Articles written in Pramana – Journal of Physics
Volume 94 All articles Published: 15 October 2020 Article ID 0151 Research Article
In this paper, the Dirac equation in the presence of some scalar potentials based on $sl$(2) Lie algebra is solved by quasi-exact solvability theory. The configuration of the classes III and VI potentials in the Turbiner’s classification is constructed. Then, the Bethe ansatz equations are calculated so that the energy eigenvalues and eigenfunctions are obtained. Also, we study the problem by using asymptotic iteration method. Finally, we compare the results obtained by these two methods.
Volume 94 All articles Published: 3 November 2020 Article ID 0158 Research Article
In this paper, the single bunch fast transverse instabilities of the electron beam in the ILSF storage ring due to the RF cavity impedance are investigated. We consider Satoh’s formalism (that studied mode coupling instabilities based on the Vlasov equation) and Lindberg’s formalisms (that studied mode coupling instabilities based on the Fokker–Planck equation). The Lindberg formalisms are rewritten to broad-band RF cavity impedance. It is shown that the zero chromaticity limits of both approaches completely coincide. In addition, we discuss the current threshold at high chromaticity that includes higher-order azimuthal and radial modes.
Volume 95, 2021
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