The AMIT (Advanced Molecular Imaging Techniques) cyclotron will be a 8.5 MeV, 10 μA, CW, H accelerator for the purpose of radioisotope production. It includes a superconducting, weak focusing, 4 T magnet, which allows for a small extraction radius and a compact design. The RF cavity design has to deal with challenging requirements: high electric fields created by the required accelerating voltage (60 kV), a narrow aperture of the magnet leading to high capacitances and thermal losses, and a requirement for a small overall size of the cavity. A quarter wave resonator with one dee (two acceleration gaps) design was chosen. Calculations with numerical codes such as HFSS and ANSYS have been performed to compute the main RF parameters and the stresses and deformations of the cavity due to the power losses and vacuum operation. Finally, the fluid dynamics of the cooling circuits have been carefully studied.