Grant: Subatomic Physics Envelope - Individual

The objective of this proposal is to develop an on-line model of TRIUMF's 500 MeV cyclotron. This can be achieved by developing a radically novel algorithm, that would bridge the gap between the existing fast envelope codes, and the relatively slow multiparticle codes used to model high-intensity cyclotrons. For an additional speed up, we also intend to use our newly developed code to train a neural network to serve as a surrogate model of the accelerators. On-line models are changing the way we operate particle accelerators and beamlines at TRIUMF. The key to on-line modelling is speed. The model needs to run in a very short time, on the order of a second or less, to allow real time interaction between the model, the machine, and the human operator. Speed is also essential for automatic machine optimization, which may make a large number of calls to the model before converging to an optimum tune. The workhorse of on-line modelling at TRIUMF is an envelope code, which tracks the evolution of the second moments of the particle distribution, without tracking individual particles. Based on the algorithm developed by Sacherer, this code accurately takes into account the electromagnetic interactions between particles within the beam. This is essential to accurately model high-intensity machines. Among other things, this code is used routinely to model, in real-time, the TRIUMF high-intensity 30 MeV electron linear accelerator, with great success. The other high-intensity driver accelerator at TRIUMF is the 500 MeV cyclotron. Unfortunately, an envelope code is a poor model for such a machine. The reasons are fundamental. The alternative is to use a multiparticle code, but such a code is orders of magnitude too slow for on-line modelling. One such simulation of the TRIUMF cyclotron requires in the order of 106 macro-particles, and takes on the order of 10 hours to complete (on a single processor core). To speed up the calculations by orders of magnitude, we propose to develop a hybrid algorithm, where statistical moments are used in some dimensions, while a particle-in-cell-like method is use in the others. A similar hybrid model has recently been derived by a graduate student working in our group. We propose to expand this work for application to our cyclotron. If we use moments in the vertical direction, and a particle-in-cell in the other two directions, we reduce the required number of macro-particles by a power 2/3, changing 106  into 104, and potentially turning hours-long simulations into minutes-long ones. With this fast code in hand, it will become possible to run a large enough number of simulations to train a neural network to serve as an extremely fast-running surrogate model of the cyclotron.