  There is great need for high intensity proton beams from compact particle
accelerators in particle physics, medical isotope production, and materials-
and energy-research. To this end, the DAE$\delta$ALUS/IsoDAR collaboration is
developing a compact isochronous cyclotron that will be able to deliver 10 mA
of protons - an order of magnitude higher than on-market compact cyclotrons and
a factor four higher than research machines. For the first time, vortex motion
is incorporated in the design of a cyclotron, which is key to reaching high
extracted beam current. We present high-fidelity simulations of the
acceleration of a 5 mA H$_2^+$ beam (equivalent to 10 mA of protons) in this
cyclotron, using the particle-in-cell code OPAL, demonstrating the feasibility
of constructing this machine. The simulations are based on the latest cyclotron
design and through them, we show that sufficient turn separation between the
$(\mathrm{N}-1)^{th}$ and $\mathrm{N}^{th}$ turn can be achieved even with
initially mismatched beams by careful placement of collimators to scrape away
halo particles before the beam energy has reached 1.5 MeV/amu. We describe in
detail the process for placement of electrostatic extraction channels. Beam
losses on the septa of these channels stay below 50 W with beam quality
sufficient for transport to the target. Furthermore, we present an uncertainty
quantification of select beam input parameters using machine learning, showing
the robustness of the design.
