Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems

Beam envelope calculations in general linear coupled lattices

Nonlinear Dynamics and Chaos in Many-Particle Hamiltonian Systems

We report the results of studies of nonlinear dynamics and dynamical chaos in Hamiltonian systems composed of many interacting particles. The importance of the Lyapunov exponents and the Kolmogorov-Sinai entropy is discussed in the context of ergodic theory and nonequilibrium statistical mechanics. Two types of systems are studied: hard-ball models for the motion of a tracer or Brownian particl...

Sequential second derivative general linear methods for stiff systems

‎Second derivative general linear methods (SGLMs) as an extension‎ ‎of general linear methods (GLMs) have been introduced to improve‎ ‎the stability and accuracy properties of GLMs‎. ‎The coefficients of‎ ‎SGLMs are given by six matrices‎, ‎instead of four matrices for‎ ‎GLMs‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually Runge--Kutta stability conditions‎. ‎In this p...

Symmetric multistep methods for charged - particle dynamics

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 o...

General formalism for singly thermostated Hamiltonian dynamics.

A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their r...