Global Sensitivity Analysis of Plasma Instabilities
Project Goals and Description:
Active subspace analysis is a useful computational tool to identify and exploit the most important linear combinations in the space of a model's input parameters. These directions depend inherently on a quantity of interest, which can be represented as a function from input parameters to model outputs. As the dynamics of many plasma models are driven by potentially uncertain parameter values, the utilization of active subspaces to perform global sensitivity analysis represents an important tool to understand how certain physical phenomena depend upon fluctuations in the values of these parameters. Hence, this project focuses on the construction and implementation of new computational methods to quantify the uncertainty within the rate of instability generated by perturbations in a collisionless electrostatic or electromagnetic plasma near an unstable, spatially-homogeneous equilibrium. In this way, instabilities in such plasmas may be tamed by altering their parametric dependence.
Publications on my research website:
Interested students should have familiarity with partial differential equations (MATH 455), linear algebra (MATH 332), and scientific computing (MATH 307). Additionally, they should be open to learning more about the foundational aspects of plasma physics that are inherent to the problems of interest.
TIME COMMITMENT (HRS/WK)
The student will gain analytical skills by deriving linear dispersion relations, possibly using complex analysis, and hone their computational skills by coding in MATLAB and/or Python while conducting simulations in an HPC environment.
The student will meet weekly with Prof. Pankavich, and often a graduate student or international collaborator.