Magnetocentrifugal Winds in 3D: Nonaxisymmetric Steady State

Outflows can be loaded and accelerated to high speeds along rapidly rotating, open magnetic field lines by centrifugal forces. Whether such magnetocentrifugally driven winds are stable is a longstanding theoretical problem. As a step towards addressing this problem, we perform the first large-scale 3D MHD simulations that extend to a distance $\sim 10^2$ times beyond the launching region, starting from steady 2D (axisymmetric) solutions. In an attempt to drive the wind unstable, we increase the mass loading on one half of the launching surface by a factor of $\sqrt{10}$, and reduce it by the same factor on the other half. The evolution of the perturbed wind is followed numerically. We find no evidence for any rapidly growing instability that could disrupt the wind during the launching and initial phase of propagation, even when the magnetic field of the magnetocentrifugal wind is toroidally dominated all the way to the launching surface. The strongly perturbed wind settles into a new steady state, with a highly asymmetric mass distribution. The distribution of magnetic field strength is, in contrast, much more symmetric. We discuss possible reasons for the apparent stability, including stabilization by an axial poloidal magnetic field, which is required to bend field lines away from the vertical direction and produce a magnetocentrifugal wind in the first place.Comment: 10 pages, 2 figures, accepted for publication in ApJ

Unstable coronal loops : numerical simulations with predicted observational signatures

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 unstableto 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.Comment: 13 pages, 9 figure

On the role of injection in kinetic approaches to nonlinear particle acceleration at non-relativistic shock waves

The dynamical reaction of the particles accelerated at a shock front by the first order Fermi process can be determined within kinetic models that account for both the hydrodynamics of the shocked fluid and the transport of the accelerated particles. These models predict the appearance of multiple solutions, all physically allowed. We discuss here the role of injection in selecting the real solution, in the framework of a simple phenomenological recipe, which is a variation of what is sometimes referred to as thermal leakage. In this context we show that multiple solutions basically disappear and when they are present they are limited to rather peculiar values of the parameters. We also provide a quantitative calculation of the efficiency of particle acceleration at cosmic ray modified shocks and we identify the fraction of energy which is advected downstream and that of particles escaping the system from upstream infinity at the maximum momentum. The consequences of efficient particle acceleration for shock heating are also discussed

Periodic traveling compression regions during quiet geomagnetic conditions and their association with ground Pi2

Recently, Keiling et al. (2006) showed that periodic (~90 s) traveling compression regions (TCRs) during a substorm had properties of Pi2 pulsations, prompting them to call this type of periodic TCRs "lobe Pi2". It was further shown that time-delayed ground Pi2 had the same period as the lobe Pi2 located at 16 <I>R<sub>E</sub></I>, and it was concluded that both were remotely driven by periodic, pulsed reconnection in the magnetotail. In the study reported here, we give further evidence for this association by reporting additional periodic TCR events (lobe Pi2s) at 18 <I>R<sub>E</sub></I> all of which occurred in succession during a geomagnetically very quiet, non-substorm period. Each quiet-time periodic TCR event occurred during an interval of small <I>H</I>-bay-like ground disturbance (<40 nT). Such disturbances have previously been identified as poleward boundary intensifications (PBIs). The small <I>H</I> bays were superposed by Pi2s. These ground Pi2s are compared to the TCRs in the tail lobe (Cluster) and both magnetic pulsations and flow variations at 9 <I>R<sub>E</sub></I> inside the plasma sheet (Geotail). The main results of this study are: (1) Further evidence is given that periodic TCRs in the tail lobe at distances of 18 <I>R<sub>E</sub></I> and ground Pi2 are related phenomena. In particular, it is shown that both had the same periodicity and occurred simultaneously (allowing for propagation time delays) strongly suggesting that both had the same periodic source. Since the TCRs were propagating Earthward, this source was located in the outer magnetosphere beyond 18 <I>R<sub>E</sub></I>. (2) The connection of periodic TCRs and ground Pi2 also exists during very quiet geomagnetic conditions with PBIs present in addition to the previous result (Keiling et al., 2006) which showed this connection during substorms. (3) Combining (1) and (2), we conclude that the frequency of PBI-associated Pi2 is controlled in the outer magnetosphere as opposed to the inner magnetosphere. We propose that this mechanism is pulsed reconnection based on previous results which combined modeled results and observations of substorm-related periodic TCRs and ground Pi2. (4) We show that TCRs with small compression ratios (ΔB/B<1%) can be useful in the study of magnetotail dynamics and we argue that other compressional fluctuations with ΔB/B<1% (without having all of the characteristic signatures of TCRs) seen in the tail lobe could possibly be related to the same mechanism that generates TCR with ΔB/B>1% (which are more commonly studied). (5) Finally, it is noted that both quiet time and substorm-related periodic TCRs had remarkably similar periods in spite of the drastically different geomagnetic conditions prevailing during the events which poses the important question of what causes this periodicity under these different conditions

A cosmic ray current driven instability in partially ionised media

We investigate the growth of hydromagnetic waves driven by streaming cosmic rays in the precursor environment of a supernova remnant shock. It is known that transverse waves propagating parallel to the mean magnetic field are unstable to anisotropies in the cosmic ray distribution, and may provide a mechanism to substantially amplify the ambient magnetic field. We quantify the extent to which temperature and ionisation fractions modify this picture. Using a kinetic description of the plasma we derive the dispersion relation for a collisionless thermal plasma with a streaming cosmic ray current. Fluid equations are then used to discuss the effects of neutral-ion collisions. We calculate the extent to which the environment into which the cosmic rays propagate influences the growth of the magnetic field, and determines the range of possible growth rates. If the cosmic ray acceleration is efficient, we find that very large neutral fractions are required to stabilise the growth of the non-resonant mode. For typical supernova parameters in our galaxy, thermal effects do not significantly alter the growth rates. For weakly driven modes, ion-neutral damping can dominate over the instability at more modest ionisation fractions. In the case of a supernova shock interacting with a molecular clouds, such as in RX J1713.7-3946, with high density and low ionisation, the modes can be rapidly damped.Comment: 5 pages, 2 figures, accepted to A&A. Corrections made. Applications adde

