Particle methods for plasma physics

A plasma is an ionized gas with positively and negatively charged particles (ions and electrons). One promising method of generating electricity with nuclear fusion uses tokamak reactors filled with an extremely hot plasma, similar to what happens inside the Sun. A strong magnetic field keeps the plasma away from the reactor walls. This shows the importance of simulating a plasma in an electromagnetic field.<br /> <br /> One approach is to use particle methods: write down the equations of motion of the particles inside the plasma and couple them to Maxwell's equations for the electromagnetic field. The standard method for this has only moderate accuracy (it is second order). Past research on numerical methods for solving these differential equations established that it is possible to improve the accuracy in time, but that to get maximal benefit from this, the accuracy in space should also be improved.<br /> <br /> The aim of this project is to implement a method with high spatial accuracy, combine it with our accurate time stepper, and test the combined algorithm to see in what circumstances the improved accuracy is beneficial. This project requires some prior knowledge of numerical methods for both ordinary and partial differential equations and solid programming skills. An interest in plasma physics and high-performance computing are also needed.

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;s website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT</strong></em> and&nbsp;in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Particle methods for plasma physics</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/4067/dr-jitse-niesen">Jitse Niesen</a> as your proposed supervisor&nbsp;and in the finance section, please state clearly&nbsp;<em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing">Applications will be considered after the closing date. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents in support of your application by the closing date of 3 April 2024 for&nbsp;Leeds Opportunity Research Scholarship and 8 April 2024 for Leeds Doctoral Scholarship:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>,&nbsp;<a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a>&nbsp;and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">School of Mathematics Scholarships</a><span style="font-size:11.0pt"><span style="line-height:107%"><span style="font-family:&quot;Calibri&quot;,sans-serif">&nbsp;</span></span></span>are available to UK applicants (open from October 2023). <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong> &ndash;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China (now closed for 2024/25 entry). The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Important:&nbsp;</strong> Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are <strong>not</strong> covered under this studentship.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For general enquiries about applications, contact our admissions team by email to&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For questions about the research project, contact Jitse Niesen by email to&nbsp;<a href="mailto:j.niesen@leeds.ac.uk">j.niesen@leeds.ac.uk</a></p>