Transverse Ion Beam Shaping Using Nonlinear Optics

Taking an advantage of the unique capabilities of heavy ion beams and continuously increasing beam intensity, many successful experiments on high energy density (HED) matter have been carried out at GSI over the past few years. New fascinating experimental proposals such as investigation of equation-of-state of matter under extreme conditions [1] and generation of metallic hydrogen utilizing ion-beam driven cylindrical implosion schemes [2, 3] have been also worked out. The possibility of transverse beam shaping, i.e. modification of the beam intensity distribution is crucial for these experiments. Typical examples of beam shaping are the generation of a uniform intensity distribution in the focal spot or creation of a ring focus (annular beam), whereas initial beam intensity distribution is Gaussian. Other applications of transverse beam shaping include nuclear medicine, isotope production, final focusing systems of colliders and ion implantation. Recently, two different beam shaping methods for HED matter experiments have been proposed. First, to use a special operating mode of a plasma lens [4] and second, an rf wobbler (beam rotating system) [5]. However, employing these methods meets a number of difficulties and an extensive R&D work is still needed before appropriate technical solutions can be found. It is important to note that transverse beam shaping is also possible using conventional nonlinear optical elements such as octupoles and dodecapoles, installed in a beamline. There are several papers devoted to this problem that appeared during the two past decades [6, 7, 8, 9]. Besides theoretical studies (e.g., [10, 11]), there is also work done which demonstrates the possibility of transverse ion beam shaping using octupoles experimentally [12]. In one-dimensional treatment of an arbitrary ion optical system, the number of particles dN inside an element [x, x + dx] is invariable and the initial ρ(xo) = dN/dxo and final ρ(x) = dN/dx beam intensity distributions are therefore related as ρ(xo)dxo = ρ(x)dx or, equally,