On the nonexistence of plane-polarized large amplitude Alfven waves

A theorem is presented which shows that purely Alfvenic plane-polarized large-amplitude disturbances in the solar wind are not possible and will never be observed. The theorem establishes that there is no nontrivial plane-polarized magnetic-field configuration in which the parameter B-squared is constant throughout all space. It is noted, however, that more general nonplanar Alfvenic disturbances may well exist.