R. O. Dendy

Self-organization of internal pedestals in a sandpile

The temperature profiles of magnetically confined plasmas can display distinctive longlived internal pedestals, caused by self-created transport barriers. This raises theoretical physics issues, distinct from the plasma physics modelling challenge, which concern the class of transport processes, physical principles, and control parameters that can generate such phenomenology. Here, we show that such structures can arise naturally through avalanching transport in a sandpile model. A single control parameter, that governs the spatial range of each rapid critical-gradient-triggered redistribution event, determines the occurrence and regularity of these effects.

Electron Preacceleration Mechanisms in the Foot Region of High Alfvénic Mach Number Shocks

High Mach number, collisionless perpendicular shocks are known to accelerate electrons to strongly relativistic energies by diffusive shock acceleration. This presupposes the existence of mildly relativistic electrons, whose preacceleration mechanism from lower ambient energies (the injection problem) remains an open question. Here a particle in cell simulation is used to investigate the preacceleration mechanism. Depending on the parameters of the upstream plasma and the shock velocity, the growth rate of instabilities in the foot of the shock can be significant, leading to the existence of nonlinear modes and the formation of electron phase space holes. It is found that these are associated with electron preacceleration, which can be divided into three phases. In the initial phase electrons are accelerated in the shock foot by the surfatron mechanism, which involves particle trapping in nonlinear wave modes. This mechanism is strongly linked to the existence of solitary electron phase space holes. The second phase is characterized by fluctuations in the magnetic field strength together with μ-conserving motion of the electrons. Finally, in the third phase the magnetic moment μ is no longer conserved, perhaps due to turbulent scattering processes. Energies up to Lorentz factors of 6 are achieved, for simulations in which the inflow kinetic energy of upstream electrons is 3.5 keV.

Numerical Simulations of Local Shock Reformation and Ion Acceleration in Supernova Remnants

The identification of preacceleration mechanisms for cosmic rays in supernova remnant shocks is an outstanding problem in astrophysics. Recent particle-in-cell (PIC) shock simulations have shown that the inclusion of the full electron kinetics yields non-time-stationary solutions, in contrast to previous hybrid (kinetic ions, fluid electrons) simulations. Here, by running a PIC code at high phase space resolution, we identify a new ion acceleration mechanism associated with the time dependence of the shock. From simple scaling arguments, these results suggest that for realistic parameters at supernova remnant shocks, such as an inflow speed of around 2.5 × 107 m s-1, an accelerated ion population is created at energies of order 10-20 MeV. These simulations indicate the importance of capturing the full self-consistent plasma dynamics in order to study preacceleration.

THE INFLUENCE OF ELECTRON TEMPERATURE AND MAGNETIC FIELD STRENGTH ON COSMIC-RAY INJECTION IN HIGH MACH NUMBER SHOCKS

Electron preacceleration from thermal to mildly relativistic energies in high Mach number shocks (the injection problem) is an outstanding issue in understanding synchrotron radiation from supernova remnants. At high Alfvenic Mach numbers, collisionless perpendicular shocks reflect a fraction of the upstream ions. This gives rise to two-stream instabilities, which in turn can accelerate ions. However, in astrophysical plasmas, the value of β—the ratio of kinetic pressure to magnetic pressure—is not well known. We have used a particle in cell simulation code to investigate the influence of β on the shock structure and on the electron acceleration (assuming thermodynamic equilibrium in the undisturbed plasma, β = βi = βe). Previous simulations at low values of β showed that the phase space distributions of electrons and ions became highly structured: characteristic holes appear in the electron phase space, and the shock dynamics exhibit reformation processes. However, we find that all these features disappear at higher β due to the high initial thermal velocity of the electrons. It follows that the electron cosmic-ray injection mechanism depends strongly on β, that is, on the electron temperature normalized to the magnetic field upstream.

Mutual information as a tool for identifying phase transitions in dynamical complex systems with limited data

We use a well-known model [T. Vicsek, Phys. Rev. Lett. 15, 1226 (1995)] for flocking, to test mutual information as a tool for detecting order-disorder transitions, in particular when observations of the system are limited. We show that mutual information is a sensitive indicator of the phase transition location in terms of the natural dimensionless parameters of the system which we have identified. When only a few particles are tracked and when only a subset of the positional and velocity components is available, mutual information provides a better measure of the phase transition location than the susceptibility of the data.

Mutual information between geomagnetic indices and the solar wind as seen by WIND: Implications for propagation time estimates

The determination of delay times of solar wind conditions at the sunward libration point to effects on Earth is investigated using mutual information. This measures the amount of information shared between two timeseries. We consider the mutual information content of solar wind observations, from WIND, and the geomagnetic indices. The success of five commonly used schemes for estimating interplanetary propagation times is examined. Propagation assuming a fixed plane normal at 45 degrees to the GSE x-axis (i.e. the Parker Spiral estimate) is found to give optimal mutual information. The mutual information depends on the point in space chosen as the target for the propagation estimate, and we find that it is maximized by choosing a point in the nightside rather than dayside magnetosphere. In addition, we employ recurrence plot analysis to visualize contributions to the mutual information, this suggests that it appears on timescales of hours rather than minutes.

