Energy Balance, Radiation and Stability During Rapid Plasma Termination via Impurity Pellet Injections on DIII-D

Injections of impurity {open_quotes}killer{close_quotes} pellets on DIII-D have demonstrated partial mitigation of undesirable disruption phenomena; namely reducing the convected heat loss to the wall, and the halo current`s magnitude and toroidal asymmetry. However, the appearance of a runaway electron population and large magnetic fluctuations (B/B{sub T} {approx} 1%) is coincident with the measured rapid loss of the plasma`s thermal energy ({approx}1 MJ in 1 ms) due to impurity radiation. A numerical code is developed to simulate the impurity radiation and predict the rapid plasma cooling observed. The simulation predicts two mechanisms for the generation of runaway electrons: the {open_quotes}slideaway{close_quotes} of hot tail electrons due to rapid cooling or the transport of hot electrons into the thermally collapsed plasma due to instabilities. Pressure gradients caused by the rapid non-adiabatic cooling of the impurity are identified as the probable source of these instabilities which also lead to convective heat losses. Results of a modeling effort to optimize pellet content, impurity species and cooling time for the avoidance of instabilities and runaway electrons are shown

Design of a 3rd harmonic electron cyclotron emission diagnostic for ballooning mode fluctuations in PBX-M

A third harmonic electron cyclotron emission diagnostic using ultrawide bandwidth ( = 40 GHz) heterodyne receivers centered on 120 GHz with 14 channels per radial view is describecj for localized, long wavelength (5 % X s 50 cm), fast time response ( = 1 ps) fluctuation studies in the PBX-M tokamak. The optically gray emission signal will have a y ie/ne + (3/0)Te/Te dependence on temperature and density fluctuations where y S 1 and 1 _ P: 3 depending on local optical depth. Electron temperature fluctuation sensitivity is estimated to be 0.2 % se ' Te/Te s 2.9 % depending on local optical depth and fluctuation frequency in the 0.1-1 MHz range. Spatial resolution of approximately 3 cm radially and 5 cm vertically are estimated for 2 keV plasmas with low suprathermal electron emission

Plasma Dynamics

Contains reports on eight research projects split into two sections.National Science Foundation (Grant ENG79-07047)U.S. Air Force - Office of Scientific Research (Grant AFOSR-77-3143D)U.S. Department of Energy (Contract DE-ACO2-78ET-51013)U.S. Department of Energy (Contract DE-ACO2-78ET-53073.AO02)U.S. Department of Energy (Contract DE-ACO2-78ET-53074)U.S. Department of Energy (Contract DE-ACO2-78ET-53076)U.S. Department of Energy (Contract DE-ACO2-78ET-51002

Plasma Dynamics

Contains reports on six research projects.National Science Foundation (Grant ENG79-07047)U.S. Air Force - Office of Scientific Research (Grant AFOSR77-3143D)U.S. Air Force - Office of Scientific Research (Contract AFOSR82-0063)U.S. Department of Energy (Contract DE-ACO2-78-ET-51013)U.S. Department of Energy (Contract DE-AC02-78ET-53073.A002

Plasma Dynamics

Contains reports on ten research projects divided into two sections.National Science Foundation (Grant ENG79-07047)U.S. Air Force - Office of Scientific Research (Grant AFOSR-77-3143)U.S. Department of Energy (Contract DE-ACO2-78ET51013)U.S. Department of Energy (Contract DE-ASO2-78ET53073.AO02)U.S. Department of Energy (Contract ET-78-S-02-4682)U.S. Department of Energy (Contract DE-AS02-78ET53074)U.S. Department of Energy (Contract DE-ASO2-78ET53050)U.S. Department of Energy (Contract DE-AS02-78ET51002)U.S. Department of Energy (Contract DE-ASO2-78ET53076

Turing machines on represented sets, a model of computation for Analysis

We introduce a new type of generalized Turing machines (GTMs), which are intended as a tool for the mathematician who studies computability in Analysis. In a single tape cell a GTM can store a symbol, a real number, a continuous real function or a probability measure, for example. The model is based on TTE, the representation approach for computable analysis. As a main result we prove that the functions that are computable via given representations are closed under GTM programming. This generalizes the well known fact that these functions are closed under composition. The theorem allows to speak about objects themselves instead of names in algorithms and proofs. By using GTMs for specifying algorithms, many proofs become more rigorous and also simpler and more transparent since the GTM model is very simple and allows to apply well-known techniques from Turing machine theory. We also show how finite or infinite sequences as names can be replaced by sets (generalized representations) on which computability is already defined via representations. This allows further simplification of proofs. All of this is done for multi-functions, which are essential in Computable Analysis, and multi-representations, which often allow more elegant formulations. As a byproduct we show that the computable functions on finite and infinite sequences of symbols are closed under programming with GTMs. We conclude with examples of application