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(Abridged for ArXiv) An injection of energy towards a magnetic null point can drive reversals of current sheet polarity leading to time-dependent Oscillatory Reconnection, which is a possible explanation of how periodic phenomena can be generated when reconnection occurs in the solar atmosphere. However, the details of what controls the period of these oscillations is poorly understood, despite being crucial in assessing whether OR can account for observed periodic behaviour. This paper aims to highlight that different types of reconnection reversal are supported about null points, and that these are distinct from the oscillation on the closed-boundary, linear systems considered in the 1990s. In particular, we explore the features of a nonlinear oscillation local to the null point, and examine the effect of resistivity and perturbation energy on the period, contrasting it to the linear case. It is found that in the linear systems, the inverse Lundquist number dictates the period, provided the perturbation energy is small relative to the inverse Lundquist number defined on the boundary, regardless of the broadband structure of the initial perturbation. However, when the perturbation energy exceeds the threshold required for 'nonlinear' null collapse to occur, a complex oscillation of the magnetic field is produced which is, at best, only weakly-dependent on the resistivity. The resultant periodicity is strongly influenced by the amount of free energy, with more energetic perturbations producing higher-frequency oscillations. Crucially, with regards to typical solar-based and astrophysical-based input energies, we demonstrate that the majority far exceed the threshold for nonlinearity to develop. This substantially alters the properties and periodicity of both null collapse and subsequent OR. Therefore, nonlinear regimes of OR should be considered in solar and astrophysical contexts., Comment: Accepted in A&A, 5 Figures (1 animated)

Implosive formation of current sheets is a fundamental plasma process. Previous studies focused on the early time evolution, while here our primary aim is to explore the longer-term evolution, which may be critical for determining the efficiency of energy release. To address this problem we investigate two closely-related problems, namely: (i) 1D, pinched anti-parallel magnetic fields and (ii) 2D, null point containing fields which are locally imbalanced ('null-collapse' or 'X-point collapse'). Within the framework of resistive MHD, we simulate the full nonlinear evolution through three distinct phases: the initial implosion, its eventual halting mechanism, and subsequent evolution post-halting. In a parameter study, we find the scaling with resistivity of current sheet properties at the halting time is in good agreement - in both geometries - with that inferred from a known 1D similarity solution. We find that the halting of the implosions occurs rapidly after reaching the diffusion scale by sudden Ohmic heating of the dense plasma within the current sheet, which provides a pressure gradient sufficient to oppose further collapse and decelerate the converging flow. This back-pressure grows to exceed that required for force balance and so the post-implosion evolution is characterised by the consequences of the current sheet `bouncing' outwards. These are: (i) the launching of propagating fast MHD waves (shocks) outwards and (ii) the width-wise expansion of the current sheet itself. The expansion is only observed to stall in the 2D case, where the pressurisation is relieved by outflow in the reconnection jets. In the 2D case, we quantify the maximum amount of current sheet expansion as it scales with resistivity, and analyse the structure of the reconnection region which forms post-expansion, replete with Petschek-type slow shocks and fast termination shocks., Comment: Published open access in Physics of Plasmas - go to main journal for animations https://doi.org/10.1063/1.5035489

Null collapse is an implosive process whereby MHD waves focus their energy in the vicinity of a null point, forming a current sheet and initiating magnetic reconnection. We consider, for the first time, the case of collapsing 3D magnetic null points in nonlinear, resistive MHD using numerical simulation, exploring key physical aspects of the system as well as performing a detailed parameter study. We find that within a particular plane containing the 3D null, the plasma and current density enhancements resulting from the collapse are quantitatively and qualitatively as per the 2D case in both the linear and nonlinear collapse regimes. However, the scaling with resistivity of the 3D reconnection rate - which is a global quantity - is found to be less favourable when the magnetic null point is more rotationally symmetric, due to the action of increased magnetic back-pressure. Furthermore, we find that with increasing ambient plasma pressure the collapse can be throttled, as is the case for 2D nulls. We discuss this pressure-limiting in the context of fast reconnection in the solar atmosphere and suggest mechanisms by which it may be overcome. We also discuss the implications of the results in the context of null collapse as a trigger mechanism of Oscillatory Reconnection, a time-dependent reconnection mechanism, and also within the wider subject of wave-null point interactions. We conclude that, in general, increasingly rotationally-asymmetric nulls will be more favourable in terms of magnetic energy release via null collapse than their more symmetric counterparts., Comment: Accepted in ApJ, will be published gold open access, refer to main journal

