Penetration of an alternating magnetic field into plasma in the presence of the Hall effect

In this work we have found the depth of penetration of a travelling magnetic field into plasma in the presence of electron increase owing to Hall effect. Since the electrons move in the direction of the field displacement, penetration depth increases in comparison with the case of electrons that are motionless on the average and is determined by the effective frequency Ω = k|V − ν0|; V is field velocity, ν0 electron velocity (that is, there occurs a peculiar "Doppler effect"). Velocity ν0 for a non-linear case is a function of the coordinates and depends on the magnitude of the field, its displacement velocity and also on conduction. The electrons are entrained in the direction of the field motion, which always leads to skin-depth increase. A rough calculation of the penetration depth can be made according to the formula δ = δ0 (1 – ⟨B⟩2/B02)−1 δ0=C/(4πσkV)½ is the "normal" skin depth; B0 is the alternating-magnetic-field amplitude on the plasma surface; ⟨B⟩ is the magnetic-field magnitude on the plasma surface; this field creates a current of entrained electrons. Calculation is applicable in order of magnitude up to ⟨B⟩≈B0.