Session XI2: Basic Plasma Physics: Theory, Reconnection and Dusty Plasmas

Nonlinear Energetic Particle Modes with Time-dependent Frequencies

The near-threshold regimes of wave excitation by energetic particles reveal a rich family of nonlinear scenarios ranging from benign mode saturation to explosive behavior. The choice between these scenarios depends on relaxation processes that restore the unstable distribution function. The processes of interest are velocity-space diffusion and electron drag. Recent analysis shows that the instability is always explosive when drag dominates at the wave-particle resonance [1]. This gives rise to a ``hard'' non-linear scenario in which the saturation level is insensitive to the small initial growth rate. Alfv\'{e}nic instabilities driven by beam injection in MAST tend to follow this scenario. In contrast, the instabilities excited in JET via ion cyclotron resonance heating (ICRH) are typically in a soft nonlinear regime, because the ICRH-produced fast ions are less affected by drag than by velocity-space diffusion. The explosive development of the hard nonlinear regime serves as a seed for spontaneous generation of phase space holes and clumps. In previous work, description of such structures was limited to the case of small frequency deviations from the bulk plasma eigenfrequency. However, there are numerous observations of frequency sweeping events in which the change in frequency is comparable to the frequency itself. The need to interpret such dramatic phenomena requires a non-perturbative theoretical formalism, which this new work provides. The underlying idea is that coherent structures represent traveling waves in fast-particle phase space. A rigorous solution of this type is obtained for a simple one-dimensional model [2]. This model captures the essential features of resonant particles in more general multidimensional problems. The presented solution suggests an efficient approach to quantitative modeling of actual experiments.\\[4pt] [1] M. K. Lilley, B. N. Breizman, S. E. Sharapov, Phys. Rev. Lett. \textbf{102}, 195003 (2009).\\[0pt] [2] B. N. Breizman, Nucl. Fusion, to be published (2010).   

Subdominant Stable Eigenmodes in Plasma Microturbulenc

In gyrokinetic simulations, thousands of degrees of freedom for each perpendicular wavevector (corresponding to the resolution of the velocity space and parallel discretization) are available to contribute to the fluctuation spectrum. For wavevectors with a linear instability, the unstable eigenmode accounts for one of these degrees of freedom. Little has been known about the role of the remaining degrees of freedom in the turbulent dynamics. We use eigenmode analysis and proper orthogonal decomposition (POD) to demonstrate the excitation of a hierarchy of damped modes at the same spatial scales as the driving instabilities. The higher amplitude (low order) modes are weakly damped and exhibit smooth, large-scale structure in velocity space and in the direction parallel to the magnetic field. Lower amplitude (high order) modes are characterized by increasingly fine scale structure and, as a result, are highly dissipative. These modes are excited to exponentially decreasing (in mode number) amplitudes, yet in aggregate provide a potent energy sink. This leads to an overlap of the spatial scales of energy injection and peak dissipation, a feature that is in contrast with more traditional turbulent systems. In many cases, the high order modes exhibit equipartition in energy dissipation, i.e. the modes' increasing damping rates are balanced by decreasing amplitudes in such a way that on average each mode dissipates energy at the same rate. This motivates a novel statistical description of gyrokinetic turbulence. Finally, in electromagnetic simulations, a low order subdominant mode is characterized by micro-tearing parity: symmetric parallel mode structure for the magnetic vector potential. This damped mode is driven to high amplitude in the nonlinear state and thus offers a mechanism for the observed magnetic stochasticity even at very low values of beta.   

Wheels within wheels: Hamiltonian dynamics as a hierarchy of action variables

In Hamiltonian systems where one coordinate oscillates, the remaining coordinates may undergo a net displacement during one period of the oscillating coordinate. The archetypal example from plasma physics is charged particle motion in a magnetic field where the particle's position across field lines increases with every gyration, resulting in the well known guiding center drifts. We show that the net displacements of the non-periodic coordinates can be obtained by appropriate partial differentiation of the action integral associated with the periodic coordinate. This result is then used to demonstrate that the action integral acts as a Hamiltonian for the other coordinates providing time is scaled to the period, or ``tick-time,'' of the oscillating coordinate. This generalizes the concept of guiding center drifts to a broad range of Hamiltonian systems and allows one to compute such drifts in regimes where the guiding center approximation fails. As an example, we derive the guiding center formulas for the grad-B drift and magnetic mirror force by taking partial derivatives of the first adiabatic invariant mu. Other examples, including a relativistic coupling effect and a mechanical analog of magnetic mirroring, are supplied to illustrate the varied application of these results.   

