1 / 47

Numerical Modeling of Plasmas: Magnetic Reconnection Magnetic Explosions

Explore the phenomenon of magnetic reconnection and its simulation in plasmas, including its applications in space weather, fusion energy, and outside the solar system. Learn about the different scales and approximations used in the study of magnetic fields, and discover the challenges in simulating reconnection.

jgillan
Download Presentation

Numerical Modeling of Plasmas: Magnetic Reconnection Magnetic Explosions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Numerical Modeling of Plasmas: Magnetic ReconnectionMagnetic Explosions Michael Shay University of Maryland http://www.glue.umd.edu/~shay/presentations

  2. Overview • What is Reconnection? • How do you simulate it?

  3. Part I: What is Reconnection?

  4. What is a Plasma?

  5. The Sun is a Big Ball of Plasma Put animated picture here http://science.msfc.nasa.gov/ssl/pad/solar/flares.htm

  6. Space Weather • Plasma streams away from the sun and hits the Earth. • Astronaut safety. • Satellite disruptions. • Communication disruptions.

  7. Unlimited Clean Energy: Fusion • Hydrogen gas must have: • Very high temperature and density. • Plasma

  8. Fusion 1: Tokamaks • Compress and heat the plasma using magnetic fields.

  9. Fusion 2: Laser Fusion • Compress and Heat the plasma with multiple lasers

  10. Outside the Solar System • Clumps of matter gradually compress due to gravity and heat. • Star formation. Eagle Nebula

  11. Accretion Disks • When matter collects onto an object, it tends to form a disk. • Difficult for matter to accrete: • Plasma Turbulence is key. Hubble Telescope Image Jim Stone’s Web Page

  12. The Wide Range of Plasmas

  13. A Normal Gas (non-plasma) • All dynamics is controlled through sound wave physics (Slinky Example).

  14. N N S S Plasmas are More Complicated

  15. Magnetic Fields • Wave a magnet around with a plasma in it and you will created wind! • In fact, in the simplest type of plasmas, magnetic fields play an extremely important role.

  16. Frozen-in Condition • In a simple form of plasma, the plasma moves so that the magnetic flux through any surface is preserved.

  17. Magnetic Field Waves • Magnetic field waves have tension and pressure. • Think of them as rubber tubes. • Magnetic fields can store a lot of energy! • bmagnetosphere  0.003 bsurface of Earth  3 ·107 • bsun 0.01

  18. Magnetic Fields: Rubber Tubes Bi R w Bf L • Disparate scales: w << R << L • Incompressible: Lw ~ R2 • Conservation of Magnetic Flux: Bf ~ (w/R) Bi • Change in Magnetic Energy: B energy density ~ B2/8 Ef ~ (w/L) Ei << Ef

  19. Magnetic Field Lines Can’t Break =>

  20. Everything Breaks Eventually

  21. Approximations • Magnetic fields acting like rubber tubes assumes the slow plasma response. • Good for slow motions • Large scales • Slinky • It will break: • Fast Timescales/motions • Small lengths.

  22. Field Lines Breaking: Reconnection Vin d CA Process breaking the frozen-in constraint determines the width of the dissipation region, d.

  23. Field Lines Breaking: Reconnection Jz and Magnetic Field Lines Y X

  24. What “Reconnection” Isn’t

  25. Reconnection Application – Solar Flares

  26. Reconnection in Solar Flares • X-class flare: t ~ 100 sec. • B ~ 100 G, n ~ 1010 cm-3 , L ~ 109 cm • tA ~ L/cA ~ 10 sec. F. Shu, 1992

  27. Dayside Reconnection Magnetotail Reconnection Application - Magnetospheric Physics To Sun

  28. Part II: Simulating Reconnection

  29. Reconnection is Hard • Remember slinky? • Now global (important) answers are strongly dependent on very fast/small timescales. • If you have to worry about very small timescales, it makes the problem very hard.

  30. Currently, Two Choices • Macro Simulations: • Treat reconnection in a non-physical way. • Simulate Large Systems. • Micro Simulations • Treat reconnection physically. • Simulate small idealized systems.

  31. Our General Simulations • Initial Value Problems • You give me the system initially, and I’ll tell you how it will behave in the future.

  32. A “Real” Plasma • Individual charge particles (on board) • Simply Calculate forces between each particle. • Problem: N total particles. • For each N particle, have to calculate force from (N-1) particles. • Calculations per time step: N2. Prohibitively expensive.

  33. One Simplification: The Fluid Approximation

  34. Fluid Approximation • Break up plasma into infinitesmal cells. • Define average properticies of each cell (fluid element) • density, velocity, temperature, etc. • Okay as long as sufficient particles per cell.

  35. The Simplest Plasma Fluid: MHD • Magnetohydrodynamics (MHD): • Describes the slow, large scale behavior of plasmas. • Now, very straightforward to solve numerically.

  36. Simulating Fluid Plasmas • Define Fluid quantities on a grid cell. • Dynamical equations tell how to step forward fluid quantities. • Problem with Numerical MHD: • No reconnection in equations. • Reconnection at grid scale. Grid cell n,V,B known.

  37. MHD Macro Simulations • Courtesy of the University of Michigan group: • Remember that reconnection occurs only at grid scale.

  38. Non-MHD Micro Fluid Simulations • Include smaller scale physics but still treat the system as a fluid.

  39. Effective Gyration Radius Ions: B E Electrons: • Frozen-in constraint broken when scales of variation of B are the same size as the gyro-radius. Electron gyroradius << Ion gyroradius => Dissipation region develops a 2-scale structure.

  40. Vin CA y x z Removing this Physics me/mi = 1/25 Out of Plane Current Y X Hall Term No Hall Term

  41. Simulating Particles • Still have N2 problem. How do we do it? • Forces due to electric and magnetic fields. • Fields exist on grids => Fluid • Extrapolate to each particles location. • Particles can be thought of as a Monte-Carlo simulation.

  42. Simulating Kinetic Reconnection • Finite Difference • Fluid quantities exist at grid points. • E,B treated as fluids always • Maxwell’s equations • Two-Fluid • E,B,ions, electrons are fluid • Kinetic Particle in Cell • E,B fluids • Ions and electrons are particles. • Stepping fluids: particle quantities averaged to grid. • Stepping particles: Fluids interpolated to particle position. Grid cell Macro-particle

  43. 3-D Magnetic Reconnection: with guide field • Particle simulation with 670 million particles • Bz=5.0Bx, mi/me=100, Te=Ti=0.04, ni=ne=1.0 • Development of current layer with high electron parallel drift • Buneman instability evolves into electron holes y x

  44. Formation of Electron holes • Intense electron beam generates Buneman instability • nonlinear evolution into “electron holes” • localized regions of intense positive potential and associated anti-parallel electric field Ez z x

  45. Electron Holes • Localized region of positive potential in three space dimensions • ion and electron dynamics essential • different from structures studied by Omura, et al. 1996 and Goldman, et al. 1999 in which the ions played no role • scale sizeVd/pein all directions • drift speed ~Vd/3 • dynamic structures (spontaneously form, grow and die)

  46. Electron drag due to scattering by parallel electric fields y • Drag Dz has complex spatial and temporal structure with positive and negative values • quasilinear ideas fail badly • Dz extends along separatrices at late time • Dz fluctuates both positive and negative in time. x

  47. The End

More Related