Energy Differential Structure and Exchange of A Micro Flux Increment of Charged Particles in Longitudinal Acceleration

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.