Abstract
Charged-particle motion is studied in the self-electric and self-magnetic fields of a well-matched, intense charged-particle beam and an applied periodic solenoidal magnetic focusing field. The beam is assumed to be in a state of adiabatic thermal equilibrium. The phase space is analyzed and compared with that of the well-known Kapchinskij-Vladimirskij (KV)-type beam equilibrium. It is found that the widths of nonlinear resonances in the adiabatic thermal beam equilibrium are narrower than those in the KV-type beam equilibrium. Numerical evidence is presented, indicating almost complete elimination of chaotic particle motion in the adiabatic thermal beam equilibrium.
Highlights
High-brightness beams in particle accelerators and beam devices and facilities are often generated in a regime where space charge plays an important role
Exploration of equilibrium states of charged-particle beams and their stability properties is critical to the advancement of basic particle accelerator physics
Of particular concern are emittance growth and beam losses, which are related to the evolution of charged-particle beams in their nonequilibrium states
Summary
High-brightness beams in particle accelerators and beam devices and facilities are often generated in a regime where space charge plays an important role. Wellknown equilibria for periodically focused intense beams include the Kapchinskij-Vladimirskij (KV) equilibrium in an alternating-gradient (AG) quadrupole magnetic focusing field [1,2] and the periodically focused rigid-rotor Vlasov equilibrium of the KV type in a periodic solenoidal magnetic focusing field [3,4] Both of these beam equilibria [1,2,3,4] have a singular (-function) distribution in the four-dimensional phase space. The importance of this result is twofold: First, the elimination of chaotic particle motion provides a further numerical proof that the scaled transverse Hamiltonian defined in Eq (25) in [6] is a very good approximate constant of motion This approximate constant of motion and the exact contact of motion of the canonical angular momentum assure that the motion of charged particles is approximately integrable in the fourdimensional phase space of the adiabatic thermal beam equilibrium.
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