Experiments conducted using a 200TW 60 fs laser have demonstrated up to 720 MeV electrons in the self-guided laser wakefield regime using pure Helium gas jet targets. Charge and energy of the accelerated electrons was measured using an electron spectrometer with a 0.5T magnet and charge callibrated image plates. The self-trapped charge in a helium plasma was shown to fall off with decreasing electron density with a threshold at 2.5 × 10 18 (cm −3 ) below which no charge is trapped. Self-guiding however is shown to continue below this density limitation over distances of 14 mm with an exit spot size of 25µm. Simulations show that injection of electrons at these densities can be assisted through ionization induced trapping in a mix of Helium with 3% Oxygen.

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We present a numerical method for solving the time-independent thermal radiative transfer (TRT) equation or the neutron transport (NT) equation when the opacity or cross-section varies rapidly in energy (frequency) on the microscale ε; ε corresponds to the characteristic spacing between absorption lines or resonances, and is much smaller than the macroscopic energy (frequency) variation of interest. The approach is based on a rigorous homogenization of the TRT/NT equation in the energy (frequency) variable. Discretization of the homogenized TRT/NT equation results in a multigroup-type system, and can therefore be solved by standard methods.We demonstrate the accuracy and efficiency of the approach on three model problems. First we consider the Elsasser band model with constant temperature and a line spacing ε = 10 −4 . Second, we consider a neutron transport application for fast neutrons incident on iron, where the characteristic resonance spacing ε necessitates ≈ 16, 000 energy discretization parameters if Planck-weighted cross sections are used. Third, we consider an atmospheric TRT problem for an opacity corresponding to water vapor over a frequency range 1000 − 2000 cm −1 , where we take 12 homogeneous layers between 1 km -15 km, and temperature/pressure values in each layer from the standard US atmosphere. For all three problems, we demonstrate that we can achieve between 0.1 and 1 percent relative error in the solution, and with several orders of magnitude fewer parameters than a standard multigroup formulation using Planck-weighted opacities for a comparable accuracy. BackgroundThermal radiative transfer (TRT) plays a key role in a number of scientific and engineering disciplines. For example, resolving the radiation field in three-dimensional cloudy atmospheres is key to understanding a number of atmospheric science and remote sensing problems [12]. In many TRT problems, there is rapid variation in the opacity with energy (or frequency) due to bound-bound and bound-free transitions. In fact, for broad-band TRT problems there can be hundreds of thousands of absorption lines, whose widths are many times smaller than the overall energy range of interest. This fine scale structure in the opacities, coupled with discretizing the spatial and angular variables, places large demands on computational resources. Thus, researchers have sought methods to "average" or "homogenize" the opacities and derive so-called "grey" or frequency independent approximations, thereby reducing the complexity of solving the full TRT problem. Many opacity homogenization techniques have been developed over the years. Here we mention only those most closely related with the method developed in this paper.1

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