Particle acceleration in the presence of weak turbulence at an X-type neutral point

We simulate the likely noisy situation near a reconnection region by superposing many 2D linear reconnection eigenmodes. The superposition of modes on the steady state X-type magnetic field creates multiple X- and O-type neutral points close to the original neutral point and so increases the size of the non-adiabatic region. We study test particle trajectories of initially thermal protons in these fields. Protons become trapped in this region and are accelerated by the turbulent electric field to energies up to 1 MeV in time scales relevant to solar flares. Higher energies are achieved due to the interaction of particles with increasingly turbulent electric and magnetic fields

Effect of binary collisions on electron acceleration in magnetic reconnection

Context. The presence of energetic X-ray sources in the solar corona indicates there are additional transport effects in the acceleration region. A prime method of investigation is to add collisions into models of particle behaviour at the reconnection region.<p></p> Aims. We investigate electron test particle acceleration in a simple model of an X-type reconnection region. In particular, we explore the possibility that collisions will cause electrons to re-enter the acceleration more frequently, in turn causing particles to be accelerated to high energies.<p></p> Methods. The deterministic (Lorentz) description of particle gyration and acceleration has been coupled to a model for the effects of collisions. The resulting equations are solved numerically using Honeycutt’s extension of the RK4 method to stochastic differential equations. This approach ensures a correct description of collisional energy loss and pitch-angle scattering combined with a sufficiently precise description of gyro-motion and acceleration.<p></p> Results. Even with initially mono-energetic electrons, the competition between collisions and acceleration results in a distribution of electron energies. When realistic model parameters are used, electrons achieve X-ray energies. A possible model for coronal hard X-ray sources is indicated. Conclusions. Even in competition with energy losses, pitch-angle scattering results in a small proportion of electrons reaching higher energies than they would in a collisionless situation.<p></p&gt

Particle Acceleration in Dynamical Collisionless Reconnection

The work presented in this thesis is concerned with how particle acceleration can take place in the context of dynamical magnetic reconnection in collisionless coronal plasmas. The energy production mechanism in solar flares has been a long standing problem of solar physics. The mechanism that provides the energy during solar flares is thought to be magnetic reconnection. However, timescales from different models disagree. Most rnagnetohydrodynamic models do not explain the high energy particles observed during solar flares and most collisionless models fail in that they do not account for the dynamic evolution of the solar flare environment. This thesis is divided in seven chapters. I will summarise each chapter individually. Chapter 1 contains a brief overview of the properties of the Sun and the structure of its atmosphere. Then follows a much more detailed discussion of energetic phenomena in the Sun concentrating primarily on solar flares and solar noise storms, and their manifestations in the electromagnetic spectrum and production of high energy particles. An introduction to magnetic reconnection is given in Chapter 2. Magnetic reconnection is defined as the process whereby plasma flows across a surface that separates regions containing topologically different magnetic field lines. We briefly discuss some of the most important models for magnetic reconnection. The models are divided in hydro- magnetic and collisionless models. We also discuss mechanism for particle acceleration in cosmic plasmas. The mechanisms of particle acceleration are: diffusive shock acceleration, stochastic acceleration and electric field acceleration. I review some mechanism of particle accelaration in X-type neutral points and their implications for energy distributions produced. In Chapter 3 we present the results of a non self-consistent calculation for collisionless magnetic reconnection. First we assume the form of the electric and magnetic fields, a procedure which is not necessarily self-consistent. The magnetic field is taken to have an X-type neutral point. Two cases for the imposed electric fields are considered, one constant and the other time-varying. The amplitude of the electric field is treated as a parameter. We calculate the particle orbits in these fields and the resulting energy distributions and show that protons and electrons may gain relativistic energies in times < 15 for plausible (small) electric field amplitudes and active region magnetic fields. We note the effectiveness of acceleration of protons and electrons varies according to the frequency of oscillation invoked. It seems that electrons, when they are accelerated, are accelerated more rapidly than protons, although numerical limitations prevented us from investigating this possibility in full. Protons are accelerated to 7 ray producing energies. In Chapter 4 we formally derive an analytical description for the time and space dependence of a linear incompressible, azimuthally symmetric disturbance propagating in a medium with a neutral point. In deriving the expression for the magnetic disturbance we follow Craig and McClymont (1991) fairly closely. There are however the important differences between our treatment and theirs: we recast the problem in dimensionless variables for consistency with the integration of the particle orbits, and introduce a slight restriction on the possible modes of interest. The latter has the consequence that the final, hypergeometric function form of the solution is always exact (cf. Craig, 1994). Also we give heavier emphasis than other work to the numerical evaluation of the eigenfunctions. We use this description to study the detailed form and behaviour of reconnective eigenvalues, as a preliminary step in addressing the problem of the particle orbits. In the Chapter 5 we study particle orbits in the presence of such a disturbance. A general feature of the orbits is that particles remain relatively close to the neutral point during the integration time of 1 second. The particles that are accelerated to high energies are those that are trapped close to neutral point area. This happens for specific values of the 'resistivity' owing to the spatial form of the electric and magnetic field perturbation. Particle orbits are calculated for the fundamental and higher eigenmodes. In Chapter 6 we attempt to match the MHD and test particle calculations. To do this we compare the energy loss of the wave during 1 second and the energy gained by the particles during the same time. For all the vaues of the resistivity investigated, the wave loses energy much faster than the particles gain energy. The calculations presented in this Chapter force us to re-examine the nature of 'resistivity'. Particles trapped for long periods near the neutral point are freely accelerated and clearly extract energy from the wave. However, they do not contribute to the resistivity. Despite the difficulties in defining the 'correct' value of the 'resistivity', we have demonstrated that the passage of such a reconnective disturbance may accelerate protons to ? ray producing energies, and certainly to energies where they could play a role in energy transport