Here we detail the dynamic evolution of localised reconnection regions about three-dimensional (3D) magnetic null points by using numerical simulation. We demonstrate for the first time that reconnection triggered by the localised collapse of a 3D null point due to an external MHD wave involves a self-generated oscillation, whereby the current sheet and outflow jets undergo a reconnection reversal process during which back-pressure formation at the jet heads acts to prise open the collapsed field before overshooting the equilibrium into an opposite-polarity configuration. The discovery that reconnection at fully 3D nulls can proceed naturally in a time-dependent and periodic fashion is suggestive that oscillatory reconnection mechanisms may play a role in explaining periodicity in astrophysical phenomena associated with magnetic reconnection, such as the observed quasi-periodicity of solar and stellar flare emission. Furthermore, we find a consequence of oscillatory reconnection is the generation of a plethora of freely-propagating MHD waves which escape the vicinity of the reconnection region, Comment: Accepted in ApJ, will be published gold open access, refer to main journal for animated content

Previous theoretical considerations of electron beam relaxation in inhomogeneous plasmas have indicated that the effects of the irregular solar wind may account for the poor agreement of homogeneous modelling with the observations. Quasi-linear theory and Hamiltonian models based on Zakharov's equations have indicated that when a level of density fluctuations is above a given threshold, density irregularities act to de-resonate the beam-plasma interaction, restricting Langmuir wave growth on the expense of beam energy. This work presents the first fully kinetic particle-in-cell (PIC) simulations of beam relaxation under the influence of density irregularities. We aim to independently determine the influence of background inhomogeneity on the beam-plasma system, and to test theoretical predictions and alternative models using a fully kinetic treatment. We carry out 1D PIC simulations of a bump-on-tail unstable electron beam in the presence of increasing levels of background inhomogeneity using the fully electromagnetic, relativistic EPOCH PIC code. We find that in the case of homogeneous background plasma density, Langmuir wave packets are generated at the resonant condition and then quasi-liear relaxation leads to a dynamic increase of wavenumbers generated. No electron acceleration is seen - unlike in the inhomogeneous experiments, all of which produce high-energy electrons. For the inhomogeneous experiments we also observe the generation of backwards propagating Langmuir waves, which is shown directly to be due to the refraction of the packets off the density gradients. Our fully kinetic PIC simulations broadly confirm the findings of quasi-linear theory and the Hamiltonian model based on Zakharov's equations. Strong density fluctuations modify properties of excited Langmuir waves altering their dispersion properties., Comment: Animations can be found at https://jonathanthurgood.wordpress.com/myresearch/thurgood-and-tsiklauri-2016-movies/

Aims. The simulation of three-wave interaction based plasma emission, thought to be the underlying mechanism for Type III solar radio bursts, is a challenging task requiring fully-kinetic, multi-dimensional models. This paper aims to resolve a contradiction in past attempts, whereby some studies indicate that no such processes occur. Methods. We self-consistently simulate three-waved based plasma emission through all stages by using 2D, fully kinetic, electromagnetic particle-in-cell simulations of relaxing electron beams using the EPOCH2D code. Results. Here we present the results of two simulations; Run 1 (nb/n0 = 0.0057, vb/{\Delta}vb = vb/Ve = 16) and Run 2 (nb/n0 = 0.05, vb/{\Delta}vb = vb/Ve = 8), which we find to permit and prohibit plasma emission respectively. We show that the possibility of plasma emission is contingent upon the frequency of the initial electrostatic waves generated by the bump-in-tail instability, and that these waves may be prohibited from participating in the necessary three-wave interactions due to frequency conservation requirements. In resolving this apparent contradiction through a comprehensive analysis, in this paper we present the first self-consistent demonstration of fundamental and harmonic plasma emission from a single-beam system via fully kinetic numerical simulation. We caution against simulating astrophysical radio bursts using unrealistically dense beams (a common approach which reduces run time), as the resulting non-Langmiur characteristics of the initial wave modes significantly suppresses emission. Comparison of our results also indicates that, contrary to the suggestions of previous authors, an alternative plasma emission mechanism based on two counter-propagating beams is unnecessary in an astrophysical context.

