Thermal Distribution of Relativistic Particle Beams with Space Charge

Phys. Rev. Lett. 71, 2911 (1993)https://ireap.umd.edu/10.1103/PhysRevLett.71.29111993Journal ArticlePlasma, Accelerator, and Nuclear Physics

The Maxwell-Boltzmann (‘‘thermal’’) distribution constitutes the natural thermodynamic equilibrium state for a charged particle beam, and knowledge of its properties is therfore of fundamental importance. The Boltzmann relation for the particle density has a nonanalytic form when the space-charge force is included.