J. H. Foote

Observation of scaling laws of ion confining potential versus thermal barrier depth and of axial particle confinement time in the tandem mirror GAMMA 10

In the thermal barrier tandem mirror GAMMA 10, the scaling law governing the enhancement of the ion confining potential, c, resulting from thermal barrier formation, is obtained experimentally, and is consistently interpreted in terms of the weak and strong ECH theories set up by Cohen and co-workers. The scaling law on the axial particle confinement time, τp||, related to this c formation, is also demonstrated in detail; it is in good agreement with the Pastukhov theory as modified by Cohen and co-workers. This scaling is verified at any radial position in the core plasma region and at any time through the various stages of a discharge; this indicates a scaling with drastic improvement of τp||, due to the potential formation in the tandem mirror plasma.

Nonadiabaticity in mirror machines

An analytic technique for calculating magnetic‐moment jumps Δμ of particles in magnetic traps, previously derived for particular two‐dimensional vacuum fields, is generalized to nonvacuum fields of arbitrary complexity and applied to high‐β mirror machines. The size of a jump depends on the behavior of the magnetic‐field strength B (s) near the singularities of B in the complex s plane, where real s measures position along a field line. It is demonstrated that an intrinsic complication of mirror‐machine magnetic configurations is the presence of multiple singularities of B, which become closely spaced for field lines near the axis. An expansion in r2 is used to determine Δμ in the closely spaced regime. The analytic theory is compared with results from a particle‐orbit code for several axisymmetric nonvacuum fields, and is found to be in excellent agreement in both the well separated and closely spaced singularity regimes. Finite‐β effects are examined using axisymmetric model fields derived from the long...

Low‐frequency oscillations in the central cell of the TMX tandem mirror experiment

Two modes of low‐frequency oscillations have been observed in the central cell of the tandem mirror experiment (TMX). A mode at about 7 kHz has m=1 and probably drives radial transport at large radii. The mode identification is uncertain. A mode at about 13 kHz has m=0. The two end plugs oscillate 180° out of phase with each other and in phase with the amplitude (envelope) of the ion cyclotron frequency oscillations in each plug. This mode is identified as a sound wave; the frequency is apparently locked to the E×B rotation frequency, probably through an associated m=1 component. Neither mode severely limits confinement in the central cell, and both may be controllable. The lower‐frequency mode is sensitive to the density profile and to the fueling and is not always present. The higher‐frequency mode may be less important (or absent) in devices in which the plugs are stable at the plug’s ion cyclotron frequencies.

Design of the divertor Thomson scattering system on DIII-D

Local measurements of ne and Te in the divertor region are necessary for a more complete understanding of divertor physics. We have designed an extension to the existing multipulse Thomson scattering system [Carlstrom et al., Rev. Sci. Instrum. 63, 4901 (1992)] to measure ne in the range 5×1018–5×1020 m−3 and Te in the range 5–500 eV with 1 cm resolution from 1 to 21 cm above the floor of the DIII‐D vessel (eight spatial channels) in the region of the X point for lower single‐null diverted plasmas. One of the existing, 20 Hz, Nd:YAG lasers will be redirected to a separate vertical port and viewed radially with a specially designed f/6.8 lens. Fiber optics carry the light to polychromators whose interference filters have been optimized for low Te measurements. Other aspects of the system, including the beam path to the vessel, polychromator design, real‐time data acquisition, laser control, calibration facility, and DIII‐D timing and data acquisition interface, will be shared with the existing multipulse T...

E∥B end‐loss‐ion analyzer for Tandem‐Mirror Experiment‐Upgrade

We are constructing and testing a diagnostic instrument to investigate, in detail, ions emanating along magnetic field lines from the plasma region of the TMX‐U tandem‐mirror experiment. This analyzer (of Tokamak Fusion Test Reactor design) contains parallel electric and magnetic fields, which yield ion mass and energy spatial separation, respectively. A two‐dimensional array of 128 copper collector plates detects the particles. The entering ion flux is first well collimated and then focused onto the detector plane during the 180° bending in the magnetic field. This instrument is designed to measure higher particle energies than the present gridded end‐loss analyzers as well as determine the energy spectra more accurately. Tandem‐mirror plasma parameters to be investigated with this analyzer include end‐plug potential, average central‐cell‐ion energy, and plasma potential in the thermal barrier and nearby regions. We plan a time resolution of up to 2 kHz for each detector.

