The mission of the U.S. Muon Accelerator Program (MAP) is to develop and demonstrate the concepts and critical technologies required to produce, capture, condition, accelerate, and store intense beams of muons for Muon Colliders and Neutrino Factories [1,2]. Current plans involve staged facilities beginning with neutrino factories, possibly followed by a low energy collider (Higgs Factory), and eventually leading to a multi-TeV energy collider. Muon-based facilities have the potential to discover and explore new exciting fundamental physics, but will require the development of demanding technologies and innovative concepts. Grant applications are sought, as described in greater detail below, related to the production of muon beams, muon cooling, and rapid muon acceleration. 1) 6D Cooling of Muon Beams Utilizing Rectilinear channels: To meet the proposed Muon Collider performance goals, 6D ionization cooling is required down to transverse emittances of less than 0.3 mm-rad and longitudinal emittances of approximately 2 mm. Rectilinear channels have been proposed with demonstrated capability to achieve 6D cooling of muon beams of both charge species simultaneously: a Helical FOFO Snake ; and a Rectilinear Planar Snake[4,5,6]. In both cases, plane parallel absorbers are employed and cooling of both signs occurs simultaneously. The Helical FOFO lattice must be modified and scaled in order to meet the above transverse emittance requirement. Scaling of the Planar Snake lattice has been successfully demonstrated. Grant applications are sought to examine in greater detail either of the referenced lattice types. The magnet designs should be refined, including the use of different conductor materials in areas with differing fields. Required superconductor current densities should then be compared with published conductor performances for the chosen geometry. Radial and other forces and strains within the coils should be calculated, together with the forces between the coils. In a second phase, the dimensions of structures required to restrain these forces should be calculated, and estimates made of the required specifications for such structures. Estimates should also be made of specifications needed for thermal isolation, rf feeds and other needed structures. 2) Large Aperture Kickers for Muon Cooling Rings: A significant cost savings in both capital construction and operations could be realized if cooling rings could be employed in the cooling chain for a Muon Collider. The injection and extraction systems for each ring will be challenging in that the muon beams have large emittances especially at the beginning of the cooling chain. Transverse emittances on the order of 1 to 5 mm-rad are expected; hence the kicker apertures must be larger than typical. Several types of cooling rings [7,8,9] have been considered but all will require these technically advanced kickers. Initial studies of the necessary kicker parameters  have confirmed the basic challenge of these kickers. Grant applications are sought for both the design of kicker hardware and an accompanying pulsed power system. 3) R&D for Rapid Acceleration of Muons- Dogbone RLA with Multi-Pass Arcs: Recirculating Linear Accelerators (RLAs) are a fast, compact and efficient way of accelerating lepton and possibly ion beams to medium and high energies by reusing the same linac for multiple passes, or to recycle the energy of the beam. In a conventional RLA, the different-energy passes coming out the linac are separated and directed into individual return arcs for recirculation. Thus, each pass through the linac requires a separate fixed energy arc, increasing the complexity, size, and cost of the RLA. A novel RLA concept involves return-arc optics design based on linear combined function magnets with variable dipole and quadrupole field components, which allows two consecutive passes with very different energies to be transported through the same string of magnets [11,12]. Grant applications are sought to develop a complete conceptual design for a scaled electron model of such an RLA (i.e. a model developed by scaling a GeV muon design for electrons yielding a machine that fits in a compact area). Along with a conceptual design, a cost comparison to an alternative separate-arc design should also be done. Proposals are also invited on the conceptual engineering design of the above-mentioned multi-pass arc magnets, capable of handling wide energy ranges, and related systems. 4) A Pulsed Dipole for Muon Beam Acceleration in an RCS: A Muon Collider will require final acceleration of muons to TeV-scale energies. For this purpose, a final acceleration stage based on a Rapid Cycling Synchrotron (RCS) [13,14] is envisioned. At these energies, the RCS lattice contains a sequence of fixed field superconducting dipoles and pulsed warm dipoles capable of +-- 1.8T swings at a rate of 2 to 8 T-ms . Grant applications are sought to develop a detailed magnet design achieving the required performance along with a cost effective pulsed power supply system. In a second phase, prototypes of the magnet and power supply system could be built and tested.