Grant W. Hart

Verification of the Taylor (minimum energy) state in a spheromak

Experimental measurements of the equilibrium in the S‐1 spheromak [M. Yamada, J. Sinnis, H. P. Furth, M. Okabayashi, G. Sheffield, T. H. Stix, and A. M. M. Todd, in Proceedings of the US‐Japan Symposium on Compact Toruses and Energetic Particle Injection (Princeton Plasma Physics Laboratory, Princeton, NJ, 1979), p. 171] by use of magnetic probes inside the plasma show that the final magnetic equilibrium is one that has relaxed close to the Taylor (minimum‐energy) state, even though the plasma is far from that state during formation. The comparison is made by calculating the two‐dimensional μ profile of the plasma from the probe data, where μ is defined as μ0 j∥/B. Measurements using a triple Langmuir probe proved evidence to support the conclusion that the pressure gradients in the relaxed state are confined to the edge region of the plasma.Experimental measurements of the equilibrium in the S‐1 spheromak [M. Yamada, J. Sinnis, H. P. Furth, M. Okabayashi, G. Sheffield, T. H. Stix, and A. M. M. Todd, in Proceedings of the US‐Japan Symposium on Compact Toruses and Energetic Particle Injection (Princeton Plasma Physics Laboratory, Princeton, NJ, 1979), p. 171] by use of magnetic probes inside the plasma show that the final magnetic equilibrium is one that has relaxed close to the Taylor (minimum‐energy) state, even though the plasma is far from that state during formation. The comparison is made by calculating the two‐dimensional μ profile of the plasma from the probe data, where μ is defined as μ0 j∥/B. Measurements using a triple Langmuir probe proved evidence to support the conclusion that the pressure gradients in the relaxed state are confined to the edge region of the plasma.

Experimental studies of spheromak formation

Studies in the PS‐1 spheromak configuration can be effectively formed by a combined z‐ and θ‐pinch technique on both a fast (τformation≂τAlfven) and a much slower timescale. The gross tilt and shift instability of the toroid can be suppressed by a combination of conduction walls, shaping the separatrix by externally applied fields, and the use of ‘‘figure‐eight’’ coils. Optimum stabilty is obtained for almost spherical toroids. Maximum field‐reversal times for stable, well‐confined toroids are ≥40 /μsec, consistent with resistive decay. Temperatures during the stable decay are 5–10 eV; impurity radiation is an important energy‐loss mechanism.

The effect of a tilted magnetic field on the equilibrium of a pure electron plasma

If the magnetic field in a pure electron plasma containment device is not aligned with the axis of the conducting walls, the electrons in the device will accumulate at the ends of the plasma where the magnetic field lines come closest to the walls and the electrons bound to the field lines can be closest to their image charges. If the plasma is also offset radially from the center (as with an l=1 diocotron mode), then more density will accumulate at one end than the other. As the plasma revolves around the center, the electrons will slosh from one end to the other, creating a measurable signal. This signal has been experimentally measured and its origin verified using a three‐dimensional equilibrium code. This signal can be used experimentally to align the magnetic field with the conducting walls.

Peak Coalescence, Spontaneous Loss of Coherence, and Quantification of the Relative Abundances of Two Species in the Plasma Regime: Particle-In-Cell Modeling of Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) is often limited by space-charge effects. Previously, particle-in-cell (PIC) simulations have been used to understand these effects on FTICR-MS signals. However, none have extended fully into the space-charge dominated (plasma) regime. We use a two-dimensional (2-D) electrostatic PIC code, which facilitates work at very high number densities at modest computational cost to study FTICR-MS in the plasma regime. In our simulation, we have observed peak coalescence and the rapid loss of signal coherence, two common experimental problems. This demonstrates that a 2-D model can simulate these effects. The 2-D code can handle a larger numbers of particles and finer spatial resolution than can currently be addressed by 3-D models. The PIC method naturally takes into account image charge and space charge effects in trapped-ion mass spectrometry. We found we can quantify the relative abundances of two closely spaced (such as 7Be+ and 7Li+) species in the plasma regime even when their peaks have coalesced. We find that the frequency of the coalesced peak shifts linearly according to the relative abundances of these species. Space charge also affects more widely spaced lines. Singly-ionized 7BeH and 7Li have two separate peaks in the plasma regime. Both the frequency and peak area vary nonlinearly with their relative abundances. Under some conditions, the signal exhibited a rapid loss of coherence. We found that this is due to a high order diocotron instability growing in the ion cloud.

