Global Tearing Modes Research Articles

Global linear and nonlinear gyrokinetic simulations of tearing modes

To better understand multi-scale interactions between global tearing modes and microturbulence in the Madison Symmetric Torus (MST) reversed-field pinch (RFP), the global gyrokinetic code Gene is modified to describe global tearing mode instability via a shifted Maxwellian (SM) distribution consistent with experimental equilibria. The implementation of the SM is tested and benchmarked by comparisons with different codes and models. Good agreement is obtained in code-code and code-theory comparisons. Linear stability of tearing modes of a non-reversed MST discharge is studied. A collisionality scan is performed to the lowest order unstable modes (n = 5, n = 6) and shown to behave consistently with theoretical scaling. The nonlinear evolution is simulated, and saturation is found to arise from mode coupling and transfer of energy from the most unstable tearing mode to small-scale stable modes mediated by the m = 2 tearing mode. The work described herein lays the foundation for nonlinear simulation and analysis of the interaction of tearing modes and gyroradius-scale instabilities in RFP plasmas.

Observation of trapped-electron-mode microturbulence in reversed field pinch plasmas

Density fluctuations in the large-density-gradient region of improved confinement Madison Symmetric Torus reversed field pinch (RFP) plasmas exhibit multiple features that are characteristic of the trapped-electron mode (TEM). Core transport in conventional RFP plasmas is governed by magnetic stochasticity stemming from multiple long-wavelength tearing modes. Using inductive current profile control, these tearing modes are reduced, and global confinement is increased to that expected for comparable tokamak plasmas. Under these conditions, new short-wavelength fluctuations distinct from global tearing modes appear in the spectrum at a frequency of f ∼ 50 kHz, which have normalized perpendicular wavenumbers k⊥ρs≲0.2 and propagate in the electron diamagnetic drift direction. They exhibit a critical-gradient threshold, and the fluctuation amplitude increases with the local electron density gradient. These characteristics are consistent with predictions from gyrokinetic analysis using the Gene code, including increased TEM turbulence and transport from the interaction of remnant tearing magnetic fluctuations and zonal flow.

Evidence for drift waves in the turbulence of reversed field pinch plasmas

A detailed characterization of the high-frequency range of the fluctuation spectrum in reversed field pinch plasmas is presented, revealing a variety of new features distinct from global tearing modes and the cascade that they are thought to drive. The anisotropic broadband spectrum of the fluctuating electric field is measured. The power in the fluctuating kinetic energy (1/2)miniṼẼ×B02, previously measured to be smaller than the magnetic energy in the tearing-mode-unstable frequency range, becomes greater than and diverges from the magnetic energy above 60–80 kHz. The lack of equipartition at high frequencies coincides with the measured signatures of the independent fluctuation activity broadly consistent with the drift-wave fluctuations. Statistical coherence measurements reveal the mode activity that is compressive with a large amplitude in the vicinity of strong density gradients and with a phase speed comparable to the electron drift speed. There is a distinct high-frequency correlation between the fluctuations of density and the parallel magnetic field. Elevated coherences associated with this fluctuation feature return more quickly after a sawtooth event than the corresponding coherences associated with tearing activity.

High-frequency fluctuation measurements by far-infrared laser Faraday-effect polarimetry-interferometry and forward scattering system on MST.

Magnetic fluctuation-induced transport driven by global tearing modes has been measured by Faraday-effect polarimetry and interferometry (phase measurements) in the MST reversed field pinch. However, the role of small-scale broadband magnetic and density turbulence in transport remains unknown. In order to investigate broadband magnetic turbulence, we plan to upgrade the existing detector system by using planar-diode fundamental waveguide mixers optimized for high sensitivity. Initial tests indicate these mixers have ×10 sensitivity improvement compared to currently employed corner-cube Schottky-diode mixers and ×5 lower noise. Compact mixer design will allow us to resolve the wavenumbers up to k ∼ 1-2 cm(-1) for beam width w = 1.5 cm and 15 cm(-1) for beam width w = 2 mm. The system can also be used to measure the scattered signal (amplitude measurement) induced by both plasma density and magnetic fluctuations.

2D image of local density and magnetic fluctuations from line-integrated interferometry-polarimetry measurements.

Combined polarimetry-interferometry capability permits simultaneous measurement of line-integrated density and Faraday effect with fast time response (∼1 μs) and high sensitivity. Faraday effect fluctuations with phase shift of order 0.05° associated with global tearing modes are resolved with an uncertainty ∼0.01°. For physics investigations, local density fluctuations are obtained by inverting the line-integrated interferometry data. The local magnetic and current density fluctuations are then reconstructed using a parameterized fit of the polarimetry data. Reconstructed 2D images of density and magnetic field fluctuations in a poloidal cross section exhibit significantly different spatial structure. Combined with their relative phase, the magnetic-fluctuation-induced particle transport flux and its spatial distribution are resolved.

