Abstract
Eigenfrequencies are calculated for the transverse oscillations of a round beam radially confined in a solenoidal magnetic field. Under the assumption of a linear restoring force in the equilibrium beam, with partial or total neutralization by an immobile background charge, the influence of different distribution functions on stability is investigated. It is found that the well-known extended instabilities of a microcanonical (Kapchinskij–Vladimirsky) distribution are replaced by apparently insignificant patches of instability if the distribution function is broadened, hence the loss-cone is partially filled up. The water-bag distribution indicates transition to only stable eigenfrequencies and it is found that this transition is accompanied by suppression of negative energy oscillations, which are responsible for the instabilities of loss-cone or nonmonotonically decreasing distributions. The method employed consists of infinite series expansion for the eigenfunctions and approximating the infinite determinant dispersion relation by rapidly converging finite order subdeterminants.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
