Microscopic processes in global relativistic jets containing helical magnetic fields

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton (e−–p+) and electron–positron (e±) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of “global” jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e−–p+ jet simulation a recollimation-like instability occurs and jet electrons are strongly perturbed. In the e± jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields.

Computational studies of the transverse structure of AGN jets

Both the emission properties and the evolution of the radio jets of Active Galactic Nuclei are dependent on the magnetic (B) fields that thread them. A number of observations of AGN jets suggest that the B fields they carry have a significant helical component, at least on parsec scales. This thesis uses a model, first proposed by Laing and then developed by Papageorgiou, to explore how well the observed properties of AGN jets can be reproduced by assuming a helical B field with three parameters; pitch angle, viewing angle and degree of entanglement. This model has been applied to multifrequency Very Long Baseline Interferometry (VLBI) observations of the AGN jets of Markarian 501 and M87, making it possible to derive values for the helical pitch angle, the viewing angle and the degree of entanglement for these jets. Faraday rotation measurements are another important tool for investigating the B fields of AGN jets. A helical B field component should result in a systematic gradient in the observed Faraday rotation across the jet. Real observed radio images have finite resolution; typical beam sizes for cm-wavelength VLBI observations are often comparable to or larger than the intrinsic jet widths, raising questions about how well resolved a jet must be in the transverse direction in order to reliably detect transverse Faraday-rotation structure. This thesis presents results of Monte Carlo simulations of Faraday rotation images designed to directly investigate this question, together with a detailed investigation into the probabilities of observing spurious Faraday Rotation gradients as a result of random noise and finite resolution. These simulations clearly demonstrate the possibility of detecting transverse Faraday-rotation structures even when the intrinsic jet widths are appreciably smaller than the beam width.

The development of new methods for high resolution radio astronomy imaging

Very Long Baseline Interferometry (VLBI) polarisation observations of the relativistic jets from Active Galactic Nuclei (AGN) allow the magnetic field environment around the jet to be probed. In particular, multi-wavelength observations of AGN jets allow the creation of Faraday rotation measure maps which can be used to gain an insight into the magnetic field component of the jet along the line of sight. Recent polarisation and Faraday rotation measure maps of many AGN show possible evidence for the presence of helical magnetic fields. The detection of such evidence is highly dependent both on the resolution of the images and the quality of the error analysis and statistics used in the detection. This thesis focuses on the development of new methods for high resolution radio astronomy imaging in both of these areas. An implementation of the Maximum Entropy Method (MEM) suitable for multi-wavelength VLBI polarisation observations is presented and the advantage in resolution it possesses over the CLEAN algorithm is discussed and demonstrated using Monte Carlo simulations. This new polarisation MEM code has been applied to multi-wavelength imaging of the Active Galactic Nuclei 0716+714, Mrk 501 and 1633+382, in each case providing improved polarisation imaging compared to the case of deconvolution using the standard CLEAN algorithm. The first MEM-based fractional polarisation and Faraday-rotation VLBI images are presented, using these sources as examples. Recent detections of gradients in Faraday rotation measure are presented, including an observation of a reversal in the direction of a gradient further along a jet. Simulated observations confirming the observability of such a phenomenon are conducted, and possible explanations for a reversal in the direction of the Faraday rotation measure gradient are discussed. These results were originally published in Mahmud et al. (2013). Finally, a new error model for the CLEAN algorithm is developed which takes into account correlation between neighbouring pixels. Comparison of error maps calculated using this new model and Monte Carlo maps show striking similarities when the sources considered are well resolved, indicating that the method is correctly reproducing at least some component of the overall uncertainty in the images. The calculation of many useful quantities using this model is demonstrated and the advantages it poses over traditional single pixel calculations is illustrated. The limitations of the model as revealed by Monte Carlo simulations are also discussed; unfortunately, the error model does not work well when applied to compact regions of emission.

Electromagnetic tracking and steering for catheter navigation

This thesis explores the use of electromagnetics for both steering and tracking of medical instruments in minimally invasive surgeries. The end application is virtual navigation of the lung for biopsy of early stage cancer nodules. Navigation to the peripheral regions of the lung is difficult due to physical dimensions of the bronchi and current methods have low successes rates for accurate diagnosis. Firstly, the potential use of DC magnetic fields for the actuation of catheter devices with permanently magnetised distal attachments is investigated. Catheter models formed from various materials and magnetic tip formations are used to examine the usefulness of relatively low power and compact electromagnets. The force and torque that can be exerted on a small permanent magnet is shown to be extremely limited. Hence, after this initial investigation we turn our attention to electromagnetic tracking, in the development of a novel, low-cost implementation of a GPS-like system for navigating within a patient. A planar magnetic transmitter, formed on a printed circuit board for a low-profile and low cost manufacture, is used to generate a low frequency magnetic field distribution which is detected by a small induction coil sensor. The field transmitter is controlled by a novel closed-loop system that ensures a highly stable magnetic field with reduced interference from one transmitter coil to another. Efficient demodulation schemes are presented which utilise synchronous detection of each magnetic field component experienced by the sensor. The overall tracking accuracy of the system is shown to be less than 2 mm with an orientation error less than 1°. A novel demodulation implementation using a unique undersampling approach allows the use of reduced sample rates to sample the signals of interest without loss of tracking accuracy. This is advantageous for embedded microcontroller implementations of EM tracking systems. The EM tracking system is demonstrated in the pre-clinical environment of a breathing lung phantom. The airways of the phantom are successfully navigated using the system in combination with a 3D computer model rendered from CT data. Registration is achieved using both a landmark rigid registration method and a hybrid fiducial-free approach. The design of a planar magnetic shield structure for blocking the effects of metallic distortion from below the transmitter is presented which successfully blocks the impact of large ferromagnetic objects such as operating tables. A variety of shielding material are analysed with MuMetal and ferrite both providing excellent shieling performance and an increased signal to noise ratio. Finally, the effect of conductive materials and human tissue on magnetic field measurements is presented. Error due to induced eddy currents and capacitive coupling is shown to severely affect EM tracking accuracy at higher frequencies.