Finding the radial parallel temperature profile in a non-neutral plasma using equilibrium calculations on experimental data

In 1992, Eggleston et al. [D. L. Eggleston et al., Phys. Fluids B 4, 3432 (1992)] reported on a technique for measuring the radial temperature profile in a pure-electron plasma confined in a Malmberg-Penning trap by partially dumping the plasma onto a charge collector at the end of the trap. For short plasmas and short confining rings, the assumptions in their paper are violated and a more general calculation is needed. This paper presents a variation of the standard equilibrium calculation to find the temperature profile of a pure-electron plasma. Eggleston’s shortcut “evaporation” temperature method is found to require a correction factor that can be calculated using methods described in this paper. For typical conditions, the evaporation method overstates the actual temperature by a factor ranging from 1.1 to 1.5 or more, depending on the plasma’s total charge and temperature and the geometry of the trap.

Experimental spheromak MHD stability studies

Abstract The n = 1 tilt and radial shift instability of spheromaks is shown to be stabilized by the use of conducting wall ( r w r s ≅1.2) and stabilization coils.

Properties of axisymmetric Bernstein modes in an infinite-length non-neutral plasma

We have observed axisymmetric Bernstein modes in an infinite-length particle-in-cell code simulation of a non-neutral plasma. The plasmas considered were in global thermal equilibrium and there were at least 50 Larmor radii within the plasma radius. The density of the plasma in the simulation is parameterized by β, the ratio of the central density to the density at the Brillouin limit. These modes have m = 0 and kz=0, where the eigenfunctions vary as ei(mθ+kzz). The modes exist both near the Coriolis-shifted (by the plasma rotation) upper-hybrid frequency, ωuh=ωc2−ωp2, and near integer multiples (2, 3, etc.) of the Coriolis-shifted cyclotron frequency (called the vortex frequency, ωv=ωc2−2ωp2). The two modes near ωuh and 2ωv are the main subject of this paper. The modes observed are clustered about these two frequencies and are separated in frequency at low plasma density roughly by δω≈10(rL/rp)2ωp2/ωc. The radial velocity field of the modes has a J1(kr) dependence in the region of the plasma where the de...

Linear theory of non‐neutral plasma equilibrium in a tilted magnetic field

A linear perturbation expansion has been found that allows the rapid and accurate calculation of the response of a non‐neutral plasma to a tilted magnetic field. The results of the calculation have been found to agree with previous three‐dimensional equilibrium calculations, and also to agree with Keinigs’ [Phys. Fluids 24, 860 (1981)] calculation of zero‐frequency resonances caused by magnetic field errors. This expansion also allows the perturbed velocity to be calculated. It is speculated that this perturbed flow may be related to the enhanced radial transport in a non‐neutral plasma with a tilted magnetic field.

An interchangeable-cathode vacuum arc plasma source

A simplified vacuum arc design [based on metal vapor vacuum arc (MeVVA) concepts] is employed as a plasma source for a study of a (7)Be non-neutral plasma. The design includes a mechanism for interchanging the cathode source. Testing of the plasma source showed that it is capable of producing on the order of 10(12) charges at confinable energies using a boron-carbide disk as the cathode target. The design is simplified from typical designs for lower energy and lower density applications by using only the trigger spark rather than the full vacuum arc in high current ion beam designs. The interchangeability of the cathode design gives the source the ability to replace only the source sample, simplifying use of radioactive materials in the plasma source. The sample can also be replaced with a completely different conductive material. The design can be easily modified for use in other plasma confinement or full MeVVA applications.

A pedagogical note on the relativistic velocity addition formula

The velocity addition formula for special relativity in one dimension (along the direction of relative motion of the two coordinate systems) is easier to apply if written using the same subscript notation usually used with classical relative velocity vectors.