Related papers: Van Kampen modes for bunch longitudinal motion
Conditions for the existence, uniqueness and stability of self-consistent bunch steady states are considered. For the existence and uniqueness problems, simple algebraic criteria are derived for both the action and Hamiltonian domain…
Van Kampen modes are eigen-modes of Jeans-Vlasov equation. Their spectrum consists of continuous and, possibly, discrete parts. Onset of a discrete van Kampen mode means emergence of a coherent mode without any Landau damping; thus, even a…
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation…
Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge, and resistive wall wakefield taken into account. Boxcar model is used for all-round analysis, and Gaussian distribution is invoked for…
This paper describes a general investigation of stationary oscillations of galaxies. It begins with a linear analysis of modes of oscillation with continuous spectra of real frequencies. Such modes are gravitational analogues of the van…
This paper sheds new light on the stability properties of solitary wave solutions associated with models of Korteweg-de Vries and Benjamin\&Bona\&Mahoney type, when the dispersion is very lower. Via an approach of compactness, analyticity…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…
Landau damping mechanism plays a crucial role in providing single-bunch stability in LHC, High-Luminosity LHC, other existing as well as previous and future (like FCC) circular hadron accelerators. In this paper, the thresholds for the loss…
This research was stimulated by the recent studies of damping solutions in dynamically stable spherical stellar systems. Using the simplest model of the homogeneous stellar medium, we discuss nontrivial features of stellar systems. Taking…
Landau damping is a natural stabilization mechanism that mitigates coherent beam instabilities. In the longitudinal plane, loss of Landau damping (LLD) occurs when a coherent mode of oscillation emerges from the incoherent band of the bunch…
For a single hadron bunch affected by longitudinal space charge in a stationary rf bucket we analyze the frequency spectrum close to the expected loss of Landau damping for the lowest order dipole mode. For different bunch intensity…
Observations of single bunch beam-beam coherent modes during dedicated experiments in the LHC are presented. Their role in standard operation for physics is discussed and, in particular, candidates of beam-beam coherent mode driven unstable…
An equation is derived for the energy of a small disturbance in a system that is generated by a distribution function (DF) of the form $f(\vJ)$ -- most galaxies and star clusters can be closely approximated by such a DF. The theory of van…
We study the longitudinal motion of beam particles under the action of a single resonator wave induced by the beam itself. Based on the method of multiple scales we derive a system of coupled amplitude equations for the slowly varying part…
Landau damping is the mechanism of plasma and beam stabilization; it arises through energy transfer from collective modes to the incoherent motion of resonant particles. Normally this resonance requires the resonant particle's frequency to…
We present a practical method to detect, diagnose and engineer higher order Van Hove singularities in multiband systems, with no restrictions on the number of bands and hopping terms. The method allows us to directly compute the Taylor…
Pattern formation in biological, chemical and physical problems has received considerable attention, with much attention paid to dissipative systems. For example, the Ginzburg--Landau equation is a normal form that describes pattern…
We consider the time evolution of a lattice branching random walk with local perturbations. Under certain conditions, we prove the Carleman type estimation for the moments of a particle subpopulation number and show the existence of a…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
The effect of the beam-beam interactions on the stability of impedance mode is discussed. The detuning is evaluated by the means of single particle tracking in arbitrarily complex collision configurations, including lattice non-linearities,…