Slide #1.

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)
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Slide #2.

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 
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Slide #3.

Astrophysical Plasma Review equations of MHD Newton II: ma F dv      P  J B vol vol dt v    v v P  J B t  Ohm’s Law: V IR   E'E  v B J   Maxwell’s eqs:  B 0 J and  E  B t induction eq. (curl of Ohm):  B  (v B)  2 B t 0
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Slide #4.

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 20 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 00 t smallest scale : mv 2 mv v ion F eE evB    ri   r eB  ci 
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Slide #5.

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!
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Slide #6.

 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 2r VI so... S  and S dA VI 2rL ...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
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Slide #7.

 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 20 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
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Slide #8.

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
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