    ρis= 2.9 cm

Grid: ∆Rmin = 1x10-4 m, ∆Zmin = 4x10-5 m

  • However, large aspect ratio current sheet is unstable to island formation (for ηH≤ 10-8).

  • In Cartesian geometry a central island stalls the reconnection.

  • Stronger BT: weaker density asymmetry. Multiple, shorter wavelength islands.

  • Order 1 density variations in “quadrupole” structure.

  • Electrons accelerated in low density regions.

  • Similar to reduced two-fluid reconnection model of Kleva et al. 1995.


Summary in the MAST Spherical

  • We use merging start-up in MAST as a magnetic reconnection experiment.

  • Resistive and Hall-MHD simulations were run in Cartesian and toroidalaxisymmetric 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 < ρis) 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.

We have also simulated separate ion and electron temperature profiles.

(Stanier et al. 2013).

  • Resistive MHD simulations in the sloshing regime.

  • Three regimes in Hall-MHD simulations: collisional (δ >> ρis), open X-point (δ < ρis) and intermediate

  • Tilt of outflow jets, and ion temperature profiles in two-fluid case – signature of two-fluid effects with guide field.

  • Toroidal geometry has little effect on reconnection process (eg. the reconnection rate) but can modify density profiles.

  • Simulated 1D density profiles show same time evolution as in TS profiles – motivation to look for density “quadroupole” with 2D measurement.

  • Resistive MHD simulations in the sloshing regime.

  • Three regimes in Hall-MHD simulations: collisional (δ >> ρis), open X-point (δ < ρis) and intermediate

  • Tilt of outflow jets, and ion temperature profiles in two-fluid case – signature of two-fluid effects with guide field.

  • Toroidal geometry has little effect on reconnection process (eg. the reconnection rate) but can modify density profiles.

  • Simulated 1D density profiles show same time evolution as in TS profiles – motivation to look for density “quadroupole” with 2D measurement.


Additional: Reconnection rates in the MAST Spherical

Resistive MHD

  • Several studies have shown length-scale ρis = (Te/mi)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).

t=7 t0

(eg. Kleva et al. 1995., Simakov et al. 2010)


Additional: Numerical grid and convergence in the MAST Spherical

25 cells across CS width

NR=360, NZ=540, NP=4

NR=180, NZ=270, NP=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 %.


Direction of island ejection depends upon radial positions of O-points and X-point

Additional slide: q-profile

t=60 midplane

Vacuum field

  • 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.


Additional: Resistive MHD sloshing of O-points and X-point

  • 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)

S = 105, mu = 10-3, BT= 0.5 T, a=0.6, Iplasma = 268 kA


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