Universally Unstable Nature of Velocity Ring Distributions

Although it is typically believed that an ion ring velocity distribution has a stability threshold, we find that they are universally unstable. This can substantially impact the understanding of dynamics in both laboratory and space plasmas. A high ring density neutralizes the stabilizing effect of ion Landau damping in a warm plasma and the ring is unstable to the generation of waves below the lower hybrid frequency- even for a very high temperature plasma. For ring densities lower than the background plasma density there is a slow instability with growth rate less than the background ion cyclotron frequency and consequently the background ion response is magnetized. This is in addition to the widely discussed fast instability where the wave growth rate exceeds the background ion cyclotron frequency and hence the background ions are effectively unmagnetized. Thus, even a low density ring is unstable to waves around the lower hybrid frequency range for any ring speed. This implies that effectively there is no velocity threshold for a sufficiently cold ring. The importance of these conclusions on the nonlinear evolution of space plasmas, in particular to solar wind-comet interaction, post-magnetospheric storm conditions, and chemical release experiments in the ionosphere will be discussed.   

Experimental Measurement of Viscoelasticity of Strongly-Coupled Dusty Plasma

Until recently, the basic physics concept of strongly-coupled plasmas was studied mainly theoretically. This research area is now more active because experiments are possible, due to the development of laboratory plasmas that are strongly-coupled and allow convenient diagnostics. A dusty plasma consists of highly-charged microspheres immersed in a typical electron-ion plasma. The microspheres self-organize, arranging themselves with equal spacing, forming a spatial structure like a crystalline lattice. In these experiments, video microscopy is a diagnostic that allows measurement of the positions and velocities of all microspheres, as functions of time. This has opened up a wide range of experiments of fundamental physical interest that are impossible with any other experimental system. This talk is a report of the first experimental measurement, in any physical system, of viscoelasticity of a liquid as characterized by the wavenumber-dependent viscosity. A two-dimensional crystalline lattice is formed by levitating charged polymer microspheres in an argon RF plasma. This lattice is then melted, using random energy added by rastered laser beams that push the microspheres. The microspheres are analogous to molecules in a normal liquid, but the dusty-plasma experiment has the advantage that unlike molecules, the microspheres are large enough to be tracked individually using image analysis methods. A recently-developed method of computing the wavenumber-dependent viscosity, based on particle positions and velocities, is then used. It is shown that viscosity diminishes as length scales become smaller. This serves as a measure of viscoelasticity: energy dissipation (viscosity) diminishes while energy storage (elasticity) increases as scale lengths become smaller in a liquid. This experiment result for the wavenumber-dependent viscosity is consistent with a molecular dynamics simulation.   

Experimental Investigation of the Trigger Problem in Magnetic Reconnection

Magnetic reconnection is a fundamental process in plasma physics, which involves the often explosive release of magnetically stored energy in both space and laboratory plasmas. In order for this sudden release of energy to occur, there must be a period of slow reconnection, in which magnetic stress accumulates in the system, followed by a quick transition to fast reconnection. The question of what causes this transition is known as the ``trigger problem'' and is not well understood. We address the trigger problem using the Versatile Toroidal Facility (VTF) at MIT, which we operate in the strong magnetic guide field regime. The resulting reconnection occurs in spontaneous events, in which there is a transition to fast reconnection [1]. The reconnection in these events is asymmetric: it begins at one toroidal location and propagates toroidally in both directions [2]. The spontaneous onset is facilitated by an interaction between the x-line current channel and a global mode, which breaks axisymmetry. We model the onset using an empirical Ohm's law and current continuity, which is maintained by ion polarization currents associated with the mode. The model reproduces the exponential growth of the reconnection electric field, and the model growth rate agrees well with the experimentally measured growth rate. \\[4pt] [1] J. Egedal et al. Phys. Rev. Lett. 98, 015003 (2007) \\[0pt] [2] N. Katz et al. Phys. Rev. Lett. 104, 255004 (2010)