Jeffrey B. Parker

Generation of zonal flows through symmetry breaking of statistical homogeneity

In geophysical and plasma contexts, zonal flows (ZFs) are well known to arise out of turbulence. We elucidate the transition from homogeneous turbulence without ZFs to inhomogeneous turbulence with steady ZFs. Starting from the equation for barotropic flow on a β plane, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking zonostrophic instability and show that it is an example of a Type instability within the pattern formation literature. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the ZF wavelength is not unique. In an idealized, infinite system, there is a continuous band of ZF wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors are shown numerically to hold in the CE2 system. We also conclude that the stability of the equilibria near the bifurcation point, which is governed by the Eckhaus instability, is independent of the Rayleigh–Kuo criterion.

Zonal flow as pattern formation

Zonal flows are well known to arise spontaneously out of turbulence. We show that for statistically averaged equations of the stochastically forced generalized Hasegawa-Mima model, steady-state zonal flows, and inhomogeneous turbulence fit into the framework of pattern formation. There are many implications. First, the wavelength of the zonal flows is not unique. Indeed, in an idealized, infinite system, any wavelength within a certain continuous band corresponds to a solution. Second, of these wavelengths, only those within a smaller subband are linearly stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets.

Studies of Rotating Spoke Oscillations in Cylindrical Hall Thrusters

In recent experiments with cylindrical and annular Hall thrusters, the enhanced crossfield electron transport induced by the rotating spoke was directly measured using a segmented anode. Approximately 50% of the total current was found to pass through the spoke. For the cylindrical Hall thrusters, the spoke oscillations were characterized using emissive and biased electrostatic probes and high speed imaging. The findings revealed a perturbed electric field which enhances electron transport across the field. Control and suppression of the spoke can be achieved by varying the effective boundaries of the thruster discharge from its cathode and anode sides. This includes recently demonstrated spoke suppression with a feedback control at the segmented anode. The magnetic field configuration of the thruster and the background gas pressure in the vacuum vessel can also affect the spoke oscillations.

Operation and Plume Measurements of Miniaturized Cylindrical Hall Thrusters with Permanent Magnets

*§ ** § Two permanent magnet versions of the miniaturized cylindrical Hall thruster (CHT) with different channel outer diameters, 1.5 cm and 2.6 cm, were operated in the power range of 50W-300 W. With twice smaller total power consumption, the 2.6 cm CHT is twice lighter than its electromagnet counterpart. Results of the discharge and plasma plume measurements suggest that the CHT with permanent magnets and electromagnet coils operate rather differently. In particular, the plasma flow from the permanent magnet thrusters has an unusual halo shape of the angular ion current density distribution with a majority of high energy ions flowing at the angles of 50°-70° with respect to the thruster centerline. This divergence of the energetic ion flow leads to the reduced efficiency of the thrust production in these thrusters.

Background Gas Pressure Effects in the Cylindrical Hall Thruster

A weakly collisional plasma discharge of the cylindrical Hall thruster with the cusp magnetic field and the thruster plume are strongly affected by variations of the low background pressure from 3 µtorr to 50 µtorr. High speed imaging measurements revealed that the increase of the background pressure leads to the suppression of two key modes of low frequency discharge oscillations in this thruster, including longitudinal breathing mode and rotating spoke mode. These effects occur in spite of insignificant changes of the plasma collisionality in this pressure range.

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.

Bringing global gyrokinetic turbulence simulations to the transport timescale using a multiscale approach

The vast separation dividing the characteristic times of energy confinement and turbulence in the core of toroidal plasmas makes first-principles prediction on long timescales extremely challenging. Here we report the demonstration of a multiple-timescale method that enables coupling global gyrokinetic simulations with a transport solver to calculate the evolution of the self-consistent temperature profile. This method, which exhibits resiliency to the intrinsic fluctuations arising in turbulence simulations, holds potential for integrating nonlocal gyrokinetic turbulence simulations into predictive, whole-device models.

Comment on “Three-dimensional numerical investigation of electron transport with rotating spoke in a cylindrical anode layer Hall plasma accelerator” [Phys. Plasmas 19, 073519 (2012)]

The oscillation behavior described by Tang et al. [Phys. Plasmas 19, 073519 (2012)] differs too greatly from previous experimental and numerical studies to claim observation of the same phenomenon. Most significantly, the rotation velocity by Tang et al. [Phys. Plasmas 19, 073519 (2012)] is three orders of magnitude larger than that of typical “rotating spoke” phenomena. Several physical and numerical considerations are presented to more accurately understand the numerical results of Tang et al. [Phys. Plasmas 19, 073519 (2012)] in light of previous studies.

Investigation of a Multiple-Timescale Turbulence-Transport Coupling Method in the Presence of Random Fluctuations

One route to improved predictive modeling of magnetically confined fusion reactors is to couple transport solvers with direct numerical simulations (DNS) of turbulence, rather than with surrogate models. An additional challenge presented by coupling directly with DNS is the inherent fluctuations in the turbulence, which limit the convergence achievable in the transport solver. In this article, we investigate the performance of one numerical coupling method in the presence of turbulent fluctuations. To test a particular numerical coupling method for the transport solver, we use an autoregressive-moving-average model to generate stochastic fluctuations efficiently with statistical properties resembling those of a gyrokinetic simulation. These fluctuations are then added to a simple, solvable problem, and we examine the behavior of the coupling method. We find that monitoring the residual as a proxy for the error can be misleading. From a pragmatic point of view, this study aids us in the full problem of transport coupled to DNS by predicting the amount of averaging required to reduce the fluctuation error and obtain a specific level of accuracy.