Dispersion-Induced Beam Instability in Circular Accelerators

Abstract

The envelope instability near the 90° phase advance in periodically focused space charge dominated beams is a well-known phenomenon in linear transport sections or linacs. The corresponding stop band is usually avoided because of the resulting strong mismatch oscillations and beam loss. We show that in circular accelerators or transport sections including bending magnets the instability is modified due to the effect of dispersion. Using the two-dimensional envelope equations extended by the dispersion equation we identify an additional stop band above 120°. For periodic focusing the stop band results from the confluence of an envelope mode with the newly identified coherent dispersion mode. Results from perturbation theory are compared with the full envelope model and particle-in-cell simulation, which all show good agreement. The newly identified mode has several implications and applications for the characterization of intense beams in circular machines.

Intensity limitations due to space charge for bunch compression in synchrotrons

“…By including the space-charge modified dispersion, the transverse envelope equations become a useful tool to study the transverse collective motion in synchrotrons (for example, see Refs. [16,19]). During bunch compression, both space charge and its effect on dispersion are increasing.…”

“…In order to further study the mechanism of the 90°-related intensity limitation, and distinguish the role of fourth-order resonance and envelope instability during bunch compression, we calculate the envelope modes (the fast mode ϕ 1 , the slow mode ϕ 2 ) and dispersion mode ϕ d [16] during bunch compression from the coupled envelope model, as shown in Fig. 11.…”

“…Thus, a fourth-order single particle resonance and the wellknown envelope instability-both entirely driven by space charge-are of potential concern with practically overlapping stop bands [15]. Furthermore, in the horizontal plane, bunch compression may lead to crossing of 120°, and the recently discovered dispersion-induced instability [16] could be a potential limitation of bunch intensity.…”

Modeling of second order space charge driven coherent sum and difference instabilities

“…(11). Analogous to the treatment of the usual envelope instabilities [7,21], the four eigenvalues can be calculated by integrating Eqs. (10) and Eqs.…”

Space charge compensation with pulsed electron lenses for intense ion beams in synchrotrons

“…The shift of the lower edge of the two stopbands (in x and y) is well described by Equation 9 with α = 0 and S = 12. The white dot indicates the reference highcurrent working point in the SIS, which lies inside the unstable area for the chosen beam intensity.Very weakly visible are the parametric sum resonance (the diagonal line)[14] and the dispersion induced envelope resonance (the vertical line at Q x = 4.3)[13].The lower part ofFigure 2shows a tune scan performed with N e = 12 electron lenses (one in each SIS lattice period). The lenses are adjusted to provide a partial compensation of the space charge tune shift by one-third (α = 0.33), limited by the integer resonance.…”