On the Behavior of Plasma at Ionic Resonance

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Abstract
An electromagnetic wave having its wave vector parallel to the direction of the steady magnetic field Ĥ is attenuated in plasma very effectively when the frequency ω is equal to the ionic resonance frequency Ωg of the plasma. A small localized periodic disturbance initiated in a plasma in thermodynamic equilibrium at t = − ∞ and having frequency ω = Ωg produces along the direction of the magnetic field a wave motion characterized by a complex wave vector k ∼ (Ω0Ωg/c2u0i) ⅓ (√3 + i) where Ω0 is the Langmuir frequency and u0i is the mean thermal velocity of the ions in the plasma. The attenuation per wavelength at the resonance frequency is substantial since Imk/Rek = 1/√3. However, the attenuation per unit of length is not at maximum at ionic resonance since it increases for increasing frequencies when ω passes through the resonance. This is shown by the fact that for ω = Ωg we have Im(dk/dω) > 0 since at resonance Im(dk/dω) = K1/u0i + (K2/u02ui0) ⅓ where K1 and K2 are appropriate positive constants and u0 is the velocity of the magnetohydrodynamic wave.

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