  The Cornell-BNL FFAG-ERL Test Accelerator (C$\beta$) will comprise the first
ever Energy Recovery Linac (ERL) based on a Fixed Field Alternating Gradient
(FFAG) lattice. In particular, we plan to use a Non Scaling FFAG (NS-FFAG)
lattice that is very compact and thus space- and cost- effective, enabling
multiple passes of the electron beam in a single recirculation beam line, using
the superconducting RF (SRF) linac multiple times. The FFAG-ERL moves the cost
optimized linac and recirculation lattice to a dramatically better optimum.
  The prime accelerator science motivation for C$\beta$ is proving that the
FFAG-ERL concept works. This is an important milestone for the Brookhaven
National Laboratory (BNL) plans to build a major Nuclear Physics facility,
eRHIC, based on producing 21 GeV electron beams to collide with the RHIC ion
beams. A consequence of the C$\beta$ work would be the availability of
significantly better, cost-effective, compact CW high-brightness electron beams
for a plethora of scientific investigations and applications, such as X-ray
sources, dark-matter and dark-energy searches, and industrial high-power
Free-Electron Laser (FEL) applications.
  C$\beta$ brings together the resources and expertise of a large DOE National
Laboratory, BNL, and a leading research university, Cornell. C$\beta$ will be
built in an existing building at Cornell, for the most part using components
that have been developed under previous R&D programs, including a fully
commissioned world-leading photoemission electron injector, a large SRF
accelerator module, and a high-power beam stop. The only elements that require
design and construction from scratch is the FFAG magnet transport lattice.
  This white paper describes a project that promises to propel high-power,
high-brightness electron beam science and applications to an exciting new
level.
