Explanation of Sextupole Instability in CERN PS Booster

Dual harmonic RF systems have been discussed for many years: to promote Landau damping, to reduce transverse space-charge, and to improve Touschek lifetime. Since its introduction into the CPS booster in 1982, the dual harmonic acceleration process suffered from an unexplained longitudinal instability occurring when the 2nd harmonic cavity is anti-phased and controlled by the 1st harmonic gap signa l. The instability does not occur when the beam fundamental is used as reference, nor when the RF harmonics are in-phase. The impetus for the present study arises from the conversion from harmonic num bers h=5 and 10 to h=1 and 2 for LHC operation. The instability has recently been diagnosed as a sextupole mode. In this paper, which is a synopsis of two laboratory notes [3,4], are presented experim ental results from machine development (MD) periods, and a detailed theoretical explanation for the instability (and its correction) that considers feedback from the beam versus the cavity fundamental

Longitudinal Phase Space Tomography with Space Charge

Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the non-linearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of the vacuum chamber parametrized by a single value of distributed reactive impedance and by a geometrical coupling coefficient. This is sufficient to model the dominant collective effects in machines of low to moderate energy. In contrast to simulation codes, binning is not an issue since the profiles to be differentiated are measured ones. The program is written in Fortran 90 with High-Performance Fortran (HPF) extensions for parallel processing. A major effort has been made to identify and remove execution bottlenecks, for example by reducting floating-point calculations and re­coding slow intrinsic functions. A pointer-like mechanism which avoids the problems associated with pointers and parallel processing has been implemented. This is required to handle the large, sparse matrices that the algorithm employs. Results obtained with and without the inclusion of space charge are presented and compared for proton beams in the CERN PS Booster. Comparisons of execution times on different platforms are presented and the chosen solution for our application program, which uses a dual processor PC for the number crunching, is described

Longitudinal holes in debunched particle beams in storage rings, perpetuated by space-charge forces

Stationary, self-consistent, and localized longitudinal density perturbations on an unbunched charged-particle beam, which are solutions of the nonlinearized Vlasov-Poisson equation, have recently received some attention. In particular, we address the case that space charge is the dominant longitudinal impedance and the storage ring operates below transition energy so that the negative mass instability is not an explanation for persistent beam structure. Under the customary assumption of a bell-shaped steady-state distribution, about which the expansion is made, the usual wave theory of Keil and Schnell (1969) for perturbations on unbunched beams predicts that self-sustaining perturbations are possible only (below transition) if the impedance is inductive (or resistive) or if the bell shape is inverted. Space charge gives a capacitive impedance. Nevertheless, we report numerous experimental measurements made at the CERN Proton Synchrotron Booster that plainly show the longevity of holelike structures in coasting beams. We shall also report on computer simulations of boosterlike beams that provide compelling evidence that it is space-charge force which perpetuates the holes. We shall show that the localized solitonlike structures, i.e., holes, decouple from the steady-state distribution and that they are simple solutions of the nonlinearized time-independent Vlasov equation. We have derived conditions for stationarity of holes that satisfy the requirement of self-consistency; essentially, the relation between the momentum spread and depth of the holes is given by the Hamiltonian-with the constraint that the phase-space density be high enough to support the solitons. The stationarity conditions have scaling laws similar to the Keil-Schnell criteria except that the charge and momentum spread of the hole replaces that of the beam. (29 refs)

Hollow bunch distributions at high intensity in the PS booster

Bunches from the CERN PS Booster (PSB) with an improved bunching factor due to a hollow longitudinal distribution would facilitate the production of a high-intensity (>7´1012/bunch) proton beam needed for the future neutron time-of-flight facility. It would also provide a safety margin for the Large Hadron Collider beam, where a double-batch transfer is used in which the first PSB batch waits for 1.2 seconds at 1.4 GeV in the PS for the second one to arrive. Since the earlier reports of the successful acceleration of low-intensity hollow bunches in the PSB, theoretical studies of the Beam Transfer Function (BTF) have led to a greatly improved understanding of the stability requirements of such beams. In addition, an experimental study of the capture of hollow coasting beams has revealed that structure resulting from the linac acceleration process persists for a remarkably long time. Any inhomogeneity has to be smeared out and the degree of hollowness carefully adjusted by a controlled longitudinal blow-up before a reproducible, stable bunch can be created. A method has been developed for reliably creating hollow distributions of up to 8´1012 protons per bunch which have been routinely accelerated in the PSB

New technique for bunch shape flattening

A technique for increasing the bunching factor (Bf) is described. Typically in booster-type synchrotrons, it is important to reduce the transverse space-charge tune shift. One means to achieve this is to increase the ratio of average to peak longitudinal charge density. Essentially, the idea is to create hollow bunches by sweeping high-harmonic empty buckets into the particle beam prior to bunching and acceleration. Successful beam experiments are reported with supporting LONG1D simulation studies performed on the CERN PS Booster for both single and dual rf cases. The longitudinally hollow bunches also benefit the receiving ring during the double batch transfer where half of the PS has to wait 1.2 seconds at low energy for the second injection. A 15th harmonic rf system was used to form the empty buckets. Simulations show that for the single harmonic case, Bf is increased from 0.28 to 0.38, and for the dual harmonic one, Bf is increased from 0.45 to 0.55 (values at 100 MeV). The flattening technique has been tested successfully with the first harmonic to 1 GeV and to 100 MeV for dual harmonic acceleration

Design of a 2.2 GeV Accumulator and Compressor for a Neutrino Factory

The proton driver for a neutrino factory must provide megawatts of beam power at a few GeV, with nonosecond long bunches each containing more than 1x1012 protons. Such beam powers are within reach of a high-energy linac, but the required time structure cannot be provided without accumulation and compression. The option of a linac-based 2.2 GeV proton driver has been studied at CERN, taking into account the space charge and stability problems which make beam accumulation and bunch compression difficult at such a low-energy. A solution featuring two rings of approximately 1 km circumference has been worked out and is described in this paper. The subjects deserving further investigation are outlined

Proton Drivers for Neutrino Factories: The CERN Approach

The paper describes the CERN approach for a proton driver for a Neutrino Factory. Two main layouts are presented: the so-called CERN Reference Scenario, based on a 2.2 GeV linac and an alternative one, based on a 30 GeV synchrotron. Both produce bunches of 1 ns (r.m.s.) and a beam power of 4 MW

The PS complex produces the nominal LHC beam

The LHC [1] will be supplied, via the SPS, with protons from the pre-injector chain comprising Linac2, PS Booster (PSB) and PS. These accelerators have under-gone a major upgrading programme [2] during the last five years so as to meet the stringent requirements of the LHC. These imply that many high-intensity bunches of small emittance and tight spacing (25 ns) be available at the PS extraction energy (25 GeV). The upgrading project involved an increase of Linac2 current, new RF systems in the PSB and the PS, raising the PSB energy from 1 to 1.4 GeV, two-batch filling of the PS and the installation of high-resolution beam profile measurement devices. With the project entering its final phase and most of the newly installed hardware now being operational, the emphasis switches to producing the nominal LHC beam and tackling the associated beam physics problems. While a beam with transverse characteristics better than nominal has been obtained, the longitudinal density still needs to be increased. An alternative scheme to produce the 25 ns bunch spacing is outlined, together with other promising developments