High intensity discharge (HID) lamps are often found in high power lighting applications, such as car head lights, video projectors, or stadium lights. The characteristics of such discharges are mainly determined by the plasma in the near-cathode region. This work investigates the near-cathode region with fluid dynamic and kinetic methods. The kinetic model, which is solved by expanding the heavy particle distribution functions into Hermite and Laguerre polynomials, proves to be more powerful and accurate.