Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics

Area of Science:

• Computational physics
• Relativistic electrodynamics
• Numerical analysis

Background:

• Simulating particle dynamics in electromagnetic fields is crucial for understanding fundamental physics.
• Existing numerical methods can suffer from accumulating errors, especially in long-term simulations.
• The Lorentz-Bargmann-Michel-Telegdi equation provides a framework for describing relativistic particle spin dynamics.

Purpose of the Study:

• To develop novel explicit numerical schemes for solving the relativistic dynamics and spin of particles.
• To analyze the properties of these new schemes, including energy conservation, volume conservation, and convergence.
• To compare the performance of the new schemes against established methods like the Boris pusher.

Main Methods:

• Formulation of numerical schemes using the Clifford algebra representation of the Lorentz-Bargmann-Michel-Telegdi equation.
• Implementation of methods analogous to the leapfrog and Verlet algorithms.
• Empirical benchmarking against analytical solutions in constant uniform electrodynamic fields.
• Investigation of particle spin dynamics in a plane-wave electromagnetic field configuration.

Main Results:

• The developed numerical schemes are energy conserving, volume conserving, and second-order convergent.
• These schemes exhibit bounded numerical errors in constant magnetic fields over long simulation times.
• In contrast, the Boris pusher shows a linearly increasing angular error over time.
• The study successfully investigates complex spin dynamics in a plane-wave field.

Conclusions:

• The new explicit numerical schemes offer a robust and accurate approach for simulating relativistic particle dynamics and spin.
• These methods provide significant advantages over existing techniques, particularly for long-term simulations.
• The findings contribute to advancements in computational physics and relativistic electrodynamics.