Radial transport in the central cell of the tandem mirror experiment

An experimental study of radial transport in the Tandem Mirror Experiment is reported here. Plasma parameters were measured in a series of well‐diagnosed plasma discharges. A negative electric current (80±40 A within a 30‐cm radius) flowed to the end wall, implying an equal radial loss of plasma ions. The axial losses of plasma ions were 100 A from the same volume. The nonambipolar radial ion flux was of the same order as the flux resulting from resonant‐neoclassical and ion‐neutral transport, but the uncertainties are large. The ambipolar radial transport (of both ions and electrons) was investigated by comparing the observed end losses with calculations of the plasma fueling by gas penetration and neutral beams. The ambipolar radial losses are probably smaller than the loses through other processes and may be as small as the classical losses resulting from Coulomb collisions.

The effect of end-cell stability on the confinement of the central-cell plasma in TMX

In the Tandem Mirror Experiment (TMX), the central-cell losses provide the warm unconfined plasma necessary to stabilize the drift-cyclotron loss-cone instability in the end cells. This places a theoretical limit on central-cell confinement, which is expressed as a limit on the end-cell to central-cell density ratio. As this density ratio increases in a TMX experiment, large increases of end-cell ion-cyclotron-frequency plasma fluctuations are observed. These fluctuations cause the central-cell confinement to decrease, in agreement with a theoretical model.

Plasma measurements with the TMX‐U E∥B end‐loss‐ion spectrometers

Two E∥B end‐loss‐ion spectrometers (ELIS) are now making plasma measurements on tandem mirror experiment‐upgrade (TMX‐U). One instrument is mounted on each end of this open‐ended tandem‐mirror machine. These spectrometers observe plasma losses along magnetic‐field lines. They operate reliably and with a minimum of attention during an experimental run. Their data, which are quickly acquired and analyzed, help guide the experimental sequence. The parallel electric and magnetic fields separate the end‐loss ions according to mass (D+ and H+) and energy. Each spectrometer detects ions with an array of 128 flat collector plates that are made from copper‐coated G10 epoxy fiberglass, normally used for printed‐circuit boards. The ELIS diagnostic system produces a wealth of experimental information, including data on peak plasma potential, central‐cell ion temperature, potentials in the thermal‐barrier region, axial confinement and ion‐end‐loss plugging, energetic‐electron losses, and hydrogen/deuterium concentrations.

Plasma measurements from neutral‐beam attenuation

Extensive and informative plasma measurements have been made with the intense and energetic neutral‐particle beams that are used for fueling and heating magnetically confined, controlled‐fusion experimental plasmas. This diagnostic technique does not perturb the plasma because only the unused transmitted fraction of a neutral beam is detected. Orthogonal arrays of highly collimated detectors of the simple secondary‐electron‐emission type are used in magnetic‐mirror experiments to measure neutral‐beam attenuation (directly related to the plasma line density) along chords through the plasma volume at different radial and axial positions. Data from these arrays yield radial and axial plasma‐density profiles, ion angular distributions at the plasma midplane, estimates of the neutral‐beam input power to the plasma, and information on macroscopic plasma motion. Representative results obtained by applying this useful diagnostic technique to the recently completed tandem‐mirror experiment TMX are included here. T...

Cooperative Effects in a Tenuous Energetic Plasma Contained by a Magnetic Mirror Field

The formation and characteristics of a steady‐state hydrogen plasma contained in a magnetic mirror field are described. The mean ion energy is 20 keV. The plasma is formed by ionizing and trapping a portion of a beam of energetic hydrogen atoms passing through the confining field. The methods of measurement used to determine the plasma properties are described. Measurements of the radial and azimuthal trapped‐ion distributions, the average ion and electron densities, and the plasma potential are compared with the predictions of simple theory, neglecting cooperative plasma effects. The observed deviations from these simple predictions show that the plasma properties are dominated by cooperative phenomena. The plasma density is found to be limited to a low value (∼4 × 107 ions/cm3) by a flute or drift instability. This instability is characterized by a low frequency rotation of the plasma at a frequency typically close to the ▿B precession frequency of a 20‐keV proton in the nonuniform mirror field. The pla...