Related papers: Symplectic integrator for $s$-dependent static mag…
Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories…
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
This paper investigates the equations of motion for a relativistic charged particle in a general magnetic field. By reformulating the dynamics in four-dimensional spacetime and separating the linear and nonlinear parts, we construct an…
A transfer matrix method is presented for solving the scattering problem for the quasi one-dimensional massless Dirac equation applied to graphene in the presence of an arbitrary inhomogeneous electric and perpendicular magnetic field. It…
In this paper, explicit stable integrators based on symplectic and contact geometries are proposed for a non-autonomous ordinarily differential equation (ODE) found in improving convergence rate of Nesterov's accelerated gradient method.…
We construct a symplectic realisation of the twisted Poisson structure on the phase space of an electric charge in the background of an arbitrary smooth magnetic monopole density in three dimensions. We use the extended phase space…
We present a detailed comparison of several integration schemes applied to the dynamic system consisting of a charged particle on the Kerr background endowed with the axisymmetric electromagnetic test field. In particular, we compare the…
This report documents the development of a versatile model for longitudinal gradient bending magnets (LGB's) and its implementation in particle tracking simulations. The model presented below may be used to represent an arbitrary magnetic…
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving…
In this paper a novel compressor for static magnetic fields is proposed based on finite embedded transformation optics. When the DC magnetic field passes through the designed device, the magnetic field can be compressed inside the device.…
The AMAS group at the Paul Scherrer Institute developed an object oriented library for high performance simulation of high intensity ion beam transport with space charge. Such particle-in-cell (PIC) simulations require a method to generate…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
We present an approach to construct appropriate and efficient emulators for Hamiltonian flow maps. Intended future applications are long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations.…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
In this article we introduce a new method for constructing implicit symplectic maps using special symplectic manifolds and Liouvillian forms. This method extends, in a natural way, the method of generating functions to 1-forms which are…
Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this article, we present analytical symplectic maps describing Poincar\'e maps of the magnetic field lines in confined…
The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…