Superconducting cavities presently used for acceleration of ions in velocity range ϳ0.01c to 0.3c (where c is the speed of light) are based on quarter-wave resonators. Currently there are several design proposals in nuclear physics laboratories for application of this type of cavity for acceleration of light and heavy ions. The operating frequencies of the cavities range from ϳ50 to 360 MHz to satisfy various specifications. Electrodynamics studies of the field distributions in the beam-cavity interaction area indicate appreciable dipole components of both electric and magnetic fields, especially for higher-frequency cavities. The dipole fields induce beam steering, which is a strong function of rf phase and which couples the longitudinal and transverse motion. This can result in growth in the transverse emittance of the beam. In this paper, we propose two possible methods for the correction of such dynamic beam-steering effects in quarter-wave resonators. We analyze and discuss the correction methods for the particular examples of two quarter-wave resonators operating at 57.5 and 115 MHz designed for the driver linac of the Rare Isotope Accelerator facility.

TABLE I. Table of ML methods discussed in this Colloquium with an indication of the main type of learning (S, supervised; U, unsupervised; semi-S, semisupervised). Acronym Method Description Learning type AE, VAE Autoencoders, Variational autoencoders ANN capable of learning efficient representations of the input data without any supervision U ANN Artificial neural network Models for learning defined by connected units (or nodes) and hidden layers with well-defined inputs and outputs S BED Bayesian experimental design Bayesian inference for experimental design S BM Boltzmann machine Generative ANN that can learn a probability distribution from sets of changing inputs U BMA, BMM Bayesian model averaging, Bayesian model mixing Bayesian inference applied to model selection or the combined estimation, or performed over a mixture model S BNN Bayesian neural network ANN where the parameters of the network are represented by probabilities learned by Bayesian inference S BO Bayesian optimization Optimization of functions without an a priori knowledge of functional forms. S and semi-S CNN Convolutional neural network ANN where convolution is used to reduce dimensionalities S EMB Ensemble methods and boosting Methods based on collections of decision trees as simple learners S GAN Generative adversarial network System of two ANNs where a generative network generates outputs while a discriminative network evaluates them U GP Gaussian process Collection of random variables that have a joint Gaussian distribution used in Bayesian inference Semi-S KNN k-nearest neighbors Nonparametric method where inputs consist of the k closest training examples in a dataset S KR Kernel regression Extension of linear regression methods to include nonlinear function kernels S LR Logistic regression Convex optimization method based on maximum likelihood estimate for classification problems S LSTM Long short-term memory RNN capable of learning long-term dependencies S PCA Principal component analysis Dimensionality reduction technique based on retaining the largest eigenvalues of the covariance matrix U REG Linear regression Linear algebra methods used for modeling continuous functions in terms of their explanatory variables S RL Reinforcement learning Learning achieved by trial and error of desired and undesired events Neither S nor U RNN Recurrent neural network ANN where connections between nodes allow for temporal dynamic behavior S SVM Support vector machine Convex optimization techniques with efficient ways to distinguish features in datasets S

The proposed Rare Isotope Accelerator (RIA) Facility, an innovative exotic-beam facility for the production of high-quality beams of short-lived isotopes, consists of a fully superconducting 1.4 GV driver linac and a 140 MV postaccelerator. To produce sufficient intensities of secondary beams the driver linac will provide 400 kW primary beams of any ion from hydrogen to uranium. Because of the high intensity of the primary beams the beam losses must be minimized to avoid radioactivation of the accelerator equipment. To keep the power deposited by the particles lost on the accelerator structures below 1 W=m, the relative beam losses per unit length should be less than 10 ÿ5 , especially along the high-energy section of the linac. A new beam dynamics simulation code TRACK has been developed and used for beam loss studies in the RIA driver linac. In the TRACK code, ions are tracked through the three-dimensional electromagnetic fields of every element of the linac starting from the electron cyclotron resonance (ECR) ion source to the production target. The simulation starts with a multicomponent dc ion beam extracted from the ECR. The space charge forces are included in the simulations. They are especially important in the front end of the driver linac. Beam losses are studied by tracking a large number of particles (up to 10 6) through the whole linac considering all sources of error such us element misalignments, rf field errors, and stripper thickness fluctuations. For each configuration of the linac, multiple sets of error values have been randomly generated and used in the calculations. The results are then combined to calculate important beam parameters, estimate beam losses, and characterize the corresponding linac configuration. To track a large number of particles for a comprehensive number of error sets (up to 500), the code TRACK was parallelized and run on the Jazz computer cluster at ANL.

No abstract

An advanced facility for the production of nuclei far from stability could be based on a high-power driver accelerator providing ion beams over the full mass range from protons to uranium. A beam power of several hundred kilowatts is highly desirable for this application. At present, however, the beam power available for the heavier ions would be limited by ion source capabilities. A simple and cost-effective method to enhance the available beam current would be to accelerate multiple charge states through a superconducting ion linac. This paper presents results of numerical simulation of multiple charge state beams through a 1.3 GeV ion linac, the design of which is based on current state-of-the-art superconducting elements. The dynamics of multiple charge state beams are detailed, including the effects of possible errors in rf field parameters and misalignments of transverse focusing elements. The results indicate that operation with multiple charge state beams is not only feasible but straightforward and can increase the beam current by a factor of 3 or more.