Optimal reconstruction of magnetopause structures from Cluster data

The Grad-Shafranov (GS) reconstruction tech- nique, a single-spacecraft based data analysis method for recovering approximately two-dimensional (2-D) magneto- hydrostatic plasma/field structures in space, is improved to become a multi-spacecraft technique that produces a single field map by ingesting data from all four Cluster spacecraft into the calculation. The plasma pressure, required for the technique, is measured in high time resolution by only two of the spacecraft, C1 and C3, but, with the help of spacecraft po- tential measurements available from all four spacecraft, the pressure can be estimated at the other spacecraft as well via a relationship, established from C1 and C3 data, between the pressure and the electron density deduced from the poten- tials. Consequently, four independent field maps, one for each spacecraft, can be reconstructed and then merged into a single map. The resulting map appears more accurate than the individual single-spacecraft based ones, in the sense that agreement between magnetic field variations predicted from the map to occur at each of the four spacecraft and those actually measured is significantly better. Such a composite map does not satisfy the GS equation any more, but is op- timal under the constraints that the structures are 2-D and time-independent. Based on the reconstruction results, we show that, even on a scale of a few thousand km, the magne- topause surface is usually not planar, but has significant cur- vature, often with intriguing meso-scale structures embedded in the current layer, and that the thickness of both the current layer and the boundary layer attached to its earthward side can occasionally be larger than 3000 km

Optimization of the Fading MIMO Broadcast Channel: Capacity and Fairness Perspectives

Multiple input multiple output (MIMO) systems are now a proven area in current and future telecommunications research. MIMO wireless channels, in which both the transmitter and receiver have multiple antennas, have been shown to provide high bandwidth efficiency. In this thesis, we cover MIMO communications technology with a focus on cellular systems and the MIMO broadcast channel (MIMO-BC). Our development of techniques and analysis for the MIMO-BC starts with a study of single user MIMO systems. One such single user technique is that of antenna selection. In this thesis, we discuss various flavours of antenna selection, with the focus on powerful, yet straightforward, norm-based algorithms. These algorithms are analyzed and the results of this analysis produce a powerful and flexible power scaling factor. This power scaling factor can be used to model the gains of norm-based antenna selection via a single signal-to-noise ratio (SNR)-based parameter. This provides a powerful tool for engineers interested in quickly seeing the effects of antenna selection on their systems. A novel low complexity power allocation scheme follows on from the selection algorithms. Named “Poor Man’s Waterfilling” (PMWF), this scheme can provide significant gains in low SNR systems with very little extra complexity compared to selection alone. We then compare a variety of algorithms for the MIMO-BC, ranging from selection to beamforming, to the optimal, yet complex, iterative waterfilling (ITWF) solution. In this thesis we show that certain algorithms perform better in different scenarios, based on whether there is shadow fading or not. A power scaling factor analysis is also performed on these systems. In the cases where the user’s link gains are widely varying, such as when shadowing and distance effects are present, user fairness is impaired when optimal and near optimal throughput occurs. This leads to a key problem in the MIMO-BC, the balance between user fairness and throughput performance. In an attempt to find a suitable balance between these two factors, we modify the ITWF algorithm by both introducing extra constraints and also by using a novel utility function approach. Both these methods prove to increase user fairness with only minor loss in throughput over the optimal systems. The introduction of MIMO systems to the cellular domain has been hampered by the effects of interference between the cells. In this thesis we move MIMO to the cellular domain, addressing the interference using two different methods. We first use power control, where the transmit power of the base station is controlled to optimize the overall system throughput. This leads to promising results using low complexity methods. Our second method is a novel method of collaboration between base stations. This collaboration transforms neighbouring cell sectors into macro-cells and this results in substantial increases in performance

Optimal reconstruction of magnetopause structures from Cluster data

The Grad-Shafranov (GS) reconstruction technique, a single-spacecraft based data analysis method for recovering approximately two-dimensional (2-D) magnetohydrostatic plasma/field structures in space, is improved to become a multi-spacecraft technique that produces a single field map by ingesting data from all four Cluster spacecraft into the calculation. The plasma pressure, required for the technique, is measured in high time resolution by only two of the spacecraft, C1 and C3, but, with the help of spacecraft potential measurements available from all four spacecraft, the pressure can be estimated at the other spacecraft as well via a relationship, established from C1 and C3 data, between the pressure and the electron density deduced from the potentials. Consequently, four independent field maps, one for each spacecraft, can be reconstructed and then merged into a single map. The resulting map appears more accurate than the individual single-spacecraft based ones, in the sense that agreement between magnetic field variations predicted from the map to occur at each of the four spacecraft and those actually measured is significantly better. Such a composite map does not satisfy the GS equation any more, but is optimal under the constraints that the structures are 2-D and time-independent. Based on the reconstruction results, we show that, even on a scale of a few thousand km, the magnetopause surface is usually not planar, but has significant curvature, often with intriguing meso-scale structures embedded in the current layer, and that the thickness of both the current layer and the boundary layer attached to its earthward side can occasionally be larger than 3000km

