A recently proposed set of demagnetization diagnostics [Scudder et al., submitted to Physics of Plasmas, 2015] is related to the preconditions of Guiding Center Theory (GCT) and benchmarked in kinetic particle-in-cell simulations. Specifically, GCT requires that the time and length scales of the field are long compared to the Larmor motion of the particles. When this condition is violated, the particles become demagnetized and the assumptions of magnetohydrodynamics are no longer valid. In this thesis, these diagnostics are applied to different space plasma layers of different length scales. In the past, proxy diagnostics that are not based on fundamental GCT conditions have been used to search for, and provide evidence of, demagnetization in different space plasma layers. The problem with these proxy diagnostics is that they are not invertible to demagnetization. The diagnostics presented in this thesis are not only unique to demagnetization, but also have the additional advantages of being dimensionless, scalar, and independent of coordinate system. These diagnostics are applied to three space plasma layers of different length scales, resulting in new insights and methods for detecting particle demagnetization. First, the evidence for wave heating in the solar wind is reexamined through its fundamental assumptions of demagnetization. The proxy diagnostic commonly used for demagnetization is non-conservation of the Chew-Goldberger-Low conserved quantity. This diagnostic is a good proxy for the first adiabatic invariant in the supersonic regime. To test this and compare it to the assumptions of the Helios analysis [Marsch et al., Journal of Geophysical Research: Space Physics, 88(A4), 1983], the solar wind is modeled through a self-consistent Vlasov mapping. In addition, other experimental assumptions in that same Helios analysis are also examined. Second, a new method for estimating local length scales is demonstrated across a known bow shock crossing. This new method, based on one of the demagnetization diagnostics, is different from current methods in that it can be performed with single spacecraft data and does not require a special coordinate system. Third, a new set of invertible signatures of the electron diffusion region (EDR) is introduced and applied to five magnetopause events to search for layers of collisionless magnetic reconnection. Four of these magnetopause events have not been identified before in the literature. The five EDR diagnostics are large electron pressure anisotropy, non-perturbative GCT expansion parameters, order one electron pressure agyrotropy, and order one electron thermal mach number. These EDR diagnostics are compared to a wide range of degenerate diagnostics that are commonly used in reconnection studies. The results of this analysis show that, compared to these degenerate diagnostics, the EDR diagnostics are much more surgical in their identification of electron-scale current layers.

In this dissertation we consider the dynamics of the solar interior, with particular focus on angular momentum balance and magnetic field confinement within the tachocline. In Part I we review current knowledge of the Sun's rotation. We summarise the main mechanisms by which angular momentum is transported within the Sun, and discuss the difficulties in reconciling the observed uniform rotation of the radiative interior with purely hydrodynamical theories. Following Gough & McIntyre (1998) we conclude that a global-scale interior magnetic field provides the most plausible explanation for the observed uniform rotation, provided that it is confined within the tachocline. We discuss potential mechanisms for magnetic field confinement, assuming that the field has a roughly axial-dipolar structure. In particular, we argue that the field is confined, in high latitudes, by a laminar downwelling flow driven by turbulence in the tachocline and convection zone above. In Part II we describe how the magnetic confinement picture is affected by the presence of compositional stratification in the 'helium settling layer' below the convection zone. We use scaling arguments to estimate the rate at which the settling layer forms, and verify our predictions with a simple numerical model. We discuss the implications for lithium depletion in the convection zone. In Part III we present numerical results showing how the Sun's interior magnetic field can be confined, in the polar regions, while maintaining uniform rotation within the radiative envelope. These results come from solving the full, nonlinear equations numerically. We also show how these results can be understood in terms of a reduced, analytical model that is asymptotically valid in the parameter regime of relevance to the solar tachocline. In Part IV we discuss how our high-latitude model can be extended to a global model of magnetic confinement within the tachocline.