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1、SwinburneMarch 12 20071Magnetohydrodynamics Basicsor “MHD in one lecture?! Youve gotta be kidding!”Paul Cally, Centre for Stellar & Planetary Astrophysics, Monash UniversityMHD EquationsPhysical InterpretationMHD WavesSwinburneMarch 12 20072Solar atmosphere dominated by magnetic fieldsSwinburneMarch
2、 12 20073MHDMHD = fluid dynamics + Maxwells eqns - displacement current + Ohms “Law” j j=(EE+vXBvXB) or generalizationApplies to (at least partially) ionized gases (plasmas)NonrelativisticAssumes highly collisional, low frequency (c.f. cyclotron frequency)SwinburneMarch 12 20074MHD Approximationv2 1
3、 dominated by advectionRm1), it is advected with the plasma.SwinburneMarch 12 20079SwinburneMarch 12 200710Lorentz Force j jXBXBj B=1 B B=1 B B B2 2= BB B22Imagnetic stress tensorStress: tension along field lines B2/isotropic pressure pmag= B2/2Dv Dt=ppmagg1 B Bviscous termsSwinburneMarch 12 200711E
4、xample 1What do you expect this to do? orPressure pushing away from high B.B=0,ex2,0 j=0,0,2xex2/j B=2xe2x2,0,0/B B=0and B2/2=2xe2x2,0,0/ j B=B B/ B2/2=2xe2x2,0,0/SwinburneMarch 12 200712Example 2And this? or“Slingshot effect” to the right! important in flares and CMEsB=2y,1,0 j=0,0,2/ j B=2,4y ,0/B
5、 B=2,0,0 B2=0,8 y,0So1 B B B2 2=2 ,0,00,4y ,0SwinburneMarch 12 200713Plasma betaA simple measure of the relative importance of the gas and magnetic forcesIf 1 the gas dominates (e.g. stellar interiors)If a or ac) travelling directly along the field lines. Because it is longitudinal, it does not bend or displace them, so there is no magnetic effect.SwinburneMarch 12 200729Non-Ideal EffectsMagnetic reconnectionSolar corona (flares, CMEs)massive source of energyEarths magnetosphere (interaction with solar wind) another day perhaps.SwinburneMarch 12 200730Lunchtime!Lunchtime!
