Absolute and Convective Instabilities of Circularly Polarized Alfvén Waves
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We discuss the recent progress in studying the absolute and convective instabilities of circularly polarized Alfvén 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 U l < U < U r and convective otherwise. We study the dependences of U l and U r on a and the ratio of the sound speed to the Alfvén speed b. We also present the results of calculation of the increment of the absolute instability on U for different values of a and b. When the instability is convective (U < U l or U > U r) 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 Alfvén waves propagating in the solar wind are convectively unstable in a reference frame of any realistic spacecraft.
KeywordsMHD plasma solar wind stability waves
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