ELMO Bumpy Torus Research Articles

Reflection-symmetry effects in the perturbation series of an action integral for the field-line displacement in an ELMO bumpy torus

Deviations from this ideal geometry and less-than-perfect alignment of the field coils in an ELMO Bumpy Torus generate perturbations to the ideal magnetic field configuration, resulting generally in failure of the field lines to close on themselves and thereby causing degradation in plasma confinement. The sensitivity of the field line displacement to certain types of errors in coil parameters is studied by means of a perturbation formalism developed for an action integral representing the longitudinal adiabatic invariant. Reflection symmetry properties satisfied by the magnetic field and the vector potential are derived, and it is demonstrated both analytically and numerically that the leading term of the field line displacement per period of 2..pi.. around the major axis is second order in the perturbation parameter if the coil planes remain invariant under the perturbation. Numerical analyses for the field line displacement also reveal some more useful properties for the first- and second-order terms in the perturbation series.

ELMO Bumpy Torus with Enhanced Confinement

A toroidal array of racetrack-shaped coils whose major axes are alternately oriented vertically and horizontally ("Andreoletti coils") provides neoclassical confinement that is strikingly superior to a simple bumpy torus of similar aspect ratio but circular coils. For suitable parameters, the drift surfaces of deeply trapped and passing particles can be made concentric. At large minor radii, near the stabilizing ELMO rings, there exist closed, almost concentric drift surfaces for all pitch angles.

Dose Rates from Induced Activity in the Elmo Bumpy Torus Proof-Of-Principle Device

Calculated results of the dose rates from induced activity in the enclosure of the ELMO Bumpy Torus proof-of-principle device (EBT-P) are presented. A cylindrical model of EBT-P is used. EBT-P will have a hydrogen plasma and thus the plasma will not produce neutrons, but substantial numbers of photoneutrons will be produced and it is the induced activity from these photoneutrons that is considered. The activation dose rates are presented for a variety of operating times and times after shutdown. Dose rates about5 to 10 mrem/h at 1 h after shutdown are obtained and the major contributor to the dose rate at 1 h after shutdown is found to be /sup 24/Na (half-life = 15.0 h).

Scanning microwave interferometer for ELMO bumpy torus

A simple 4-mm scanning microwave interferometer has been developed and employed for electron density profile measurements on the ELMO bumpy torus (EBT). By making use of a pair of horizontally moving 45° mirrors that are located at the top and bottom of the plasma volume, the system avoids the deleterious effects of plasma sputtering and wall material flaking, since the microwave transmission and receiving horns do not view the plasma directly.

The role of the hot-electron distribution function in the stability of the ELMO Bumpy Torus

Several recent studies of ELMO Bumpy Torus (EBT) stability show that conflicting results can emerge when different distribution functions for the hot-electron component are used. In this paper the role of the distribution function is established by examining the stability of various modes with the aid of two models. In the ‘‘slab’’ model where the magnetic field curvature is simulated by a gravitational force it is shown that the stability of the compressional Alfvén wave is insensitive to the distribution function while the interacting interchange mode is sensitive. In the ‘‘local’’ approximation in which the curvature effects enter in a natural way it is seen that the interchange modes are insensitive so long as the anisotropy of the hot electrons is large, while other modes reflect dependence on the distribution function. Finally it is demonstrated that in the ‘‘deep well’ case the results for both modes are independent of the model and of the distribution function.

Analysis of Alpha Particle Behavior in EBT Reactors

A formalism has been developed in terms of a drift kinetic equation with a Fokker-Planck collision operator to calculate alpha-particle loss and energy-deposition-rate coefficients for one position in space and for steady-state operating conditions in an ELMO Bumpy Torus (EBT) reactor. Pitch-angle and energy-scattering terms were retained in the collision term so that the analysis provides information on alpha-particle behavior due to pitch-angle scattering into loss regions in velocity space and information on alpha energy deposition during slowing down in the device. A square-well magnetic-field shape is assumed and the resulting particle loss rates and energy-deposition rates are calculated. For typical EBT reactor parameters, results show that while 80 to 90% of the alpha particles are scattered into a pitch-angle loss region and lost from the device, more than 70% of the alpha-particle energy is deposited in the core plasma and about 1 to 2% goes to alphas retained in the plasma as ash. Parametric studies are performed, and the sensitivity to plasma potential, the pitch angle, the width of loss regions, and computational procedures are analyzed.

