Since the invention of quantum mechanics, even the simplest example of collisional breakup in a system of charged particles, e{sup {minus}} + H {r_arrow} H{sup +} + e{sup {minus}} + e{sup {minus}}, has stood as one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculating the energies and directions for a final state in which three charged particles are moving apart. Advances in the formal description of three-body breakup have yet to lead to a viable computational method. Traditional approaches, based on two-body formalisms, have been unable to produce differential cross sections for the three-body final state. Now, by using a mathematical transformation of the Schrodinger equation that makes the final state tractable, a complete solution has finally been achieved, Under this transformation, the scattering wave function can be calculated without imposing explicit scattering boundary conditions. This approach has produced the first triple differential cross sections that agree on an absolute scale with experiment as well as the first ab initio calculations of the single differential cross section.

The High Current Experiment (HCX) at Lawrence Berkeley National Laboratory is part of the US program that explores heavy-ion beam as the driver option for fusion energy production in an Inertial Fusion Energy (IFE) plant. The HCX is a beam transport experiment at a scale representative of the low-energy end of an induction linear accelerator driver. The primary mission of this experiment is to investigate aperture fill factors acceptable for the transport of space-charge-dominated heavy-ion beams at high intensity (line charge density {approx}0.2 {micro}C/m) over long pulse durations (4 {micro}s) in alternating gradient focusing lattices of electrostatic or magnetic quadrupoles. This experiment is testing transport issues resulting from nonlinear space-charge effects and collective modes, beam centroid alignment and steering, envelope matching, image charges and focusing field nonlinearities, halo and, electron and gas cloud effects. We present the results for a coasting 1 MeV K{sup +} ion beam transported through ten electrostatic quadrupoles. The measurements cover two different fill factor studies (60% and 80% of the clear aperture radius) for which the transverse phase-space of the beam was characterized in detail, along with beam energy measurements and the first halo measurements. Electrostatic quadrupole transport at high beam fill factor ({approx}80%) is …