Finite Ion Temperature, Plasma Rotation, and Electromagnetic Effects on Plasma Acceleration in the Magnetic Mirror Geometry

Converging-diverging magnetic field configurations (such as magnetic mirrors and mag-netic nozzles) are employed in various functions for nuclear fusion, electric propulsion, and material processing applications. The physics underlying the dynamics of plasmas in such geometries is not fully understood and remains an area of active research. The ambipolar ion acceleration by the electric field due to plasma compressibility in the inhomogeneous magnetic field, in some ways, is analogous to the acceleration in the de Laval nozzle in gas dynamics. However, plasma dynamics introduces many new phenomena. The aim of this thesis is to present and analyze the role of specific plasma processes and mechanisms, such as finite and anisotropic ion pressure, electromagnetic effects related to plasma rotation and azimuthal magnetic field, heat conductivity, ionization, and charge-exchange interactions on plasma acceleration in the magnetic nozzle and mirrors. The plasma dynamics was studied using a quasi-2D model in the paraxial approximation in which the effects of the radial magnetic field Br were considered up to first order. In this approximation, the general two-dimensional nonlinear equations for the axisymmetric equilibria with flow are reduced to a set of nonlinear one-dimensional equations along the magnetic surfaces. An analytical solution in terms of the Lambert function was derived for the acceleration of cold ions, neglecting plasma rotation and electromagnetic effects. In general, the hierarchy of fluid moment equations was solved numerically across the entire nozzle using the BOUT++ framework. The analysis is done using a two-fluid magnetohydrodynamic model. Our focus is on the ion dynamics, so we use the simple Boltzmann relation for electrons with an isothermal or polytropic equation of state. The latter allows for the inclusion of the effects of the electron cooling. The advanced magnetohydrodynamic models are used to describe the effects of a finite ion temperature, including pressure anisotropy. Higher-order transport equations with additional moments were used to study the effects of the ion temperature anisotropies and ion heat fluxes. It is shown that finite ion temperature increases the final ion exhaust velocity and that this effect is predominantly related to the mirror force due to the perpendicular ion energy. The effect of the collisionless heat fluxes on the ion acceleration was studied using the higher-order transport equations for the evolution of the heat fluxes (dynamic heat flux model). It is shown that the results obtained with the advanced fluid model are in good agreement with recent kinetic simulation results. The role of dissipative effects, such as ionization and charge-exchange interactions between ions and neutrals, was studied using the modified fluid equations. It is shown that the dynamic heat flux model provides a natural, physics-based limit for the collisional heat flux closures that are diverging in the limit of vanishing collisions. The effects of the azimuthal plasma rotation and electromagnetic effects related to Alfven-type dynamics were analyzed by solving the MHD equations for the cases of cold and isotropic hot ions and extended to include the effects of the ion temperature anisotropy in the absence of heat fluxes. The effects of plasma rotation and azimuthal magnetic field, their coupling, and the role of the boundary conditions were analyzed. It is demonstrated that the unique transonic (including subsonic and supersonic regions) accelerating solutions are fully determined by the regularization conditions at the critical points where plasma flow is equal to the phase velocity of the plasma eigenmodes, i.e., ion-sound in the electrostatic case and slow- and fast- magnetosonic and Alfven mode in the MHD case.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Physics

Grantor

University of Saskatchewan

Year dc:date.issued

2026

Author dc:creator

• Sabo, Andy

Advisor dc:contributor.advisor

• Smolyakov, Andrei

Committee members dc:contributor.committeemember

• Dick, Rainer
• Couedel, Lenaic
• Degenstein, Doug
• Yang, Qiaoqin
• Chang, Gap Soo
• Kabin, Konstantin

• Plasma, MHD, magnetic nozzle, temperature anisotropy, plasma rotation

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/10388/18163

OAI identifier oai:identifier

oai:harvest.usask.ca:10388/18163