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The IsoDAR cyclotron is a 60 MeV cyclotron designed to output 10mA of protonsin order to be a driver for a neutrino experiment. Coupling the high fluxgenerated by the IsoDAR system with a kiloton neutrino detector will providesterile neutrino exclusion searches covering anomalous regions indicated byshort baseline experiments. Simultaneously, the coupling of a high power targetand kiloton detector allows for the investigation of dark matter candidates,namely axion-like particles. We have shown that nuclear excitations within theIsoDAR target create a unique opportunity to produce axions and detectmonoenergetic peaks with the nearby kiloton detector. Beyond this, the highpower produced by the IsoDAR cyclotron can be used for applications beyondparticle physics. The IsoDAR cyclotron accelerates and extracts H$_2^+$, whichallows the beam to be split downstream, a versatile and important developmentto alleviate the problem of producing high-power targets for the medicalisotope community. This thesis presents a proposal for production of an morethan an order of magnitude higher rates than are available at present forcertain highly-need medical isotopes, including Ac-225.  In this thesis, we report results from a multi-cusp ion source that meetsthese requirements and produces a record level of high purity, low emittanceH$_2^+$ current. The second has been to design a radio-frequency quadrupole(RFQ) that will allow for gentle bunching of the high current before injection.This is the first use of axial direct injection with a compact cyclotron. Thisthesis reports the first application of machine learning to the RFQ design.These tools enable the high currents required by IsoDAR cyclotron, leading toimportant impact on the accelerator, medical, and physics communities.

High Power Cyclotrons: The Bridge Between Beyond the Standard Model Physics, Computation, and Medical Applications