Use of Advanced Programmable Logic Controllers to Monitor and Control the Elmo Bumpy Torus - Proof-Of-Principle Device

The Elmo Bumpy Torus - Proof-of-Principle (EBT-P) device is designed with an instrumentation and control system based upon the use of an advanced Programmable Logic Controller (PLC). The modern PLC incorporates many advanced programming features not available in earlier PLC’s intended for application to conventional relay logic replacement. The additional power and flexibility of these modern PLC’s is especially applicable to an experimental device such as EBT-P which is made up of several complex interrelated subsystems whose operational characteristics will be evolving throughout the lifetime of the device. The rationale for the selection of advanced PLC’s for EBT-P and the approach taken to design of the software developed to control EBT-P are the topics addressed in this paper.

Particle Confinement in EBT Reactors with Noncircular Mirror Coils

Methods of improving single particle confinement in the vacuum magnetic field of an ELMO Bumpy Torus (EBT) reactor have heretofore focused on enhancement of the effective magnetic aspect ratio through the addition of relatively low current supplementary coils to the basic EBT configuration of toroidally linked circular mirror coils. This method of aspect ratio enhancement is reviewed and compared to the use of noncircular, D-shaped mirror coils. A critical parameter in this evaluation is the required radial thickness delta of the blanket-shield assembly in the coil throat. Results indicate that D-coils represent an attractive alternative to the supplementary coil configurations if future neutronics calculations show that delta

Assessment of Energetic Ion Rings Versus Electron Rings for an EBT Reactor

This paper summarizes the results of a preliminary assessment of energetic ion rings for use in an ELMO Bumpy Torus (EBT) reactor. The properties of ion rings are compared with those of electron rings. Ion rings appear to require sizable devices and magnetic field strengths for stable, adiabatic confinement. Stable windows for steady-state ion ring operation having acceptable power requirements, determined mainly by Coulomb drag on the background electrons, appear to exist for EBT reactors. Power requirements for ion rings can be quantitatively lower than those for electron rings, provided the ion ring volume does not greatly exceed the electron ring volume. Some stability properties of ion rings are also discussed. Results of parametric trade-off studies for ion rings versus electron rings using an EBT reactor systems code are presented.

Design for the National RF Test Facility at ORNL

Conceptual and preliminary engineering design for the National RF Test Facility at Oak Ridge National Laboratory (ORNL) has been completed. The facility will comprise a single mirror configuration embodying two superconducting development coils from the ELMO Bumpy Torus Proof-of-Principle (EBT-P) program on either side of a cavity designed for full-scale antenna testing. The coils are capable of generating a 1.2-T field at the axial midpoint between the coils separated by 1.0 m. The vacuum vessel will be a stainless steel, water-cooled structure having an 85-cm-radius central cavity. The facility will have the use of a number of continuous wave (cw), radio-frequency (rf) sources at levels including 600 kW at 80 MHz and 100 kW at 28 GHz. Several plasma sources will provide a wide range of plasma environments, including densities as high as approx. 5 x 10/sup 13/ cm/sup -3/ and temperatures on the order of approx. 10 eV. Furthermore, a wide range of diagnostics will be available to the experimenter for accurate appraisal of rf testing.

Transport Scaling Studies for EBT Reactor

Transport simulation and modeling studies for the ELMO bumpy Torus (EBT) reactor are carried out by using 0-D and 1-1/2-D transport calculations. The time-dependent 0-D model is used for global analysis whereas the 1-1/2-D radial transport code is used for accurate determination of density, temperature, and ambipolar potential profiles and of the role of these profiles in reactor plasma performance. Analysis with the 1-1/2-D transport code shows that profile effects near the outer edge of the hot electron ring lead to enhanced confinement by a least a factor of 2 to 5 beyond the simple scaling that is obtained from the global analysis. The radial profiles of core plasma density and temperatures (or core pressure) obtained from 1-1/2-D transport calculations are found to be similar to those theoretically required for stability.

