T.P. Intrator

Phenomenological theory of the kink instability in a slender plasma column

In this paper we are concerned with the kink instability of a current-carrying plasma column whose radius a is much smaller than its length L. In the limit a⪡L, one can consider the column as a thin filament whose kinking can be adequately described simply by a two dimensional 2D displacement vector, ξx=ξx(z,t); ξy=ξy(z,t). Details of the internal structure of the column such as the radial distribution of the current, density, and axial flow can be lumped into some phenomenological parameters. This approach is particularly efficient in the problems with nonideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and with a substantial axial flow. With the sheath BC imposed at one of the endplates, we find instability in the domain well below the classical Kruskal-Shafranov limit. The presence of an axial flow causes the onset of rotation of the kink and strong axial “skewness” of the eigenfunction, with the perturbation amplitude increasing in the flow direction. ...

Current-Driven Rotating-Kink Mode in a Plasma Column with a Non-Line-Tied Free End

First experimental measurements are presented for the kink instability in a linear plasma column which is insulated from an axial boundary by finite sheath resistivity. An instability threshold below the classical Kruskal-Shafranov threshold, axially asymmetric mode structure, and rotation are observed. These are accurately reproduced by a recent kink theory, which includes axial plasma flow and one end of the plasma column that is free to move due to a non-line-tied boundary condition.

Long-lifetime current-driven rotating kink modes in a non-line-tied plasma column with a free end

[1]xa0We show the first experimental evidence for a magnetohydrodynamic kink instability in a current rope with one end that is free to move. This free end is partially insulated by sheath resistivity, so that the usual frozen in flux assumption for magnetohydrodynamics is violated in this region. The free end is therefore not line-tied to the axial boundary. We find the instability threshold is well below the classical Kruskal-Shafranov threshold, culminating in a long-lifetime saturated state. The presence of an axial flow further lowers the kink threshold and gives rise to a doppler-shifted frequency from rotation of the kink, where the eigenfunction is axially pushed in the flow direction. This lowered threshold may give rise to kink instabilities in situations with small magnetic twist that would otherwise be considered stable. Striking agreement with a theoretical analysis is demonstrated. The existence of a free end may be important for open flux tubes attached to the Sun, galactic jets associated with accretion discs, and spheromak startup.

Adiabatic model and design of a translating field reversed configuration

We apply an adiabatic evolution model to predict the behavior of a field reversed configuration (FRC) during decompression and translation, as well as during boundary compression. Semi-empirical scaling laws, which were developed and benchmarked primarily for collisionless FRCs, are expected to remain valid even for the collisional regime of FRX-L experiment. We use this approach to outline the design implications for FRX-L, the high density translated FRC experiment at Los Alamos National Laboratory. A conical theta coil is used to accelerate the FRC to the largest practical velocity so it can enter a mirror bounded compression region, where it must be a suitable target for a magnetized target fusion (MTF) implosion. FRX-L provides the physics basis for the integrated MTF plasma compression experiment at the Shiva-Star pulsed power facility at Kirtland Air Force Research Laboratory, where the FRC will be compressed inside a flux conserving cylindrical shell.

Effects of boundary conditions and flow on the kink instability in a cylindrical plasma column

An experimental investigation of the kink instability is presented in a linear plasma column where one end is line-tied to the plasma source, and the other end is not line-tied and therefore free to slide over the surface of the end-plate. This latter boundary condition is a result of plasma sheath resistance that insulates, at least partially, the plasma from the end-plate. The helical m = 1 kink mode is observed to grow when the plasma current exceeds a threshold and, close to the criticality, is characterized by an axial mode structure with maximum displacement at the free axial boundary. Azimuthal rotation of the mode is observed such that the helically kinked column always screws into the free axial boundary. The kink mode structure, rotation frequency and instability threshold are accurately reproduced by a recent kink theory [D. D. Ryutov, et al., Phys. Plasmas 13, 032105 (2006)], which includes axial plasma flow and one end of the plasma column that is free to move due to a perfect non-line-tying boundary condition which is experimentally verified. A brief review of the kink theory and its predictions for the boundary conditions relevant in the present experiments are presented.

