Survey of Collective Instabilities and Beam-Plasma Interactions in Intense Heavy Ion Beams Page: 4 of 33
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include: the electrostatic electron-ion two-stream instability; the multispecies electromagnetic
Weibel instability; dynamic stabilization of the two-stream instability during longitudinal drift
compression; and the effects of solenoidal magnetic field on collective beam-plasma instabilities.
In the accelerator and transport regions, the analysis in this paper assumes a long ion
charge bunch (bunch length lb >> bunch radius rb) with directed axial kinetic energy
(yb -1)mbc2 propagating in the z direction through a perfectly conducting cylindrical pipe with
constant radius r, . The analysis is carried out in the smooth-focusing approximation where the
applied transverse focusing force is modeled by Foc = -ybmbw fx. Here, yb = (I - p2 1/2is the
relativistic mass factor, Vb = Pfc is the directed axial velocity of the charged bunch, mb is the ion
rest mass, (of = const is the single-particle oscillation frequency associated with the applied
focusing force, and xl = xex + yeyis the transverse displacement of a beam particle from the
cylinder axis. Denoting the characteristic number density of beam particles by hb and the
particle charge by eb, it is convenient to introduce the relativistic plasma frequency (>pb defined
by Cipb = (47rhbe/ybmb )V2 and the normalized (dimensionless) beam intensity sb defined by
s= Pb/2ybcwf . Furthermore, the particle dynamics in the beam frame is assumed to be
It should be noted that one collective instability that is not summarized in the present
paper is the electron-ion two-stream (electron cloud) instability, which can occur when an
intense ion beam propagates through an (unwanted) partially-neutralizing component of
background electrons produced (for example) when energetic beam ions strike the chamber wall
or ionize background gas atoms. Advanced analytical and numerical simulation studies of this
instability have previously been reported [64-70,78] and will not be repeated here, except to note
that the conditions for eliminating or greatly reducing the effects of this instability have been
identified, e.g., through the introduction of a very modest axial momentum spread in the beam
As noted earlier, Secs. II and III provide a brief overview of the present understanding of
several collective instabilities that can develop in intense ion beams and beam-plasma systems.
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Davidson, Ronald C.; Dorf, Mikhail A.; Kaganovich, Igor D.; Qin, Hong; Startsev, Edward A.; Rose, David V. et al. Survey of Collective Instabilities and Beam-Plasma Interactions in Intense Heavy Ion Beams, article, June 19, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc898007/m1/4/?rotate=270: accessed May 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.