Discrete line integral method for the Lorentz force system
For computational physics, this provides an energy-conserving method for simulating charged particle motion, but it is incremental over existing geometric integration techniques.
The paper applies the Boole discrete line integral to solve the Lorentz force system as a non-canonical Hamiltonian system, achieving exact energy conservation for polynomial Hamiltonians of degree ≤4 and approximate conservation otherwise. Numerical experiments demonstrate the energy-preserving property compared to the Boris method.
In this paper, we apply the Boole discrete line integral to solve the Lorentz force system which is written as a non-canonical Hamiltonian system. The method is exactly energy-conserving for polynomial Hamiltonians of degree $ν\leq 4$. In any other case, the energy can also be conserved approximatively. With comparison to well-used Boris method, numerical experiments are presented to demonstrate the energy-preserving property of the method.