Cold-fluid equilibrium for a corkscrewing elliptic beam in a variably focusing channel

It is shown that there exists a new class of cold-fluid corkscrewing elliptic beam equilibria for ultrahigh-brightness, space-charge-dominated beam propagation through a linear focusing channel consisting of uniform solenoidal, periodic solenoidal, and/or alternating-gradient quadrupole focusing magnets in an arbitrary arrangement including field tapering. The equilibrium beam density and flow velocity profiles and equilibrium self-electric and self-magnetic fields are determined by solving generalized beam envelope equations. In proper limits, such cold-fluid corkscrewing elliptic beam equilibria recover many familiar beam equilibria in beam physics, including the round rigid-rotor Vlasov beam equilibria in uniform and periodic solenoidal focusing fields and the Kapchinskij-Vladimirskij beam equilibrium in an alternating-gradient quadrupole focusing field. For beams with negligibly small emittance, the equilibrium solutions are validated with self-consistent simulations. Examples and applications of the present equilibrium beam theory are discussed. As an important application of the present equilibrium beam theory, a general technique is developed and demonstrated with an example to control large-amplitude density and flow velocity fluctuations (such as beam hollowing and halo formation) often observed in ultrahigh-brightness beams.