Collinearity alignment of probe beams in a laser-based Faraday effect diagnostic

Two counter-rotating circularly polarized beams are used in a laser-based polarimetry diagnostic providing a phase measurement of the Faraday effect. Collinearity of these beams is a key issue that affects measurement accuracy. Spatial offset from even small misalignment induces systematic error due to density gradient and path length difference. Here, we report an alignment technique using a rotating dielectric wedge, which is capable of reducing spatial offset of two probe beams below 0.1 mm for beams with 40 mm diameter. With optimized alignment, 0.05° Faraday effect fluctuations associated with global tearing modes are resolved with an uncertainty below 0.01°.

Role of the pressure force in the explosive dynamics of magnetic islands in double tearing modes

The evolution of magnetic islands at two resonant surfaces during the development of a global tearing mode is investigated via numerical simulations of a reduced set of magneto-hydrodynamic equations in slab plasmas. The explosive dynamics of the islands resulting in an interchange follows a Rutherford-like regime, also referred to as a weakly coupled double tearing mode. It is found that the latent mechanism of this dynamics is the reduction of the total pressure around the opposite X-point and the abrupt growth is associated with an imbalance of the pressure around the islands. Once this imbalance is well established, each plasmoid is pushed to the opposite X-point, increasing the drive for the field merging. A feedback loop then takes place as the reconnection itself decreases the strength of the magnetic field between the tearing layers, i.e., reinforces the pressure imbalance. This loop accelerates reconnection, thus leading to the observed explosive growth.

The tearing instabilities driven by lower hybrid waves in the current sheet

We have investigated the excitation of tearing instabilities driven by lower hybrid waves in the current sheet. Considering a two‐dimensional equilibrium, we have shown that lower hybrid waves observed throughout the plasma sheet can cause large anomalous resistivity as a consequence of nonlinear interactions and significantly influence the excitation of tearing mode in the layer, where Bx (z) reverses sign. We have found that the perturbed ponderomotive force gives two new physical effects, one due to current gradients in the inner core of the current sheet (z ≪ δ ≪ λ, where λ is the current sheet width and δ is the thickness of the field reversal layer) and the other due to anomalous resistivity in the outer core (δ ≪ z ≤ λ). In the presence of these effects, we have demonstrated that global tearing modes with growth times ranging from fraction of a second to several tens of milliseconds are excited for wave electric fields of order of a few mV/m and scale lengths in the range koyLz < 1 or koyLz > 1, where koy is the wavenumber of the lower hybrid waves and Lz is the perturbation scale length. Finally, we have discussed the relevance of this wave‐driven mode to the magnetic reconnection and the substorm onset processes.

Midtail plasma flows and the relationship to near‐Earth substorm activity: A case study

Recent simulations of magnetotail reconnection have pointed to a link between plasma flows, dipolarization, and the substorm current wedge. In particular, Hesse and Birn (1991) have proposed that earthward jetting of plasma from the reconnection region transports flux into the near‐Earth region. At the inner edge of the plasma sheet this flux piles up, producing a dipolarization of the magnetic field. The vorticity produced by the east‐west deflection of the flow at the inner edge of the plasma sheet gives rise to field‐aligned currents that have region 1 polarity. Thus in this scenario the earthward flow from the reconnection region produces the dipolarization and the current wedge in a self‐consistent fashion. In this study we examine observations made on April 8,1985 by the Active Magnetospheric Particle Tracer Explorers/Ion Release Module (IRM), the geosynchronous satellites 1979‐053,1983‐019, and 1984‐037, and Syowa station, as well as AE. This event is unique because IRM was located near the neutral sheet in the midnight sector for an extended period of time. Ground data show that there was ongoing activity in the IRM local time sector for several hours, beginning at 1800 UT and reaching a crescendo at 2300 UT. This activity was also accompanied by energetic particle variations, including injections, at geosynchronous orbit in the nighttime sector. Significantly, there were no fast flows at the neutral sheet until the great intensification of activity at 2300 UT. At that time, IRM recorded fast earthward flow simultaneous with a dipolarization of the magnetic field. We conclude that while the aforementioned scenario for the creation of the current wedge encounters serious problems explaining the earlier activity, the observations at 2300 UT are consistent with the scenario of Hesse and Birn (1991). On that basis it is argued that the physics of substorms is not exclusively rooted in the development of a global tearing mode. Processes at the inner edge of the cross‐tail current that cause a disruption of the current and a consequent dipolarization and current wedge may be unrelated to the formation of a macroscale reconnection region. Thus the global evolution of a substorm is probably a complicated superposition of such processes operating on a very localized scale and a global macroscale process that allows for such things as releasing the energy stored in lobe flux and the creation of plasmoids.

Finite ion temperature effects on collisional and semicollisional tearing modes

The finite ion gyroradius effects on the stability of global tearing modes are studied using analytic and numerical techniques. It is found that in the collisional regime the modes are weakly stabilized compared to the zero ion temperature case. In the semicollisional regime, the stabilization is weaker than the polarization drift stabilization in the zero ion temperature case. There is overall a very minor finite ion temperature modification of the stability boundary in the plasma beta, collisionality space.