B. Roberts

Wave propagation in a magnetic cylinder

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvénic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvénic-type, oscillations arise only in high density (strictly, low Alfvén velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.

Wave propagation in a magnetically structured atmosphere

The solar atmosphere, from the photosphere to the corona, is structured by the presence of magnetic fields. We consider the nature of such inhomogeneity and emphasis that the usual picture of hydromagnetic wave propagation in a uniform medium may be misleading if applied to a structured field. We investigate the occurrence of magnetoacoustic surface waves at a single magnetic interface and consider in detail the case where one side of the interface is field-free. For such an interface, a slow surface wave can always propagate. In addition, a fast surface wave may propagate if the field-free medium is warmer than the magnetic atmosphere.

Vertical motions in an intense magnetic flux tube

In a recent discussion of intense photospheric magnetic fields we gave an expansion procedure that lead to a tractible system of differential equations governing vertical motions in a slender flux tube embedded in a quiescent environment. Transverse variations were taken into account in our discussion. In support of this expansion scheme we considered the special case of a straight flux tube in a uniform atmosphere. Wilson (1978, 1979b) has now criticised our treatment of this special case. We discuss his objections here, and show them to be without foundation.The cause of the disparity between our results and his lies not in a breakdown of the slender flux tube approximation but rather in the differing assumptions as to the nature of pressure variations in the tubes exterior. We generalize the slender flux tube approximation in a uniform tube, and obtain the governing dispersion relation. This dispersion relation contains, as special cases, both the results of Roberts and Webb (1978) and those of Wilson (1979a).

WAVES AND OSCILLATIONS IN THE CORONA (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earths crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.

Pulse propagation in a magnetic flux tube

The linear development of a pulse as it propagates adiabatically along an isothermal magnetic flux tube embedded in a gravitationally stratified atmosphere is studied. It is shown that, for a quiescent environment, longitudinal disturbances in the tube are governed by an equation of the Klein-Gordon type. An impulsively generated disturbance results in a wave front propagating at the subsonic and subAlfvenic tube speed; the wave front trails a wake oscillating at the tube frequency. The results are illustrated for solar photospheric conditiions.

Alfvén Wave Phase Mixing as a Source of Fast Magnetosonic Waves

The nonlinear excitation of fast magnetosonic waves by phase mixing Alfvén waves in a cold plasma with a smooth inhomogeneity of density across a uniform magnetic field is considered. If initially fast waves are absent from the system, then nonlinearity leads to their excitation by transversal gradients in the Alfvén wave. The efficiency of the nonlinear Alfvén–fast magnetosonic wave coupling is strongly increased by the inhomogeneity of the medium. The fast waves, permanently generated by Alfvén wave phase mixing, are refracted from the region with transversal gradients of the Alfvén speed. This nonlinear process suggests a mechanism of indirect plasma heating by phase mixing through the excitation of obliquely propagating fast waves.

Waves in Twisted Magnetic Flux Tubes

The modes of oscillation of a twisted magnetic flux tube in an incompressible medium are investigated analytically. An exact dispersion relation for the case of uniform twist is obtained. In contrast to the case of an untwisted incompressible tube, body, surface, and hybrid (surface-body) modes arise.

On fast magnetosonic coronal pulsations

The linear properties of the fast magnetosonic modes of a coronal loop modelled as a smooth density inhomogeneity in a uniform magnetic field are compared with the case of a step function slab. It is shown that the group velocityCgof the modes, important in determining the structure of impulsively excited wave packets, possesses a minimum for a wide class of profile including the slab, with the exception of the Epstein profile for which the minimum inCgmoves out to infinity. Results for the simple step profile are thus of wider validity, and likely to be applicable to coronal loops.

Solitary waves in a magnetic flux tube

Magnetic flux tubes (slabs or cylinders) are of considerable physical interest because of their occurrence in the sun’s atmosphere. The propagation of weakly nonlinear, long‐wavelength (weakly dispersive), sound waves in both a magnetic slab and a magnetic cylinder is discussed. The slab geometry leads to the Benjamin–Ono equation, viz., ∂v/∂t+cT(∂v/∂z) +βv(∂v/∂z) +(α/π)(∂2/∂z2) ×∫/∞−∞[v(s,t)ds/(s−z)]=0, and the cylindrical geometry yields its allied form, viz., ∂v/∂t+cT(∂v/∂z)+βv(∂v/∂z) +α’(∂3/∂z3)∫∞−∞{v(s,t)ds/ [λ2+(s−z)2]1/2}=0, an equation known also to arise in waves on concentrated vortices in fluids. The magnetic flux tube thus provides a simple illustration of these two equations, hitherto only considered in separate physical systems.

The influence of a chromospheric magnetic field on the solar p- and f-modes

The influence of a chromospheric magnetic field on p- and f-mode frequencies is evaluated theoretically for a simple model of the solar plasma, consisting of a polytrope in the solar interior, above which is an isothermal atmosphere. The atmosphere is permeated by a horizontal magnetic field. Frequency changes and shifts in phase factors due to the presence of a magnetic atmosphere are calculated analytically in the long-wavelength limit, and numerically for arbitrary wavelength. The results reveal that, at low to moderate degree l, an increase in chromospheric magnetic field leads to a frequency increase for the n = 1 p-mode, whereas the overtones (n = 2, 3, etc.) suffer a frequency decrease. At high l, all the p-modes suffer a frequency decrease. 35 refs.