Calculations of the Electron Energy Distribution Function in a Uranium Plasma by Analytic and Monte Carlo Techniques

Electron energy distribution functions were calculated in a U235 plasma at 1 atmosphere for various plasma temperatures and neutron fluxes. The distributions are assumed to be a summation of a high energy tail and a Maxwellian distribution. The sources of energetic electrons considered are the fission-fragment induced ionization of uranium and the electron induced ionization of uranium. The calculation of the high energy tail is reduced to an electron slowing down calculation, from the most energetic source to the energy where the electron is assumed to be incorporated into the Maxwellian distribution. The pertinent collisional processes are electron-electron scattering and electron induced ionization and excitation of uranium. Two distinct methods were employed in the calculation of the distributions. One method is based upon the assumption of continuous slowing and yields a distribution inversely proportional to the stopping power. An iteration scheme is utilized to include the secondary electron avalanche. In the other method, a governing equation is derived without assuming continuous electron slowing. This equation is solved by a Monte Carlo technique

Sample Size Calculation and Blinded Recalculation for Analysis of Covariance Models with Multiple Random Covariates

When testing for superiority in a parallel-group setting with a continuous outcome, adjusting for covariates is usually recommended. For this purpose, the analysis of covariance is frequently used, and recently several exact and approximate sample size calculation procedures have been proposed. However, in case of multiple covariates, the planning might pose some practical challenges and pitfalls. Therefore, we propose a method, which allows for blinded re-estimation of the sample size during the course of the trial. Simulations confirm that the proposed method provides reliable results in many practically relevant situations, and applicability is illustrated by a real-life data example

The TITAN oscillating-field current-drive system

The TITAN study uses oscillating-field current drive (OFCD) for steady-state operation in a reversed-field-pinch (RFP) fusion reactor. A circuit model which simulates the plasma, first wall, blanket, and coils has been developed and applied to two TITAN reactor designs to assess OFCD efficiency and power-supply requirements. Methods for optimizing current-drive efficiency and minimizing power-supply requirements have been identified. 15 refs

The TITAN magnet configuration

The TITAN study uses copper-alloy ohmic-heating coils (OHC) to startup inductively a reversed-field-pinch (RFP) fusion reactor. The plasma equilibrium is maintained with a pair of superconducting equilibrium-field coils (EFCs). A second pair of copper EFCs provides the necessary trimming of the equilibrium field during plasma transients. A compact toroidal-field-coil (TFC) set is provided by an integrated blanket/coil (IBC). The IBC concept also is applied to the toroidal-field divertor coils. Steady-state operation is achieved with oscillating-field current drive, which oscillates at low amplitude and frequency the OHCs, EFCs, the TFCs, and divertor coils about their steady-state currents. An integrated magnet design, which uses low-field, low technology coils, and the related design basis is given. 18 refs

Combining Stochastic Tendency and Distribution Overlap Towards Improved Nonparametric Effect Measures and Inference

A fundamental functional in nonparametric statistics is the Mann-Whitney functional ${\theta} = P (X < Y )$ , which constitutes the basis for the most popular nonparametric procedures. The functional ${\theta}$ measures a location or stochastic tendency effect between two distributions. A limitation of ${\theta}$ is its inability to capture scale differences. If differences of this nature are to be detected, specific tests for scale or omnibus tests need to be employed. However, the latter often suffer from low power, and they do not yield interpretable effect measures. In this manuscript, we extend ${\theta}$ by additionally incorporating the recently introduced distribution overlap index (nonparametric dispersion measure) $I_2$ that can be expressed in terms of the quantile process. We derive the joint asymptotic distribution of the respective estimators of ${\theta}$ and $I_2$ and construct confidence regions. Extending the Wilcoxon- Mann-Whitney test, we introduce a new test based on the joint use of these functionals. It results in much larger consistency regions while maintaining competitive power to the rank sum test for situations in which {\theta} alone would suffice. Compared with classical omnibus tests, the simulated power is much improved. Additionally, the newly proposed inference method yields effect measures whose interpretation is surprisingly straightforward.Comment: Submitted to Electronic Journal of Statistic