Rainbow lenses

Abstract

This review paper is devoted to transmission of protons through rainbow lenses, being novel ion beam optical elements analogous to crystal channels. We begin with a brief description of the crystal rainbow effect, which has proven to be the basic effect in ion channeling in thin crystals. Then, we concentrate on the transmission of a parallel proton beam through a square electrostatic rainbow lens. The initial proton kinetic energy is 10 keV and the potential of the electrodes is chosen to be between 10 and 100 kV. It is demonstrated that the evolution of the spatial distribution of transmitted protons is determined by the evolution of the corresponding rainbow pattern. The beam after the lens is clearly separated into the bright and dark components, corresponding to the bright and dark sides of the rainbow, respectively. All the focused protons are confined within the rainbow line. After that, we explore more accurately the focusing properties of the same electrostatic rainbow lens. This is done with the parallel and nonparallel initial beams of the kinetic energy of 10 keV. The electrode potential is chosen to be 2 kV. In the continuation of the paper, we analyze the acceleration properties of a square radiofrequency rainbow lens. This is done with a nonparallel initial beam of the kinetic energy of 10 keV. The lens electrodes excitation potential is a harmonic function of time of the amplitude of 20 keV and frequency of about 3 MHz. We explain the spatial, angular, and kinetic energy distributions of protons propagating through the lens. The transmitted proton beam contains a squarelike core, which is defined by the focused protons. Finally, we discuss the possible applications of rainbow lenses. © 2014 Elsevier Inc. All rights reserved.