  Differential energy structure of a micro multi-charged-particle system and
the beam internal potential energy is derived with consequent property and
ecessary inference. Then by combining the energy differential structure with
differential transfer relations of physical flux density between different time
domains, we present a general explicit formula for energy exchange in the beam
element's transfer or accelerating process between source and observer, further
give an analysis on relativistic beam's mass-energy relation and beam's energy
up limits for resonant frequency (rf) and DC acceleration. Finally we discuss
the property of elementary charge density field and consequences.
