  Vertical excursion fixed-field alternating gradient accelerators can be
designed with tunes that are invariant with respect to momentum and
trajectories that are scaled images of each other displaced only in the
vertical direction. This is possible using guiding fields that have a vertical
exponential increase, with a skew quadrupole component in the magnet body and a
solenoid component at the magnet ends. Because of the coupling this introduces,
orbit and optics calculations and optimisation of parameters need to be
performed numerically. In this paper, idealised magnetic fields are calculated
from first principles, taking into account end fields. The parameter dependence
of the optics and the dynamic aperture of the ring are calculated for the
example of a ring with an approximately 25 m circumference that accelerates
proton beams from 3 MeV to 12 MeV. The paper reports for the first time the
design of such an accelerator lattice using tools specifically devised to
analyse transverse coupled optics without the need for approximations.
