01. Research Overview
Resonant wave-particle interactions (WPI) are a fundamental driver of transport in both magnetic confinement fusion devices (like tokamaks and stellarators) and astrophysical plasmas (such as Earth's radiation belts). Standard models often assume idealized symmetries that break down in realistic 3D magnetic configurations.
My research focuses on bridging this gap by developing a reduced-order kinetic simulation model. By isolating the resonant population evolution from the background thermal evolution, we can efficiently model complex nonlinear phenomena like mode chirping, bursting, and phase-space clumping without the computational cost of fully resolving the background timescales.
02. Technical Methodology
The Vlasov-Poisson Model
We utilize the Vlasov-Poisson system to model the "bump-on-tail" instability as a paradigm for general WPI. The electric field amplitude \( \hat{E}(t) \) and phase \( \phi(t) \) are evolved via coupling equations derived from Ampere's law, driven by the current density \( j_b \) of energetic beam electrons.
Algorithm
δf Method: To reduce Monte-Carlo sampling noise, we split the distribution function into a static equilibrium \( f_0 \) and a perturbed part \( \delta f \). Only the deviation is evolved, significantly improving signal-to-noise ratio.
Numerical Stability
Pseudo-Cartesian Coordinates: To avoid singularities when the mode amplitude vanishes (\( \hat{u} \to 0 \)), we integrate in a transformed coordinate system:
u_c = u * cos(φ)
u_s = u * sin(φ)
03. Current Status & Roadmap
Phase 1: Code Implementation (WISP)
Implementing the Wave Interaction Simulation Platform (WISP). Developing the Langmuir mode stepping equations and particle trajectory integration.
Phase 2: Benchmarking
Validating the code against analytic predictions for linear growth rates and nonlinear saturation amplitudes (e.g., \( \omega_b \approx 3.2\gamma_L \)).
Phase 3: 3D Field Integration
Extending the model to include non-symmetric background magnetic fields to study drift orbit bifurcations.
Repository
This is an active research project. The codebase is updated regularly with new benchmarks and optimization routines.
View Source CodeDr. Elizabeth Paul
Kamil Ahmed Syed
Columbia Fusion Energy Research Center