An advanced set of scaling laws for Hall e¨ect thrusters running with Xenon as propellant is established on the basis of the existence of an optimum atom number density that warrants a high e©ciency thruster operation. A set of general relationships between macroscopic quantities, like thrust and input power, dimensions, including the channel length, the channel width and the channel mean diameter, and magnetic ¦eld strength are inferred from the main physical processes at work in a Hall thruster discharge. The ¤atom density constraint¥ of which the nature is here critically interpreted allows simplifying those relationships as it leads to a linear dependency between the channel length and mean diameter. Scaling laws which represent an essential tool for sizing up and down Hall thrusters are eventually obtained after proportionnality co-e©cients are determined. This last step is realized by means of a vast database that presently encompasses 33 single-stage Hall thrusters. In order to illustrate the usefulness of this new set of scaling laws, two practical applications are given and discussed. The scaling laws are ¦rst employed to calculate the dimensions and the operating parameters for a 20-kilowatt Hall thruster capable of producing 1 N of thrust. Such an electrical engine would permit orbit transfer of large communication satellites. Finally, the geometry of a Hall thruster is determined for tolerating 100 kW, an interesting power level for interplanetary trips.