Particle interactions with single or multiple 3D solar reconnecting current sheets

The acceleration of charged particles (electrons and protons) in flaring solar active regions is analyzed by numerical experiments. The acceleration is modelled as a stochastic process taking place by the interaction of the particles with local magnetic reconnection sites via multiple steps. Two types of local reconnecting topologies are studied: the Harris-type and the X-point. A formula for the maximum kinetic energy gain in a Harris-type current sheet, found in a previous work of ours, fits well the numerical data for a single step of the process. A generalization is then given approximating the kinetic energy gain through an X-point. In the case of the multiple step process, in both topologies the particles' kinetic energy distribution is found to acquire a practically invariant form after a small number of steps. This tendency is interpreted theoretically. Other characteristics of the acceleration process are given, such as the mean acceleration time and the pitch angle distributions of the particles.Comment: 18 pages, 9 figures, Solar Physics, in pres

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

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

Fluctuating electric field particle acceleration at a magnetic field null point

Release of stored magnetic energy via particle acceleration is a characteristic feature of astrophysical plasmas. Magnetic reconnection is one of the primary candidate mechanisms for releasing non-potential energy from magnetized plasmas. A collisionless magnetic reconnection scenario could provide both the energy release mechanism and the particle accelerator in flares. We studied particle acceleration consequences from fluctuating (in-time) electric fields superposed on an X-type magnetic field in collisionless hot solar plasma. This system is chosen to mimic generic features of dynamic reconnection, or the reconnective dissipation of a linear disturbance. Time evolution of thermal particle distributions are obtained by numerically integrating particle orbits. A range of frequencies of the electric field is used, representing a turbulent range of waves. Depending on the frequency and amplitude of the electric field, electrons and ions are accelerated to different degrees and often have energy distributions of bimodal form. Protons are accelerated to gamma-ray producing energies and electrons to and above hard X-ray producing energies in timescales of less than 1 second. The acceleration mechanism could be applicable to all collisionless plasmas

Particle acceleration by fluctuating electric fields at a magnetic field null point

Particle acceleration consequences from fluctuating electric ields superposed on an X-type magnetic field in collisionless solar plasma are studied. Such a system is chosen to mimic generic features of dynamic reconnection, or the reconnective dissipation of a linear disturbance. Explore numerically the consequences for charged particle distributions of fluctuating electric ields superposed on an X-type magnetic field. Particle distributions are obtained by numerically integrating individual charged particle orbits when a time varying electric field is superimposed on a static X-type neutral point. This configuration represents the effects of the passage of a generic MHD disturbance through such a system. Different frequencies of the electric field are used, representing different possible types of wave. The electric field reduces with increasing distance from the X-type neutral point as in linear dynamic magnetic reconnection. The resulting particle distributions have properties that depend on the amplitude and frequency of the electric field. In many cases a bimodal form is found. Depending on the timescale for variation of the electric field, electrons and ions may be accelerated to different degrees and often have energy distributions of different forms. Protons are accelerated to gamma-ray producing energies and electrons to and above hard X-ray producing energies in timescales of 1 second. The acceleration mechanism is possibly important for solar flares and solar noise storms but is also applicable to all collisionless plasmas