Mesoscale ionospheric plasma irregularities and scintillation over Svalbard

This thesis investigates how navigation signals are compromised by ionospheric plasma irregularities in the auroral and polar ionosphere over Svalbard. In 2013, four multiconstellation global navigation satellite system (GNSS) receivers were installed in NyÅlesund, Longyearbyen, Hopen, and Bjørnøya. These receivers provide unprecedented coverage of scintillation and plasma density (total electron content) in the region. The four research papers in this thesis are detailed case studies investigating mesoscale irregularities and scintillation.We use data from these GNSS receivers, all-sky imagers, coherent and incoherent scatter radars, ionosondes, and in-situ satellite measurements. Paper I [van der Meeren et al., 2014] investigates scintillation and irregularities on the front of a tongue of ionization (TOI) in the polar cap. Moderate scintillation and structuring is observed on the leading edge of the TOI. We employ a novel method where we use spectrograms of the phase of raw GNSS signals to show that the structuring is real and not due to erroneous data detrending of the σφ phase scintillation index. Paper II [Oksavik et al., 2015] investigates irregularities in the dayside auroral region, specifically in relation to poleward-moving auroral forms (PMAFs). Scintillation is strongly localized to these intense and transient features, even in the presence of polar cap patches. Paper III [van der Meeren et al., 2015] investigates scintillation from substorm auroral emissions as polar cap patches enter the nightside auroral oval. The most severe scintillation is found when the auroral precipitation coincides with polar cap patches. The scintillation is strongly localized to signals intersecting intense auroral emissions. Paper IV [van der Meeren et al., 2016] investigates irregularities during quiet geomagnetic conditions. We find weak irregularities in relation to a stable and intense transpolar arc, but no scintillation is seen. The main results in this thesis are: Scintillation-producing irregularities can exist on the leading edge of TOIs, in PMAFs, and in substorm auroral precipitation when patches enter the nightside auroral oval. Of these, auroral precipitation on top of pre-existing plasma patches seems to produce the strongest scintillation. The scintillation generally shows a high degree of localization, varying significantly over distances of ∼ 100km. This clearly indicates the need for a dense network of scintillation receivers in the polar ionosphere to fully resolve this spatial variation. It also shows that detailed case studies are important to complement the averaged, static, large-scale picture common in statistical studies. We have developed a novel method of using spectrograms of the phase of raw GNSS signals to get a more complete view of irregularities than aggregate scintillation indices like σφ . Furthermore, our method does not require data detrending, and it is therefore more robust than traditional scintillation indices that are frequently used by the community. The observed irregularities cover a wide range of spatial scale sizes, from decameters to several kilometers. Irregularities at these spatial scale sizes can affect radio wave propagation from HF to GNSS frequencies. </ul

Connecting the two worlds: well-partial-orders and ordinal notation systems

Kruskal claims in his now-classical 1972 paper [47] that well-partial-orders are among the most frequently rediscovered mathematical objects. Well partial-orders have applications in many fields outside the theory of orders: computer science, proof theory, reverse mathematics, algebra, combinatorics, etc. The maximal order type of a well-partial-order characterizes that order’s strength. Moreover, in many natural cases, a well-partial-order’s maximal order type can be represented by an ordinal notation system. However, there are a number of natural well-partial-orders whose maximal order types and corresponding ordinal notation systems remain unknown. Prominent examples are Friedman’s well-partial-orders of trees with the gap-embeddability relation [76]. The main goal of this dissertation is to investigate a conjecture of Weiermann [86], thereby addressing the problem of the unknown maximal order types and corresponding ordinal notation systems for Friedman’s well-partial orders [76]. Weiermann’s conjecture concerns a class of structures, a typical member of which is denoted by T (W ), each are ordered by a certain gapembeddability relation. The conjecture indicates a possible approach towards determining the maximal order types of the structures T (W ). Specifically, Weiermann conjectures that the collapsing functions #i correspond to maximal linear extensions of these well-partial-orders T (W ), hence also that these collapsing functions correspond to maximal linear extensions of Friedman’s famous well-partial-orders