MATLAB Source Code for 1D Plasma FDTD Simulation in Electromagnetics

The one-dimensional Finite-Difference Time-Domain (FDTD) method for plasma is a classic numerical technique in computational electromagnetics for simulating interactions between electromagnetic waves and plasma. This method discretizes Maxwell's equations coupled with plasma fluid equations to achieve time-domain stepping solutions. At the implementation level, the algorithm typically comprises three core modules: The electromagnetic field update module employs Yee's staggered grid scheme to discretize Faraday's law and Ampere's circuital law; The plasma module handles electron density dynamics using Drude model or cold plasma assumptions; The boundary condition module commonly utilizes Perfectly Matched Layer (PML) absorbing boundaries to truncate the computational domain. A typical implementation alternates between electric-magnetic field updates and plasma current density calculations, where magnetic field components are offset by half a time step to maintain numerical stability. The time step must satisfy the Courant stability condition, while spatial discretization intervals need to be smaller than the minimum wavelength in plasma. For MATLAB implementations, matrix operations significantly enhance computational efficiency by avoiding explicit loops. Common optimization techniques include pre-allocating array memory, using sparse matrices for non-uniform plasma parameters, and employing vectorized operations for full-field updates. In post-processing, Fourier transforms convert time-domain results to frequency-domain responses for analyzing plasma frequency selection characteristics. The method's extensibility allows for incorporating collision frequency models to simulate dissipation effects, handling anisotropy in magnetized plasmas, and implementing multi-fluid models to distinguish different particle species. These enhancements can be achieved by adding corresponding source terms or state equations within the existing framework. Key implementation details include: - Using central difference approximations for spatial derivatives - Implementing leapfrog time stepping for field updates - Handling plasma dispersion through auxiliary differential equations - Applying PML implementation using split-field or unsplit formulations - Optimizing code structure with modular function design for easier modification