Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis

The Flare-energy Distributions Generated by Kink-unstable Ensembles of Zero-net-current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold

Modeling the Longitudinal Asymmetry in Sunspot Emergence -- the Role of the Wilson Depression

The distributions of sunspot longitude at first appearance and at disappearance display an east-west asymmetry that results from a reduction in visibility as one moves from disk centre to the limb. To first order, this is explicable in terms of simple geometrical foreshortening. However, the centre-to-limb visibility variation is much larger than that predicted by foreshortening. Sunspot visibility is also known to be affected by the Wilson effect: the apparent dish shape of the sunspot photosphere caused by the temperature-dependent variation of the geometrical position of the tau=1 layer. In this article we investigate the role of the Wilson effect on the sunspot appearance distributions, deducing a mean depth for the umbral tau=1 layer of 500 to 1500 km. This is based on the comparison of observations of sunspot longitude distribution and Monte Carlo simulations of sunspot appearance using different models for spot growth rate, growth time and depth of Wilson depression.Comment: 18 pages, 10 figures, in press (Solar Physics

Cost and Outcome of Behavioural Activation versus Cognitive Behavioural Therapy for Depression (COBRA): a randomised, controlled, non-inferiority trial

Background Depression is a common, debilitating, and costly disorder. Many patients request psychological therapy, but the best-evidenced therapy—cognitive behavioural therapy (CBT)—is complex and costly. A simpler therapy—behavioural activation (BA)—might be as effective and cheaper than is CBT. We aimed to establish the clinical efficacy and cost-effectiveness of BA compared with CBT for adults with depression. Methods In this randomised, controlled, non-inferiority trial, we recruited adults aged 18 years or older meeting Diagnostic and Statistical Manual of Mental Disorders IV criteria for major depressive disorder from primary care and psychological therapy services in Devon, Durham, and Leeds (UK). We excluded people who were receiving psychological therapy, were alcohol or drug dependent, were acutely suicidal or had attempted suicide in the previous 2 months, or were cognitively impaired, or who had bipolar disorder or psychosis or psychotic symptoms. We randomly assigned participants (1:1) remotely using computer-generated allocation (minimisation used; stratified by depression severity [Patient Health Questionnaire 9 (PHQ-9) score of <19 vs ≥19], antidepressant use, and recruitment site) to BA from junior mental health workers or CBT from psychological therapists. Randomisation done at the Peninsula Clinical Trials Unit was concealed from investigators. Treatment was given open label, but outcome assessors were masked. The primary outcome was depression symptoms according to the PHQ-9 at 12 months. We analysed all those who were randomly allocated and had complete data (modified intention to treat [mITT]) and also all those who were randomly allocated, had complete data, and received at least eight treatment sessions (per protocol [PP]). We analysed safety in the mITT population. The non-inferiority margin was 1·9 PHQ-9 points. This trial is registered with the ISCRTN registry, number ISRCTN27473954. Findings Between Sept 26, 2012, and April 3, 2014, we randomly allocated 221 (50%) participants to BA and 219 (50%) to CBT. 175 (79%) participants were assessable for the primary outcome in the mITT population in the BA group compared with 189 (86%) in the CBT group, whereas 135 (61%) were assessable in the PP population in the BA group compared with 151 (69%) in the CBT group. BA was non-inferior to CBT (mITT: CBT 8·4 PHQ-9 points [SD 7·5], BA 8·4 PHQ-9 points [7·0], mean difference 0·1 PHQ-9 points [95% CI −1·3 to 1·5], p=0·89; PP: CBT 7·9 PHQ-9 points [7·3]; BA 7·8 [6·5], mean difference 0·0 PHQ-9 points [–1·5 to 1·6], p=0·99). Two (1%) non-trial-related deaths (one [1%] multidrug toxicity in the BA group and one [1%] cancer in the CBT group) and 15 depression-related, but not treatment-related, serious adverse events (three in the BA group and 12 in the CBT group) occurred in three [2%] participants in the BA group (two [1%] patients who overdosed and one [1%] who self-harmed) and eight (4%) participants in the CBT group (seven [4%] who overdosed and one [1%] who self-harmed). Interpretation We found that BA, a simpler psychological treatment than CBT, can be delivered by junior mental health workers with less intensive and costly training, with no lesser effect than CBT. Effective psychological therapy for depression can be delivered without the need for costly and highly trained professionals. Funding National Institute for Health Research

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.Comment: This is a chapter in a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011

Flux-rope twist in eruptive flares and CMEs : due to zipper and main-phase reconnection

Funding: UK Science and Technology Facilities CouncilThe nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D “main phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (2π radians of twist), and then main phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist.PostprintPublisher PDFPeer reviewe

New Insights into White-Light Flare Emission from Radiative-Hydrodynamic Modeling of a Chromospheric Condensation

