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Matteo Bocchi Bas Ummels Jerry Chittenden Sergei Lebedev Adam Frank Eric Blackman

M.A.G.P.I.E. Centre of Excellence in High Energy Density Plasma Physics. Numerical simulations of Z-Pinch experiments to create supersonic differentially-rotating plasma flows. Matteo Bocchi Bas Ummels Jerry Chittenden Sergei Lebedev Adam Frank Eric Blackman. Accretion Discs.

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Matteo Bocchi Bas Ummels Jerry Chittenden Sergei Lebedev Adam Frank Eric Blackman

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  1. M.A.G.P.I.E. Centre of Excellence in High Energy Density Plasma Physics Numerical simulations of Z-Pinch experiments to create supersonic differentially-rotating plasma flows Matteo Bocchi Bas Ummels Jerry Chittenden Sergei Lebedev Adam Frank Eric Blackman

  2. Accretion Discs • Ubiquitous: • Protostars • AGNs • Black holes • Brown dwarfs • Main ingredient of jet formation Protostar disc • Differentially rotating: • Keplerian velocity: V  R-1/2 • Supersonic: • M~ R/h ~ 10 • Radiatively cooled (Dust) • Very high Reynolds and magnetic Reynolds numbers (size). Galactic disc Hubble space telescope (NASA, ESA)

  3. Experimental approach • Proposed experiment by Ryutov (2011 Ap&SS 336): • Small number of laser driven jets • Miss the axis () • Rotating plasma • We use pulsed power instead • Driving extended in time • Previously: • Rotating jet from twisted conical array (Ampleford et al, 2008) • Modified cylindrical wire array • Magnetic deflection for plasma Ryutov, 2011 Ampleford et al, 2008

  4. Lebedev et al, 2001 Lebedev et al, 2001 Proposed setups • Displaced Return-Posts • Cusp B Field JxBR BR X X X Lebedev et al, 2001 Wires Plasma Streams Cathode Anode Support posts Return posts

  5. Computational setup • Return Post array • 12 Copper wires • RArray = 8 mm • lArray = 1.4 mm • Anode-Cathode gap = 1mm • Return-posts angular displacement = 2/128 • MAGPIE generator • 1.4 MA in 250 ns • Simulation • 496x496x324 points • dx = 50 μm • 20 hours on 384 CPUs • 3D MHD code GORGON • Successfully used to model Z-pinches

  6. Flow Dynamics • Plasma streams miss the axis and collide one with each other • Rotating plasma cylinder or “ring” • Plasma ejected in a pair of thermally driven conical outflows • Low density, wide angle flow from wires contributes to the outflow • Thick wires -> • non-imploding array • 3D MHD code GORGON • Successfully used to model Z-pinches

  7. 500 ns Flow Structure Averaged radial profiles 500 ns XZ Plane Cuts of mass density in logarithmic scale Red: mass density Blue: Rotation velocity XY Plane • Plasma streams interact in complicated patterns • Plasma ring and outflow develop internal non-uniform structures • Non uniformities seeded by plasma streams • Differential rotation – MRI unstable

  8. Typical Parameters • Average temporal evolution: • Radius: 1.1 – 1.2 mm • Density: 1 – 18 x 10-3 g/cm3 • Velocity: 50 – 20 Km/s • Mach number: 8 - 3 • Temperature: 10 – 5 eV • Z: 6 – 3 • Dimensionless quantities: • Re: ~107 • Pe: ~104 • Beta: ~105 • =tcool/thydro<<1 M

  9. Parameter Study • Wires • Material • Number • Length • Return Posts displacement () • Array radius • Cathode-Anode Gap  

  10. Wires Material 300 ns Al Cu W • Big difference in cooling: • Aluminium (Al): Weak • Copper (Cu): Medium • Tungsten (W): Strong • Similar structure • Similar plasma radius and velocity • Differences • Stronger cooling -> more non-uniform structures • Stronger cooling -> higher Mach number • Stronger cooling -> higher Re XZ Plane XY Plane M

  11. External Magnetic Field 1 T BZ: • Uniform vertical magnetic field • 2 coils, above and below the array • Relevant for magnetic field line bending by differential rotation and/or accretion XZ Plane XY Plane 300 ns • Dipolar magnetic field • Permanent magnet or small coil at the centre of the array • Relevant to magnetospheric accretion on protostars

