Emittance growth of an electron beam in a periodic focusing channel due to transfer of longitudinal energy to transverse energy

Most discussions about emittance growth and halo production for an intense electron beam in a periodic focusing channel assume that the total transverse energy is constant (or, in other words, that the transverse and longitudinal Hamiltonians are separable). Previous analyses that include variations in the total transverse energy are typically based on a transverse-longitudinal coupling that is either from two-dimensional space-charge modes or particle-particle Coulomb collisions. With the space-charge modes, the energy exchange between the transverse and longitudinal directions is periodic, and of constant magnitude. The total energy transfer for the case of the Coulomb collisions is negligible. This limited increase of energy in the transverse direction from these other effects will limit the amount of transverse emittance growth possible. In this paper, the authors investigate a mechanism in which there is a continual transfer of energy from the longitudinal direction to the transverse direction, leading to essentially unlimited potential transverse emittance growth. This mechanism is caused by an asymmetry of the beam`s betatron motion within the periodic focusing elements. This analysis is based on thermodynamic principles. This mechanism exists for both solenoids and quadrupole focusing, although only solenoid focusing is studied here.