(abridged) The heating mechanism at high densities during M dwarf flares is poorly understood. Spectra of M dwarf flares in the optical and near-ultraviolet wavelength regimes have revealed three continuum components during the impulsive phase: 1) an energetically dominant blackbody component with a color temperature of T $\sim$ 10,000 K in the blue-optical, 2) a smaller amount of Balmer continuum emission in the near-ultraviolet at lambda $<$ 3646 Angstroms and 3) an apparent pseudo-continuum of blended high-order Balmer lines. These properties are not reproduced by models that employ a typical "solar-type" flare heating level in nonthermal electrons, and therefore our understanding of these spectra is limited to a phenomenological interpretation. We present a new 1D radiative-hydrodynamic model of an M dwarf flare from precipitating nonthermal electrons with a large energy flux of $10^{13}$ erg cm$^{-2}$ s$^{-1}$. The simulation produces bright continuum emission from a dense, hot chromospheric condensation. For the first time, the observed color temperature and Balmer jump ratio are produced self-consistently in a radiative-hydrodynamic flare model. We find that a T $\sim$ 10,000 K blackbody-like continuum component and a small Balmer jump ratio result from optically thick Balmer and Paschen recombination radiation, and thus the properties of the flux spectrum are caused by blue light escaping over a larger physical depth range compared to red and near-ultraviolet light. To model the near-ultraviolet pseudo-continuum previously attributed to overlapping Balmer lines, we include the extra Balmer continuum opacity from Landau-Zener transitions that result from merged, high order energy levels of hydrogen in a dense, partially ionized atmosphere. This reveals a new diagnostic of ambient charge density in the densest regions of the atmosphere that are heated during dMe and solar flares.Comment: 50 pages, 2 tables, 13 figures. Accepted for publication in the Solar Physics Topical Issue, "Solar and Stellar Flares". Version 2 (June 22, 2015): updated to include comments by Guest Editor. The final publication is available at Springer via http://dx.doi.org/10.1007/s11207-015-0708-

Why are flare ribbons associated with the spines of magnetic null points generically elongated?

Coronal magnetic null points exist in abundance as demonstrated by extrapolations of the coronal field, and have been inferred to be important for a broad range of energetic events. These null points and their associated separatrix and spine field lines represent discontinuities of the field line mapping, making them preferential locations for reconnection. This field line mapping also exhibits strong gradients adjacent to the separatrix (fan) and spine field lines, that can be analysed using the `squashing factor', $Q$. In this paper we make a detailed analysis of the distribution of $Q$ in the presence of magnetic nulls. While $Q$ is formally infinite on both the spine and fan of the null, the decay of $Q$ away from these structures is shown in general to depend strongly on the null-point structure. For the generic case of a non-radially-symmetric null, $Q$ decays most slowly away from the spine/fan in the direction in which $|{\bf B}|$ increases most slowly. In particular, this demonstrates that the extended, elliptical high-$Q$ halo around the spine footpoints observed by Masson et al. (Astrophys. J., 700, 559, 2009) is a generic feature. This extension of the $Q$ halos around the spine/fan footpoints is important for diagnosing the regions of the photosphere that are magnetically connected to any current layer that forms at the null. In light of this, we discuss how our results can be used to interpret the geometry of observed flare ribbons in `circular ribbon flares', in which typically a coronal null is implicated. We conclude that both the physics in the vicinity of the null and how this is related to the extension of $Q$ away from the spine/fan can be used in tandem to understand observational signatures of reconnection at coronal null points.Comment: Pre-print version of article accepted for publication in Solar Physic

Imaging Observations of Quasi-Periodic Pulsatory Non-Thermal Emission in Ribbon Solar Flares

Using RHESSI and some auxiliary observations we examine possible connections between spatial and temporal morphology of the sources of non-thermal hard X-ray (HXR) emission which revealed minute quasi-periodic pulsations (QPPs) during the two-ribbon flares on 2003 May 29 and 2005 January 19. Microwave emission also reveals the same quasi-periodicity. The sources of non-thermal HXR emission are situated mainly inside the footpoints of the flare arcade loops observed by the TRACE and SOHO instruments. At least one of the sources moves systematically both during the QPP-phase and after it in each flare that allows to examine the sources velocities and the energy release rate via the process of magnetic reconnection. The sources move predominantly parallel to the magnetic inversion line or the appropriate flare ribbon during the QPP-phase whereas the movement slightly changes to more perpendicular regime after the QPPs. Each QPP is emitted from its own position. It is also seen that the velocity and the energy release rate don't correlate well with the flux of the HXR emission calculated from the sources. The sources of microwaves and thermal HXRs are situated near the apex of the loop arcade and are not stationary either. Almost all QPPs and some spikes of HXR emission during the post-QPP-phase reveal the soft-hard-soft spectral behavior indicating separate acts of electrons acceleration and injection, rather than modulation of emission flux by some kinds of magnetohydrodynamic (MHD) oscillations of coronal loops. In all likelihood, the flare scenarios based on the successively firing arcade loops are more preferable to interpret the observations, although we can not conclude exactly what mechanism forces these loops to flare up.Comment: 22 pages, 10 figure