Tandem Mirror Experiment Research Articles

Electron temperature differences and double layers

Electron temperature differences across plasma double layers are studied experimentally. It is shown that the temperature differences across a double layer can be varied and are not a result of thermalization of the bump-on-tail distribution. The implications of these results for electron thermal energy transport in laser-pellet and tandem-mirror experiments are also discussed.

Control of Plasma/Wall Interactions in Tandem Mirrors

Data from the Tandem Mirror Experiment (TMX) and other recent research show how to control plasma/wall interactions in tandem mirrors (TMs). Based on current knowledge, plasma/wall interactions will not limit the performance of TM reactors-either at the end walls or the radial walls. Magnetic field expansion and gas pumping can be used to regulate the plasma conditions at the end wall. Specifically, in TMX the plasma density at the end wall was found to be approx. =2 x 10/sup 9/ cm/sup -3/, whereas the end-plug density was approx. =2 x 10/sup 13/ cm/sup -3/; also, the sheath potential at the wall (8 V) was <10% of the end-plug electron temperature. The ''natural divertor'' effect-by which positively charged plasmas in magnetic mirror machines exhaust particles and energy to the end wallcan be used to both control the plasma conditions at the radial walls and divert impurities to the end wall. These techniques, the data that support them, and needed areas of further research are discussed.

The whistler instability at relativistic energies

The effects of a relativistic electron population on the temporal and spatial growth rates of the whistler instability are considered. It is found that relativistic effects tend to reduce the temporal growth rate of the whistler but are not sufficient, by themselves, to completely stabilize the mode. Relativistic effects are also found to reduce the volume of parameter space over which temporal growth can occur; the residual rate of spatial growth, however, is substantial. The results obtained are applied to two plasmas with significant relativistic electron content—the ELMO Bumpy Torus and the Tandem Mirror Experiments.

Fokker-Planck calculations of hot-electron formation by electron cyclotron resonance heating in the TMX-Upgrade tandem mirror

The paper studies cold plasma trapping and heating of hot electrons in mirror geometry using a time-dependent, bounce-averaged Fokker-Planck code with quasi-linear diffusion due to RF heating at fundamental and second harmonic frequencies. With the restriction k‖ = 0, the code models the beam-controlled heating (spatially restricted electric fields) that will be used to create thermal barriers in the TMX-Upgrade tandem-mirror experiment. By spatially localizing the microwave beams, which are strongly absorbed in a single pass, the mean hot-electron energy may be controlled. Heating is away from the midplane to control anisotropy (P⊥/P‖ ). For a given magnetic field geometry and cold-plasma source temperature Ts, the parameters of the hot electrons scale with the quantity χ ≡ ϵ2/nsω, where ϵ is the electric field, ns is the cold-plasma density, and ω is the frequency.

Magnetic Field Errors in Quadrupole Tandem Mirrors

Coil misalignments in quadrupole tandem mirrors generate dipole and quadrupole field errors. The effects of these errors on the magnetic field are calculated. Misalignments in the thin, quadrupole fans have particularly large effects on field lines. The results are applied to the Tandem Mirror Experiment (TMX) and to the TMX Upgrade.

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.

TMX upgrade magnet system: Design characteristics and physics considerations

Summarized in this article are the design characteristics of the magnet-system configuration constructed for use in the modified Tandem Mirror Experiment (TMX Upgrade), and a description of the resulting vacuum magnetic field. Many engineering and physics considerations and limitations governed the design. Several of the physics issues are discussed here, including single-particle drift surfaces and adiabaticity, central-cell resonant radial transport, magnetohydrodynamic stability analysis, and finite-beta equilibrium. The described design procedures can be applied to other tandem-mirror experiments or reactor studies.

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.

End-wall plasma characteristics in the Tandem Mirror Experiment

An array of emitting and collecting probes was used to measure the characteristics of the plasma at the end wall of TMX. The emitting probes indicated a plasma potential with a characteristic value of approximately 8 V, measured at 2 cm and 10 cm from the grounded wall. The potential in the plug varied from 300 to 1000 V. The collecting probes indicated a cold plasma present near the wall, with an electron temperature of about 5 eV and a cold-electron density of about 2 × 109 cm−3, while the hot-ion density at the wall was about 6 × 108 cm−3. The density of electrons in the plug was about 2 × 1013 cm−3. The electron temperature measured at the wall was decoupled from the temperature of the electrons in the plug and the central cell. The plasma wall sheath was established to balance the flux of hot ions and cold electrons. An additional species of electrons, i.e. secondary electrons produced at the end wall, was also identified. These secondary electrons had a directed energy comparable to the local plasma potential, an energy spread of less than 7 eV, and a density of about 4 × 108 cm−3. The experimental results are shown to be consistent with a simple model involving cold-gas recycling from the end wall.

