The Solar Wind.pdf
The Solar Wind.pdf
The Solar Wind.pdf
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• Let us express the magnetic field in the equatorialrplane in polar coordinates as B = B , B )(r ϕ1 ∂ 2– Gauss’s Law in spherical coordinates is ∇ ⋅ B r = r2 r=r ∂rB2 2since the field depends only on r so that r B = .rr0B0– <strong>The</strong> magnetic flux through radial shells is conserved and the radialcomponent of the field decreases as2⎛ r0⎞B r= B0⎜⎟⎝⎠r r– <strong>The</strong> frozen-in field condition ∇×( v × B)= 0 gives1 ∂( r(vϕ Br− vrB ϕ)) = 0r ∂ror r( v B v B )) const.If we assume thatϕ r−r ϕ=get2rvϕ Br− rvrBϕ=BϕB=ϕrvϕv=Bϕr− r20rvr− rωvrr 0ω BB ω0Sun BrSunSun0B r( ) 0is radial at r 0we