  12. Cusp B Field • Behaviour similar to previous cases • Supersonic plasma ring • Differential rotation • Plasma outflow Experiment Simulation • Experiment on MAGPIE • Plasma streams deflection • Rotating plasma • Compatible with simulations

  13. Conclusions • Differentially rotating, supersonic plasma flow • Very high Reynolds number (107) • Relevant to aspects of accretion discs physics Experiment Simulation • Preliminary experiments on MAGPIE, London consistent with simulations

  14. Feasibility • Return-Posts Array • Swirly Array • Small anode-cathode gap could short circuit • A magnetic field is always present

  15. Numerical Code • Numerical code: GORGON • 3D Magneto-Hydro-Dynamic • Separate Ion and Electron temperatures • Ohmic heating • Radiation losses • Computational Vacuum (10-4 Kg/m3) • MPI parallelization • Successfully used to model Z-pinches

  16. Flow Dynamics • Plasma streams miss the axis and collide one with each other • Rotating plasma cylinder or “ring” • Plasma ejected in a pair of thermally driven conical outflows • Thick wires -> • non-imploding array • 3D MHD code GORGON • Successfully used to model Z-pinches

  17. Flow Structure Averaged radial profiles 160 ns 500 ns XZ Plane Cuts of mass density in logarithmic scale 160 ns 500 ns XY Plane Red: mass density Blue: Rotation velocity • Plasma streams interact in complicated patterns • Plasma ring and outflow develop internal non-uniform structures • Non uniformities seeded by plasma streams • Differential rotation

  18. Typical Parameters • Average temporal evolution: • Radius: 1.1 – 1.2 mm • Density: 1 – 18 Kg/m3 • Velocity: 50 – 20 Km/s • Mach number: 7- 4 • Temperature: 10 – 5 eV • Z: 6 – 3 • Phases: • Adjustment (A) • Peak (B) • Non-linear (C) A A B B C C R  V M Te Z

  19. Typical Parameters A A B B C C • Average temporal evolution: • Radius: 1.1 – 1.2 mm • Density: 1 – 18 Kg/m3 • Velocity: 50 – 20 Km/s • Mach number: 7- 4 • Temperature: 10 – 5 eV • Z: 6 – 3 • Dimensionless quantities: • Re: ~107 • Pe: ~103 • Beta: ~104 • ReM: ~0.2 R  V M Te Z ReM

  20. Number of wires Wires: 8 12 16 250 ns • Number of wires influences deflection • Posts displacement chosen to produce the same deflection. • Similar structure • Similar plasma radius and velocity • Lower number of wires • Develops non-uniform structures earlier • Higher number of wires • Still develops non-uniform structures XZ Plane XY Plane

  21. Return-Posts Displacement : 2/64 2/128 2/256 300 ns • In general, post displacement    Plasma stream deflection. • Small deflection • Smaller ring radius • Higher density • More non-uniform structures • Big deflection • Bigger ring radius • Lower density • Less non-uniform structures XZ Plane XY Plane

  22. External Magnetic Field • Uniform vertical magnetic field • 2 coils, above and below the array • Relevant for magnetic field line bending by differential rotation and/or accretion • Dipolar magnetic field • Permanent magnet or small coil at the centre of the array • Relevant to magnetospheric accretion on protostars

  23. Vertical Magnetic Field BZ: 0 T 0.1 T 1 T 300 ns • Higher field -> stronger non-uniform behavior • Potentially observable • Modest field strengths necessary • 1 T initial field -> Beta ~4 at time of plasma formation XZ Plane XY Plane

  24. Dipolar Magnetic Field 38 T 100 T 3.8 T • Sufficiently strong field • Plasma forms “accretion columns” • Low intensity • Strong non uniformities and irregular structures • Effects similar to vertical field • Strong field required • Need more study to optimise setup for experiments 250 ns BDipole: XZ Plane

  25. Conclusions • Differentially rotating, supersonic plasma flow • Very high Reynolds number (107) • Relevant to aspects of accretion discs physics Experiment Simulation • Preliminary experiments on MAGPIE, London consistent with simulations

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