- Seminars at CIPS

In a series of experiments magnetic flux ropes as well as long and narrow current sheets are generated in a background magnetoplasma capable of supporting Alfen waves. The flux ropes are kink unstable and smash into one another as they move. When they do, reconnection events occur. The current sheet rapidly tears into a series of magnetic islands when viewed in a cross-sectional plane, but are three-dimensional flux ropes. At the onset of the current, magnetic field line reconnection is observed between the flux ropes. The sheet on the whole is kink unstable, and after kinking exhibits large scale, low frequency (f<<fci) rotation about the background field with an amplitude that grows with distance from the source of the current. Three-dimensional data (at up to 50,000 spatial locations and thousands of time steps) of the magnetic and total electric field is acquired throughout the duration of the two experiments and the parallel resistivity is derived from it. The parallel resistivity, for the most part, is not largest in the reconnection regions; rather it peaks in the neighborhood of the current gradient. Quasi-separatrix layers - regions in which magnetic field lined rapidly diverge - are observed in both cases. The dynamics of multiple ropes is similar to that of the ropes that the current sheet tears into. The permutation entropy is calculated from time series of the magnetic field or flow data and used to calculate the Jensen Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or chaotic. The complexity is a function of space and time. The entropy and complexity change in space and time, which reflects the change, and possibly type, of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion, Levi flights...) and underlying dynamical process. The power spectra of much of the magnetic field and flow data is exponential and Lorentzian structures in the time domain are embedded within them.

Solar flares produce non-thermal electrons with energies up to tens of MeVs. To understand the origin of energetic electrons, coronal hard X-ray (HXR) sources, in particular above-the-looptop sources, have been studied extensively. However, it still remains unclear how energies are partitioned between thermal and non-thermal electrons within the above-the-looptop source. Here we show that the kappa distribution, when compared to conventional spectral models, can better characterize the above-the-looptop HXRs (>~ 15 keV) observed in four different cases. Based on the kappa distribution model, we found that the 2012 July 19 flare showed the largest non-thermal fraction of electron energies about 50%, suggesting equipartition of energies. Considering the results of particle-in-cell simulations, as well as density estimates of the four cases studied, we propose a scenario in which electron acceleration is achieved primarily by collisionless magnetic reconnection, but the electron energy partition in the above-the-looptop source depends on the source density. In low-density above-the-looptop regions (few times 10^9 cm^-3 ), the enhanced non-thermal tail can remain and a prominent HXR source is created, whereas in higher densities (>10^10 cm^-3), the non-thermal tail is suppressed or thermalized by Coulomb collisions.

Nonlinear energy fluxes are known to redistribute the energies according to the detailed conservation laws. For example, the energy produced in the linearly unstable plasma is transported by the nonlinear flux toward larger or smaller scales where it is dissipated by the viscosity. As such a role is crucial in sustaining a steady state, most analyses on the flux focus in terms of the transport. Yet, there is another side of the nonlinear flux altering the temporal response of the plasma from the linear reaction. In this seminar the features of this part of the flux, to be called in the presentation as non-transporting flux (NTF), are highlighted in the context of the electrostatic resistive-drift fluid turbulence. Simulations are performed for three cases of adiabaticity parameter of the Hasegawa-Wakatani model. When the zonal flow ( ) is not present, the time scales of the energy-transporting flux and the NTF are of the same order. The energy NTF is found to be anisotropic and advective in the sense that it is approximately proportional to the gradient of the energy in the direction of the Fourier space with the proportionality coefficient being dimensionally advecting velocity. When the zonal flow is allowed to be excited, the time scale of the NTF becomes much shorter than that of the energy- redistributing flux as the plasma comes to be adiabatic where the zonal part of the energy is much larger than the non-zonal counterpart. Details will be discussed at the presentation.

We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron MHD (EMHD). We argue there is no energy principle in EMHD: any stationary closed configuration is neutrally stable.

We derive the Hamiltonian formulation of EMHD in a canonical form; we calculate the matrix elements for the three-wave interaction of whistlers and show that (i) harmonic whistlers are exact non-linear solutions; (ii) co-linear whistlers do not interact (including counter- propagating); (iii) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (iv) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles.

