Alfvén Waves in Dusty Interstellar Clouds.

N. F. Cramer, S. V. Vladimirov, PASA, 14 (2), in press.

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The Dispersion Relation

We now write the fields in terms of circularly polarized mode amplitudes:
where the +(-) sign corresponds to the left(right) hand circularly polarized wave.

Using (11) in (7)-(10) yields, after some algebra,


In our case of tex2html_wrap_inline658 very close to 1, tex2html_wrap_inline660.

Equation (13) shows that for oblique propagation (tex2html_wrap_inline662), the amplitudes of opposite circular polarization are coupled together, i.e. the modes are not purely circularly polarized. We then obtain from (13):

The cutoffs of tex2html_wrap_inline632 (where tex2html_wrap_inline666) correspond to
which is the parallel propagation case treated by Pilipp et al. (1987). For no collisions, a case previously treated by Shukla (1992) and Mendis and Rosenberg (1992), the parallel propagation dispersion relation is, from (18),
showing, for the right hand polarized mode, the cutoff where tex2html_wrap_inline668 at tex2html_wrap_inline670, and the resonance where tex2html_wrap_inline672 at tex2html_wrap_inline674. This mode was discussed by Shukla (1992). For tex2html_wrap_inline676, we obtain the modification of the parallel propagating Alfvén wave due to dust discussed by Vladimirov and Cramer (1996) as the basis for a discussion of nonlinear effects: the right hand circularly polarized mode with a cutoff in tex2html_wrap_inline678 at tex2html_wrap_inline680, and the left hand circularly polarized mode with tex2html_wrap_inline682 as tex2html_wrap_inline684.

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