Guiding of relativistically intense laser pulses with peak power of 0.85 PW over 15 diffraction lengths was demonstrated by increasing the focusing strength of a capillary discharge waveguide using laser inverse Bremsstrahlung heating. This allowed for the production of electron beams with quasi-monoenergetic peaks up to 7.8 GeV, double the energy that was previously demonstrated. Charge was 5 pC at 7.8 GeV and up to 62 pC in 6 GeV peaks, and typical beam divergence was 0.2 mrad.

A one-dimensional dissipative magnetohydrodynamics code is used to investigate the discharge dynamics of a waveguide for high-intensity laser pulses: the gas-filled capillary discharge waveguide. Simulations are performed for the conditions of a recent experimental measurement of the electron density profile in hydrogen-filled capillaries [D. J. Spence et al., Phys. Rev. E 63, 015401 (R) (2001)], and are found to be in good agreement with those results. The evolution of the discharge in this device is found to be substantially different to that found in Z-pinch capillary discharges, owing to the fact that the plasma pressure is always much higher than the magnetic pressure. Three stages of the capillary discharge are identified. During the last of these the distribution of plasma inside the capillary is determined by the balance between ohmic heating, and cooling due to electron heat conduction. A simple analytical model of the discharge during the final stage is presented, and shown to be in good agreement with the magnetohydrodynamic simulations.

We study the probability distribution P(H, t, L) of the surface height h(x = 0, t) = H in the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimension when starting from a parabolic interface, h(x, t = 0) = x 2 /L. The limits of L → ∞ and L → 0 have been recently solved exactly for any t > 0. Here we address the early-time behavior of P(H, t, L) for general L. We employ the weak-noise theory -a variant of WKB approximation -which yields the optimal history of the interface, conditioned on reaching the given height H at the origin at time t. We find that at small H P(H, t, L) is Gaussian, but its tails are non-Gaussian and highly asymmetric. In the leading order and in a proper moving frame, the tails behave as − ln P = f+|H| 5/2 /t 1/2 and f−|H| 3/2 /t 1/2 . The factor f+(L, t) monotonically increases as a function of L, interpolating between time-independent values at L = 0 and L = ∞ that were previously known. The factor f− is independent of L and t, signalling universality of this tail for a whole class of deterministic initial conditions.

This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations between neighboring sites. In extinction scenario I, the zero population size is a repelling fixed point of the on-site deterministic dynamics. In extinction scenario II, the zero population size is an attracting fixed point, corresponding to what is known in ecology as the Allee effect. Assuming a large population size, we develop a WKB (Wentzel-Kramers-Brillouin) approximation to the master equation. The resulting Hamilton's equations encode the most probable path of the population toward extinction and the mean time to extinction. In the fast-migration limit these equations coincide, up to a canonical transformation, with those obtained, in a different way, by Elgart and Kamenev [Phys. Rev. E 70, 041106 (2004)]. We classify possible regimes of population extinction with and without an Allee effect and for different types of refuge, and solve several examples analytically and numerically. For a very strong Allee effect, the extinction problem can be mapped into the overdamped limit of the theory of homogeneous nucleation due to Langer [Ann. Phys. (NY) 54, 258 (1969)]. In this regime, and for very long systems, we predict an optimal refuge size that maximizes the mean time to extinction.

Compact, tunable, radially symmetric focusing of electrons is critical to laser-plasma accelerator (LPA) applications. Experiments are presented demonstrating the use of a discharge-capillary active plasma lens to focus 100-MeV-level LPA beams. The lens can provide tunable field gradients in excess of 3000 T/m, enabling cm-scale focal lengths for GeV-level beam energies and allowing LPA-based electron beams and light sources to maintain their compact footprint. For a range of lens strengths, excellent agreement with simulation was obtained.