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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Adam stanier 1 p browning 1 m gordovskyy 1

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


Adam stanier 1 p browning 1 m gordovskyy 1

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.

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.


Adam stanier 1 p browning 1 m gordovskyy 1

Merging start-up

  • 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


Adam stanier 1 p browning 1 m gordovskyy 1

Merging start-up

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


Adam stanier 1 p browning 1 m gordovskyy 1

Fluid model

  • 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).


Adam stanier 1 p browning 1 m gordovskyy 1

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).

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


Adam stanier 1 p browning 1 m gordovskyy 1

Hall-MHD simulation in toroidal geometry

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.


Adam stanier 1 p browning 1 m gordovskyy 1

Density profiles: Comparison with experiment

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?


Adam stanier 1 p browning 1 m gordovskyy 1

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.

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


Adam stanier 1 p browning 1 m gordovskyy 1

Cartesian Hall-MHD: Effect of collisions

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.


Adam stanier 1 p browning 1 m gordovskyy 1

Summary

  • 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.


Adam stanier 1 p browning 1 m gordovskyy 1

Additional: Reconnection rates

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)


Adam stanier 1 p browning 1 m gordovskyy 1

Additional: Numerical grid and convergence

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 %.


Adam stanier 1 p browning 1 m gordovskyy 1

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.


Adam stanier 1 p browning 1 m gordovskyy 1

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)

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


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