An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Transition region velocity oscillations observed by EUNIS-06

Spectroscopic measurements of NOAA AR 10871, obtained with the Extreme Ultraviolet Normal Incidence Spectrograph (EUNIS) sounding rocket instrument on 2006 April 12, reveal velocity oscillations in the He II 303.8 angstrom emission line formed at T approximate to 5; 10(4) K. The oscillations appear to arise in a bright active region loop arcade about 25 '' wide which crosses the EUNIS slit. The period of these transition region oscillations is 26 +/- 4 s, coupled with a velocity amplitude of +/- 10 km s(-1), detected over four complete cycles. Similar oscillations are observed in lines formed at temperatures up to T approximate to 4; 10(5) K, but we find no evidence for the coupling of these velocity oscillations with corresponding phenomena in the corona. We interpret the detected oscillations as originating from an almost purely adiabatic plasma, and infer that they are generated by the resonant transmission of MHD waves through the lower active region atmospheres. Through the use of seismological techniques, we establish that the observed velocity oscillations display wave properties most characteristic of fast body global sausage modes.

Mono-energetic ion beam acceleration in solitary waves during relativistic transparency using high-contrast circularly polarized short-pulse laser and nanoscale targets

In recent experiments at the Trident laser facility, quasi-monoenergetic ion beams have been obtained from the interaction of an ultraintense, circularly polarized laser with a diamond-like carbon target of nm-scale thickness under conditions of ultrahigh laser pulse contrast. Kinetic simulations of this experiment under realistic laser and plasma conditions show that relativistic transparency occurs before significant radiation pressure acceleration and that the main ion acceleration occurs after the onset of relativistic transparency. Associated with this transition are a period of intense ion acceleration and the generation of a new class of ion solitons that naturally give rise to quasi-monoenergetic ion beams. An analytic theory has been derived for the properties of these solitons that reproduces the behavior observed in kinetic simulations and the experiments. © 2011 American Institute of Physics.

A study of velocity fields in the transition region of ε Eri (K2 V)

Analyses of the widths and shifts of optically thin emission lines in the ultraviolet spectrum of the active dwarf e Eri (K2 V) are presented. The spectra were obtained using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer. The linewidths are used to find the non-thermal energy density and its variation with temperature from the chromosphere to the upper transition region. The energy fluxes that could be carried by Alfvén and acoustic waves are investigated, to test their possible roles in coronal heating. Acoustic waves do not appear to be a viable means of coronal heating. There is, in principle, ample flux in Alfvén waves, but detailed calculations of wave propagation are required before definite conclusions can be drawn concerning their viability. The high sensitivity and spectral resolution of the above instruments have allowed two-component Gaussian fits to be made to the profiles of the stronger transition region lines. The broad and narrow components that result share some similarities with those observed in the Sun, but in e Eri the broad component is redshifted relative to the narrow component and contributes more to the total line flux. The possible origins of the two components and the energy fluxes implied are discussed. On balance our results support the conclusion of Wood, Linsky & Ayres, that the narrow component is related to Alfvén waves reaching to the corona, but the origin of the broad component is not clear.

Multiwavelength studies of MHD waves in the solar chromosphere: An Overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.