Non-modal analysis of the diocotron instability for cylindrical geometry with conducting boundary

Abstract

The temporal evolution of the linear diocotron instability of a cylindrical annular plasma column surrounded by a conducting boundary has been investigated by using the methodology of the cylindrical shearing modes. The linear solution of the initial and boundary-value problems is obtained which is valid for any time at which linear effects dominate. The solution reveals that the initial perturbations of the electron density pass through the stage of the non-modal evolution when the perturbation experiences spatio-temporal distortion pertinent to the considered geometry of the electron column. The result is confirmed by a two-dimensional cylindrical particle-in-cell simulation.

Halo removal experiments with hollow electron lens in the BNL Relativistic Heavy Ion Collider

“…The temporal evolution frequency ω l and the instability growth rate γ l of the diocotron instability are both proportional to the effective diocotron frequency ω D ðrÞ and can be expressed as [56][57]…”

“…If the vacuum pipe radius is much greater than the beam size, Eq. (11) can be simplified to [56][57] 4…”

“…For a nonuniform density of the electron beam, the recent hollow beam diocotron instability study [56] shows that small azimuthally initial disturbances or the asymmetry of the electron density may lead to significant beam density distortions.…”

The development and interaction of instabilities in intense relativistic electron beams

“…It leads to the development of the azimuthal and radial nonuniformities in the REB, particularly, to the formation of vortex and spiral structures and to the filamentation of the beam. [23][24][25][26][27][28][29][30][31][32][33] These effects are often undesirable for the operation of systems using beams of charged particles. The diocotron and slipping instabilities usually occur in HPM devices, beam collimator systems in high-energy colliders (such as the Tevatron or the Large Hadron Collider in CERN), Penning traps, etc.…”

“…In this case, the intense high-energy beams of charged particles are used on relatively long distances or for long times (like in the beam traps). 8,[33][34][35][36] Different methods for mitigation or control of such instabilities are actively studied at present. 34,37,38 At the same time, the diocotron and slipping instabilities could be useful for the development of novel methods for HPM generation (see, for example, the work 23 where the effect of the microwave generation from the filamentation and vortex formation within magnetically confined electron beams was discovered and investigated).…”