## 34 Citations

### Explicit high-order symplectic integrators for charged particles in general electromagnetic fields

- PhysicsJ. Comput. Phys.
- 2016

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

- PhysicsJ. Comput. Phys.
- 2015

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

- PhysicsPhysical review. E
- 2021

A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-Bargmann-Michel-Telegdi equation…

### Long term analysis of splitting methods for charged-particle dynamics

- PhysicsAppl. Math. Comput.
- 2023

In this paper, we rigorously analyze the energy, momentum and magnetic moment behaviours of two splitting methods for solving charged-particle dynamics. The near-conservations of these invariants are…

### Continuous-stage symplectic adapted exponential methods for charged-particle dynamics with arbitrary electromagnetic fields

- MathematicsArXiv
- 2022

. This paper is devoted to the numerical symplectic approximation of the charged- particle dynamics (CPD) with arbitrary electromagnetic ﬁelds. By utilizing continuous-stage methods and exponential…

### Energy behavior of Boris algorithm

- Physics
- 2020

The energy behavior of the Boris method is found to be strongly related to the integrability of the Hamiltonian system, and if the invariant tori is preserved under Boris discretization, the energy error can be bounded for an exponentially long time, otherwise the error will show a linear growth.

### Symmetric multistep methods for charged-particle dynamics

- Physics
- 2017

A class of explicit symmetric multistep methods is proposed for integrating the equations of motion of charged particles in an electro-magnetic field. The magnetic forces are built into these methods…

### Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field

- PhysicsNumerische Mathematik
- 2020

The numerical discretisation is studied for a variational integrator that is an analogue for charged-particle dynamics of the Störmer–Verlet method to yield near-conservation of a modified magnetic moment and a modified energy over similarly long times.

### Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field

- PhysicsNumerische Mathematik
- 2020

The differential equations of motion of a charged particle in a strong non-uniform magnetic field have the magnetic moment as an adiabatic invariant. This quantity is nearly conserved over long time…

### Asymptotically preserving particle methods for strongly magnetizedplasmas in a torus

- Computer ScienceSSRN Electronic Journal
- 2022

A class of particle methods for the Vlasov equation with a strong external magnetic ﬁeld in a torus conﬁguration based on higher-order semi-implicit numerical schemes already validated on dissipative systems and for magneticﬂelds pointing in a ﬂxed direction is proposed and analyzed.

## References

SHOWING 1-10 OF 13 REFERENCES

### Construction of higher order symplectic integrators

- Mathematics, Physics
- 1990

### Discrete mechanics and variational integrators

- MathematicsActa Numerica
- 2001

This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of…

### RUNGE-KUTTA SCHEMES FOR HAMILTONIAN SYSTEMS

- Computer Science
- 2005

The application of Runge-Kutta schemes to Hamiltonian systems of ordinary differential equations and the issue of exact conservation in the time-discretization of the continuous invariants of motion is considered.

### A Can0nical Integrati0n Technique

- MathematicsIEEE Transactions on Nuclear Science
- 1983

The class of differential equations of interest to this paper is that in which the equations are derivable from a Hamiltonian by the use of Hamilton's equations. The exact solution of such a system…

### Geometric integration for particle accelerators

- Physics, Education
- 2006

This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not…

### Exact charge conservation scheme for Particle-in-Cell simulation with an arbitrary form-factor

- Physics
- 2001

### Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media

- Mathematics
- 1966

Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a…

### Plasma Physics via Computer Simulation

- Physics
- 1985

PART 1: PRIMER Why attempting to do plasma physics via computer simulation using particles makes good sense Overall view of a one dimensional electrostatic program A one dimensional electrostatic…

### Simulation of beams or plasmas crossing at relaticistic velocity

- Physics
- 2007

Simulation of beams or plasmas crossing at relativistic velocity. J.-L. Vay Lawrence Berkeley National Laboratory, CA, U.S.A. ∗ Abstract This paper addresses the numerical issues related to the…