Nonlinear theory of mirror instability near threshold

An asymptotic model based on a reductive perturbative expansion of the drift kinetic and the Maxwell equations is used to demonstrate that, near the instability threshold, the nonlinear dynamics of mirror modes in a magnetized plasma with anisotropic ion temperatures involves a subcritical bifurcation,leading to the formation of small-scale structures with amplitudes comparable with the ambient magnetic field

The transport of cosmic rays in self-excited magnetic turbulence

The process of diffusive shock acceleration relies on the efficacy with which hydromagnetic waves can scatter charged particles in the precursor of a shock. The growth of self-generated waves is driven by both resonant and non-resonant processes. We perform high-resolution magnetohydrodynamic simulations of the non-resonant cosmic-ray driven instability, in which the unstable waves are excited beyond the linear regime. In a snapshot of the resultant field, particle transport simulations are carried out. The use of a static snapshot of the field is reasonable given that the Larmor period for particles is typically very short relative to the instability growth time. The diffusion rate is found to be close to, or below, the Bohm limit for a range of energies. This provides the first explicit demonstration that self-excited turbulence reduces the diffusion coefficient and has important implications for cosmic ray transport and acceleration in supernova remnants.Comment: 8 pages, 8 figures, accepted for publication in MNRA

Correlation functions of small-scale fluctuations of the interplanetary magnetic field

The Interplanetary Magnetic Field shows complex spatial and temporal variations. Single spacecraft measurements reveal only a one dimensional section of this rich four dimensional phenomenon. Multi-point measurements of the four Cluster spacecraft provide a unique tool to study the spatiotemporal structure of the field. Using Cluster data we determined three dimensional correlation functions of the fluctuations. By means of the correlation function one can describe and measure field variations. Our results can be used to verify theoretical predictions, to understand the formation and nature of solar wind turbulence. We found that the correlation length varies over almost six orders of magnitude. The IMF turbulence shows significant anisotropy with two distinct populations. In certain time intervals the ratio of the three axes of the correlation ellipse is 1/2.2/6 while in the remaining time we found extremely high correlation along one axis. We found favoured directions in the orientation of the correlation ellipsoids.Comment: accepted to Solar Physics on June 14, 2010. 10 pages, 8 figure

Three-Dimensional Simulations of Jets from Keplerian Disks: Self--Regulatory Stability

We present the extension of previous two-dimensional simulations of the time-dependent evolution of non-relativistic outflows from the surface of Keplerian accretion disks, to three dimensions. The accretion disk itself is taken to provide a set of fixed boundary conditions for the problem. The 3-D results are consistent with the theory of steady, axisymmetric, centrifugally driven disk winds up to the Alfv\'en surface of the outflow. Beyond the Alfv\'en surface however, the jet in 3-D becomes unstable to non-axisymmetric, Kelvin-Helmholtz instabilities. We show that jets maintain their long-term stability through a self-limiting process wherein the average Alfv\'enic Mach number within the jet is maintained to order unity. This is accomplished in at least two ways. First, poloidal magnetic field is concentrated along the central axis of the jet forming a ``backbone'' in which the Alfv\'en speed is sufficiently high to reduce the average jet Alfv\'enic Mach number to unity. Second, the onset of higher order Kelvin-Helmholtz ``flute'' modes (m \ge 2) reduce the efficiency with which the jet material is accelerated, and transfer kinetic energy of the outflow into the stretched, poloidal field lines of the distorted jet. This too has the effect of increasing the Alfv\'en speed, and thus reducing the Alfv\'enic Mach number. The jet is able to survive the onset of the more destructive m=1 mode in this way. Our simulations also show that jets can acquire corkscrew, or wobbling types of geometries in this relatively stable end-state, depending on the nature of the perturbations upon them. Finally, we suggest that jets go into alternating periods of low and high activity as the disappearance of unstable modes in the sub-Alfv\'enic regime enables another cycle of acceleration to super-Alfv\'enic speeds.Comment: 57 pages, 22 figures, submitted to Ap

Motion of flux transfer events: a test of the Cooling model

The simple model of reconnected field line motion developed by Cooling et al. (2001) has been used in several recent case studies to explain the motion of flux transfer events across the magnetopause. We examine 213 FTEs observed by all four Cluster spacecraft under a variety of IMF conditions between November 2002 and June 2003, when the spacecraft tetrahedron separation was ~5000 km. Observed velocities were calculated from multi-spacecraft timing analysis, and compared with the velocities predicted by the Cooling model in order to check the validity of the model. After excluding three categories of FTEs (events with poorly defined velocities, a significant velocity component out of the magnetopause surface, or a scale size of less than 5000 km), we were left with a sample of 118 events. 78% of these events were consistent in both direction of motion and speed with one of the two model de Hoffmann-Teller (dHT) velocities calculated from the Cooling model (to within 30° and a factor of two in the speed). We also examined the plasma signatures of several magnetosheath FTEs; the electron signatures confirm the hemisphere of connection indicated by the model in most cases. This indicates that although the model is a simple one, it is a useful tool for identifying the source regions of FTEs