Four-spacecraft determination of magnetopause orientation, motion and thickness: comparison with results from single-spacecraft methods

In this paper, we use Cluster data from one magnetopause event on 5 July 2001 to compare predictions from various methods for determination of the velocity, orientation, and thickness of the magnetopause current layer. We employ established as well as new multi-spacecraft techniques, in which time differences between the crossings by the four spacecraft, along with the duration of each crossing, are used to calculate magnetopause speed, normal vector, and width. The timing is based on data from either the Cluster Magnetic Field Experiment (FGM) or the Electric Field Experiment (EFW) instruments. The multi-spacecraft results are compared with those derived from various single-spacecraft techniques, including minimum-variance analysis of the magnetic field and deHoffmann-Teller, as well as Minimum-Faraday-Residue analysis of plasma velocities and magnetic fields measured during the crossings. In order to improve the overall consistency between multi- and single-spacecraft results, we have also explored the use of hybrid techniques, in which timing information from the four spacecraft is combined with certain limited results from single-spacecraft methods, the remaining results being left for consistency checks. The results show good agreement between magnetopause orientations derived from appropriately chosen single-spacecraft techniques and those obtained from multi-spacecraft timing. The agreement between magnetopause speeds derived from single- and multi-spacecraft methods is quantitatively somewhat less good but it is evident that the speed can change substantially from one crossing to the next within an event. The magnetopause thickness varied substantially from one crossing to the next, within an event. It ranged from 5 to 10 ion gyroradii. The density profile was sharper than the magnetic profile: most of the density change occured in the earthward half of the magnetopause.<br><br> <b>Key words.</b> Magnetospheric physics (magnetopause, cusp and boundary layers; instruments and techniques) – Space plasma physics (discontinuities

Plasma convection in the magnetotail lobes: statistical results from Cluster EDI measurements

A major part of the plasma in the Earth's magnetotail is populated through transport of plasma from the solar wind via the magnetotail lobes. In this paper, we present a statistical study of plasma convection in the lobes for different directions of the interplanetary magnetic field and for different geomagnetic disturbance levels. The data set used in this study consists of roughly 340 000 one-minute vector measurements of the plasma convection from the Cluster Electron Drift Instrument (EDI) obtained during the period February 2001 to June 2007. The results show that both convection magnitude and direction are largely controlled by the interplanetary magnetic field (IMF). For a southward IMF, there is a strong convection towards the central plasma sheet with convection velocities around 10 km s<sup>−1</sup>. During periods of northward IMF, the lobe convection is almost stagnant. A <I>B<sub>y</sub></I> dominated IMF causes a rotation of the convection patterns in the tail with an oppositely directed dawn-dusk component of the convection for the northern and southern lobe. Our results also show that there is an overall persistent duskward component, which is most likely a result of conductivity gradients in the footpoints of the magnetic field lines in the ionosphere

Alfvén waves in the near-PSBL lobe: Cluster observations

Electromagnetic low-frequency waves in the magnetotail lobe close to the PSBL (Plasma Sheet Boundary Layer) are studied using the Cluster spacecraft. The lobe waves show Alfvénic properties and transport their wave energy (Poynting flux) on average toward the Earth along magnetic field lines. Most of the wave events are rich with oxygen (O+) ion plasma. The rich O+ plasma can serve to enhance the magnetic field fluctuations, resulting in a greater likelihood of observation, but it does not appear to be necessary for the generation of the waves. Taking into account the fact that all events are associated with auroral electrojet enhancements, the source of the lobe waves might be a substorm-associated instability, i.e. some instability near the reconnection site, or an ion beam-related instability in the PSBL

The effect of diamagnetic drift on motion of the dayside magnetopause reconnection line

Magnetic reconnection at the magnetopause occurs with a large density asymmetry and for a large range of magnetic shears. In these conditions, a motion of the X line has been predicted in the direction of the electron diamagnetic drift. When this motion is super Alfvenic, reconnection should be suppressed. We analysed a large data set of Double Star TC-1 dayside magnetopause crossings, which includes reconnection and nonreconnection events. Moreover, it also includes several events during which TC-1 is near the X line. With these close events, we verified the diamagnetic suppression condition with local observations near the X line. Moreover, with the same close events, we also studied the motion of the X line along the magnetopause. It is found that, when reconnection is not suppressed, the X line moves northward or southward according to the orientation of the guide field, which is related to the interplanetary magnetic field BY component, in agreement with the diamagnetic drift