Session PO5: Waves, Oscillations and Instabilities

Relativistic Fluid Theory of Electromagnetic Instabilities

Electromagnetic instabilities are analyzed within the context of a manifestly covariant fluid formalism. Starting from an arbitrary adiabatic background fluid state, and using perturbation theory, we derive a minimal set of four 3$^{\mathrm{rd}}$ order PDEs in the 4-potential perturbation. A general dispersion relation is derived for plane waves, and analyzed for convective and absolute instabilities. This theory applies to several physical systems, such as coherent radiation sources, high-energy accelerators, ICF and astrophysical plasmas. Prepared by LLNL under Contract DE-AC52-07NA27344.   

The Residual Zonal Flow in Toroidally Rotating Tokamak Plasmas

The residual zonal flow, initially driven by ion-temperature-gradient turbulence, is considered for a toroidally rotating tokamak plasma. The gyro-kinetic equation is solved for two limiting cases: low speed toroidal rotation and sonic speed rotation. The general expression of the residual zonal flow for the two cases is the same as that of the static plasma but the numerical result is different due to the different evaluation of particle orbit average and the non-uniformity of density on magnetic surfaces. The level of the residual zonal flow decreases as the rotation velocity increases. For rotation at sonic speed the value of residual zonal flows is approximately one third of static cases. The presented result may be important in the fluid simulation of turbulence for rotating tokamak plasmas.   

Numerical Investigation of Landau Damping in Arbitrarily Degenerate Fermi-Dirac Quantum Plasmas

Plasma phenomena in environments where the inter-particle spacing approaches the thermal de Broglie wavelength are modified because of quantum statistical and tunnelling effects. Models of these systems are applicable to the study of microelectronics, dense laser-produced plasmas, and some extreme astrophysical environments. The question of the existence of Landau damping in completely degenerate plasmas has received attention in the literature, but many problems remain open. In this presentation, linear dispersion and Landau damping of electrostatic waves, in a quantum plasma with arbitrarily-degenerate Fermi-Dirac equilibrium distribution, are investigated numerically. The analysis uses a self-consistent mean-field quantum kinetic model (the Wigner-Poisson system). The problem of applying the Landau prescription for the integration contour in the presence of complex poles in the Fermi-Dirac distribution function and the effect of these poles on dispersion is addressed. The application of the method to equilibria containing velocity space anisotropies with the potential for kinetic instabilities is discussed.   

Experimental Characterization of Microtearing Modes in the RFX-mod Reversed-Field Pinch Plasmas

We present direct experimental observations in a laboratory fusion plasma of microtearing modes, obtained in the RFX-mod reversed-field pinch (RFP) plasma. The so-called Quasi Single Helicity magnetic equilibrium features in RFX-mod a central plasma volume with good magnetic surfaces and transport barriers with reduced heat transport. Recently, a theoretical stability analysis performed with the gyrokinetic GS2 code revealed the QSH states to be prone to microtearing modes. Measurements are carried out with a system of in-vessel probes located at the wall, capable of detecting magnetic fluctuations with high time and space resolution. Small-scale electromagnetic modes are revealed during the helical states of the plasma: their amplitude is correlated to the electron temperature gradient strength in the core. The identification in terms of microtearing modes derives from the comparison of experimental data with linear gyrokinetic simulations. The relation between the spectral properties of microtearing modes and the magnetic topology, mainly in terms of the helical safety factor profile, is investigated. The effects on the time evolution of the temperature profiles and on heat transport in RFP plasma are also discussed.   

New insights into ion acoustic wave decay

The stability of Ion Acoustic Waves (IAWs) is of importance to inertial confinement fusion experiments due to its potential to saturate stimulated Brillouin scattering. Using high-resolution fully-kinetic (for both electron and ion species) Vlasov simulations, the nature of IAW decay is investigated over a broad parameter space for both driven and undriven (free) waves. Scalings of the instability growth rate with the fundamental IAW amplitude and wave number are presented which are applicable across most of the relevant parameter space. The onset of turbulence arising due to the growth of subharmonic IAW modes is found to greatly change the plasma response to a fixed-frequency driver. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the Laboratory Research and Development Program at LLNL under project tracking code 12-ERD-061.   