Measurement of the tandem mirror experiment x-ray spectrum

We measured x-ray spectrum at the Tandem Mirror Experiment (TMX) facility as a function of time using a new x-ray spectrometer with medium energy resolution that measures as well as identifies x rays in intense and varied particle and radiation backgrounds. The x-ray spectrum was deconvoluted from single-channel energy responses recorded one at a time for each shot. The data for each channel were normalized to the total x-ray energy, which was measured separately for each shot. After a few milliseconds during which conditions within the plasma pulse stabilized, the spectrum consisted of a broad peak with a typical median energy of 0.66±0.04 keV, which can be interpreted as predominantly line emission. Resolution studies indicate that neonlike titanium may be a better interpretation than heliumlike oxygen; however, no quantitative model has been compared.

Equilibrium and stability of nonaxisymmetric minimum-B mirrors

Analytic three-dimensional mirror equilibria are calculated from the tensor-pressure fluid equations by means of an asymptotic expansion procedure. The class of equilibria described here is of interest to the minimum-B end cells of current tandem mirror experiments. It is shown that in the shallow-well approximation, a small plasma pressure can produce a relative change of order unity in the vacuum magnetic well, thereby leading to interchange instability. In addition, if the axial dependence of the quadrupole field is not chosen in a specific way, ’’long thin’’ corrections set an upper limit on the maximum allowable plasma radius. The proper choice of quadrupole field to avoid this limitation is discussed, and an analytic expression is derived for the interchange beta limit.

Observation of Alfvén Ion-Cyclotron Fluctuations in the End-Cell Plasma in the Tandem Mirror Experiment

Ion-cyclotron fluctuations in the tandem mirror experiment have wave characteristics consistent with the Alfv\'en ion-cyclotron instability. The oscillations are coherent, have small azimuthal mode numbers, and have frequencies as low as 12% below the diamagnetically depressed, minimum ion-cyclotron frequency in the end cell. Polarization is in the direction of ion gyration, and azimuthal propagation is in either the electron or the ion diamagnetic direction, with the former prevailing.

The LLNL tandem mirror experiment (TMX) upgrade vacuum system

The tandem mirror experiment (TMX) upgrade is a large, tandem, magnetic‐mirror fusion experiment with stringent requirements on base pressure (10−8 Torr), low H reflux from the first walls, and peak gas pressure (5×10−7 Torr) due to neutral beam gas during plasma operation. The 225 m3 vacuum vessel is initially evacuated by turbopumps. Cryopumps provide a continuous sink for gases other than helium, deuterium, and hydrogen. The neutral beam system introduces up to 480 l/s of H or D. The hydrogen isotopes are pumped at very high speed by titanium sublimed onto two cylindrical radially separated stainless steel quilted liners with a total surface area of 540 m2. These surfaces (when cooled to about 80 K) provide a pumping speed of 6×107 l/s for hydrogen. The titanium getter system is programmable and is used for heating as well as gettering. The inner plasma liner can be operated at elevated temperatures to enhance migration of gases away from the surfaces close to the plasma. Glow discharge cleaning is part of the pumpdown procedure. The design features are discussed in conjunction with the operating procedures developed to manage the dynamic vacuum conditions.

Design of first walls and beam dumps for Tandem Mirror Experiment Upgrade

Neutral reflux from the first walls and beam dumps of the Tandem Mirror Experiment (TMX) Upgrade could erode the neutral-beam-fueled end-cell plasma or cool the neutral-beam-heated central-cell plasma. To allow the TMX Upgrade to meet its design parameters, the neutral reflux to the plasma must be much less than the fluxes of both charge-exchange neutral products to the first walls and transmitted neutral-beam atoms to the beam dumps. To achieve this, we intend to evaporate titanium as a getter on the first wall and install vanadium-foil beam dumps. The vanadium beam dumps will be heated by the neutral beam during the shot, releasing most of the implanted hydrogen as they cool radiatively after the shot. The deposited titanium will be thick enough to retain the implanted charge-exchange neutral products. We describe our design of these components, report our estimates of their performance, and compare their performance to the needs of TMX Upgrade.

‘Ballistic damping’ – a possible technique for stabilizing resonant ion cyclotron modes in mirror systems

A technique called ‘ballistic damping’ is proposed for the control of ion cyclotron instabilities of the highly coherent type characteristically observed in mirror-confined plasmas at high plasma density. Ion beams, launched parallel to the field lines, transit the plasma resonantly gaining perpendicular energy from the unstable wave. These ions exit through the far mirror, thereby extracting energy from the wave. Critical beam currents required to achieve marginal stability, as estimated from power balance considerations, lie well within existing beam technology, both for present mirror or tandem mirror experiments and for scaled-up systems.

