Related papers: Dancing bunches as Van Kampen modes
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…
Conditions for existence, uniqueness and stability of bunch steady states are considered. For the existence uniqueness problem, simple algebraic equations are derived, showing the result both for the action and Hamiltonian domain…
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…
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…
In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation…
Long lived modes of elliptical galaxies can exist {\it \`a la} van Kampen. Specific systems may possess long lived oscillations which Landau damp on time scales longer than a Hubble time. Some physical processes such as a close encounter,…
We examine the decay of perturbations in an infinite homogeneous self-gravitating model with a Maxwellian distribution function (DF) when weak collisions are present. In collisionless systems within the stable parameter range, the…
Landau damping of head-tail modes in bunches due to spreads in the tune shift can be a deciding factor for beam stability. We demonstrate that the coherent tune shifts due to reactive impedances can enhance the space-charge induced damping…
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…
We investigate the structure of damped two-dimensional perturbations in unstable plane-parallel shear flows with an inflection point. In inviscid flows within the stable wavenumber region $k$, no regular eigenmodes exist -- the frequency…
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…
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…
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…
Transverse mode coupling instability of bunched beam is investigated in the paper at different form of the bunches with space charge included. Equation of transverse motion of the bunch in parabolic potential well of synchrotron…
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…
Landau-damped oscillations in collisionless plasmas, described by van Kampen and Case, are quasi-modes, representing a continuous superposition of singular eigenfunctions, not true eigenmodes. Recent work by Ng et al. shows that even rare…
We consider the spectrum of eigenmodes in a stellar system dominated by gravitational forces in the limit of zero collisions. We show analytically and numerically using the Lenard-Bernstein collision operator that the Landau modes, which…
We present a theoretical framework for analyzing longitudinal coupled-bunch instabilities in double-rf systems with even filling patterns, accounting for potential-well distortion and multiple azimuthal modes. The linearized Vlasov equation…