ICFA Beam Dynamics Newsletter 14 (August 1997)

Significant statistics (95% confidence level) were gathered on the dynamic aperture (D.A.) of the former version 4 of LHC to estimate better the relationship between the tracking results and the D.A. of the actual machine (longer times, more initial conditions, tune ripple,...). A factor of 2 seems necessary. The present D.A. of 9.5 sigma shall be increased to 12 sigma to ensure that the beam dynamics is weakly perturbed at the primary collimators positioned at 6 sigma. A new table of magnet imperfections was synthesized to fulfil this goal. Part of the required improvement are already met by the new dipole coil design and the others are under study. The first tracking results show the same D.A. for LHC version 5 with however a more significant reduction for a mostly horizontal motion. This point is under investigation.

Synchrotron radiation from proton bunches in the LHC creates photoelectrons at the beam screen wall. These photoelectrons are pulled toward the positively charged proton bunch. When they hit the opposite wall, they generate secondary electrons which can in turn be accelerated by the next bunch. Depending on several assumptions about surface reflectivity, photoelectron and secondary electron yield, this mechanism can lead to the fast build-up of an electron cloud with potential implications for beam stability and heat load on the beam screen. A crash program has been set up to measure the relevant physical quantities (by EPA irradiation tests and multipacting tests in a superconducting magnet), thus `calibrating' analytic estimates and numeric simulations. The ongoing activity is documented in the World-wide web page http://wwwslap.cern.ch/collective/electron-cloud/electron-cloud.html

Surface resistance measurements for the copper coated LHC beam screen at cryogenic temperatures indicate a beam-induced ohmic heating about a factor two larger than previously estimated. For frequencies up to 1.5 GHz, the additional effect of an 8.4 T magnetic field is only 10 to 15%: an absolute measurement precision of a few per cent is reached by comparing the quality factors of even and odd TEM modes in a cylindrical structure with two inner conductors.

Impedance estimates have been completed for several LHC components, such as bellows, monitors, and experimental chambers (whose design is being modified to reduce coherent losses). Stability studies based on Landau damping thresholds with two-dimensional betatron tune spread, for a detuning at 1 \sigma of 10^{-4} in both planes achieved by two octupole families, show that a pilot bunch with poorly controlled chromaticity is stable against the head-tail instability for currents as high as 10% of the nominal current. Multiple bunches in the same current range remain stable without feedback for negative chromaticities as large as -15.

ICFA Beam Dynamics Newsletter 13 (February 1997)

Map analysis was used to compute resonance coefficients and attempt to relate them to the dynamic aperture results. A rather clear correlation appears between the latter and simulataneously two difference resonances driven by a_4 and b_4. The tune split of version 5 may thus have a positive impact on dynamic aperture.

The optimistic results obtained on the influence of long-range beam-beam effects at injection on the dynamic aperture were not confirmed by a more comprehensive 6D tracking. The separation of 7 sigmas appears to be not sufficient, with a dynamic aperture of 6.5 sigmas. The flexibility of the new version 5 will allow to decrease the beta-values so as to obtain a sufficient beam separation.

The version 9 of MAD (based on the Classic project) is progressing. Version 8 of MAD is being reorganized as well around a small database common to the two versions. MAD algorithms will be implemented as independent modules interacting through the database.

Surface resistance measurements for the copper coated LHC beam screen are in progress. Preliminary results at 4 K and without magnetic field, for frequencies in the range 600-900 MHz, indicate a surface resistance above 2 mOhm, i.e., more than a factor two larger then previously estimated.

Coasting beam longitudinal echo signals have been observed at 120 GeV in the SPS even after 2 minutes from the last RF pulse, corresponding to diffusion coefficients as small as 10^-13 sec^-1. These results have been cross-calibrated by independent Schottky measurements of the energy spread induced by an additional RF noise. Bunched-beam longitudinal quadrupole echoes have also been recently observed.

An impedance database program (ZBASE) has been set-up and already successfully applied to estimate the LEP impedance budget: it helps keeping track of all the known impedance sources and of the input files used by different programs, such as ABCI or MAFIA, to compute HOM and loss factors for several bunch lengths. In the near future, a further interface is foreseen to existing beam dynamics codes for detailed calculations of multibunch transverse mode-coupling and microwave instability thresholds both in the LHC and SPS.

The existing LHC impedance budget has been used in conjunction with the program VLASOV for calculations of transverse instability thresholds and rise times including multibunch mode coupling: the transverse mode-coupling threshold is about a factor two higher than the nominal current, but the feedback bandwidth required to damp all multibunch dipole modes should be increased by a factor of two.

Landau damping of the rigid dipole oscillations with two-dimensional betatron tune spread has been investigated for Gaussian and quasi-parabolic transverse beam distributions. The results have been applied to specify the strength of the LHC octupole correctors required to stabilize dipole and higher order head-tail modes during the ramp and at collision energy. The two-dimensional analysis shows that the damping by octupoles is significantly more efficient than predicted by a one-dimensional approach.

ICFA Beam Dynamics Newsletter 12 (November 1996)

The minimum (amongst 60 seeds) medium term dynamic aperture has increased to 9 sigmas, but is still clearly limited by the systematic part of the a4/b4 imperfection of the dipole (about 11 sigmas if they would be corrected by small coils at the end of the dipoles). Yet, no clear correlation could be established yet between dynamic aperture and either the average of a_4/b_4 over one turn nor the driving term of the 4th order difference coupling resonance, neither with detunings.

First tracking results show that the linear imperfections (closed orbit, beta-beating and linear coupling corrected to reasonable values) and the long-range beam-beam interactions at injection do not reduce the dynamic aperture.

A conjecture [Giovannozzi et al.] on the evolution in time of the dynamic apertures averaged over the (x,y) projection of phase space appears to fit well the LHC survival plots and could give hints to beam stability after very long times.