Guthrie Miller

Force free equilibria in toroidal geometry

The equation ∇×B−λB=0, where B is the magnetic field and λ is constant, is solved analytically in toroidally curved cylindrical coordinates, assuming a large aspect ratio torus.

Using exact Poisson likelihood functions in Bayesian interpretation of counting measurements.

A technique for computing the exact marginalized (integrated) Poisson likelihood function for counting measurement processes involving a background subtraction is described. An empirical Bayesian method for determining the prior probability distribution of background count rates from population data is recommended and would seem to have important practical advantages. The exact marginalized Poisson likelihood function may be used instead of the commonly used Gaussian approximation. Differences occur in some cases of small numbers of measured counts, which are discussed. Optional use of exact likelihood functions in our Bayesian internal dosimetry codes has been implemented using an interpolation-table approach, which means that there is no computation time penalty except for the initial setup of the interpolation tables.

Oscillating field current drive experiments in a reversed field pinch

Steady‐state current sustainment by oscillating field current drive (OFCD) utilizes a technique in which the toroidal and poloidal magnetic fields at the plasma surface are modulated at audio frequencies in quadrature. Experiments on the ZT‐40M reversed field pinch [Fusion Technol. 8, 1571 (1985)] have examined OFCD over a range of modulation amplitude, frequency, and phase. For all cases examined, the magnitude of the plasma current is dependent on the phase of the modulations as predicted by theory. However, evidence of current drive has only been observed at relatively low levels of injected power. For larger modulation amplitudes, the data suggest that substantial current drive is offset by increased plasma resistance as a result of modulation enhanced plasma–wall interactions. The initial experimental results and supporting theoretical interpretations of OFCD are discussed.

Quasi-steady-state toroidal discharges

A method for maintaining toroidal current in toroidal plasmas is discussed. The method requires application of suitably phased oscillating toroidal and poloidal voltages to the plasma resulting in a magnetic field configuration with small oscillations around some mean state. In such quasi‐steady states the usual v sec limitation on discharge duration is eliminated. The current drive effect is caused by a nonlinear interaction between the toroidal and poloidal circuits that can be understood in general terms from symmetry considerations. Specific calculations of the effect are made using two models: (1) a zero‐dimensional relaxation model, relevant to the reversed‐field pinch, and (2) a one‐dimensional resistive diffusion model (assuming slab geometry). The results for the relaxation model indicate a useful current drive effect that may be of importance for the reversed‐field‐pinch program.

Fluctuations and transport in a reversed field pinch edge plasma

Edge fluctuations are characterized and their associated transport is determined from Langmuir probe measurements in the ZT-40M reversed field pinch. It is found that the fluctuations have high normalized amplitudes and |n|/n = 0.4). There are significant contributions from magnetic perturbations acting on the equilibrium gradients. Compared to the global estimates, the fluctuation driven particle flux is large, whereas the corresponding electron energy flux is not. In the limiter shadow, the equilibrium density and electron temperature scale lengths are shorter and the fluctuation levels are higher. The fluctuation driven particle flux in the limiter shadow is 60% less than that in the plasma edge; most of the reduction is in the low frequency spectral region, which is where global MHD magnetic fluctuations are strongest.

Error magnetic fields in a cylindrical plasma: Stability with zero pressure

The importance of error magnetic fields is that, if large enough, they cause the destruction of magnetic surfaces. In this paper error fields in a cylindrical plasma are described by nonlinear tearing mode theory, which deals with plasma equilibria having concentrated currents flowing along closed magnetic field lines. Because of the small spatial scale of the current distribution, resistive diffusion is significant even for small resistivity and, in certain cases, causes instability. An energy principle exists and is discussed. This conceptual framework is used in a study of the stability of zero pressure equilibria toward spontaneous generation of error fields, relevant for the reversed field pinch program. Cylindrical Ohmic states are shown to be extremely unstable. Relaxed states (having flattened current profiles) have much better stability. Both completely relaxed states of the Taylor type and partially relaxed Robinson‐type states are studied. A new class of metal–liner stabilized profiles is found, which offers one explanation for the apparent stability observed in experiments with distant conducting shells. The possibility that relaxed states have weakly stochastic magnetic field lines is discussed.

Rotational instability in a linear theta pinch

The m=1 ’’wobble’’ instability of the plasma column in a 5‐m linear theta pinch has been studied using an axial array of orthogonally viewing position detectors to resolve the wavelength and frequency of the column motion. The experimental results are compared with recent theoretical predictions that include finite Larmor orbit effects. The frequency and wavelength characteristics at saturation agree with the predicted dispersion relation for a plasma rotating faster than the diamagnetic drift speed. Measurements of the magnetic fields at the ends of the pinch establish the existence of currents flowing in such a way that they short out the radial electric fields in the plasma column. The magnitude of rotation, the observed delay in the onset of m=1 motion, and the magnitude of end‐shorting currents can all be understood in terms of the torsional Alfven waves that communicate to the central plasma column the information that the ends have been shorted. The same waves are responsible for the torque which r...

UNCERTAINTIES IN INTERNAL DOSES CALCULATED FOR MAYAK WORKERS—A STUDY OF 63 CASES

This study makes use of 63 cases of Mayak workers exposed to Pu-239 with autopsy data and some late-time urine bioassay data. In addition, air-concentration data--used to construct monthly average values--are available for each case, which provide the time dependence and potential magnitudes of normal inhalation intakes for each case. The purpose of the study is to develop and test Bayesian methods of dose calculation for the Mayak workers. The first part of the study was to quantitatively characterise the uncertainties of the bioassay data. Then, starting with three different published biokinetic models, the data are fit by varying intake and model perturbation parameters, e.g., parameters influencing the lung, thoracic lymph nodes, liver and bone retention. Statistical self-consistency arguments are used to check the measurement uncertainty parameters within the Poisson-lognormal model. The second part of the study is to set up and test Bayesian dose calculations, which use the point determinations of biokinetic parameters from the study cases within a discrete, empirical Bayes approximation. The main conclusion of the study is that these methods are now ready to be applied to the entire Mayak worker population.

Steady‐state discharges

The properties of steady‐state discharges with stochastic magnetic fields are considered using a fluid model. Magnetic field stochasticity provides a simple explanation of the phenomenon of relaxation of a discharge, defined by J. B. Taylor.

METHODS USED TO CALCULATE DOSES RESULTING FROM INHALATION OF CAPSTONE DEPLETED URANIUM AEROSOLS

The methods used to calculate radiological and toxicological doses to hypothetical persons inside either a U.S. Army Abrams tank or Bradley Fighting Vehicle that has been perforated by depleted uranium munitions are described. Data from time- and particle-size-resolved measurements of depleted uranium aerosol as well as particle-size-resolved measurements of aerosol solubility in lung fluids for aerosol produced in the breathing zones of the hypothetical occupants were used. The aerosol was approximated as a mixture of nine monodisperse (single particle size) components corresponding to particle size increments measured by the eight stages plus the backup filter of the cascade impactors used. A Markov Chain Monte Carlo Bayesian analysis technique was employed, which straightforwardly calculates the uncertainties in doses. Extensive quality control checking of the various computer codes used is described.