Expansion of a singularly perturbed equation with a two-scale converging convection term

In many physical contexts, evolution convection equations may present some very large amplitude convective terms. As an example, in the context of magnetic confinement fusion, the distribution function that describes the plasma satisfies the Vlasov equation in which some terms are of the same order as $\epsilon^{-1}$, $\epsilon \ll 1$ being the characteristic gyrokinetic period of the particles around the magnetic lines. In this paper, we aim to present a model hierarchy for modeling the distribution function for any value of $\epsilon$ by using some two-scale convergence tools. Following Fr\'enod \\& Sonnendr\"ucker's recent work, we choose the framework of a singularly perturbed convection equation where the convective terms admit either a high amplitude part or a an oscillating part with high frequency $\epsilon^{-1} \gg 1$. In this abstract framework, we derive an expansion with respect to the small parameter $\epsilon$ and we recursively identify each term of this expansion. Finally, we apply this new model hierarchy to the context of a linear Vlasov equation in three physical contexts linked to the magnetic confinement fusion and the evolution of charged particle beams

Geodesic least squares regression on information manifolds

We present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the response variable suggested by the data need not be the same as the modeled distribution. Instead they are matched by minimizing the Rao geodesic distance between them. This yields a more flexible regression method that is less constrained by the assumptions imposed through the regression model. As an example, we demonstrate the improved resistance of our method against some flawed model assumptions and we apply this to scaling laws in magnetic confinement fusion

Selection of alternative central-station technologies for the Satellite Power System (SPS) comparative assessment

An important effort is the Satellite Power System (SPS) comparative Assessment is the selection and characterization of alternative technologies to be compared with the SPS concept. The ground rules, criteria, and screening procedure applied in the selection of those alternative technologies are summarized. The final set of central station alternatives selected for comparison with the SPS concept includes: (1) light water reactor with improved fuel utilization, (2) conventional coal combustion with improved environmental controls, (3) open cycle gas turbine with integral low Btu gasifier, (4) terrestrial photovoltaic, (5) liquid metal fast breeder reactor, and (6) magnetic confinement fusion

Spheromak Experiment Using Separate Guns For Formation And Sustainment

An experiment is described that incorporates the use of separate magnetized plasma guns for formation and sustainment of a spheromak. It is shown that energy coupling efficiency approaches unity if the gun and spheromak are of comparable size. A large gun should be able to operate at lower current and therefore lower voltage. In addition, it is expected that a gun matched to the size of the spheromak will cause less perturbation to the equilibrium. It is proposed to use a smaller gun for spheromak formation and a large, efficient gun for sustainment. The theoretical basis for the experiment is developed, and the details of the experiment are described. A prediction of the equilibrium magnetic flux surfaces using the EFIT code is presented