Stages of homogeneous nucleation in solid isotopic helium mixtures

Abstract

Photonic bandgap (PBG) fibers with hollow core defects have been suggested for use as laser driven accelerator structures. The modes of a photonic crystal fiber he in a set of allowed bands. A fiber with a central vacuum defect can support so-called defect modes with frequencies in the bandgap and electromagnetic fields confined spatially near the defect. A defect mode suitable for relativistic particle acceleration must have a longitudinal electric field in the central defect and a phase velocity at the speed of light (SOL). We explore the design of the defect geometry to support well confined accelerating modes in such PBG fibers. The dispersion diagram of an accelerating mode must cross the SOL line, and such modes form a special class of defect modes known as surface modes, which are lattice modes of the original PBG crystal that have been perturbed into the bandgap. The details of the surface boundary separating the defect from the surrounding PBG matrix are found to be the critical ingredients for optimizing the accelerator mode properties. Photonic Bandgap (PBG) structures have recently been proposed as optical accelerators for their high coupling impedance and high damage threshold. As a first step in preparing a PBG accelerator, we propose to observe the optical wakefield induced by an electron beam traversing the structure in the absence of a coupled laser pulse. The electrons are focused into the fiber via a permanent magnet quadrupole triplet. The electrons excite fiber modes with speed-of-light (SOL) phase velocities. By observing the wakefield using a spectrometer, the SOL mode frequencies are determined. We have made pressure and NMR measurements during the evolution of phase separation in solid helium isotopic mixtures. Our observations indicate clearly all three stages of the homogeneous nucleation-growth process: (1) creation of nucleation sites; (2) growth of the new-phase component at these nucleation sites; and (3) coarsening: the dissolution of subcritical droplets with the consequent further late-stage growth of the supercritical droplets. The time exponent for the coarsening, a=1/3, is consistent with the conserved order parameter Lifshitz-Slezov evaporation-condensation mechanism.