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By Bichowsky F.R., Urey H.C.

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The conductivity tensor becomes σ jk = σ δ jk. The medium, consisting of neutral gas and plasma, then obeys Ohm’s law: J = σ E. Copyright © 2005 IOP Publishing Ltd. 3 Anisotropic conductivity with infinite conductivity along the field If e νe and σjk νi , the conductivity tensor may be written in the form  Ne σi 1 + νii νee 0 B   . 84) = 1 + 0 − σ   i B i e 0 0 σe + σi i  The mean free paths for collisions of electrons and ions with neutrals are of the same order of magnitude. For √ isothermal conditions, the ratio of the electron and ion thermal velocities is m i /m e and, hence, the ratio between the collision frequencies is of the same order.

48), this may be written in the form VG = Copyright © 2005 IOP Publishing Ltd. M × ∇B . 51), changes, then the guiding centre has an acceleration ∂V0 dV 0 ≡ + (V 0 · ∇)V 0 . 7) dt ∂t In the non-inertial reference frame moving with the guiding centre, this acceleration gives rise to a fictitious force −m dV 0 /dt. This force gives rise to an F × B drift velocity relative to the guiding centre: V= dV 0 mµ ˆ d 1 µ ˆ ×m = × {µv ˆ + V E }. 8): d(µv ˆ ) mv dµ ˆ mµ ˆ × = µ ˆ × . 10) dt ∂t Rc where Rc = κ −1 is the radius of curvature of the field line.

In Cartesian tensor notation, after a little manipulation, we get ∂ ∂ (ρv j ) = − ∂t ∂ xk pδ j k + ρv j vk − B j Bk − 12 B 2 δ j k µ0 . 101) In this formulation, the expression on the right-hand side is the force density which is given by the divergence of a stress tensor. The quantity pδ j k is the isotropic pressure. The quantity ρvi vk is the result of momentum transport through the motion of the plasma: if this term is integrated over a volume V , the result is the net rate at which momentum is transported into the volume through the surface as a result of the plasma motion.

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