Strong electron-scale instability in relativistic shear flows

Collisionless shear-driven plasma instabilities have recently been shown to be capable of generating strong and large-scale magnetic fields and may therefore play an important role in relativistic astrophysical outflows. We present a new collisionless shear-driven plasma instability, which operates in the plane transverse to the Kelvin Helmholtz instability (KHI). We develop the linear stability analysis of electromagnetic modes in the transverse plane and find that the growth rate of this instability is greater than the competing KHI in relativistic shears. The analytical results are confirmed with 2D particle-in-cell (PIC) simulations. Simulations also reveal the nonlinear evolution of the instability which leads to the development of mushroom-like electron-density structures, similar to the Rayleigh Taylor instability. Finally, the interplay between the competing instabilities is investigated in 3D PIC simulations.   

Nonlinear evolution of electron density in microwave plasma source with abnormal-permeability metamaterial

High electron-density plasmas beyond cutoff density were generated by high-power microwaves in an abnormal-permeability space, in which negative permittivity achieved in high density plasma makes refractive index real and negative. Experimental results using a high power microwave source and abnormal-permeability metamaterials verify that this plasma generation is in bifurcated states: high density and low density cases. This indicates that the process is quite nonlinear, partly predicted by our previous study [1]. In the case of negative permeability, after high-density plasma generation, transmitted microwaves increased, which is quite abnormal in usual microwave plasma sources. In the case of near-zero permeability, we also observed high-electron-density or overdense plasmas. Our previous report [2] demonstrates ``plasma metamaterials'' which include array of microplasmas and metallic microstructures with functional roles as media of electromagnetic waves with small amplitudes. The state of plasmas generated by high-power microwaves and immersed in the metallic metamaterial microstructures will open novel functions of plasma metamaterials; they are nonlinear metamaterials for scientific interests, potential high-density microwave sources for plasma processing, and potential switches for high-power microwaves. \\[4pt] [1] O. Sakai et al., J. Appl. Phys., vol. 109 (2011), 084914.\\[0pt] [2] O. Sakai et al., Plasma Sources Sci. Technol., vol. 21 (2012), 013001.   

Theoretical Issues on the Spontaneous Rotation of Axisymmetric Plasmas*

An extensive series of experiments have confirmed that the observed phenomenon of ``spontaneous rotation'' in axisymmetric plasmas is related to the confinement properties of the concerned plasmas and connected to the excitation of relevant collective modes [1]. Localized modes can extract angular momentum from the plasma column from which they grow while, the background plasma has to recoil in the direction opposite to that of mode phase velocity. In the case of the excitation of plasma edge modes, the loss of their angular momentum can be connected to the directed particle ejection to the surrounding medium. The recoil angular momentum is then redistributed inside the plasma column mainly by such processes as an effective viscous diffusion and inward flow (pinch) that is connected, for instance, to ITG driven modes. The linear and quasi-linear theories of the collisionless trapped electron modes and of the toroidal ion temperature gradient driven modes are re-examined in the considered context. Relevant features of the weakly collisional drift tearing mode and of the $m^{0}=1$ internal mode, are pointed out. *Sponsored in part by the US DOE.\\[4pt] [1] B. Coppi, 18th IAEA Fusion Energy Conf. THP 1/17 (2000). and \textit{Nucl. Fus.} {\bf 42}, 1 (2002).   

Energy-Conserving Semi-Lagrangian Discontinuous Galerkin Schemes for Vlasov-Poisson Systems

In many laboratory settings a common approach is to model the plasma via kinetic equations (i.e., some form of the Boltzmann equation). In this description the plasma is represented through a probability density function (PDF) that self-interacts through electromagnetic forces. Kinetic models are valid over most of the spatial and temporal scales that are of physical relevance in many application problem; however, they are computationally expensive due to the high-dimensionality of phase space and the disparate length and time scales that they resolve. In this work we describe efforts to develop high-order accurate numerical methods for collisionless plasma. In this setting the canonical model is the Vlasov-Poisson system. After briefly reviewing key properties of the Vlasov-Poisson system, we describe a class of numerical methods for solving Vlasov-Poisson based on coupling high-order discontinuous Galerkin finite element methods with semi-Lagrangian time-stepping. We show how to modify such numerical schemes to maintain important physical properties such as charge, mass, and energy conservation, as well positivity of the probability density function. The resulting numerical method is tested on several numerical examples.