The effect of parallel static and microwave electric fields on excited hydrogen atoms

Motivated by recent experiments we analyse the classical dynamics of a hydrogen atom in parallel static and microwave electric fields. Using an appropriate representation and averaging approximations we show that resonant ionisation is controlled by a separatrix, and provide necessary conditions for a dynamical resonance to affect the ionisation probability. The position of the dynamical resonance is computed using a high-order perturbation series, and estimate its radius of convergence. We show that the position of the dynamical resonance does not coincide precisely with the ionisation maxima, and that the field switch-on time can dramatically affect the ionisation signal which, for long switch times, reflects the shape of an incipient homoclinic. Similarly, the resonance ionisation time can reflect the time-scale of the separatrix motion, which is therefore longer than conventional static field Stark ionisation. We explain why these effects should be observed in the quantum dynamics. PACs: 32.80.Rm, 33.40.+f, 34.10.+x, 05.45.Ac, 05.45.MtComment: 47 pages, 20 figure

Magnetic dipoles and electric currents

We discuss several similarities and differences between the concepts of electric and magnetic dipoles. We then consider the relation between the magnetic dipole and a current loop and show that in the limit of a pointlike circuit, their magnetic fields coincide. The presentation is accessible to undergraduate students with a knowledge of the basic ideas of classical electromagnetism.Comment: 7 pages, 1 figur

Sub-au imaging of water vapour clouds around four Asymptotic Giant Branch stars

We present MERLIN maps of the 22-GHz H2O masers around four low-mass late-type stars (IK Tau U Ori, RT Vir and U Her), made with an angular resolution of ~ 15 milliarcsec and a velocity resolution of 0.1 km s-1. The H2O masers are found in thick expanding shells with inner radii ~ 6 to 16 au and outer radii four times larger. The expansion velocity increases radially through the H2O maser regions, with logarithmic velocity gradients of 0.5--0.9. IK Tau and RT Vir have well-filled H2O maser shells with a spatial offset between the near and far sides of the shell, which suggests that the masers are distributed in oblate spheroids inclined to the line of sight. U Ori and U Her have elongated poorly-filled shells with indications that the masers at the inner edge have been compressed by shocks; these stars also show OH maser flares. MERLIN resolves individual maser clouds, which have diameters of 2 -- 4 au and filling factors of only ~ 0.01 with respect to the whole H2O maser shells. The CSE velocity structure gives additional evidence the maser clouds are density bounded. Masing clouds can be identified over a similar timescale to their sound crossing time (~2 yr) but not longer. The sizes and observed lifetimes of these clouds are an order of magnitude smaller than those around red supergiants, similar to the ratio of low-mass:high-mass stellar masses and sizes. This suggests that cloud size is determined by stellar properties, not local physical phenomena in the wind.Comment: 21 pages, including 14 figures and 8 tables. Accepted for publication in MNRA

Aperiodic invariant continua for surface homeomorphisms

We prove that if a homeomorphism of a closed orientable surface S has no wandering points and leaves invariant a compact, connected set K which contains no periodic points, then either K=S and S is a torus, or $K$ is the intersection of a decreasing sequence of annuli. A version for non-orientable surfaces is given.Comment: 8 pages, to appear in Mathematische Zeitschrif

Fine forecasts: encouraging the media to include ultraviolet radiation information in summertime weather forecasts

Melanoma and skin cancer are largely attributable to over-exposure to solar ultraviolet radiation (UVR). Reports of UVR levels within media weather forecasts appear to be well received by the public and have good potential to communicate the need for appropriate sun protection to a broad audience. This study describes provision of UVR messages by New Zealand newspapers, radio and TV stations over a 4-year period, and examines the impact of an intervention which aimed to address media concerns about the financial costs of accessing UVR information for broadcast. Newspaper and radio presentation of UVR information increased immediately after these costs were removed; however, among radio stations it dropped in subsequent years. Among those media that were presenting UVR, this information was broadcast throughout the summer period and repeated throughout the day. Furthermore, most reports included concomitant, behavioral sun protection messages. At the final assessment (summer 2001/02), 66% of radio stations, both TV channels and 48% of newspapers reported UVR information in summertime weather reports. Efforts to further increase UVR presentation will need to address media concerns about time constraints on weather forecasts and media perceptions of poor audience demand or understanding of some UVR message