  The production of an intense, high energy and low emittance muon beam is
interesting for a possible muon collider. The Low EMittance Muon Accelerator
(LEMMA) team at the Istituto Nazionale di Fisica Nucleare (INFN), in Italy, is
studying the production of a 22.5 GeV low emittance muon beam from a high
energy positron beam at twice the muon energy impinging on a fixed thin target.
The LEMMA scheme proposes to perform the muon accumulation from multiple
($10^2$ to $10^3$) positron bunches to increase the population of a single muon
bunch that is recirculated through the target using two small accumulator
rings, one per muon species. The three beams ($\mu^+$ and $\mu^-$ at 22.5 GeV
and $e^+$ at twice the muon energy) share the same phase space at the target on
every positron bunch interaction, producing new muons inside the preserved beam
emittance. We study the requirements and optics design of the accumulator to
recirculate the muons over the target using a Fixed Field Alternating Gradient
(FFA) arc. As a result, we achieve a compact 230 m long accumulator with two
Interaction Points, energy acceptance of $\pm5$ %, low twiss beta function at
the target $\beta^*_\mu=20$ cm, and a drift space 2$L^*$ of 20 cm enough to
accommodate 1 % of a radiation length $X_0$ for several material options. These
optics parameters are obtained with magnets similar to those foreseen for new
colliders like FCC or CLIC, and could be extended further with new magnet
designs. The current muon accumulation results will serve as input for beam
combination studies.
