Frank James Sacherer

A Longitudinal Stability Criterion for Bunched Beams

The unstable motion of a bunched beam consists of rigid-bunch (dipole) and higher bunch-shape oscillations of the individual bunches (individual-bunch modes), plus perhaps coupled motion of the different bunches (coupled-bunch modes). Stability is achieved either by decoupling the bunches or by a spread in synchrotron frequencies within a bunch. A stability criterion analogous to the Keil-Schnell criterion for coasting beams is given which includes the effect of a beam interacting with perfectly conducting walls, resistive walls, and resonant structures. Some examples for the CERN accelerators are included.

Bunch Lengthening and Microwave Instability

A single-bunch instability that leads to blow-up of bunch area and microwave signals (100 MHz to 3 GHz) has been observed in the pS1) and the ISR2). A similar instability may cause bunch lengthening in electron storage rings. Attempts to explain this as a high-frequency coasting-beam instability require e-folding rates faster than a synchrotron period, and wavelengths shorter than a bunch length. In this case, the usual Keil-Schnell coasting-beam criterion3) is used, but with local values of bunch current and momentum spread, as suggested by Boussard1). This yields |Z/n| ¿ 13 ¿ for the ISR, and values about five to ten times larger for the PS. The restricitons mentioned above, however, are not fulfilled near threshold, or for frequencies as low as 100 MHz.

Theory and Performance of the Longitudinal Active Damping System for the CERN PS Booster

Longitudinal instabilities have long been trouble-some in the Booster1). They are described by the coupledbunch mode number n = 0 to 4 for five bunches, and by the within-bunch mode number m = 1 for dipole, m = 2 for quadrupole, m = 3 for sextupole, and so on (Fig. 1). The normal beam control system damps the rigid-bunch oscillation (m = 1) when all five bunches move togethier (n = 0)2). The new feedback system3) damps the other coupled-bunch modes n = 1 to 4 for the three lowest orders, m = l to 3. With the damping system off, one can display the evolution of any mode along the cycle, which helps in locating coupling impedances that cause instability. One can also excite the various modes and measure the amplitude-phase response (RF knockout applied to a bunched beam). This gives the frequency spread within the bunch, the coherent frequent shifts, plus the usual stability diagram in the U-V plane.

Methods for measuring transverse coupling impedances in circular accelerators

Abstract Charged particle beams in circular accelerators often become unstable and execute coherent transverse oscillations that grow in amplitude. These are driven by deflecting fields set up by currents induced in the vacuum chamber walls or other equipment by the oscillating beam itself. This unwanted interaction between the beam and its surroundings is characterized by a transverse coupling impedance Z T . We show that it is relatively easy to measure Z T for accelerator components with large impedance such as kicker magnets, and that useful results can also be obtained for components with small impedance, such as vacuum chambers, although in this case one is close to the limits of accuracy with ordinary laboratory equipment.

Beam Dynamics Experiments in the PS Booster

The main problems encountered on the way to 1013 ppp have been emittance blow-up and coherent instabilities. The observations and counter measures are described in the text.

Experiments on Stochastic Cooling in ICE (Initial Cooling Experiment)

Recent experiments on stochastic cooling have resulted in cooling rates several orders of magnitude higher than obtained previously in the ISR. Two cooling systems reduce betatron oscillations. A third system reduces momentum spread, using the so-called filter method. The favourable signal-to-noise ratio of this method has led to cooling times (e-folding of peak density) of 15 s with 7.107 protons in ICE. Betatron cooling times are longer due to the lower signal-to-noise ratio. Simultaneous cooling in all three planes has yielded lifetimes of about 100 h, a value consistent with losses caused by single scattering on the residual gas. The existing stochastic cooling theory has been confirmed.

Longitudinal Bunch Dilution Due to RF Noise

The effect of phase noise on a tightly bunched proton beam is investigated taking into account the frequency spread in the beam, the wall impedance and the phase feedback loop. Under normal conditions the measured dilution rates in the ISR correspond typically to a doubling of the bunch length in one to a few hours, and are consistent with the measured noise spectra. Amplitude noise is not investigated.