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Absolute and convective instabilities of parallel propagating circularly polarized Alfven waves: Beat instability

Simpson, D. and Ruderman, M.S. (2005) Absolute and convective instabilities of parallel propagating circularly polarized Alfven waves: Beat instability. Physics of Plasmas, 12 (6). Art. No. 062103. ISSN 1089-7674


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Ruderman and Simpson [Phys. Plasmas 11, 4178 (2004)] studied the absolute and convective decay instabilities of parallel propagating circularly polarized Alfven waves in plasmas where the sound speed c(S) is smaller than the Alfven speed upsilon(A). We extend their analysis for the beat instability which occurs in plasmas with c(S)>upsilon(A). We assume that the dimensionless amplitude of the circularly polarized Alfven wave (pump wave), a, is small. Applying Briggs' method we study the problem analytically using expansions in power series with respect to a. It is shown that the pump wave is absolutely unstable in a reference frame moving with the velocity U with respect to the rest plasma if U-l< U < U-r, where U-l=-upsilon(A)+O(a) and U-r=upsilon(A)+O(a). When U < U-l or U>U-r, the instability is convective. The signaling problem is studied in a reference frame where the pump wave is convectively unstable. It is shown that the spatially amplifying waves exist only when the signaling frequency is in two narrow symmetric frequency bands with the widths of the order of a(3). These results enable us to extend for the case when c(S)>upsilon(A) the conclusions, previously made for the case when c(S)<upsilon(A), that circularly polarized Alfven waves propagating in the solar wind are convectively unstable in a reference frame of any spacecraft moving with the velocity not exceeding a few tens of km/s in the solar reference frame. The characteristic scale of spatial amplification for these waves exceeds 1 a.u.

Item Type: Article
Copyright, Publisher and Additional Information: © AIP 2005. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Repository Assistant
Date Deposited: 31 Oct 2006
Last Modified: 18 Nov 2015 01:50
Published Version: http://dx.doi.org/10.1063/1.1919407
Status: Published
Publisher: American Institute of Physics
Refereed: Yes
Identification Number: 10.1063/1.1919407
URI: http://eprints.whiterose.ac.uk/id/eprint/1671

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