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 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

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

Nonlinear dependence of ion-acoustic anomalous resistivity on electron drift velocity

Collisionless magnetic reconnection requires the violation of ideal MHD by various kinetic-scale effects. Recent research has highlighted the potential importance of wave-particle interactions by showing that Vlasov simulations of unstable ion-acoustic waves predict an anomalous resistivity that can be significantly higher in the nonlinear regime than the quasi-linear estimate. Here, we investigate the dependence on the initial electron drift velocity of the current driven ion-acoustic instability and its resulting anomalous resistivity. We examine the properties of statistical ensembles of 10 Vlasov simulations with real mass ratios for a range of drift velocities and for electron to ion temperature ratios of 0.9, 1, and 2, relevant to both solar and magnetospheric physics. We show that the ion-acoustic anomalous resistivity depends nonlinearly on the electron drift velocity for the low temperature ratios examined, in contrast to the linear dependence predicted by theory and commonly assumed in models of magnetic reconnection. Specifically we find that (1) anomalous resistivity is a power-law function of the electron drift velocity ( ), approximately with exponent , and (2) anomalous resistivity is a power-law function of the normalized drift velocity ( , approximately with exponent . An anomalous resistivity model consistent with our results could be important for simulations of magnetic reconnection in astrophysical plasmas