The scaling properties of dissipation in incompressible isotropic three-dimensional magnetohydrodynamic turbulence

The statistical properties of the dissipation process constrain the analysis of large scale numerical simulations of three-dimensional incompressible magnetohydrodynamic (MHD) turbulence, such as those of Biskamp and Muller [Phys. Plasmas 7, 4889 (2000)]. The structure functions of the turbulent flow are expected to display statistical self-similarity, but the relatively low Reynolds numbers attainable by direct numerical simulation, combined with the finite size of the system, make this difficult to measure directly. However, it is known that extended self-similarity, which constrains the ratio of scaling exponents of structure functions of different orders, is well satisfied. This implies the extension of physical scaling arguments beyond the inertial range into the dissipation range. The present work focuses on the scaling properties of the dissipation process itself. This provides an important consistency check in that we find that the ratio of dissipation structure function exponents is that predicte...

Characterization and interpretation of strongly nonlinear phenomena in fusion, space and astrophysical plasmas

Much of plasma behaviour is governed by multiple distinct nonlinear processes, operating on a wide range of lengthscales and timescales, that are coupled together in innumerable feedback loops. Capturing and quantifying this nonlinear behaviour is crucial at all levels of description, ranging from individual events to global phenomenology. In recent years, a range of techniques derived from complex systems science has been applied successfully to nonlinear plasma datasets. The present paper reviews several of these techniques in the context of applications spanning fusion, space, solar and astrophysical plasmas. Topics include non-Gaussian probability density functions, notably extreme event distributions in fusion and astrophysics and power law distributions in the solar context; differencing and rescaling of fluctuation data, which has yielded information on the number of dominant plasma turbulent processes, and the spatiotemporal ranges over which they operate, in plasmas ranging from microquasar accretion discs to L-mode and dithering H-mode fusion plasmas in the MAST tokamak; quantitative measures of mutual information content and pattern repetition between causally linked but spatiotemporally separated nonlinear events in solar wind and magnetospheric plasmas; global statistics of full-disc solar irradiance; and ELMing, considered as a sequence of pulsed events, in H-mode fusion plasmas in the JET tokamak. These developments in nonlinear plasma data characterization provide fresh additional insights into the underlying plasma physics. They also provide new opportunities for comparing models with data, and with each other, and open avenues for the development of a more rigorous predictive capability in this field.

Finite Larmor radius effects on test particle transport in drift wave-zonal flow turbulence

The effect of finite Larmor radius on the transport of passive charged test particles moving in turbulent electrostatic fields is investigated. The turbulent field is governed by a flexible model which is able to produce turbulence where zonal flows are damped or free to self-generate. A subtle interplay between trapping in small scale vortices and entrainment in larger scale zonal flows determines the rate, character and Larmor radius dependence of the test particle transport. When zonal flows are damped, the transport is classically diffusive, with Gaussian statistics, and the rate of transport decreases with increasing Larmor radius. Once the Larmor radius is larger than the typical radius of the turbulent vortices, the rate of transport remains roughly constant. When zonal flows are allowed non-Gaussian statistics are observed. Radial transport (across the zones) is subdiffusive and decreases with the Larmor radius at a slower rate. Poloidal transport (along the zones), however, is superdiffusive and increases with small values of the Larmor radius.

The Signature of Evolving Turbulence in Quiet Solar Wind as Seen by Ulysses

Solar wind fluctuations, such as magnetic field or velocity, show power-law power spectra suggestive both of an inertial range of intermittent turbulence (with �� 5/3 exponent), and at lower frequencies, of fluctuations of coronal origin (with �� 1 exponent). The Ulysses spacecraft spent many months in the quiet fast solar wind above the Sun’s polar coronal holes in a highly ordered magnetic field. We use statistical analysis methods such as the generalized structure function (GSF) and extended self-similarity (ESS) to quantify the scaling of the moments of the probability density function of fluctuations in the magnetic field. The GSFs give power law scaling in the f � 1 range of the form hjy(t þ � ) � y(t)j m i� � � (m) , but ESS is required to reveal scaling in the inertial range, which is of the form hjy(t þ � ) � y(t)j m i�½ g(� )� � (m) .W e fi nd thatg(� ) is independent of spacecraft position and g(� ) � � � log10( ˜ k� ) .T he f � 1 scaling fluctuates with radial spacecraft position. This confirms that, whereas the f � 1 fluctuations are directly influenced by the corona, the inertial range fluctuations are consistent with locally evolving turbulence, but with an envelope g(� ), which captures the formation of the quiet fast solar wind. Subject headingg magnetic fields — solar wind — turbulence