In this paper we present the first automatically constructed LASCO CME catalog, a result of the application of the Computer Aided CME Tracking software (CACTus) on the LASCO archive during the interval September 1997 -January 2007. We have studied the CME characteristics and have compared them with similar results obtained by manual detection (CDAW CME catalog). On average CACTus detects less than 2 events per day during solar minimum up to 8 events during maximum, nearly half of them being narrow (< 20 • ). Assuming a correction factor, we find that the CACTus CME rate is surprisingly consistent with CME rates found during the past 30 years. The CACTus statistics show that small scale outflow is ubiquitously observed in the outer corona. The majority of CACTus-only events are narrow transients related to previous CME activity or to intensity variations in the slow solar wind, reflecting its turbulent nature. A significant fraction (about 15%) of CACTus-only events were identified as independent events, thus not related to other CME activity. The CACTus CME width distribution is essentially scale invariant in angular span over a range of scales from 20 to 120 • while previous catalogues present a broad maximum around 30 • . The possibility that the size of coronal mass outflows follow a power law distribution could indicate that no typical CME size exists, i.e. that the narrow transients are not different from the larger well-defined CMEs.

Context. The paper is concerned with heating of the solar corona by nanoflares: a superposition of small transient events in which stored magnetic energy is dissipated by magnetic reconnection. It is proposed that heating occurs in the nonlinear phase of an ideal kink instability, where magnetic reconnection leads to relaxation to a state of minimum magnetic energy. Aims. The aim is to investigate the nonlinear aspects of magnetic relaxation on a current loop with zero net axial current. The dynamical processes leading to the establishment of a relaxed state are explored. The efficiency of loop heating is investigated. Methods. A 3D magnetohydrodynamic numerical code is used to simulate the evolution of coronal loops which are initially in ideally unstable equilibrium. The initial states have zero net current. The results are interpreted by comparison both with linear stability analysis and with helicity-conserving relaxation theory. Results. The disturbance due to the unstable mode is strongly radially confined when the loop carries zero net current. Strong current sheets are still formed in the nonlinear phase with dissipation of magnetic energy by fast reconnection. The nonlinear development consists first of reconnection in a large scale current sheet, which forms near the quasi-resonant surface of the equilibrium field. Subsequently, the current sheet extends and then fragments, leading to multiple reconnections and effective relaxation to a constant α field. Conclusions. Magnetic reconnection is triggered in the nonlinear phase of kink instability in loops with zero net current. Initially, reconnection occurs in a single current sheet, which then fragments into multiple reconnection sites, allowing almost full relaxation to the minimum energy state. The loop is heated to high temperatures throughout its volume.

Context. The heating of solar coronal plasma to millions of degrees is likely to be due to the superposition of many small energyreleasing events, known as nanoflares. Nanoflares dissipate magnetic energy through magnetic reconnection. Aims. A model has been recently proposed in which nanoflare-like heating naturally arises, with a sequence of dissipation events of various magnitudes. It is proposed that heating is triggered by the onset of ideal instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. The aim is to use numerical simulations to investigate this heating process. Methods. Three-dimensional magnetohydrodynamic numerical simulations of energy release are presented for a cylindrical coronal loop model. Initial equilibrium magnetic-field profiles are chosen to be linearly unstable, with a two-layer parameterisation of the current profile. The results are compared with calculations of linear instability, with line-tying, which are extended to account for a potential field layer surrounding the loop. The energy release is also compared with predictions that the field relaxes to a state of minimum magnetic energy with conserved magnetic helicity (a constant α force-free field). Results. The loop initially develops a helical kink, whose structure and growth rate are generally in accordance with linear stability theory, and subsequently a current sheet forms. During this phase, there is a burst of kinetic energy while the magnetic energy decays. A new relaxed equilibrium is established that corresponds quite closely to a constant α field. The fraction of stored magnetic energy released depends strongly on the initial current profile, which agrees with the predictions of relaxation theory. Conclusions. Energy dissipation events in a coronal loop are triggered by the onset of ideal kink instability. Magnetic energy is dissipated, leading to large or small heating events according to the initial current profile.

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Abstract.A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed "nanoflares". We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of α (the ratio of current density to field strength). Different initial α profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events.

We present numerical studies of the nonlinear, resistive magnetohydrodynamic (MHD) evolution of coronal loops. For these simulations we assume that the loops carry no net current, as might be expected if the loop had evolved due to vortex flows. Furthermore the initial equilibrium is taken to be a cylindrical flux tube with line-tied ends. For a given amount of twist in the magnetic field it is well known that once such a loop exceeds a critical length it becomes unstable to ideal MHD instabilities. The early evolution of these instabilities generates large current concentrations. Firstly we show that these current concentrations are consistent with the formation of a current sheet. Magnetic reconnection can only occur in the vicinity of these current concentrations and we therefore couple the resistivity to the local current density. This has the advantage of avoiding resistive diffusion in regions where it should be negligible. We demonstrate the importance of this procedure by comparison with simulations based on a uniform resistivity. From our numerical experiments we are able to estimate some observational signatures for unstable coronal loops. These signatures include: the timescale of the loop brightening; the temperature increase; the energy released and the predicted observable flow speeds. Finally we discuss to what extent these observational signatures are consistent with the properties of transient brightening loops.

Oscillations with toroidal mode number n=1 are ubiquitous in helicity injected spheromaks and spherical tokamaks, and play a crucial role in current drive. It has been proposed that these arise from a current driven instability of the open flux tube. Stability calculations are presented to confirm this, and they are compared with experimental data from the Spheromak Experiment (SPHEX) [M. Rusbridge et al., Plasma Phys. Control. Fusion 39, 683 (1997)]. The equilibria are modelled as piece-wise constant μ profile force-free plasmas with different values for the μ in the open (μc) and closed (μa) flux regions. A stability map in μc,μa space is then calculated. The SPHEX experimental data is also reduced to the same space both as a culmination of direct single point measurements of μ and as a time history of the reconstructed equilibrium from a particular shot. The results show a favorable comparison of the stability map with experiment, both in magnitude and shape. The effect of inserting a central current-carrying rod on the stability is also discussed.

Context. It is thought likely that vast numbers of nanoflares are responsible for the corona having a temperature of millions of degrees. Current observational technologies lack the resolving power to confirm the nanoflare hypothesis. An alternative approach is to construct a magnetohydrodynamic coronal loop model that has the ability to predict nanoflare energy distributions. Aims. This paper presents the initial results generated by a coronal loop model that flares whenever it becomes unstable to an ideal MHD kink mode. A feature of the model is that it predicts heating events with a range of sizes, depending on where the instability threshold for linear kink modes is encountered. The aims are to calculate the distribution of event energies and to investigate whether kink instability can be predicted from a single parameter. Methods. The loop is represented as a straight line-tied cylinder. The twisting caused by random photospheric motions is captured by two parameters, representing the ratio of current density to field strength for specific regions of the loop. Instability onset is mapped as a closed boundary in the 2D parameter space. Dissipation of the loop's magnetic energy begins during the nonlinear stage of the instability, which develops as a consequence of current sheet reconnection. After flaring, the loop evolves to the state of lowest energy where, in accordance with relaxation theory, the ratio of current to field is constant throughout the loop and helicity is conserved. Results. There exists substantial variation in the radial magnetic twist profiles for the loop states along the instability threshold. These results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Hence, an energy distribution of the nanoflares produced is collated. This paper also presents the calculated relaxation states and energy releases for all instability threshold points. Conclusions. The final energy distribution features two nanoflare populations that follow different power laws. The power law index for the higher energy population is more than sufficient for coronal heating.