Characterizing Electrons in Primary and Secondary Magnetic Islands During Magnetic Reconnection

The physics underlying particle-in-cell simulations that are widely employed in studying plasma dynamics are reviewed. Results from a two-dimensional particle-in-cell simulation of fully kinetic, undriven, collisionless magnetic reconnection are studied to compare the electrons in a primary magnetic island formed from an ion current sheet and the electrons in a secondary island formed in an electron current layer. We find that the secondary island is born with a strong out-of-plane current density due to localized peaks in the electron density and out-of-plane electron velocity; the secondary island retains these features as it evolves, distinguishing it from the primary island. For the first time distinct features in electron velocity distributions are established for both types of islands. These magnetic island comparisons and their connection to in situ Cluster observations are analysis techniques valuable to NASA’s Magnetospheric Multiscale mission to launch in 2014 which is capable of resolving the various types of electron distributions discussed in this thesis

Attitude analysis in Flatland: The plane truth

Many results in attitude analysis are still meaningful when the attitude is restricted to rotations about a single axis. Such a picture corresponds to attitude analysis in the Euclidean plane. The present report formalizes the representation of attitude in the plane and applies it to some well-known problems. In particular, we study the connection of the 'additive' and 'multiplicative' formulations of the differential corrector for the quaternion in its two-dimensional setting

New quests for better attitudes

During the past few years considerable insight was gained into the QUEST algorithm both as a maximum likelihood estimator and as a Kalman filter/smoother for systems devoid of dynamical noise. The new algorithms and software are described and analytical comparisons are made with the more conventional attitude Kalman filter. It is also described how they may be accommodated to noisy dynamical systems