There is intense interest in determining the precise contribution of Alfv\'enic waves propagating along solar structures to the problems of coronal heating and solar wind acceleration. Since the launch of SDO/AIA, it has been possible to resolve transverse oscillations in off-limb solar polar plumes and recently McIntosh et al. (2011, Nature, 475, 477) concluded that such waves are energetic enough to play a role in heating the corona and accelerating the fast solar wind. However, this result is based on comparisons to Monte Carlo simulations and confirmation via direct measurements is still outstanding. Thus, this letter reports on the first direct measurements of transverse wave motions in solar polar plumes. Over a 4 hour period, we measure the transverse displacements, periods and velocity amplitudes of 596 distinct oscillations observed in the 171 \AA channel of SDO/AIA. We find a broad range of non-uniformly distributed parameter values which are well described by log-normal distributions with peaks at $234$ km, $121$ s and $8$ km s$^{-1}$, and mean and standard deviations of $407\pm297$ km, $173\pm118$ s and $14\pm10$ km s$^{-1}$. Within standard deviations, our direct measurements are broadly consistent with previous results. However, accounting for the whole of our observed non-uniform parameter distribution we calculate an energy flux of $9-24$ W m$^{-2}$, which is $4-10$ times below the energy requirement for solar wind acceleration. Hence, our results indicate that transverse MHD waves as resolved by SDO/AIA cannot be the dominant energy source for fast solar wind acceleration in the open-field corona., Comment: 16 pages, 4 figures, 1 table

Context: MHD waves and magnetic null points are both prevalent in many astrophysical plasmas, including the solar atmosphere. Interaction between waves and null points has been implicated as a possible mechanism for localised heating events. Aims: Here we investigate the transient behaviour of the Alfven wave about fully 3D proper and improper 3D magnetic null points. Previously, the behaviour of fast magnetoacoustic waves at null points in 3D, cold MHD was considered by Thurgood & McLaughlin (Astronomy & Astrophysics, 2012, 545, A9). Methods: We introduce an Alfven wave into the vicinity of both proper and improper null points by numerically solving the ideal, $\beta=0$ MHD equations using the LARE3D code. A magnetic fieldline and flux-based coordinate system permits the isolation of resulting wave-modes and the analysis of their interaction. Results: We find that the Alfven wave propagates throughout the region and accumulates near the fan-plane, causing current build up. For different values of null point eccentricity, the qualitative behaviour changes only by the imposition of anisotropic pulse dilation, due to the differing rates at which fieldlines diverge from the spine. For all eccentricities, we find that the fast and Alfven waves are linearly decoupled. During the driving phase, an independently propagating fast wave is nonlinearly generated due to the ponderomotive force. Subsequently, no further excitation of fast waves occurs. Conclusions: We find that the key aspects of the theory of Alfv\'en waves about 2D null points extends intuitively to the fully 3D case; i.e. the wave propagates along fieldlines and thus accumulates at predictable parts of the topology. We also highlight that unlike in the 2D case, in 3D Alfven-wave pulses are always toroidal and thus any aspects of 2D Alfven-wave-null models that are pulse-geometry specific must be reconsidered in 3D., Comment: Accepted for publication in Astronomy & Astrophysics

Context : In the linear, {\beta}=0 MHD regime, the transient properties of MHD waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfv\'en waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfv\'en speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfv\'en waves about a 2D magnetic null point in nonlinear, {\beta}= 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfv\'en waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfv\'en wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfv\'en wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfv\'en wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfv\'en-speed profile (Grad c_A \neq 0) there is no further nonlinear generation of fast waves. Conclusions: We find that Alfv\'en waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances - effects absent in the linear regime - due to nonlinear magnetic pressure gradients., Comment: 7 pages. 4 figures, Pre-print: Accepted for publication in Astronomy & Astrophysics

Where spatial gradients in the amplitude of an Alfven wave are non-zero, a nonlinear magnetic-pressure gradient acts upon the medium (the ponderomotive force). We investigate the nature of such a force in inhomogeneous 2.5D MHD plasmas by analysing source terms in the nonlinear wave equations for the general case of inhomogeneous B and {\rho}, and consider supporting nonlinear numerical simulations. Our equations indicate there are two distinct classes of ponderomotive effect induced by Alfven waves in general 2.5D MHD, each with both a longitudinal and transverse manifestation; i) Geometric Effects: Gradients in the pulse geometry relative to the background magnetic field cause the wave to sustain cospatial disturbances, the longitudinal and transverse daughter disturbances - where we report on the transverse disturbance for the first time. ii) Grad (c_A) Effects: Where a pulse propagates through an inhomogeneous region (where the non-zero gradients in the Alfven-speed profile are non-zero), the nonlinear magnetic-pressure gradient acts to accelerate the plasma. Transverse gradients (phase mixing regions) excite independently propagating fast magnetoacoustic waves (generalising the result of Nakariakov et al. 1997, Solar Physics, 175, 93) and longitudinal gradients perturb along the field (thus creating static disturbances in {\beta} = 0, and slow waves in {\beta} \= 0). We additionally demonstrate that mode conversion due the nonlinear Lorentz force is a one-way process, and does not act as a mechanism to nonlinearly generate Alfven waves due to propagating magnetoacoustic waves. We conclude that these ponderomotive effects are induced by an Alfven wave propagating in any MHD medium, and have the potential to have significant consequences on the dynamics of energy transport and aspects of dissipation provided the system is sufficiently nonlinear and inhomogeneous., Comment: Pre-print, Accepted for publication in Solar Physics Feb 2013

