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

Transverse-Longitudinal Coupling by Space Charge in Cyclotrons

A method is presented that enables to compute the parameters of matched beams with space charge in cyclotrons with emphasis on the effect of the transverse-longitudinal coupling. Equations describing the transverse-longitudinal coupling and corresponding tune-shifts in first order are derived for the model of an azimuthally symmetric cyclotron. The eigenellipsoid of the beam is calculated and the transfer matrix is transformed into block-diagonal form. The influence of the slope of the phase curve on the transverse-longitudinal coupling is accounted for. The results are generalized and numerical procedures for the case of an AVF cyclotron are presented. The algorithm is applied to the PSI Injector II and Ring cyclotron and the results are compared to TRANSPORT.Comment: 8 pages, 2 figure

Tune-stabilized linear-field FFAG for carbon therapy

A hybrid design for a Fixed-Field Alternating-Gradient (FFAG) accelerator has been invented which uses edge and alternating-gradient focusing principles applied in a specific configuration to a combined-function magnet to stabilize tunes through an acceleration cycle which extends over a factor of 2-6 in momentum. Using normal conducting magnets, the final, extracted energy from this machine attains 400 MeV/nucleon and thus supports a carbon ion beam in the energy range of interest for cancer therapy. Competing machines for this application include superconducting cyclotrons[1], synchrotrons[2], and, more recently, scaling FFAGs. The machine proposed here has the high average current advantage of the cyclotron with smaller radial aperture requirements that are more typical of the synchrotron; and as such represents a desirable innovation for therapy machines