Issue |
A&A
Volume 452, Number 2, June III 2006
|
|
---|---|---|
Page(s) | 641 - 646 | |
Section | The Sun | |
DOI | https://doi.org/10.1051/0004-6361:20053595 | |
Published online | 22 May 2006 |
Absolute and convective instabilities of parallel propagating circularly polarized Alfvén waves: numerical results
Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
Received:
8
June
2005
Accepted:
27
February
2006
Context.The stability of parallel propagating circularly polarized Alfvén waves (pump waves) has been studied for more than four decades with the use of normal mode analysis. It is well known that the normal mode analysis does not answer the question if a pump wave looks stable or unstable in a particular reference frame. To answer this question it is necessary to find out if the instability is absolute or convective in this reference frame.
Aims.We extend our previous study of absolute and convective instabilities of pump waves with small amplitude to pump waves with arbitrary amplitude.
Methods.To study the absolute and convective instabilities of pump waves with arbitrary amplitude we numerically implement Brigg's method.
Results.We show that the wave is absolutely unstable in a reference frame
moving with the velocity U with respect to the rest plasma if U satisfies
the inequality and convectively unstable otherwise, and
calculate the dependences of Ul and Ur on the dimensionless wave
amplitude a . We also calculate the dependence of the increment of the
absolute instability on U for different values of a . When the instability
is convective (
or
) we study the signalling problem. We show
that spatially amplifying waves exist only when the signalling frequency is in
two symmetric frequency bands, and calculate the dependences of the boundaries
of these bands on U for different values of a . We also obtain the
dependences of the maximum spatial amplification rate on U for different
values of a . The implication of these 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.
Key words: plasmas / magnetohydrodynamics (MHD) / waves / instabilities / solar wind
© ESO, 2006
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.