# Undergraduate summer project

## A systematic analysis of transverse loop oscillations in the corona of the Sun (Summer 2009)

**Funding:** URSS

**Student:** Christopher Smith

The corona is the outer rarefied part of the atmosphere of the Sun. It’s high temperature in excess of one million degrees is one of the longstanding mysteries of plasma physics and astronomy. Studying this high-temperature plasma provides us with insight into the workings of other stars and as a natural plasma laboratory into physical processes in fusion experiments. The dominating force in the corona is magnetism and it structures the coronal plasma into magnetic loops. Unfortunately, it is difficult to measure accurately the coronal magnetic field strength and it therefore does not permit to constrain theoretical models.

In the last decade a panoply of observations of coronal plasma waves have been compiled. In particular, many cases of transverse oscillations of coronal loops have been unearthed and studied. The measurement of the oscillation parameters allows for an indirect measurement of the local magnetic field strength through the application of the technique of coronal seismology. The Centre for Fusion, Space and Astrophysics (CFSA) at Warwick, of which Dr Erwin Verwichte is a member, is particularly strong in this research field.

Only a fraction of transverse loop oscillations have been studied so far. Furthermore, different research groups have used different analysis techniques and it is not clear whether the various approaches are mutually consistent. The aim of this project is for the student, in collaboration with the supervisor, to identify multiple interesting oscillatory events in data catalogues from the TRACE space craft and then to analyse them in a systematic way using scientific data and visualization software. Both new and previously (but differently) studied events will be investigated. Also, the student will learn the underlying analytical theory of magnetohydrodynamic waves in structured, magnetized plasmas in order to understand how the seismological techniques are applied.

## A virtual plasma wave laboratory (Summer 2009)

**Funding:** FUSENET

**Student:** Jan Graf-von-Pahlen

Waves and instabilities play a pivotal role in the physics of high-temperature laboratory and astrophysical plasmas such as magnetically confined fusion devices and the atmosphere of the Sun. They are important for the two most fundamental outstanding questions in plasma: achieving controlled nuclear fusion with the potential of providing humanities future energy needs, and understanding the physical processes responsible for heating the corona of the Sun, our nearest star. Plasma waves are responsible for energy transport and deposition (e.g. ion-cyclotron heating in tokamaks) and may be used for plasma diagnostics though the application of techniques such as magnetohydrodynamic (MHD) coronal seismology and MHD spectroscopy. Large-scale MHD instabilities are responsible for the plasma limitations on a fusion device and cause eruptions on the Sun that can affect the Earth space environment. The Centre for Fusion, Space and Astrophysics at Warwick is particularly strong in these research fields.

The aim of the project is for the student to develop together with the supervisor an online virtual lab focused on plasma waves, which will help students and scientists to calculate quickly useful information for learning and input for scientific modeling. This involves building a physical understanding of plasma waves, performing analytical calculations to derive the suitable physical expressions, usage of visualization software to produce scientific plots, and web-based programming to construct the interactive web pages.

In particular, the student will investigate the propagation properties and observables of plasma waves depending on plasma conditions such as magnetic field strength and temperature. The key parameters, expressions and profiles will be calculated and identified (e.g. propagation speed). The interactive web page will first involve calculations of the numerical value of physical quantities but will be extended to include graphical representations of wave observables and dispersion curves. Also, initially the focus will be on low-frequency MHD waves. Later the project will be extended to high-frequency waves.

## Toroidicity-induced Alfven waves in fusion plasmas (Summer 2007)

**Funding:** URSS

**Student:** Nicholas Darvell

This project concerns the study of magnetically controlled fusion plasmas. Achieving controlled nuclear fusion is one of the holy grails of physics with the potential of providing humanities future energy needs. In a plasma, the large-scale forces can support various types of magnetohydrodynamic (MHD) waves, one of which is the Alfvén wave due to the magnetic tension. In a tokamak, the plasma is confined in a torus-shaped vessel and suspended by the strong magnetic field. Due to the twisted nature of the magnetic field and the structuring of the plasma, at most of the frequencies, Alfvén waves are strongly suppressed. However, in a few gaps in frequency, created by the curvature of the tokamak, some discrete long-lived Alfvén waves can be excited, called Toroidicity-induced Alfvén Eigenmodes (TAEs). Crucially, TAEs can influence the heating process of the tokamak during active operation. This heating occurs by alpha-particles, which are an end-product of fusion reactions. However, TAEs are excited by these particles and hence divert energy away from plasma heating. Therefore, it is important to understand the role of TAEs in fusion plasmas in context of the new international ITER fusion project.

The student will start from the general MHD equations in toroidal geometry. These equations are reduced using Fourier and perturbation techniques to calculate the governing equations for Alfvén waves in a tokamak. The appearance of TAEs are then investigated for several specific cases. For realistic tokamak plasma configurations, the student will use available numerical codes (HELENA and CASTOR) to calculate the spectrum and structure of TAEs.

The student will gain valuable experience in research in plasma physics and nuclear fusion research. This research fits into the activities of the Centre of Fusion, Space and Astrophysics of which Dr Erwin Verwichte is a member. The group currently has an EPSRC Science and Innovation grant and which involves collaborations with UKAEA, Culham. The student is encouraged to interact with other members of the group. Furthermore, this project is a potential stepping stone for starting a PhD in fusion research at Warwick in 2008.

The applied analytical techniques, such as manipulating systems of partial differential equations are generally used in mathematics, physics and engineering. Furthermore, the student will learn to operate with and understand the basics of a sophisticated numerical code. Therefore, the student will gain skills that the student will be able to apply during the fourth year of studies and in a future job or postgraduate position.