• Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos

      Gascoyne, Andrew (AIP, 2015-03-27)
      Using a full orbit test particle approach, we analyse the motion of a single proton in the vicinity of magnetic null point configurations which are solutions to the kinematic, steady state, resistive magnetohydrodynamics equations. We consider two magnetic configurations, namely, the sheared and torsional spine reconnection regimes [E. R. Priest and D. I. Pontin, Phys. Plasmas 16, 122101 (2009); P. Wyper and R. Jain, Phys. Plasmas 17, 092902 (2010)]; each produce an associated electric field and thus the possibility of accelerating charged particles to high energy levels, i.e., > MeV, as observed in solar flares [R. P. Lin, Space Sci. Rev. 124, 233 (2006)]. The particle's energy gain is strongly dependent on the location of injection and is characterised by the angle of approach β, with optimum angle of approach βopt as the value of β which produces the maximum energy gain. We examine the topological features of each regime and analyse the effect on the energy gain of the proton. We also calculate the complete Lyapunov spectrum for the considered dynamical systems in order to correctly quantify the chaotic nature of the particle orbits. We find that the sheared model is a good candidate for the acceleration of particles, and for increased shear, we expect a larger population to be accelerated to higher energy levels. In the strong electric field regime (E0=1500E0=1500 V/m), the torsional model produces chaotic particle orbits quantified by the calculation of multiple positive Lyapunov exponents in the spectrum, whereas the sheared model produces chaotic orbits only in the neighbourhood of the null point.
    • Structure of the harmonic oscillator in the space of n-particle Glauber correlators

      Zubizarreta Casalengua, E.; López Carreño, J. C.; del Valle, E.; Laussy, Fabrice; Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid E-28049, Spain; Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid E-28049, Spain; Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid E-28049, Spain; Faculty of Science Engineering, University of Wolverhampton, Wulfruna St., Wolverhampton WV1 1LY, United Kingdom (AIP, 2017-06-27)
      We map the Hilbert space of the quantum harmonic oscillator to the space of Glauber’s nth-order intensity correlators, in effect showing “the correlations between the correlators” for a random sampling of the quantum states. In particular, we show how the popular g(2) function is correlated to the mean population and how a recurrent criterion to identify single-particle states or emitters, namely, g(2)<1/2g(2)<1/2, actually identifies states with at most two particles on average. Our charting of the Hilbert space allows us to capture its structure in a simpler and physically more intuitive way that can be used to classify quantum sources by surveying which territory they can access.