Oscillatory reconnection is a time-dependent magnetic reconnection mechanism that naturally produces periodic outputs from aperiodic drivers. This paper aims to quantify and measure the periodic nature of oscillatory reconnection for the first time. We solve the compressible, resistive, nonlinear MHD equations using 2.5D numerical simulations. We identify two distinct periodic regimes: the impulsive and stationary phases. In the impulsive phase, we find the greater the amplitude of the initial velocity driver, the longer the resultant current sheet and the earlier its formation. In the stationary phase, we find that the oscillations are exponentially decaying and for driving amplitudes 6.3 - 126.2 km/s, we measure stationary-phase periods in the range 56.3 - 78.9 s, i.e. these are high frequency (0.01 - 0.02 Hz) oscillations. In both phases, we find that the greater the amplitude of the initial velocity driver, the shorter the resultant period, but note that different physical processes and periods are associated with both phases. We conclude that the oscillatory reconnection mechanism behaves akin to a damped harmonic oscillator., Comment: 8 pages, 4 figures

Context: Coronal magnetic null points have been implicated as possible locations for localised heating events in 2D models. We investigate this possibility about fully 3D null points. Aims: We investigate the nature of the fast magnetoacoustic wave about a fully 3D magnetic null point, with a specific interest in its propagation, and we look for evidence of MHD mode coupling and/or conversion to the Alfv\'en mode. Methods: A special fieldline and flux-based coordinate system was constructed to permit the introduction of a pure fast magnetoacoustic wave in the vicinity of proper and improper 3D null points. We considered the ideal, {\beta} = 0, MHD equations, which are solved using the LARE3D numerical code. The constituent modes of the resulting wave were isolated and identified using the special coordinate system. Numerical results were supported by analytical work derived from perturbation theory and a linear implementation of the WKB method. Results: An initially pure fast wave is found to be permanently decoupled from the Alfv\'en mode both linearly and nonlinearly for both proper and improper 3D null points. The pure fast mode also generates and sustains a nonlinear disturbance aligned along the equilibrium magnetic field. The resulting pure fast magnetoacoustic pulse has transient behaviour, which is found to be governed by the (equilibrium) Alfv\'en-speed profile, and a refraction effect focuses all the wave energy towards the null point. Conclusions: Thus, the main results from previous 2D work do indeed carry over to the fully 3D magnetic null points and, Comment: 11 pages, 6 figures

In this report, Thurgood Marshall Academy Public Charter High School (TMA) submits its Development Plan for the renovation and improvements to the Nichols Avenue School building and site, which will serve as the future home for their school. Working with an experienced planning, design and construction team, they have prepared a Development Plan that will revitalize this important corner, provide a state of the art educational environment for TMA and Savoy students, and provide recreational amenities to the youth and adults of the neighborhood.

This handbook presents current explanations of how each survey program of the National Center for Education Statistics (NCES) obtains and prepared the data it publishes. The handbook aims to provide users of NCES data with the most current information necessary to evaluate the suitability of the statistics for their needs, with a focus on the methodologies for survey design, data collection, and data processing. The handbook contains 18 chapters. Chapters 1 to 26 each focus on one of the 26 major NCES survey programs. Information in these chapters is presented in a uniform format of: (1) overview; (2) uses of data; (3) key concepts; (4) survey design; (5) data quality and comparability; (6) contact information; and (7) methodology and evaluation reports. These chapters are organized into these subject matter categories: (1) early childhood education survey; (2) elementary and secondary education surveys; (3) library surveys; (4) postsecondary and adult education surveys; (5) educational assessment surveys; and (6) household education surveys. The final chapters, 27 and 28, cover multiple surveys and survey systems, including the Fast Response Survey System. Five appendixes contain a glossary, information on how to obtain NCES publications, a list of tools for each survey, a list of Web sites for each survey, and an index. (SLD)