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Calculate the magnetic Reynolds number Rm and the diffusion time Td for (a) a laboratory plasma where LB= 0.1 m, V 10° m s-' and o s 100 2-' m (b) solar wind where LB = 10 solar radii, V z 400 km s-1 and o = 3 × 10ª N-1 m-1

Calculate the magnetic Reynolds number Rm and the diffusion time Td for (a) a laboratory plasma where LB= 0.1 m, V 10° m s-' and o s 100 2-' m (b) solar wind where LB = 10 solar radii, V z 400 km s-1 and o = 3 × 10ª N-1 m-1

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Calculate the magnetic Reynolds number Rm and the diffusion time Ta for (a) a laboratory plasma where LB =0.1 m, V = 103 m s-1 and o z 100 N-1 m (b) solar wind where Lg = 10 solar radii, V = 400 km s-1 and o 3 x 104 2-1 m-1.
Transcribed Image Text:Calculate the magnetic Reynolds number Rm and the diffusion time Ta for (a) a laboratory plasma where LB =0.1 m, V = 103 m s-1 and o z 100 N-1 m (b) solar wind where Lg = 10 solar radii, V = 400 km s-1 and o 3 x 104 2-1 m-1.
Expert Solution
Part (a)

Given:

Length,LB=0.1mMagnetic Permeability of the free space,μ0=4π×10-7H/mPlasma Velocity,V=103m/sElectrical Conductivity,σ=100Ω-1m-1Diffusion Coefficient, D=30m2/s

The magnetic Reynolds number is expressed as:

Rm=μ0σVLB  ..... (1)

Substitute LB=0.1m , μ0=4π×10-7H/m, V=103m/s, and σ=100Ω-1m-1 in equation (1)

Rm=4π×10-7×100×103×0.1Rm=125.6×10-4HΩ-1s-1

The diffusion time is expressed as:

τD=LB2D   .....(2)

Substitute LB=0.1m , D=30m2/s in equation (2).

τD=0.1230τD=0.0003s

 

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