KAM-tori near an analytic elliptic fixed point

We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector \o_0 is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that \o_0 has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least $d+1$ passing through 0 that is foliated by complex analytic KAM-tori with frequency $\omega_0$. This is an extension of previous results obtained in \cite{EFK} to the case of an elliptic fixed point

Solar coronal heating by short-wavelength dispersive shear Alfvén waves

The electron heating of the solar coronal plasma has remained as one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude short-wavelength (in comparison with the ion gyroradius) dispersive shear Alfven (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA wave-electron interactions

Luminosity Tuning at the Interaction Point

Minimisation of the emittance in a linear collider is not enough to achieve optimal performance. For optimisation of the luminosity, tuning of collision parameters such as angle, offset, waist, etc. is needed, and a fast and reliable tuning signal is required. In this paper tuning knobs are presented, and their optimisation using beamstrahlung as a tuning signal is studied

Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications

We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy, Marseilles, France, 31 August - 4 September 200

A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Solar coronal electron heating by short-wavelength dispersive shear Alfvén waves

This work was partially supported by the STFC through the Centre for Fundamental Physics (CfFP) at Rutherford Appleton Laboratory, Chilton, Didcot, UK. BE acknowledges support by the Engineering and Physical Sciences Research Council (EPSRC), UK, Grant no EP/M009386/1.The electron heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude short-wavelength (in comparison with the ion gyroradius) dispersive shear Alfven (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA wave-electron interactions.Publisher PDFPeer reviewe

The representation of tropical upper tropospheric water in EC Earth V2

Tropical upper tropospheric humidity, clouds, and ice water content, as well as outgoing longwave radiation (OLR), are evaluated in the climate model EC Earth with the aid of satellite retrievals. The Atmospheric Infrared Sounder and Microwave Limb Sounder together provide good coverage of relative humidity. EC Earth's relative humidity is in fair agreement with these observations. CloudSat and CALIPSO data are combined to provide cloud fractions estimates throughout the altitude region considered (500-100 hPa). EC Earth is found to overestimate the degree of cloud cover above 200 hPa and underestimate it below. Precipitating and non-precipitating EC Earth ice definitions are combined to form a complete ice water content. EC Earth's ice water content is below the uncertainty range of CloudSat above 250 hPa, but can be twice as high as CloudSat's estimate in the melting layer. CERES data show that the model underestimates the impact of clouds on OLR, on average with about 9 W m(-2). Regionally, EC Earth's outgoing longwave radiation can be similar to 20 W m(-2) higher than the observation. A comparison to ERA-Interim provides further perspectives on the model's performance. Limitations of the satellite observations are emphasised and their uncertainties are, throughout, considered in the analysis. Evaluating multiple model variables in parallel is a more ambitious approach than is customary

Electromagnetic cyclotron instabilities in bi-Kappa distributed plasmas : a quasilinear approach

Anisotropic bi-Kappa distributed plasmas, as encountered in the solar wind and planetary magnetospheres,are susceptible to a variety of kinetic instabilities including the cyclotron instabilities driven by an excess ofperpendicular temperature T⊥ > T∥ (where ∥, ⊥ denote directions relative to the mean magnetic field). Theseinstabilities have been extensively investigated in the past, mainly limiting to a linear stability analysis. Abouttheir quasilinear (weakly nonlinear) development some insights have been revealed by numerical simulationsusing PIC and Vlasov solvers. This paper presents a self-consistent analytical approach, which provides forboth the electron and proton cyclotron instabilities an extended picture of the quasilinear time evolution ofthe anisotropic temperatures as well as the wave energy densities

KAM for the quantum harmonic oscillator

In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians systems. This result extends previous works of S.B. Kuksin and J. P\"oschel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an application we show that some 1D nonlinear Schr\"odinger equations with harmonic potential admits many quasi-periodic solutions. In a second application we prove the reducibility of the 1D Schr\"odinger equations with the harmonic potential and a quasi periodic in time potential.Comment: 54 pages. To appear in Comm. Math. Phy

High-quality ion beams by irradiating a nano-structured target with a petawatt laser pulse

We present a novel laser based ion acceleration scheme, where a petawatt circularly polarized laser pulse is shot on an ultra-thin (nano-scale) double-layer target. Our scheme allows the production of high-quality light ion beams with both energy and angular dispersion controllable by the target properties. We show that extraction of all electrons from the target by radiation pressure can lead to a very effective two step acceleration process for light ions if the target is designed correctly. Relativistic protons should be obtainable with pulse powers of a few petawatt. Careful analytical modeling yields estimates for characteristic beam parameters and requirements on the laser pulse quality, in excellent agreement with one and two-dimensional Particle-in Cell simulations.Comment: 18 pages, 7 figures, accepted in New. J. Phy