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

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

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)

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

Some properties of nonlinear oscillations in a diode in the space charge–limited current regime

Both the initial and late non-linear stages of the oscillation process in a beam vacuum diode in the space-charge-limited current regime are numerically investigated. Two different numerical methods are applied: Birdsall's code (B-code) and Ender-Kuznetsov code (EK-code). The capabilities of both codes are compared. The high accuracy of the EK-code gives an opportunity to build dispersion branches of instability. The domain of the parameter values, when simultaneously several stable dynamical states (limit cycles) exist, is found. A sharp decrease in the amplitude of oscillations is revealed already under a comparatively small (about 2.5%) spread in velocities of the electron beam

Nonlinear instability and saturation of linearly stable current-carrying pair plasmas

The nonlinear instability of current-carrying pair plasmas is investigated with a Vlasov-Poisson model for the two particle species. It is shown that linearly stable configurations are unstable against small incoherent perturbations of the particle distribution functions. The instability gives rise to a self-acceleration and growth of phase space holes. After the growth of the phase-space holes, the instability reaches a chaotic saturation where the finite-amplitude holes interact and merge, and after a long time, the system attains a stable equilibrium state with a smaller drift and a larger temperature than the initial one, and where a few stable phase-space holes are presen

Two-dimensional PIC simulations of ion-beam instabilities in Supernova-driven plasma flows

Supernova remnant (SNR) blast shells can reach the flow speed $v_s = 0.1 c$ and shocks form at its front. Instabilities driven by shock-reflected ion beams heat the plasma in the foreshock, which may inject particles into diffusive acceleration. The ion beams can have the speed $v_b \approx v_s$. For $v_b \ll v_s$ the Buneman or upper-hybrid instabilities dominate, while for $v_b \gg v_s$ the filamentation and mixed modes grow faster. Here the relevant waves for $v_b \approx v_s$ are examined and how they interact nonlinearly with the particles. The collision of two plasma clouds at the speed $v_s$ is modelled with particle-in-cell (PIC) simulations, which convect with them magnetic fields oriented perpendicular to their flow velocity vector. One simulation models equally dense clouds and the other one uses a density ratio of 2. Both simulations show upper-hybrid waves that are planar over large spatial intervals and that accelerate electrons to $\sim$ 10 keV. The symmetric collision yields only short oscillatory wave pulses, while the asymmetric collision also produces large-scale electric fields, probably through a magnetic pressure gradient. The large-scale fields destroy the electron phase space holes and they accelerate the ions, which facilitates the formation of a precursor shock.Comment: 15 pages, 11 figures, accepted for publication in Plasma Physics and Controlled Fusio

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