A Computational Framework for Dimensionally Reduced Particle Dynamics in Magnetic Nozzle Fields: An Adiabatic Invariant Approach

This thesis investigates a dimensional reduction strategy for modeling charged particle trajectories in electromagnetic fields representative of magnetic nozzle expansion regions. By employing Julia’s DifferentialEquations.jl and Python’s scientific libraries, particle trajectories are integrated with high precision (achieving relative and absolute error tolerances as low as 10^{-35}). Starting from the full three-dimensional Hamiltonian formulation, the problem is reduced to two dimensions via angular momentum conservation, then further simplified to one dimension through the introduction of an adiabatic invariant J, which characterizes periodic radial motion. The validity of this dimensional reduction is evaluated using the adiabaticity parameter η, which quantifies how slowly the system parameters vary compared to the oscillation timescale. Specifically, η is defined as the normalized rate of change of the radial frequency |\frac{1}{ω²}\frac{dω}{dt}|, where values much less than unity indicate valid adiabatic conditions. Numerical results show that J reliably supports dimensional reduction when $\eta \ll 1$, but its accuracy declines as η approaches unity. This study also examines the influence of electric fields on the applicability of the adiabatic approximation. These findings provide quantitative guidelines for employing J in both analytical and numerical models to reduce problem complexity. However, the method’s validity and accuracy must be carefully evaluated, especially in rapidly varying regimes.

Name thesis:degree_name

Master of Science (M.Sc.)

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Saskatchewan

Year dc:date.issued

2025

Author dc:creator

• Bahreinijangjoo, Shahab

Advisors dc:contributor.advisor

• Spiteri, Raymond J.
• Smolyakov, Andrei

Committee members dc:contributor.committeemember

• Mondal, Debajyoti
• Shevyakov, Alexey

• Magnetic nozzle
• Plasma propulsion
• Charged particle dynamics
• Adiabatic invariant
• Radial invariant J
• Adiabaticity parameter η
• Dimensional reduction
• Electric field acceleration
• Magnetic field divergence
• Lorentz force
• Hamiltonian mechanics
• Axisymmetric fields
• Particle trajectory simulation
• Julia DifferentialEquations.jl
• Runge-Kutta solvers
• Feagin14 method
• Numerical modeling
• Kinetic modeling
• Plasma expansion region
• Electromagnetic field approximation
• Magnetic moment μ
• Far-field approximation
• Azimuthal symmetry
• Plasma detachment
• Thrust efficiency
• Particle-based simulation
• High-order ODE solvers
• Plasma beam stability
• Computational plasma physics
• Reduced-order modeling.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/10388/16821

OAI identifier oai:identifier

oai:harvest.usask.ca:10388/16821