1) Improved Accelerator Modeling Simulation Codes: Grant applications are sought to develop new or improved computational tools for the design, study, or operation of charged-particle-beam optical systems, accelerator systems, or accelerator components. These tools should incorporate innovative user-friendly interfaces, with emphasis on graphical user interfaces and windows, and tools to translate between standard formats of accelerator lattice description. Grant applications also are sought for the conversion of existing codes for the incorporation of these interfaces (provided that existing copyrights are protected and that applications include the authors' statements of permission where appropriate). 2) Improved Integration of Accelerator Codes: Grant applications also are sought for user-friendly tools in software integration for different components including preprocessors and postprocessors of existing codes or for different application codes into a framework to enhance simulation of accelerator systems. 3) Accurate Modeling and Prediction of High Gradient Breakdown Physics: Grant applications also are sought to develop simulation tools for modeling high-gradient structures, in order to predict such experimental phenomena as the onset of breakdown, post breakdown phenomena, and the damage threshold. Specific areas of interest include the modeling of: (1) Surface emission, (2) Material heating due to electron and ion bombardment, (3) Multipactoring, and (4) Ionization of atomic and molecular species. Approaches that include an ability to import-export CAD descriptions, a friendly graphical user interface, and good data visualization will be a plus. 4) Software for Multi-Physics Modeling of MAP Systems: In the past decade HEP-driven accelerator modeling codes have become increasingly sophisticated. Particularly noteworthy is the fact that accelerator codes now combine multiple phenomena, such as single particle nonlinear optics, space-charge effects, beam-beam effects, and beam-material interactions. But there are some phenomena that are important to the HEP mission that are still missing from accelerator codes. Grant applications are sought for development and deployment of codes and software modules that are important to HEP projects and for which current capabilities do not exist or are not sufficient. Regarding the simulation of MAPs muon cooling systems [2,3,4], those based on gas-filled rf cavities require complex modeling of the beam-plasma interaction . Such processes are also expected to be relevant to other advanced concepts involving beams and plasmas. Proposals are sought for codes and modules to self-consistently model the interaction of beams with plasmas, including beam-plasma interactions in gas-filled rf cavities, plasma production by incoming beams, and plasma and atomic physics processes. Proposals are also sought for developing code capabilities for modeling collective effects in matter, for modeling polarized muon processes, and for combining beam dynamics codes with neutrino interaction codes to accurately predict neutrino radiation in a muon collider.