We develop a statistical approach for characterizing uncertainty in predictions that are made with the aid of a computer simulation model. Typically, the computer simulation code models a physical system and requires a set of inputs-some known and specified, others unknown. A limited amount of field data from the true physical system is available to inform us about the unknown inputs and also to inform us about the uncertainty that is associated with a simulationbased prediction. The approach given here allows for the following: • uncertainty regarding model inputs (i.e., calibration); • accounting for uncertainty due to limitations on the number of simulations that can be carried out; • discrepancy between the simulation code and the actual physical system; • uncertainty in the observation process that yields the actual field data on the true physical system. The resulting analysis yields predictions and their associated uncertainties while accounting for multiple sources of uncertainty. We use a Bayesian formulation and rely on Gaussian process models to model unknown functions of the model inputs. The estimation is carried out using a Markov chain Monte Carlo method. This methodology is applied to two examples: a charged particle accelerator and a spot welding process.

The transverse motion of beam halo particles is described by a particle-core model which uses the space-charge field of a continuous cylindrical oscillating beam core in a uniform linear focusing channel to provide the force that drives particles to large amplitudes. The model predicts a maximum amplitude for the resonantly-driven particles as a function of the initial mismatch. We have calculated these amplitude limits and have estimated the growth times for extended-halo formation as a function of both the space-charge tune-depression ratio and a mismatch parameter. We also present formulas for the scaling of the maximum amplitudes as a function of the beam parameters. The model results are compared with multiparticle simulations and we find very good agreement for a variety of initial particle distributions. [S1098-4402(98)00022-6]

NATIONAL LABORATORYIn this paper, we present an object-oriented threedimensional parallel particle-in-cell code for beam dynamics simulation in linear accelerators. A two-dimensional parallel domain decomposition approach is employed within a message passing programming paradigm along with a dynamic load balancing. Implementing objectoriented software design provides the code with better maintainability, reusability, and extensibility compared with conventional structure based code. This also helps to encapsulate the details of communication syntax. Performance tests on SGI/Cray T3E-900 and SGI Origin 2000 machines show good scalability of the object-oriented code. Some important features of this code also include employing symplectic integration with linear maps of external focusing elements and using z as the independent variable, typical in accelerators. A successful application was done to simulate beam transport through three superconducting sections in the APT Iinac design.

A new class of self-consistent 6-D phase space stationary distributions is constructed both analytically and numerically. The beam is then mismatched longitudinally and/or transversely, and we explore the beam stability and halo formation for the case of 3-D axisymmetric beam bunches using particle-in-cell simulations. We concentrate on beams with bunch length-to-width ratios varying from 1 to 5, which covers the typical range of the APT linac parameters. We find that the longitudinal halo forms first for comparable longitudinal and transverse mismatches. An interesting coupling phenomenon -a longitudinal or transverse halo is observed even for very small mismatches if the mismatch in the other plane is large -is discovered.

In this paper, we present a three-dimensional quasistatic model for high brightness beam dynamics simulation in rf/dc photoinjectors, rf linacs, and similar devices on parallel computers. In this model, electrostatic space-charge forces within a charged particle beam are calculated self-consistently at each time step by solving the three-dimensional Poisson equation in the beam frame and then transforming back to the laboratory frame. When the beam has a large energy spread, it is divided into a number of energy bins or slices so that the space-charge forces are calculated from the contribution of each bin and summed together. Image-charge effects from conducting photocathode are also included efficiently using a shifted-Green function method. For a beam with large aspect ratio, e.g., during emission, an integrated Green function method is used to solve the three-dimensional Poisson equation. Using this model, we studied beam transport in one Linac Coherent Light Sources photoinjector design through the first traveling wave linac with initial misalignment with respect to the accelerating axis.