Diagnostics for a magnetized target fusion experiment

We are planning experiments using a field reversed configuration plasma injected into a metal cylinder, which is subsequently electrically imploded to achieve a fusing plasma. Diagnosing this plasma is quite challenging due to the short timescales, high energy densities, high magnetic fields, and difficult access. We outline our diagnostic sets in both a phase I study (where the plasma will be formed and translated), and phase II study (where the plasma will be imploded). The precompression plasma (diameter of only 8–10 cm, length of 30–40 cm) is expected to have n∼1017 cm−3, T∼100–300 eV, B∼5 T, and a lifetime of 10–20 μs. We will use visible laser interferometry across the plasma, along with a series of fiber-optically coupled visible light monitors to determine the plasma density and position. Excluded flux loops will be placed outside the quartz tube of the formation region, but inside of the diameter of the θ-pinch formation coils. Impurity emission in the visible and extreme ultraviolet range will b...

Equilibrium paradigm for field-reversed configurations and application to experiments

Fresh insights on field-reversed configurations (FRCs) are incorporated in a new paradigm for equilibria. In particular four new or unappreciated properties are accounted for: an empirically based scrape-off layer thickness; a new, more accurate axial force balance relation; viscous force regularity at the O-point; and the broken-surface effect. The new paradigm corrects glaring defects of previous models (rigid rotor, Hill’s vortex). Further, the new paradigm is simple enough to be easily used as an interpretive tool despite the limited data suite in most experiments. It is applied to the newly enhanced FRC data compendium, a database of 69 records from 15 facilities. Several important observations and corrections on the previous understanding of FRCs follow, three of which stand out. (1) The traditional axial force balance (“average-β” relation) gives an inaccurate scaling with the separatrix-to-wall radius ratio. (2) The improved equilibrium paradigm yields separatrix particle transport rates of 3–5u2002m2...

Measurements of velocity shear and ion viscosity profile in a magnetohydrodynamic plasma jet

Time-dependent, two-dimensional profiles of the axial flow velocity, density, electron temperature, and magnetic field components are measured at two axial locations in a screw pinch plasma column of the reconnection scaling experiment. The results show that the ion momentum flux for a given column radius is dissipated by the ion-ion Coulomb scattering viscosity due to a significant radial shear of the axial velocity. By comparing the terms of the magnetohydrodynamic momentum balance equation, radial profile of ion viscosity is determined. Chord-integrated ion temperature measurements performed at several radial locations using Doppler broadening spectroscopy show ion temperature of about 1 eV. Measured ion viscosity agrees within a factor of 2 with the classical Braginskii expectations.

Geometrical investigation of the kinetic evolution of the magnetic field in a periodic flux rope

Flux ropes are bundles of magnetic field wrapped around an axis. Many laboratory, space, and astrophysics processes can be represented using this idealized concept. Here, a massively parallel 3D kinetic simulation of a periodic flux rope undergoing the kink instability is studied. The focus is on the topology of the magnetic field and its geometric structures. The analysis considers various techniques such as Poincare maps and the quasi-separatrix layer (QSL). These are used to highlight regions with expansion or compression and changes in the connectivity of magnetic field lines and consequently to outline regions where heating and current may be generated due to magnetic reconnection. The present study is, to our knowledge, the first QSL analysis of a fully kinetic 3D particle in cell simulation and focuses the existing QSL method of analysis to periodic systems.

A three dimensional probe positioner

In order to sort out the physics that is important in many plasma experiments, data in three dimensions (3D) are becoming necessary. Access to the usual cylindrical vacuum vessel is typically restricted to radially or axially insertable probes that can pivot. The space that can be explored usually has significant restrictions either because probe travel must be along a travel path, or a wobbly probe positioner requires one to map between a moveable coordinate system and a preferred laboratory coordinate system. This could for example introduce errors in measurements of vector quantities such as magnetic field or flow. We describe the design and implementation of a 3D probe positioner that slides in two dimensions on a double O-ring seal and radially inserts along the third dimension. The net result is that a 3D space can be explored in a laboratory Cartesian reference frame.