5 results for Armstrong, Craig Keith

  • Topics in Energy Release and Particle Acceleration in the Heliosphere

    Armstrong, Craig Keith (2014)

    Doctoral thesis
    University of Waikato

    This thesis investigates both the release of energy in solar flares, and the acceleration and transport of particles in various astrophysical situations. While numerical simulations are central to this thesis, these are always motivated by analytical arguments. A review of flare energy release is given in Chapter 2, with results presented in Chapters 3 and 4. The main goal of the flare work is to investigate the effect of viscosity on energy release rates. Scaling arguments and exact solutions of the magnetohydrodynamic equations are used to interpret the results of two-dimensional numerical simulations of magnetic reconnection. The results support viscous energy dissipation accounting for a significant fraction of flare energy release. Chapter 5 contains an introduction to astrophysical particle acceleration, using the Fokker-Planck formulation. The theory introduced in this chapter is used to study electron transport in solar flare loops (Section 5.5). A key aspect of the analysis is the expression of the Fokker-Planck equation as a system of stochastic differential equations. A generalisation to the flare loop hard X-ray emission prediction of Conway et al. (1998) is obtained, giving a stronger dependence on density for dispersed initial distributions. Chapter 6 uses the methods of the previous chapter to study the acceleration of cosmic-rays at the heliospheric termination shock. The applicability of the focused acceleration mechanism of Schlickeiser and Shalchi (2008) is examined using numerical simulations, which are interpreted using analytical arguments based on averaging the stochastic equations. The results show significant limitations in assuming a near-isotropic distribution, a requirement for the focused acceleration mechanism. In addition, momentum diffusion provides a significant effect that cannot be neglected. The theory is extended to include focused deceleration and pure momentum diffusion.

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  • Hamilton-Jacobi Theory and Superintegrable Systems

    Armstrong, Craig Keith (2007)

    Masters thesis
    University of Waikato

    Hamilton-Jacobi theory provides a powerful method for extracting the equations of motion out of some given systems in classical mechanics. On occasion it allows some systems to be solved by the method of separation of variables. If a system with n degrees of freedom has 2n - 1 constants of the motion that are polynomial in the momenta, then that system is called superintegrable. Such a system can usually be solved in multiple coordinate systems if the constants of the motion are quadratic in the momenta. All superintegrable two dimensional Hamiltonians of the form H = (p_x)sup2 + (p_y)sup2 + V(x,y), with constants that are quadratic in the momenta were classified by Kalnins et al [5], and the coordinate systems in which they separate were found. We discuss Hamilton-Jacobi theory and its development from a classical viewpoint, as well as superintegrability. We then proceed to use the theory to find equations of motion for some of the superintegrable Hamiltonians from Kalnins et al [5]. We also discuss some of the properties of the Poisson algebra of those systems, and examine the orbits.

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  • Modeling focused acceleration of cosmic-ray particles by stochastic methods

    Armstrong, Craig Keith; Litvinenko, Yuri E.; Craig, Ian J.D. (2012)

    Journal article
    University of Waikato

    Schlickeiser & Shalchi suggested that a first-order Fermi mechanism of focused particle acceleration could be important in several astrophysical applications. In order to investigate focused acceleration, we express the Fokker-Planck equation as an equivalent system of stochastic differential equations. We simplify the system for a set of physically motivated parameters, extend the analytical theory, and determine the evolving particle distribution numerically. While our numerical results agree with the focused acceleration rate of Schlickeiser & Shalchi for a weakly anisotropic particle distribution, we establish significant limitations of the analytical approach. Momentum diffusion is found to be more significant than focused acceleration at early times. Most critically, the particle distribution rapidly becomes anisotropic, leading to a much slower momentum gain rate. We discuss the consequences of our results for the role of focused acceleration in astrophysics.

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  • Viscous effects in time-dependent planar reconnection

    Armstrong, Craig Keith; Craig, Ian J.D.; Litvinenko, Yuri E. (2011)

    Journal article
    University of Waikato

    Context. Viscous dissipation is expected to play a significant part in energy release in solar flares, yet the role of viscosity in a weakly resistive plasma of the solar corona remains unclear. Aims. We attempt to clarify the role of viscous effects in magnetic reconnection by performing simulations of reconnection in planar periodic geometry in an incompressible viscous resistive plasma. Methods. We consider magnetic reconnection, driven by large-scale vortical flows. We use both the classical shear viscosity and the Braginskii form for the ion parallel viscosity in a magnetised plasma. We determine the scalings of the current sheet parameters and the global rates of resistive and viscous dissipation. We use steady-state exact solutions and scaling arguments to interpret the numerical results. Results. We show that, regardless of the form of viscosity, the resistive non-viscous analytical solutions for flux pile-up merging provide a very good approximation of the numerical results in the reconnecting current sheet. We find no evidence for a visco-resistive scale. Numerical results for a highly sheared magnetic field, however, appear to deviate from the analytical predictions in the case of the Braginskii viscosity.

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  • Visco–resistive dissipation in transient reconnection driven by the Orszag–Tang vortex

    Armstrong, Craig Keith; Craig, Ian J.D. (2013)

    Journal article
    University of Waikato

    Viscous effects are expected to significantly contribute to reconnective energy release mechanisms in solar flares. While simple scaling arguments based on head-on reconnection suggest that viscous dissipation may dominate resistive dissipation, it is not clear whether these findings can be applied in more general merging situations. Here we perform side-by-side planar reconnection simulations driven by the Orszag-Tang vortex, for both classical and Braginskii forms of the viscosity. This formulation has the advantage of providing an autonomous MHD system that develops strong current layers, sustained by large-scale vortical shearing flows. The dissipation rates are shown to follow analytically based scaling laws, which suggest that viscous losses generated from large-scale non-uniform velocity fields are likely to dominate resistive losses in current-sheet reconnection solutions.

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