Why is Boris algorithm so good?

Abstract

Due to its excellent long term accuracy, the Boris algorithm is the de facto standard for advancing a charged particle. Despite its popularity, up to now there has been no convincing explanation why the Boris algorithm has this advantageous feature. In this paper, we provide an answer to this question. We show that the Boris algorithm conserves phase space volume, even though it is not symplectic. The global bound on energy error typically associated with symplectic algorithms still holds for the Boris algorithm, making it an effective algorithm for the multi-scale dynamics of plasmas.

Characterization of the NEPOMUC primary and remoderated positron beams at different energies

“…At each time step, after calculating the magnetic field, the positions and velocities of the particles were updated using an integrator scheme based on the Boris algorithm [15].…”

Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational

“…Interestingly, the calculations in Ref. [5] do not preclude a discrete variational formulation, as claimed in Ref. [12].…”

“…However, this claim contradicts claims made in Refs. [5,14], which demonstrate the volume-preserving property of the Boris scheme. Although symplectic integrators are also volume preserving, volume-preserving integrators are not necessarily symplectic, and Ref.…”

“…Although symplectic integrators are also volume preserving, volume-preserving integrators are not necessarily symplectic, and Ref. [5] concludes the Boris algorithm is only volumepreserving based on direct calculation of a symplecticity condition. Interestingly, the calculations in Ref.…”

“…Its popularity stems from simple implementation, rapid iteration, and excellent long-term numerical fidelity [1,5]. Excellent long-term behavior strongly suggests the numerical dynamics exhibit conservation laws analogous to those governing the continuous Lorentz force system [6].…”