Abstract :
It is assumed that fermion particles, such as electron and proton, in a matched beam follow Fermi-Dirac statistics in the equilibrium state. Parametric resonances, chaotic motion, and halo formation in transverse direction of motion are investigated analytically. The analytical expressions for the parametric resonances and the maximum transverse position deviation, above which chaotic motion starts to occur due to transverse beam envelope oscillation, are derived. Analytical formula for the current loss rate is established
Keywords :
chaos; fermion systems; particle beam dynamics; particle beam stability; resonance; space charge; Fermi-Dirac statistics; chaotic motion; current loss rate; equilibrium state; fermion particles; halo formation; matched beam; maximum transverse position deviation; parametric resonances; space charge dominated beams; transverse beam envelope oscillation; Chaos; Differential equations; Electron beams; Motion analysis; Parametric statistics; Particle beams; Production; Protons; Resonance; Space charge;
