Fly me to the Moon
The Moon is our nearest neighbour in the Solar System and it is the one object in the night sky that everyone recognises. In recent years it is receiving a renewed interest from the scientific community and space industry. For instance, the Moon's origins remain unresolved. A current theory is that it was formed from the ejecta part of the Earth's crust after a Mars size planet collided with Earth. Also, the Moon is seen as a technological stepping stone for the bigger challenge of human space travel to the planet Mars.
The most important requisite to go the Moon and planets is an understanding of celestial mechanics. What are the typical orbits available to a spacecraft? What are Lagrangian points? How much power is needed to lift a certain mass from the Earth surface into an insertion orbit that will allow you to travel to the Moon or Mars? Does transit involve one orbit or are several orbits needed? How does a sling-shot work? When and by how much do thrusters have to be fired to insert into an orbit circling our goal? Also, an important aspect is the balance between cost-effectiveness (amount of fuel needed) and travel time.
In this final year project the students will study the basic concepts of celestial mechanics, e.g. conic section orbits, three body problem, Hohmann transfer orbits. A numerical code will be used to simulate space travel that takes into account burns from spacecraft thrusters. Several cases will be studied: Apollo mission to the Moon, slow transfer to the Moon by modern space probes, a Mars mission. If time permits more exotic orbits that include sling-shots or Lagrangian points may be explored.
This project is proposed for a final year MPhys pair for the academic year 2009-2010
This project is theoretical and computational intensive
Banana orbits in tokamaks
In the development of nuclear fusion donut-shaped devices called tokamaks are used in which 100 million degrees hot plasma are confined by strong magnetic fields. These fields are composed of a strong toroidal field going around the major radius, generated by external coils, and of a much weaker poloidal field going around the minor radius, generated by a current flowing in the plasma, which confines the plasma.
Charged particles are forced to spiral along the twisted magnetic field lines. In principle, all particles would then circulate around the tokamak, visiting the inboard and outboard sides of the tokamak. However, because the magnetic field is curved and weaker on the outboard side, particles will also drift across the magnetic field. This allows for a class of particles on the outboard side that is subject to magnetic mirroring. Their orbits are not circulating but form closed paths in sections of the tokamak. Due to their shape, these orbits of trapped particles are called banana orbits.
Banana orbits are of great importance to the success of fusion in tokamak devices. They lead to a reduction of the electric conductivity and greater Ohmic heating. Furthermore, banana orbits gives rise to an additional spontaneous toroidal current, called the bootstrap current, which strengthens the poloidal magnetic field and thus plasma confinement. It is hoped that in operational fusion power plants, the confinement and heating of the plasma will be self-sustaining with help of the bootstrap current.
In this project the students will learn the basic magnetic configuration of a tokamak and calculate an analytical model of the tokamak plasma equilibrium, which incorporates the various features that lead to banana orbits. For a simple case an analytical model of banana orbits will be examined to highlight the key physical ingredients. For the general equilibrium model a numerical scheme that solves the particle's equation of (guiding) motion will be implemented. The location and fraction of particles in banana orbits will be examined as a function of equilibrium parameters such as for example plasma shape. If time remains, an equilibrium from an experimental run will be used.
This project is proposed for a final year MPhys pair for the academic year 2007-2008
This project is theoretical and computational intensive
Observing the Moon
The Moon is our nearest neighbour in the Solar System and it is the one object in the night sky that everyone recognises. In recent years it is receiving a renewed interest from the scientific community and space industry. For instance, the Moon's origins remain unresolved. A current theory is that it was formed from the ejecta part of the Earth's crust after a Mars size planet collided with Earth.
The dark regions of the Moon are giant impact basins that are filled with dark solidified lava so that they have become smooth flat plains with few craters. The light regions are the ancient Highlands which are covered in craters from meteorite impacts. At the edge of Marias large mountain ranges have been thrown up by the impact. Their names are often mirrored from ranges on Earth, e.g. Alpes, Apennines, Caucasus.
In this final year project the students will study the Moon's surface from images they will take themselves using a 10 inch Ritchey-Chretien telescope and a CCD camera. The students will be required to be present on several evenings to collect the necessary observational imaging data. The students will learn how to operate a telescope and understand its optical properties. From the images, the students will measure the shadow of lunar mountains and calculate their height. Furthermore, colour images of the Moon will be constructed and its potential for extracting geological information will be explored.
This project is proposed for a final year BSc pair in the academic year 2007-2008.
This project requires several evenings of practical observing as well as data-analysis, which is computational in nature.