From the dispersion relations obtained in problem 16.8 show that, in the limit of
Question:
From the dispersion relations obtained in problem 16.8 show that, in the limit of ω ≪ Ωci, we obtain the dispersion relation for the (shear) Alfven wave (cold plasma limit of the magnetosonic wave) when k is parallel to B0. Furthermore, for ω ≤ Ωci and k parallel to B0, determine the following approximate dispersion relation for ion cyclotron waves (assume 1 + c2 /V2A ≪ η2),
Data from Problem 16.8
Using the results of the previous problem, analyze the various modes of propagation for the particular cases when θ = 0 and θ = π/2. Compare the results with those for a cold electron gas. Make a plot analogous to the one presented in Fig. 20.
Figure 20.
Data from Problem 7
Consider the problem of wave propagation at an arbitrary direction in a cold magnetoplasma, but including the motion of the ions (one type only).
Show that the dispersion relation is obtained from an equation identical to (5.25), except that now we have (neglecting collisions)
where (with α = e, i)
Obtain the dispersion relation and show that it can be written in the form
where θ is the angle between k and B0, R = S + D, and L = S – D.
Determine and plot the resonances and reflection points as a function of θ.
Equation.
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