Fourier analysis is used to consider the characteristics of linear magnetosonic N waves propagating through a uniform background medium at rest, with constant uniform magnetic field B0. The disturbance is driven by an initial compressed and localized gas pressure perturbation, represented by a Dirac delta distribution. The solutions for the perturbed gas and magnetic field variables are expressed as second derivatives of appropriate wave potentials. The wave potentials split naturally into fast and slow magnetosonic components. The fast- and slow-mode wave potentials reduce to one-dimensional integrals over the wave normal angle ϑ between the wave vector k and B0. Alternatively, the fast-mode wave potentials can be written as Abelian integrals over the slow-mode phase speed cb, whereas the slow-mode potentials reduce to Abelian integrals over the fast-mode phase speed cf. The structure of the integrals depends on the location of the observation point relative to the fast and slow magnetosonic eikonal or group velocity surfaces. Calculations of the time evolution of the magnetic field of the N wave show a family of magnetic field lines connecting the cusps of the slow magnetosonic group velocity surface, plus a further family of field lines not connected with the cusps. The wave disturbance is confined on and within the fast magnetosonic group velocity surface. The gas pressure perturbation shows singular N wave type disturbances on the fast- and slow-mode eikonal surfaces. The Green's function for the magneto-acoustic wave operator for a uniform background medium initially at rest is also obtained. Generalization of the N wave solutions for non-singular distributions of the initial gas pressure perturbation are also obtained.
ASJC Scopus subject areas
- Condensed Matter Physics