The development of advanced accelerators often involves the modeling of systems that involve a wide range of scales in space and/or time, which can render such modeling extremely challenging. The Adaptive Mesh Refinement technique can be used to significantly reduce the requirements for computer memory and the number of operations. Its application to the modeling of beams and plasmas is especially challenging, due to issues that are specific to the Vlasov-Maxwell system of equations. In [1], we presented a summary of the main issues for electrostatic plasma simulations, their cures, and example applications; issues and a solution specific to electromagnetic plasma simulations were discussed in [2]. Novel algorithms [3,4] offer new perspectives that we are currently exploring [5,6] for the use of mesh refinement with electromagnetic plasma simulations. We will present our past and present work, and discuss its applicability and benefits to the design and understanding of advanced accelerators such as laser wakefield acceleration systems.

The guiding of intense laser pulses in plasma channels is necessary to maximize the energy of electrons accelerated in a laser wakefield accelerator. A significant fraction of the energy in the laser pulse may be lost during and after coupling from vacuum into a channel. For example, imperfect coupling can lead to enhanced leakage of laser energy transversely through the channel walls. We present 2D particle-in-cell (PIC) simulations, using the VORPAL code, of an example problem. We present a numerical diagnostic, based on simultaneous FFT s in space and time, which enables quantitative measurements of forward and backward propagating pulse energy andits spectra. Future work will be directed toward VORPAL parameter studies designed to optimize the amount of laser energy that couples into a channel.

Demonstrating the viability of Advanced Accelerator Concepts (AAC) relies on experimental validation. Over the last three decades, the U.S. has maintained a portfolio of advanced and novel accelerator test facilities to support research critical to AAC. The facilities have enabled pioneering developments in a wide variety of beam and accelerator physics, including plasma-wakefield and structure-wakefield acceleration. This paper provides an overview of the current portfolio of U.S. facilities possessing charged particle drive beams with high energies, on the order of tens of joules per pulse, or drive lasers with high peak powers, on the order of a petawatt, and are actively conducting AAC research.