Abstract
We discuss the recent progress in studying the absolute and convective instabilities of circularly polarized Alfven waves (pump waves) propagating along an ambient magnetic field in the approximation of ideal magnetohydrodynamics (MHD). We present analytical results obtained for pump waves with small dimensionless amplitude a, and compare them with numerical results valid for arbitrary a. The type of instability, absolute or convective, depends on the velocity U of the reference frame where the pump wave is observed with respect to the rest plasma. One of the main results of our analysis is that the instability is absolute when Ul Ur) we consider the signalling problem, and show that spatially amplifying waves exist only when the signalling frequency is in two symmetric frequency bands. Then, we write down the analytical expressions determining the boundaries of these frequency bands and discuss how they agree with numerically calculated values. We also present the dependences of the maximum spatial amplification rate on U calculated both analytically and numerically. The implication of the obtained results on the interpretation of observational data from space missions is discussed. In particular, it is shown that circularly polarized Alfven waves propagating in the solar wind are convectively unstable in a reference frame of any realistic spacecraft.
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