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

Tao, Molei

doi:10.1016/j.jcp.2016.09.047

Cited by 60 publications

(34 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There have been recent efforts to construct explicit symplectic integrators for this problem [9,10,12]. While such methods of arbitrary order have been shown to exist, they require many evaluations of A and A or evaluations of higher derivatives of A.…”

Section: Ehairer and C Lubichmentioning

confidence: 99%

“…While such methods of arbitrary order have been shown to exist, they require many evaluations of A and A or evaluations of higher derivatives of A. For example, the fourth-order method proposed in [10] requires 16 evaluations of each A and A per time step. This needs to be put in comparison with the two-stage Gauss-Runge-Kutta method, which is an implicit fourth-order symplectic method.…”

Section: Ehairer and C Lubichmentioning

confidence: 99%

See 1 more Smart Citation

Symmetric multistep methods for charged-particle dynamics

Hairer¹,

Lubich²

2017

The SMAI Journal of Computational Mathematics

View full text Add to dashboard Cite

Abstract.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 in a special way that respects the Lagrangian structure of the problem. It is shown that such methods approximately preserve energy and momentum over very long times, proportional to a high power of the inverse stepsize. We explain this behaviour by studying the modified differential equation of the methods and by analysing the remarkably stable propagation of parasitic solution components.Math. classification. 65L06, 65P10, 78A35, 78M25.

show abstract

Section: Ehairer and C Lubichmentioning

confidence: 99%

Section: Ehairer and C Lubichmentioning

confidence: 99%

Symmetric multistep methods for charged-particle dynamics

Hairer¹,

Lubich²

2017

The SMAI Journal of Computational Mathematics

View full text Add to dashboard Cite

show abstract

“…The Boris method was presented in [2] and it was researched further in [8,13,26]. Various other kinds of methods have also been researched for charged-particle dynamics, such as volume-preserving algorithms in [17], symplectic or K-symplectic algorithms in [18,29,33,35], and symmetric multistep methods in [14]. It is worth mentioning that, more recently, a variational integrator has been studied in [15] for solving charged-particle dynamics in a strong magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

Wang

2021

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

In this paper, exponential energy-preserving methods are formulated and analysed for solving charged-particle dynamics in a strong and constant magnetic field. The resulting method can exactly preserve the energy of the dynamics. Moreover, it is shown that the magnetic moment of the considered system is nearly conserved over a long time along this exponential energy-preserving method, which is proved by using modulated Fourier expansions. Other properties of the method including symmetry and convergence are also studied. An illustrated numerical experiment is carried out to demonstrate the long-time behaviour of the method.

show abstract

“…The method needs derivatives of the electric and magnetic field, though, which may be difficult to obtain. A recently introduced new class of methods are so-called explicit symplectic shadowed Runge-Kutta methods or ESSRK for short [11]. They are symplectic and therefore have bounded long-term energy error.…”

Section: Introductionmentioning

confidence: 99%

An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields

Tretiak

Ruprecht

2019

Journal of Computational Physics: X

View full text Add to dashboard Cite

The Lorentz equations describe the motion of electrically charged particles in electric and magnetic fields and are used widely in plasma physics. The most popular numerical algorithm for solving them is the Boris method, a variant of the Störmer-Verlet algorithm. Boris' method is phase space volume conserving and simulated particles typically remain near the correct trajectory. However, it is only second order accurate. Therefore, in scenarios where it is not enough to know that a particle stays on the right trajectory but one needs to know where on the trajectory the particle is at a given time, Boris method requires very small time steps to deliver accurate phase information, making it computationally expensive. We derive an improved version of the high-order Boris spectral deferred correction algorithm (Boris-SDC) by adopting a convergence acceleration strategy for second order problems based on the Generalised Minimum Residual (GMRES) method. Our new algorithm is easy to implement as it still relies on the standard Boris method. Like Boris-SDC it can deliver arbitrary order of accuracy through simple changes of runtime parameter but possesses better long-term energy stability. We demonstrate for two examples, a magnetic mirror trap and the Solev'ev equilibrium, that the new method can deliver better accuracy at lower computational cost compared to the standard Boris method. While our examples are motivated by tracking ions in the magnetic field of a nuclear fusion reactor, the introduced algorithm can potentially deliver similar improvements in efficiency for other applications.

show abstract

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

Cited by 60 publications

References 25 publications

Symmetric multistep methods for charged-particle dynamics

Symmetric multistep methods for charged-particle dynamics

Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields

Contact Info

Product

Resources

About