Geometrically focused neutral beam accelerators

A more reliable 40 kV, 65 A power supply drain at 0.4 A/cm2, neutral-beam accelerator was developed for the Tandem Mirror Experiment (TMX). Multiple slotted aperture grids of 60% transparency are fabricated from refractory metal wires mounted to form a spherical surface. This geometrically focuses the beam by aiming individual beamlets at the center of curvature of the spherical grid (r = 3.2 m). We attain greater reliability and faster conditioning with geometrical focusing than with the previous technique of electrostatically steering beamlets to a common point. Electrostatic steering, accomplished by offsetting grid wires, is satisfactory if the offset of a beamlet is much less than the distance from the beamlet to the grids. It was found that Pierce Angle entrance grids performed better if sharper edged. A redesigned accelerator grid support structure reduced the number of ceramic-to-metal vacuum joints, and eliminated O rings between precisely aligned parts. The suppressor grid feedthrough is required to withstand a maximum voltage of 15 kV occurring during breakdown, greatly exceeding the operating voltage of 1.5 kV. Convenient fabrication and assembly techniques have been developed. Assembly of accelerators and plasma sources in a clean room appears to reduce the conditioning time. Following the successful testing of the prototype, eight 40 kV accelerators were built for TMX. Furthermore, ten 20 kV versions were built that are modifiable to 40 kV by exchanging the entrance grid.

Large acceptance angle retarding-potential analyzers

Electrostatic retarding-potential gridded analyzers have been used to measure the current and the axial energy distributions of ions escaping along magnetic field lines in the 2XIIB magnetic fusion experiment at Lawrence Livermore National Laboratory (LLNL). Two analyzers are discussed: a large scanning analyzer with a movable entrance aperture that can measure ion losses from a different segment of the plasma diameter on each shot, and a smaller analyzer that mounts in 5-cm-diam. ports. Careful electromagnetic shielding and grounding were necessary in order to reduce spurious signals. Accurate measurements of ion current require grids that attenuate the plasma flow and isolate it from the analyzer grid potentials, several techniques to suppress secondary and primary electrons, and consideration of the space-charge limits as well as techniques to increase these limits. Accurate measurements of ion energy require, in addition, confining large-angle ion orbits within the analyzer by an axial magnetic field, limiting the sweep rate of the ion-repeller grid, and aligning the analyzer so that it is normal to the magnetic field lines. (The analyzers are also used on the Tandem Mirror Experiment, TMX, where the angular acceptance requirements are reduced). The analyzers measure the axial energy, which in 2XIIB and TMX is much greater than the transverse energy. Several pitfalls and their cures are identified in the design, construction, and operation of these analyzers.

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.

Tandem mirror confinement in the presence of ion cyclotron fluctuations

A theoretical model is developed for the effect of an electrostatic ion-cyclotron wave on central-cell ion confinement in a tandem mirror. Ion heating occurs in the central cell where the wave and local ion-cyclotron frequencies are equal. Coulomb pitch-angle collisions then scatter these ions into the loss region of velocity space. The wave heating is calculated analytically from the single-particle equations of motion, and the effect of collisions is modelled numerically by using a Monte-Carlo technique. A formula is obtained for the degradation of the ion-confinement time as a function of the RF wave amplitude. This formula reproduces the experimental results from the Livermore Tandem Mirror Experiment (TMX) as they are presented in a companion paper. The effect of the wave on density and temperature profiles is also calculated.

Gas control and wall conditioning in TMX

The Tandem Mirror Experiment (TMX) is a magnetic fusion research device at the Lawrence Livermore Laboratory which confines a center-cell plasma between two higher density end-plug plasmas. The end-plug plasmas are separated from the metal end walls by an end-fan chamber. This paper describes how we minimize the power lost through charge-exchange and electron conduction. To isolate the end-plug plasma from the end wall, we employ wall conditioning, gas pumping, and magnetic-field expansion in the end-fan chamber. The plasma density is reduced from above 10 13 cm −3 in the end-plug to well below 10 10 cm −3 at the end wall. A peak plasma potential of more than 1 kV above the grounded end wall is maintained in steady state and gas buildup near the end wall is avoided. Gas flow in the end plug is controlled and the end-plug walls are conditioned so that the end-plug plasma is not eroded by large fluxes of cold gas. Wall conditioning in the center cell provides reproducible conditions. The center cell is fueled by gas from a gas box or a pulsed valve.