High-power impulse magnetron sputtering (HiPIMS), a new physical vapor deposition technique which combines the advantages of the high ionization rates of the sputtered materials and control of electromagnetism, has been widely used to deposit high-performance coatings with a large density and high adhesion. However, HiPIMS has some intrinsic disadvantages such as the low deposition rate, unstable discharge, and different ionization rates for different materials thereby hampering wider industrial adoption. We have recently designed an optimized cylindrical source based on the hollow cathode effect to circumvent the aforementioned limitations. However, during the operation of the cylindrical source, the discharge is inhomogeneous and the etching stripes are nonuniform. In order to determine the underlying mechanism and optimize the electromagnetic control, the discharge in the HiPIMS cylindrical source is simulated. The tangential magnetic field distribution on the target surface of the cylindrical sputtering source is inhomogeneous and electron runaway is serious, resulting in a relatively low plasma density. Two solutions are proposed to improve the situations. The first one is electrical improvement by installing an electron blocking plate, and the second one is magnetic improvement by adding compensating magnets. Our simulation results of the first method show that a potential well is produced by the electron blocking plate to suppress electron runaway and the plasma density is improved significantly, especially around the central cross-section of the cylindrical sputtering source. The discharge becomes homogeneous, and the etching stripes are uniform albeit not full enough. The second method of magnetic improvement significantly improves the homogeneity of the tangential magnetic field distribution on the target surface and the target utilization rate. After adding the optimized compensating magnets, the shape of the effective area (the value of the tangential magnetic field in a range of 25-50 mT) on the target surface can be controlled and made zonal. The target utilization rate increases to over 80% from 60%. In order to obtain the optimal conditions, the two techniques are combined. A larger and more homogeneous etching ring is observed by adopting both the electrical and magnetic improvements as predicted and explained by the simulation results. It can be concluded that the combination of the two improvement techniques can improve and optimize the HiPIMS cylindrical source.