A strictly physically based design theory of a new class of Spatial Harmonic Magnetrons (SHM) is thoroughly derived which leads to analytically evaluable expressions. Thus two advantages are obtained: (1) The design parameters appear grouped into two separate categories – one just containing geometrical and material parameters, the other one exclusively containing beam current-related ones, which are in product-form determining performance. The influence of each parameter can thus easily be discovered and investigated. (2) Numerical efforts for any new design will be reduced by at least one order of magnitude. Subsequently and based on feature (1) it is derived that loading the anode structure by a suitably selected meta-material will increase output power and efficiency, will pave the way to CW operation, and can extend oscillation frequency well into the sub-THz range. Finally, it is shown that the Rising Sun Magnetron is a first step toward a meta-material loaded SHM offering the same but quantitatively reduced features and less stringent requirements to fabrication technology.