Open AccessFormation of imbedded rotational discontinuities with nearly field aligned normals
Author(s) -
Vasquez Bernard J.,
Hollweg Joseph V.
Publication year - 1998
Publication title -
journal of geophysical research: space physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/97ja02993
Subject(s) - physics , waveform , classification of discontinuities , polarization (electrochemistry) , amplitude , wavenumber , field (mathematics) , fourier transform , transverse plane , computational physics , optics , mathematical analysis , quantum mechanics , mathematics , chemistry , structural engineering , voltage , pure mathematics , engineering
We present hybrid numerical simulations of a small number of low‐frequency (much less than the proton gyrofrequency) Alfvén waves and, for the first time, show how to produce imbedded rotational discontinuities (RDs) with a small angle (θ Bn ) between their asymptotic and normal fields which are stable against dispersion. When the initial waves are linearly polarized and give a waveform whose Fourier components of B 2 have wave vectors within ≈10° of the background magnetic field B 0 , the waveform tends to steepen even for small amplitudes (|δ B |/ B ≪ 1). This produces RDs with normals nearly along B 0 and nearly constant B between the RDs. However, the waveform is not steady because these RDs widen continually due to the presence of dispersive intermediate or ion cyclotron modes which are permanently attached to their edges. This commonly occurs in simulations of isolated RDs which have small θ Bn . When the initial waveform is modified by including a transverse field component with a wavenumber equaling that from the Fourier component of B 2 along B 0 so that the field moves on an “elliptical” ( B not constant) arc, the dispersive intermediate modes no longer develop, and the waveform and imbedded RDs evolve toward a steady state with nearly constant B and a “circular” arc polarization. Spherically polarized waveforms can be made in a similar manner. Only this type of waveform produces RDs without intermediate modes on their edges for all parameters. Oblique fast modes do form, but these have phase speeds which are faster than the Alfvén phase speed and so detach from the RD's edge and do not cause the RD to widen continually. The appearance of RDs with small θ Bn varies greatly with the time of development, and this can explain the diversity of hodogram shapes of such RDs in the solar wind. We finally conclude that Alfvénic fluctuations with imbedded RDs must evolve through a succession of arc‐polarized or spherically polarized waveforms as they travel outward from the Sun: Otherwise, the RDs with small θ Bn in the solar wind would have widen to the point where they are beyond recognition.