We solve numerically the kinetic equation and show that, generally, the EMHD cascade is non-univeral - it depends on the forcing and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade ~ k^?2. The cascade remains weak (not critically- balanced). The cascade is UV-local, while the infrared locality is weakly (logarithmically) violated.

Fluctuations in magnetized laboratory plasmas are ubiquitous and complex. In addition to deleterious effects, like increasing heat and particle transport in magnetic fusion energy devices, fluctuations also provide a diagnostic opportunity. Identification of a fluctuation with a particular wave or instability gives detailed information about the properties of the underlying plasma. In this work, diagnostics and spectral analysis techniques for fluctuations are developed and applied to two different laboratory plasma experiments.

Spectral properties of coherent waves in an argon plasma column are examined using fluctuation data from fast imaging. Experimental dispersion relation estimates are constructed from imaging data alone using a cross-spectral-density technique. Electron drift waves are identified by comparison with theoretical dispersion curves, and a tentative match of a low-frequency spectral feature to Kelvin-Helmholtz-driven waves is presented.

Transient fluctuations are examined in a local spheromak merging experiment using a multi-channel magnetic probe. A histogram cross-spectral analysis technique allows experimental dispersion relation estimates to be made from magnetic measurements. Hints of waves in the range of ion-cyclotron frequency harmonics are observed in conjunction with merging events.

MHD instabilities with poloidal and toroidal harmonics m=1 and n=1 have been a paradigm for the study of toroidal effects in magnetically confined fusion plasmas. The linear perturbation theory of the 1/1 internal kink has demonstrated the fundamental importance of toroidal mode coupling to poloidal harmonics m=2,0 and higher at n=1 for incompressible and compressible modes. Nonlinear MHD simulations of the resistive internal kink and sawtooth crash routinely include compressibility and mode coupling, but most analysis has been limited to reduced MHD (RMHD), which drops both effects. A new approach shows that compressible and toroidal effects at low resistivity can be analyzed in terms of the perpendicular momentum equation, with consequences that are quite different from RMHD. MHD at low resistivity allows a fast sawtooth crash in a torus that resembles many features observed in experiments. Related effects appear in other common instabilities, such as magnetic islands and edge modes. A separate density evolution also allows the nonlinear existence of long-lived 1/1 helical ion density snakes around q=1, even in the presence of periodic sawtooth crashes, as observed in many experiments.

The Crab Nebula is considered as the high-energy astrophysical source par excellence, and as an ideal laboratory for particle acceleration in relativistic magnetized plasmas of pairs. Yet, the recent discovery of intense gamma-ray flares from the Crab Nebula does not fit into the traditional picture of pulsar wind nebulae. I will argue that the origin of the flares may lie in sudden episodes of magnetic dissipation within the nebula via magnetic reconnection. This scenario is corroborated by particle-in-cell (PIC) simulations of ultra-relativistic pair plasma reconnection subject to strong synchrotron cooling. I will discuss the conditions under which particle acceleration is most efficient, focusing on new large-scale three-dimensional PIC simulations.

Particle transport in plasmas with turbulent magnetic fields in the presence of a gradient of the mean magnetic field and weak pitch-angle diffusion is analyzed. We demonstrate that such transport is described by asymmetric diffusion: the generalization of the conventional random walk process to the case of unequal transition probabilities. We construct a toy 1D Markov chain model and analytically demonstrate that the particle density distribution becomes exponential in distance, instead of linear as is the case of the standard diffusion process. Implication of our results for the transport of cosmic rays are discussed.

I will present results of the first self-consistent reacting multi-fluid simulations of magnetic reconnection in a partially ionized plasma, where the ionized and neutral fluids are treated as coupled but distinct. Partially ionized plasma environments where release of magnetic energy and topological reconfiguration of magnetic fields via magnetic reconnection is known or conjectured to take place range from highly collisional, e.g. interstellar medium and lower solar chromosphere with ionization fraction below 0.1%, to weakly collisional, e.g. in the upper solar chromosphere with ionization fraction of 1%-10%. Different plasma processes, such as ionization and recombination, ion neutral interaction via charge-exchange collisions, Hall currents, and radiative losses can become the dominant factors in determining the reconnection rate and the structure of the reconnection region in different parameter regimes. The HiFi multi-fluid modeling framework has been used to implement all of the above processes in a single self-consistent model and to perform 2D simulations of magnetic reconnection under a variety of plasma conditions. In particular, as shown in the adjacent image, we observe the formation of previously predicted non-LTE current layers and explore the associated onset of the secondary plasmoid instability.

