National Undergraduate Fellowship Program in Plasma Physics and Fusion Engineering Plasma Astrophysics Michael Brown Swarthmore College June 2007 Outline Brief plasma review (B-fields and MHD) Two important paradigms Astrophysical objects (solar flares to galactic jets) Astrophysical processes (dynamos, reconnection and pulsars)
Astrophysical Plasma Review Magnetic fields… • related to electric fields by Lorentz transformation (E'E v B) • Q: why are there large scale B-fields but no large scale E-fields in the universe? A: ...there are lots of electric monopoles around to short out electric fields • B-fields are associated with currents but do currents cause B-fields are vice-versa? • exert forces on currents Force=JxB • contain energy W (B 2 /2 )d 3 x mag 0
Astrophysical Plasma Review ramifications of MHD B 2 (v B) B t 0 L 0 L2 characteristic times : conv and diff v v 2 B 2 B energy : v Alf 2 20 0 ratio of convection to diffusion : 0(v B) vL Rm 0 2 B why we can ignore displacement current : 0c 2 light c 0vL diff 0 J 1 E L light 00 t smallest scale : mv 2 mv v ion F eE evB ri r eB ci
Astrophysical Plasma Review Frozen-in Flux high conductivity: Coulomb collisionality drops with T (so ~ T-3/2) universe is an excellent conductor of electricity almost everywhere frozen-in flux: • assume perfectly conducting magnetofluid • no electric field in a perfect conductor • if field lines move with respect to fluid then an electric field is induced • therefore fields move with the fluid!
Poynting Vector S 1 (E B) 0 for a static resistive column of magnetofluid (currents channeled by insulator) V I E and B 0 L 2r VI so... S and S dA VI 2rL ...power source is applied voltages and currents. ...but for a perfectly conducting dynamic column of magnetofluid... (v B) B vB 2 B(v B) S 0 0 v B 2 or... S 0 power source is transverse flow... flow manipulates B, J flows to satisfy Ampere
Simple 2D Reconnection Theory (Sweet/Parker) uout L assume incompressibility: uin L uout uin Ohm's law (z - comp, outside) : E z uin Bx 0 Ohm's law (z - comp, inside) : E z J z Bx2 1 2 B energy balance : uout uout uAlf x 20 2 0 Ampere's law (around layer): Bx 0 J z Ez J z ... so we find... uin Rm 1(inside) Bx 0 J z 0 L uout ...also... Rm (outside) uin
Reconnection Rate 2 u uout uAlf u L L 0 Alf 0 2 in If we define the Alfvenic Mach number as M Alf uout 1 M Alf Rm or uin uin we find : uAlf S where Rm is based on the Alfven velocity in the bulk magnetofluid and on the largest scale of the system L. Malf is a dimensionless measure of the reconnection rate or the rate at which magnetic field lines are annihilated or the direct electric field. More sophisticated models [Petschek, 1964 and Vasyliunas, 1975] predict a faster reconnection rate 1 (M Alf ~ ln(Rm )) and a smaller ration of u /u . It appears, however that a bound exists: out in ln(Rm ) uout Rm uin