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

Nonlinear propagation of broadband intense electromagnetic waves in an electron-positron plasma

A kinetic equation describing the nonlinear evolution of intense electromagnetic pulses in electron-positron (e-p) plasmas is presented. The modulational instability is analyzed for a relativistically intense partially coherent pulse, and it is found that the modulational instability is inhibited by the spectral pulse broadening. A numerical study for the one-dimensional kinetic photon equation is presented. Computer simulations reveal a Fermi-Pasta-Ulam-like recurrence phenomena for localized broadband pulses. The results should be of importance in understanding the nonlinear propagation of broadband intense electromagnetic pulses in e-p plasmas in laser-plasma systems as well as in astrophysical plasma settings.Comment: 16 pages, 5 figures, to appear in Phys. Plasma

The Intense Radiation Gas

We present a new dispersion relation for photons that are nonlinearly interacting with a radiation gas of arbitrary intensity due to photon-photon scattering. It is found that the photon phase velocity decreases with increasing radiation intensity, it and attains a minimum value in the limit of super-intense fields. By using Hamilton's ray equations, a self-consistent kinetic theory for interacting photons is formulated. The interaction between an electromagnetic pulse and the radiation gas is shown to produce pulse self-compression and nonlinear saturation. Implications of our new results are discussed.Comment: 7 pages, 1 figure, version to appear in Europhys. Let

Self-compression and catastrophic collapse of photon bullets in vacuum

Photon-photon scattering, due to photons interacting with virtual electron-positron pairs, is an intriguing deviation from classical electromagnetism predicted by quantum electrodynamics (QED). Apart from being of fundamental interest in itself, collisions between photons are believed to be of importance in the vicinity of magnetars, in the present generation intense lasers, and in intense laser-plasma/matter interactions; the latter recreating astrophysical conditions in the laboratory. We show that an intense photon pulse propagating through a radiation gas can self-focus, and under certain circumstances collapse. This is due to the response of the radiation background, creating a potential well in which the pulse gets trapped, giving rise to photonic solitary structures. When the radiation gas intensity has reached its peak values, the gas releases part of its energy into `photon wedges', similar to Cherenkov radiation. The results should be of importance for the present generation of intense lasers and for the understanding of localized gamma ray bursts in astrophysical environments. They could furthermore test the predictions of QED, and give means to create ultra-intense photonic pulses.Comment: 4 pages, 1 figur

Instability of a thin conducting foil accelerated by a finite wavelength intense laser

We derive a theoretical model for the Rayleigh-Taylor (RT)-like instability for a thin foil accelerated by an intense laser, taking into account finite wavelength effects in the laser wave field. The latter leads to the diffraction of the electromagnetic wave off the periodic structures arising from the instability of the foil, which significantly modifies the growth rate of the RT-like instability when the perturbations on the foil have wavenumbers comparable to or larger than the laser wavenumber. In particular, the growth rate has a local maximum at a perturbation wavenumber approximately equal to the laser wavenumber. The standard RT instability, arising from a pressure difference between the two sides of a foil, is approximately recovered for perturbation wavenumbers smaller than the laser wavenumber. Differences in the results for circular and linear polarization of the laser light are pointed out. The model has significance to radiation pressure acceleration of thin foils, where RT-like instabilities are significant obstacles

Pitch angle scattering of relativistic electrons near EMIC resonances in diverging magnetic fields

A theoretical study of the propagation of left hand polarized shear Alfvén waves in spatially decreasing magnetic field geometries near the EMIC resonance, including the spectrum and amplitude of the mode converted EMIC waves and the pitch angle scattering of relativistic electrons transiting the resonant region, is presented. The objective of the paper is to motivate an experimental study of the subject using the UCLA LAPD chamber. The results are relevant in exploring the possibility that shear Alfvén waves strategically injected into the radiation belts using either ionospheric heating from ground based RF transmitters or injected by transmitters based on space platforms can enhance the precipitation rate of trapped relativistic electrons. Effects of multi-ionic composition are also investigated