Scaling up quantities in hollow cathode discharges with the invariant parameter

The use of invariant parameters in low pressure gas discharges has been shown very useful to represent many discharge quantities. For the hollow cathode discharge it has been observed that the function given by the product of the cathode length by the current density divided by the pressure lj/p is an invariant parameter. By plotting the discharge voltage as a function of the invariant parameter the experimental points follow a single curve denominated discharge characteristic. Furthermore, if two discharges are similar, the experimental voltage points of both follow the same characteristic curve if plotted against the invariant parameter. We have observed that, beside voltage, other discharge quantities also follow a characteristic curve when they are plotted as a function of the invariant parameter: sputtering rate and light intensities emitted by sputtered cathode atoms. Whenever a characteristic curve can be fitted through the experimental points, this quantity might be scaled up for other discharges with different dimensions and operated under different conditions. In this work we present results of quantities, which were scaled up for several hollow cathode discharges.