EBT-P Gamma Ray Shielding Analysis

First, a one-dimensional scoping study was performed for the gamma-ray shield of the ELMO Bumpy Torus proof-of-principle device to define appropriate shielding material and determine the required shielding thickness. The dose-equivalent results are analyzed as a function of the radiation-shield thickness for different shielding options. A sensitivity analysis for the pessimistic case is given. The recommended shielding option based on the performance and cost is discussed. Next, a three-dimensional scoping study for the coil shield was performed for four different shielding options to define the heat load for each component and check the compliance with the design criterion of 10 watts maximum heat load per coil from the gamma-ray sources. Also, a detailed biological-dose survey was performed which included: (a) the dose equivalent inside and outside the building, (b) the dose equivalent from the two mazes of the building, and (c) the skyshine contribution to the dose equivalent.

The Design Method for a Control Process for Multiple Source Electron Cyclotron Resonance Heating for the Elmo Bumpy Torus - Proof of Principle Device.

A method for generating a control process for the Elmo Bumpy Torus electron cyclotron resonance heating system was developed. The method developed was a general-to-specific method inspired by methods of structured software development. It had a dual structure which put the physical system analysis and the process analysis on equal footings. The method resulted in a two branch, multilayered product, various parts of which led directly to the several final products required for plasma heating control.

Space potential profiles in ELMO Bumpy Torus (EBT) experiment

Spatially resolved measurements of the electric space potential in the ELMO Bumpy Torus (EBT) have been made by a heavy ion beam probe. The EBT-I device is characterized by positive potentials in the surface plasma the order of 100 V and by a nearly symmetric potential well in the core plasma of up to 300 V with respect to the surface potential. The EBT-S device has a similar potential structure with well depth and peak potential similar to or greater than that of EBT-I. Peak potential and well depth increase as the edge gas pressure is lowered and as the microwave power is increased. The potential structure is strongly linked to the specific heating geometry. The ambipolar electric field is large enough generally to dominate the core electron neoclassical diffusion. The potential profile is approximately parabolic in the core, which is shown to be a natural consequence of the spatially uniform plasma source function.

Direct losses in the ELMO Bumpy Torus experiment

For resonant ions in the ELMO Bumpy Torus experiment (EBT), the width of the orbits near the resonance scales like (∂Ω/∂r)−1, where Ω is the precessional drift frequency. For (∂Ω/∂r)≊0 over most of the plasma, the ions will drift vertically out of the machine due to the toroidal magnetic field. The problem of these directly lost particles is analyzed by considering collisional diffusion into a hole in velocity space. Particle and energy loss rates including boundary layer corrections due to marginally confined particles are obtained. It is shown that these direct loss rates can be comparable to diffusion rates based on banana transport.

Monte Carlo calculation of resonant diffusion coefficients in the ELMO Bumpy Torus and the applicability of local diffusion theory

A Monte Carlo calculation of resonant diffusion coefficients in the ELMO bumpy torus (EBT) is described and is shown to agree well with analytic theory in a regime where the assumptions of local, diffusive behavior are valid. Since present and future EBT devices do not fall into this regime, local diffusion theory may not be entirely applicable.

Nonresonant electron transport in the ELMO Bumpy Torus experiment using a BGK operator

For the experimentally measured parameters in the ELMO Bumpy Torus (EBT) experiment, the electrons in the core plasma are nonresonant; that is, the average ∇B×B and E×B precessional drifts are in the same direction. Analytic transport rates exist for the electrons in the case where the ambipolar field is large relative to the plasma thermal energy. For finite fields, the diffusion coefficients have been calculated numerically. An analytic expansion away from the large field case that provides corrections to the results of Kovrizhnykh for finite fields has been developed from a BGK operator. These expressions are compared with the numerical calculations for parameters of experimental interest and it is shown that a substantially improved approximation over the Kovrizhnykh results can be obtained.

Resonant ion transport in the ELMO Bumpy Torus

Modeling the ELMO Bumpy Torus as a bumpy cylinder with toroidally induced vertical drift, neoclassical transport coefficients are obtained for resonant ions as integrals over the energy-dependent flux. A continuous approximation to this energy-dependent flux reduces to the correct results in the banana and plateau regimes and yields simple analytic formulas for the diffusion coefficients which agree well with numerical results.

A numerical analysis of flute modes in the ELMO Bumpy Torus

Allowing for realistic magnetic field and plasma density profiles, a radial eigenvalue computer code was used to investigate flute modes in the ELMO Bumpy Torus (EBT).

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.