Reflection of Alfven waves in the corona and solar wind: An impulse function approach

We consider the reflection of Alfven waves in the corona and solar wind, using variables f and g which follow sunward and antisunward characteristics, respectively. We show that the basic equations for f and g have the same structure as the Klein-Gordon equation. Unlike previous studies which used a harmonic analysis, we emphasize the impulse response of the system. This is equivalent to finding the Green's function, but it may have direct application to situations where Alfven waves are launched impulsively. We provide an approximate analysis which can be used to understand most features that appear in detailed numerical solutions. The analysis reveals the origin of a previous result that f and g each has both sunward and antisunward propagating phase in a harmonic analysis, even though f (g) follows only the sunward (antisunward) characteristic. We numerically study the propagation of an antisunward moving impulse in the corona and solar wind. We find that the sunward moving wake'' tends to become more important at greater distances beyond the Alfven critical point, possibly providing a natural explanation of the observation that outward propagating waves become less dominant at greater distances from the Sun. There is an extended region behind the initial impulse in which magnetic energy dominates kinetic energy; it is not clear, however, whether our result can explain the observed dominance of magnetic energy throughout many decades of frequency in the observed power spectrum. We also find that the outgoing wake has a tendency to ring,'' with periods of the order of 15 - 30 min. The ringing is associated mainly with propagation through a structured Alfven speed profile rather that with the cutoff in the Klein-Gordon equation. These oscillation periods seem too short to explain why Alfven waves in the solar wind have most power at periods of hours, but other Alfven speed profiles could yield longer periods. We also investigate whether the same approach can be used for acoustic-gravity waves propagating along magnetic flux tubes in the solar atmosphere.