Flux ropes form basic building blocks for magnetic dynamics, are analogues of macroscopic magnetic field lines, and are irreducibly three dimensional (3D).

We have used the Reconnection Scaling Experiment (RSX) to study flux ropes, and have found many new features involving unexpected 3D dynamics, kink instability driven reconnection, non linearly stable but kinking flux ropes, large flows, and shear flow induced magnetic fields. For example the onset threshold for external kink instability depends upon boundary conditions that can be adjusted between line tied and free. These two boundary conditions could correspond to CME eruption flux ropes that are anchored ("line tied") at one end to solar coronal holes while the other end remains "free" to drift as magnetic clouds in the solar system. The dynamics of two flux ropes form a fairly simple 3D system that allowed the first identification of how a plasma instability (in this case the kink) initiated magnetic reconnection. When there is significant guide magnetic field, flux ropes bounce off each other much of the time instead of merging and reconnecting. As we assemble large 3D experimental data sets for density, temperature, pressure, magnetic field, and current density we observe local violations of MHD, and strongly sheared flow and fields. We show data where magnetic field is generated from sheared electron fluid flow. Movies from 3D experimental data also show that MHD forces fail to balance, i.e. JxB - grad P_e does not vanish at the 30% level, and we evaluate some candidates for the missing physics. We intend to model these 3D data with a PIC code (VPIC), 2 fluid code (HiFi) and possibly other hybrid approaches, and solicit collaborators.

*DOE Fusion Energy Sciences DE-AC52-06NA25396, NASA Geospace NNHIOA044I, Basic

Magnetic reconnection transforms magnetic field energy into particle kinetic energy; it may be the mechanism for accelerating particles to high enough energies to emit energetic synchrotron radiation, which is observed in various astrophysical objects, including pulsars, active Galactic nuclei, and gamma-ray bursts. Using 2D particle-in-cell simulations of relativistic, radiating, pair plasma reconnection, this work demonstrates that reconnection accelerates particles, bunching and focusing the most energetic particles into a narrow beam that wiggles in the plane of the reconnection layer. This beaming leads to brief, intense flares of high-energy photons when the beam crosses the line of sight. A newly-developed PIC code, which includes the radiation reaction, has recently shed new light (so to speak) on the picture of relativistic reconnection under strong synchrotron cooling. The most energetic particles feel very little radiative losses while they are accelerated in a straight line deep inside the layer where the electric field exceeds the magnetic field. Eventually, the particles get kicked out of the layer and subsequently radiate >160 MeV synchrotron radiation, which would be impossible to explain with ideal MHD-based models of particle acceleration. This result is essential in understanding the origin of >100 MeV gamma-ray flares observed in the Crab Nebula.

Recent advances in imaging present tantalizing prospects for diagnosing fluctuations in laboratory plasmas. Commercially available cameras now allow recording of large arrays of simultaneous data points on relevant time scales. In this talk, I will present the status of our ongoing study of imaging-based plasma turbulence measurements in the Controlled Shear Decorrelation Experiment (CSDX) at the University of California, San Diego. CSDX is a linear machine producing dense plasmas relevant to the tokamak edge (T_e ~ 3 eV, n_e ~ 10^13/cc). Electrostatic fluctuations are measured with Langmuir probes in concert with visible-light imaging over a range of plasma parameters. Comparisons between probe and imaging data constrain operational limits for both diagnostics. Drift like modes are observed and characterized using an image correlation technique. Time-resolved velocity fields are obtained using a pattern-matching algorithm, allowing access to flow dynamics across the plasma radius. Current work includes measurements of wave dispersion, velocity profiles, and probe/imaging relationships.