Recent observational evidence for magnetic field direction effects on helioseismic signals in sunspot penumbrae is suggestive of magnetohydrodynamic (MHD) mode conversion occurring at lower levels. This possibility is explored using wave mechanical and ray theory in a model of the Sun's surface layers permeated by uniform inclined magnetic field. It is found that fast‐to‐slow conversion near the equipartition depth at which the sound and Alfvén speeds coincide can indeed greatly enhance the atmospheric acoustic signal at heights observed by Solar and Heliospheric Observatory/Michelson Doppler Imager and other helioseismic instruments, but that this effect depends crucially on the wave attack angle, i.e. the angle between the wavevector and the magnetic field at the conversion/transmission depth. A major consequence of this insight is that the magnetic field acts as a filter, preferentially allowing through acoustic signal from a narrow range of incident directions. This is potentially testable by observation.

An extensive analysis, both analytic and numerical, of waves in flux tubes imbedded in (possibly) magnetic surroundings is given. It is shown that any wave confined to the tube and its neighbourhood can be put into one of seven categories. Simple criteria for deciding the existence of each type in any particular case are derived. Many other (leaky) modes are found which excite waves in the external medium and thereby lose energy to the surroundings. A number of asymptotic analyses allow much information to be gained about these without the need for numerical solution of the complicated equations involved. Three particular cases, pertaining to photospheric flux tubes, He fibrils, and coronal loops, are considered in detail.

By using a box model for the magnetosphere and by using a matrix eigenvalue method to solve the cold hnearized ideal MHD equations, we examine the temporal evolution of the irreversible coupling between fast magnetospheric cavity modes and field hne resonances (FLRs). By considering the fast mode frequency to be of the form wy = wy• -iwyi, and using a Fourier transform approach, we have determined the full time-dependent evolution of resonance energy widths. We find that at short times the resonances are broad, and narrower widths continue to develop in time. Ultimately, an asymptotic resonance Alfv6n frequency full width at half maximum (FWHM) of Aw• = 2coyi develops on a timescale of ryi -c0•/1. On timescales longer than ryi, we find that the resonance perturbations can continue to develop even finer scales by phase mixing. Thus, at any time, the finest scales within the resonance are governed by the phase mixing length Lph(t) -2•r (tdwA/dx) -1. The combination of these two effects naturally explains the localisation of pulsations in L shells observed in data, and the finer perturbation scales which may exist within them. During their evolution, FLRs may have their finest perturbation scales limited by either ionospheric dissipation or by kinetic effects (including the breakdown of single fluid MHD). For a continually driven resonance, we define an ionospheric limiting timescale wI in terms of the height-integrated Pealersen conductivity Ep, and hence derive a limiting ionospheric perturbation scale Li -2•r(ri&oA/dx) -1, in agreement with previous steady state analyses. For sufficiently high •p, FLR might be able to evolve so that their radial scales reach a kinetic scale length Lk. For this to occur, we require the pulsations to live for longer than r/• -27r (LkdcoA/dx) -1. For t < r/•, ri, kinetic effects and ionospheric dissipation are not dominant, and the ideal MHD results presented here may be expected to model realistically the growth phase of ULF pulsations. ground-based magnetometers, in the form of ultralow frequency (ULF) waves standing on dipolar field lines. The Doppler signatures of these pulsations are also of-Copyright 1995 by the American Geophysical Union. Paper number 95JA00820. 0148-0227/95/95JA-00820505.00 ten observed by HF radar at the ionospheric footpoints of oscillating field lines. Dungey [1954, 1967] first suggested that pulsations were standing Alfvdn waves on dipolar field lines (toroidal modes). He also identified fast poloidal compressional waves, which should propagate across the background magnetic field, and subsequently completed the first decoupled studies of these modes. Southwood [1974] and Chen and Hasegawa [1974] independently presented the first attempts at a full theoretical analysis of the coupled pulsation problem. They proposed that the solar wind, incident upon the magnetospheric cavity and driving magnetosheath flows, could excite a travelling Kelvin-Helmholtz surface wave on the magnetopause. Having an evanescent structure within the magnetosphere, this wave mode...

The efficacy of fast/slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical "scattering experiment", placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30• - 40• from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60• -80• .

Local helioseismology seeks to probe the near surface regions of the Sun, and in particular of active regions. These are distinguished by their strong magnetic fields, yet current local techniques do not take proper account of this. Here, we first derive appropriate gravito-magneto-acoustic dispersion relations, and then use these to examine how acoustic rays entering regions of strong field split into fast and slow components, and the subsequent fates of each. Specifically, two types of transmission point, where wave energy can transfer from the fast to slow branch (or vice versa) are identified; one close to the equipartition level where the sound and Alfvén speeds coincide, and one higher up near the acoustic cutoff turning point. This second type only exists for rays of low frequency or low l though. In accord with recent studies of fast-to-slow mode conversion from the perspective of p-modes, magnetic field inclination is found to have significant consequences for wave splitting.

We present evidence for the dependence of helioseismic Doppler signatures in active regions on the line-ofsight angle in inclined magnetic fields. Using data from the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory, we performed phase-sensitive holography in the penumbrae of sunspots over the course of several days as the spots traversed the solar disk. Control correlations, which comprise a correlation of the surface wave amplitude with the incoming acoustic wave amplitude from a surrounding region, were mapped. There is a direct dependence of control-correlation phase signatures on the line-of-sight angle in the plane defined by the vertical and magnetic field vectors. The phase shift of waves observed along directions close to the orientation of the magnetic field is smaller than the phase shift observed when the line of sight is at a significant angle with respect to the field orientation. These findings have important implications for local helioseismology. The variation in phase shift (or the equivalent acoustic travel-time perturbations) with line-ofsight direction suggests that a substantial portion of the phase shift occurs in the photospheric magnetic field. Observations of the vector components of the field may be used to develop a proxy to correct these phase perturbations (known as the acoustic showerglass) that introduce uncertainties in the signatures of acoustic perturbations below the surface.

We study the conversion of fast magneto-acoustic waves to Alfvén waves by means of 2.5D numerical simulations in a sunspot-like magnetic configuration. A fast, essentially acoustic, wave of a given frequency and wave number is generated below the surface and propagates upward though the Alfvén/acoustic equipartition layer where it splits into upgoing slow (acoustic) and fast (magnetic) waves. The fast wave quickly reflects off the steep Alfvén speed gradient, but around and above this reflection height it partially converts to Alfvén waves, depending on the local relative inclinations of the background magnetic field and the wavevector. To measure the efficiency of this conversion to Alfvén waves we calculate acoustic and magnetic energy fluxes. The particular amplitude and phase relations between the magnetic field and velocity oscillations help us to demonstrate that the waves produced are indeed Alfvén waves. We find that the conversion to Alfvén waves is particularly important for strongly inclined fields like those existing in sunspot penumbrae. Equally important is the magnetic field orientation with respect to the vertical plane of wave propagation, which we refer to as "field azimuth". For field azimuth less than 90 • the generated Alfvén waves continue upwards, but above 90 • downgoing Alfvén waves are preferentially produced. This yields negative Alfvén energy flux for azimuths between 90 • and 180 • . Alfvén energy fluxes may be comparable to or exceed acoustic fluxes, depending upon geometry, though computational exigencies limit their magnitude in our simulations.

No abstract