Longitudinal phase space tomography with space charge

Abstract

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 nonlinearity 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 extensions for parallel processing. A major effort has been made to identify and remove execution bottlenecks, for example, by reducing floating-point calculations and recoding slow intrinsic functions. A pointerlike 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 protron synchrotron 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.

Space charge effects on the third order coupled resonance

“…2). Furthermore, the beam intensity was recorded using a beam current transformer [27] and the longitudinal phase space was reconstructed applying the tomography technique [28]. In order to compare the different profiles and to gain statistical significance, each measurement was repeated three times.…”

Generation of initial kinetic distributions for simulation of long-pulse charged particle beams with high space-charge intensity

“…If the total beam propagation distance is not too long and the injector is amenable to modeling, then the beam emission from the source can be simulated and the subsequent evolution through the transport and acceleration cycle of the machine simulated for high-level ''first-principles'' modeling with limited assumptions [24][25][26][27]. Alternatively, the loaded distribution can be synthesized based on reasonable extrapolations of limited experimental measurements of the beam phase space at a diagnostic location in the machine lattice [28,29]. Or finally, the initial beam distribution can be assumed to be of a particular (ansatz) form motivated by physical insight or generated by relaxation processes from a relatively simple initial ansatz distribution.…”

Bunch-by-bunch linac beam energy profile diagnostics using storage ring phase rotation and synchrotron radiation

“…Since the linac bunch lengths are very short, the beam occupancy resembles a short, straight line in the rf bucket of the storage ring. A complicated tomographic analysis is therefore unnecessary [5,6]. The transverse oscillation contribution is negligible, since only the longitudinal phase space profile is used.…”