Single-particle structure and dynamics

Anisotropic single-particle dissipative particle dynamics model

Single Particle Linear and Nonlinear Dynamics ∗

I will give a comprehensive review of existing particle tracking tools to assess long-term particle stability for small and large accelerators in the presence of realistic magnetic imperfections and machine misalignments. The emphasis will be on the tracking and analysis tools based upon the differential algebra, Lie operator, and “polymorphism”. Using these tools, a uniform linear and non-line...

Single particle tracking of correlated bacterial dynamics.

Pattern formation in 3D random media has been a topic of interest in soft matter and biological systems. However, the onset of long-range microscopic ordering has not been explored in randomly moving self-propelled particles due to a lack of model systems as well as local probe techniques. In this article, we report on a novel experiment, using motile Escherichia coli bacteria as a model system...

Overview of single-particle nonlinear dynamics

We give an overview of the single-particle non linear dynamics in circular accelerators. The main topics are: integration of equations of motion, fast symplectic tracking, dynamic aperture definition, long-term methods, quality factors and lattice optimization. Special emphasis is put on ideas and tools developed during the last decade.

SINGLE PARTICLE DYNAMICS IN i , ; ‘ - . CIRCULAR ACCELERATORS

6. The Nonlinear Terms ........................ 6.1 The Sources of Nonlinearity and Chromaticity .......... _ . ._n. 6.2 Sextupoles for Chromatic Correction .............. ;. 7. Canonical Perturbation Theory ................... 7.1 The Equation for the Generating Function ........... -_ 7.2 The Solution for the Generating Function ........... 7.3 The New Hamiltonian and the Amplitude Dependence...