Nonlinear instability in simulations of Large Plasma Device turbulence

Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model, but different axial boundary conditions. They employ either periodic, zero-value, zero-derivative, or sheath axial boundaries. The linear stability physics is different between the scenarios because the various boundary conditions allow the drift wave instability to access different axial structures, and the sheath boundary simulation contains a conducting wall mode instability which is just as unstable as the drift waves. Nevertheless, the turbulence in all the simulations is relatively similar because it is primarily driven by a robust nonlinear instability that is the same for all cases. The nonlinear instability preferentially drives $k_parallel = 0$ potential energy fluctuations, which then three-wave couple to $k_parallel e 0$ potential energy fluctuations in order to access the adiabatic response to transfer their energy to kinetic energy fluctuations. The turbulence self-organizes to drive this nonlinear instability, which destroys the linear eigenmode structures, making the linear instabilities ineffective.

Current Induced Nuclear Spin Depolarization at Landau Level Filling Factor nu=1/2

Hyperfine interactions between electron and nuclear spins in the quantum Hall regime provide powerful means for manipulation and detection of nuclear spins. In this work we demonstrate that significant changes in nuclear spin polarization can be created by applying an electric current in a 2-dimensional electron system at Landau level filling factor nu=1/2. Electron spin transitions at nu= 2/3 and 1/2 are utilized for the measurement of the nuclear spin polarization. Consistent results are obtained from these two different methods of nuclear magnetometry. The finite thickness of the electron wavefunction is found to be important even for a narrow quantum well. The current induced effect on nuclear spins can be attributed to electron heating and the efficient coupling between the nuclear and electron spin systems at nu=1/2. The electron temperature, elevated by the current, can be measured with a thermometer based on the measurement of the nuclear spin relaxation rate. The nuclear spin polarization follows a Curie law dependence on the electron temperature. This work also allows us to evaluate the electron g-factor in high magnetic fields as well as the polarization mass of composite fermions.

Energy dynamics in a simulation of LAPD turbulence

Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flute-like ($k_parallel = 0$) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to $k_parallel e 0$ fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through suppressing $k_parallel=0$ modes, the turbulence develops a coherent frequency spectrum which is inconsistent with experimental data.

A Quantized $ u =5/2$ State in a Two-Subband Quantum Hall System

The evolution of the fractional quantum Hall state at filling 5/2 is studied in density tunable two-dimensional electron systems formed in wide wells in which it is possible to induce a transition from single to two subband occupancy. In 80 and 60 nm wells, the quantum Hall state at 5/2 filling of the lowest subband is observed even when the second subband is occupied. In a 50 nm well the 5/2 state vanishes upon second subband population. We attribute this distinct behavior to the width dependence of the capacitive energy for intersubband charge transfer and of the overlap of the subband probability densities.

Modeling of plasma turbulence and transport in the Large Plasma Device

Numerical simulation of plasma turbulence in the Large Plasma Device (LAPD) [Gekelman et al, Rev. Sci. Inst., 62, 2875, 1991] is presented. The model, implemented in the BOUndary Turbulence (BOUT) code [M. Umansky et al, Contrib. Plasma Phys. 180, 887 (2009)], includes 3-D collisional fluid equations for plasma density, electron parallel momentum, and current continuity, and also includes the effects of ion-neutral collisions. In nonlinear simulations using measured LAPD density profiles but assuming constant temperature profile for simplicity, self-consistent evolution of instabilities and nonlinearly-generated zonal flows results in a saturated turbulent state. Comparisons of these simulations with measurements in LAPD plasmas reveal good qualitative and reasonable quantitative agreement, in particular in frequency spectrum, spatial correlation and amplitude probability distribution function of density fluctuations. For comparison with LAPD measurements, the plasma density profile in simulations is maintained either by direct azimuthal averaging on each time step, or by adding particle source/sink function. The inferred source/sink values are consistent with the estimated ionization source and parallel losses in LAPD. These simulations lay the groundwork for more a comprehensive effort to test fluid turbulence simulation against LAPD data.

BOUT++: a framework for parallel plasma fluid simulations

A new modular code called BOUT++ is presented, which simulates 3D fluid equations in curvilinear coordinates. Although aimed at simulating Edge Localised Modes (ELMs) in tokamak X-point geometry, the code is able to simulate a wide range of fluid models (magnetised and unmagnetised) involving an arbitrary number of scalar and vector fields, in a wide range of geometries. Time evolution is fully implicit, and 3rd-order WENO schemes are implemented. Benchmarks are presented for linear and non-linear problems (the Orszag-Tang vortex) showing good agreement. Performance of the code is tested by scaling with problem size and processor number, showing efficient scaling to thousands of processors. Linear initial-value simulations of ELMs using reduced ideal MHD are presented, and the results compared to the ELITE linear MHD eigenvalue code. The resulting mode-structures and growth-rate are found to be in good agreement (BOUT++ = 0.245, ELITE = 0.239). To our knowledge, this is the first time dissipationless, initial-value simulations of ELMs have been successfully demonstrated.

Towards identification of a non-abelian state: observation of a quarter of electron charge at $ u=5/2$ quantum Hall state

The fractional quantum Hall effect, where plateaus in the Hall resistance at values of coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. Current flows along the edges carried by charged excitations (quasi particles) whose charge is a fraction of the electron charge. While earlier research concentrated on odd denominator fractional values of $ u$, the observation of the even denominator $ u=5/2$ state sparked a vast interest. This state is conjectured to be characterized by quasiparticles of charge e/4, whose statistics is non-abelian. In other words, interchanging of two quasi particles may modify the state of the system to an orthogonal one, and does not just add a phase as in for fermions or bosons. As such, these quasiparticles may be useful for the construction of a topological quantum computer. Here we report data of shot noise generated by partitioning edge currents in the $ u=5/2$ state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other potentially possible values, such as e/2 and e. While not proving the non-abelian nature of the $ u=5/2$ state, this observation is the first step toward a full understanding of these new fractional charges.