EDP Sciences
Free Access
Volume 406, Number 2, August I 2003
Page(s) 735 - 740
Section Diffuse matter in space
DOI https://doi.org/10.1051/0004-6361:20030822

A&A 406, 735-740 (2003)
DOI: 10.1051/0004-6361:20030822

On the generation of Alfvén waves by solar energetic particles

R. Vainio

Department of Physical Sciences, PO Box 64, 00014 University of Helsinki, Finland
(Received 18 March 2003 / Accepted 16 May 2003 )

A simple analytical theory of Alfvén waves amplified by streaming solar energetic particles (SEPs) is studied. It is pointed out that a finite time-integrated net flux of energetic protons has to pass each point in space before we can expect Alfvén waves to be significantly modified by the streaming instability. The time-integrated net proton flux needed for the time-integrated wave growth rate (or wave growth, for short) to exceed unity is evaluated. Assuming that protons stream much faster than the waves, we evaluate the wave growth as a function of position and wavenumber for a specified proton injection energy spectrum, dN/dE. The wave growth is found to be proportional to $vp\, \mathrm{d}N/\mathrm{d}E$, where v and p are the particle speed and momentum, and to the local Alfvén speed VA. Thus, maximum wave growth is achieved at the location of maximum VA (at a few solar radii), and the minimum value of dN/dE required for the wave growth to exceed unity there is a few times 10 32/vp protons per unit solid angle (in coordinate space) at the solar surface. If dN/dE is below this value, test-particle theory is a valid description of particle transport and acceleration. The value is not exceeded (above 1 MeV energies) in small gradual SEP events having peak 1-MeV proton intensities below $\sim $10 protons (cm $^{2}\, $sr s MeV) -1 at 1 AU. The spatial and momentum dependence of the wave growth can also be used to estimate the maximum emission strength of a moving proton source in the interplanetary medium. For a strong source moving through the solar wind at constant super-Alfvénic speed, the number of escaping particles per unit time and flux-tube cross section is approximately constant in time, predicting a plateau-type time-intensity profile observed ahead of the source. The model reproduces observations of streaming-limited intensities at energies around 10 MeV and explains the double peaked injection profiles observed in large SEP events.

Key words: instabilities -- Sun: particle emission -- turbulence

© ESO 2003

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.