#### Date Awarded

2017

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Department

Physics

#### Advisor

Eugene R. Tracy

#### Abstract

Mode conversion is a phenomenon that is of interest as a method for heating in fusion reactors. A magnetosonic wave with dispersion relation DMS propagates toward the interior of the plasma, where it excites an ion-hybrid wave with dispersion relation DIH and thereby transfers energy to the plasma. We wish to study this process using ray-based methods. The 2 2 dispersion matrix D, which is, in general, a function of the phase space variables (x; y; kx; ky), must be put into normal form, in which the diagonals of D, identied as the uncoupled dispersion relations, DMS and DIH, Poisson-commute with the o-diagonals, identied as the coupling constants. Once in this form, we look at the points in the four- dimensional phase space that satisfy DMS(x; y; kx; ky) = 0 = DIH(x; y; kx; ky), which, in general, will be a two-dimensional surface we call the conversion surface. We implement our normal form algorithm on two models. First, we consider a slab model, in which D depends only on (x; kx; ky). Then we consider a two-dimensional model of the polodial cross section of a tokamak reactor with a DT plasma with a density ratio of one- to-one. Using numerical methods, we put D into normal form and identify the conversion surface. For both models, we nd that there are regions in the four-dimensional phase space where the normal form transformation is well behaved and the conversion surface is what we expect. These are where the two dispersion surfaces DMS(x; y; kx; ky) = 0 and DIH(x; y; kx; ky) = 0 intersect transversely. However, there are also regions in the phase space where the normal form transformation is not well behaved. These coincide with tangential conversions, that is, where the two dispersion surfaces intersect tangentially. In this case, we must revisit the normal form theory and adapt it to this non-generic situation. Finally, we compute the transmission and conversion coecients for such tangential conversions.

#### DOI

http://dx.doi.org/doi:10.21220/S2F66F

#### Rights

© The Author

#### Recommended Citation

Johnston, David Gregory, "A global normal form for two-dimensional mode conversion" (2017). *Dissertations, Theses, and Masters Projects.* William & Mary. Paper 1516639767.

http://dx.doi.org/doi:10.21220/S2F66F