Quantum corrected electron holes

The theory of electron holes is extended into the quantum regime. The Wigner--Poisson system is solved perturbatively based in lowest order on a weak, standing electron hole. Quantum corrections are shown to lower the potential amplitude and to increase the number of deeply trapped electrons. They, hence, tend to bring this extreme non--equilibrium state closer to thermodynamic equilibrium, an effect which can be attributed to the tunneling of particles in this mixed state system.Comment: 12 pages, 3 figure

Kinetic theory of periodic holes in debunched particle beams

A self-consistent theory of periodic hole structures in coasting beams in synchrotrons and storage rings is presented, extending the theory on localized holes. The analysis reveals new intrinsic nonlinear modes which owe their existence to a deficiency of particles trapped in the self-sustained potential well, showing up as notches in the thermal range of the distribution function. It is therefore the full set of Vlasov-Poisson equations which is invoked; linearized treatments as well their nonlinear extensions fundamentally fail to cope with this strongly nonthermodynamic phenomenon. Qualitative agreement with the holes recently found at the CERN proton synchrotron booster is shown. (24 refs)

On deformation of electron holes in phase space

This Letter shows that for particularly shaped background particle distributions momentum exchange between phase space holes and the distribution causes acceleration of the holes along the magnetic field. In the particular case of a non-symmetric ring distribution (ring with loss cone) this acceleration is nonuniform in phase space being weaker at larger perpendicular velocities thus causing deformation of the hole in phase space.Comment: Original MS in EPL style, 1 Figur

Width-amplitude relation of Bernstein-Greene-Kruskal solitary waves

Inequality width-amplitude relations for three-dimensional Bernstein-Greene-Kruskal solitary waves are derived for magnetized plasmas. Criteria for neglecting effects of nonzero cyclotron radius are obtained. We emphasize that the form of the solitary potential is not tightly constrained, and the amplitude and widths of the potential are constrained by inequalities. The existence of a continuous range of allowed sizes and shapes for these waves makes them easily accessible. We propose that these solitary waves can be spontaneously generated in turbulence or thermal fluctuations. We expect that the high excitation probability of these waves should alter the bulk properties of the plasma medium such as electrical resistivity and thermal conductivity.Comment: 5 pages, 2 figure

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Computational and Mathematical Modelling of the EGF Receptor System

This chapter gives an overview of computational and mathematical modelling of the EGF receptor system. It begins with a survey of motivations for producing such models, then describes the main approaches that are taken to carrying out such modelling, viz. differential equations and individual-based modelling. Finally, a number of projects that applying modelling and simulation techniques to various aspects of the EGF receptor system are described