Engineering topics

Webb, G M

Publications and source records attributed to Webb, G M.

5 records

DOE OSTI2012

Solitons in two-fluid plasma

We examine ion-acoustic solitons in two-fluid plasmas without the usual simplification of setting electron mass to zero. Assuming one-dimensional, electrostatic and cold protons, the system is treated analytically, resulting in an integral form solution. We present numerical calculations which resolve the ion-acoustic solitary wave signatures. Also, we consider the conditions for which ion-acoustic solitons may exist. The existence conditions set up a Mach number threshold. Our result shows that the Mach number threshold depends on the electron-to-proton mass ratio and the electron adiabatic index; for a special adiabatic index {gamma}= 2, the condition reduces to a cubic equation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

A FOCUSED TRANSPORT APPROACH TO THE TIME-DEPENDENT SHOCK ACCELERATION OF SOLAR ENERGETIC PARTICLES AT A FAST TRAVELING SHOCK

Some of the most sophisticated models for solar energetic particle (SEP) acceleration at coronal mass ejection driven shocks are based on standard diffusive shock acceleration theory. However, this theory, which only applies when SEP pitch-angle anisotropies are small, might have difficulty in describing first-order Fermi acceleration or the shock pre-heating and injection of SEPs into first-order Fermi acceleration accurately at lower SEP speeds where SEP pitch-angle anisotropies upstream near the shock can be large. To avoid this problem, we use a time-dependent focused transport model to reinvestigate first-order Fermi acceleration at planar parallel and quasi-parallel spherical traveling shocks between the Sun and Earth with high shock speeds associated with rare extreme gradual SEP events. The focused transport model is also used to investigate and compare three different shock pre-heating mechanisms associated with different aspects of the nonuniform cross-shock solar wind flow, namely, the convergence of the flow (adiabatic compression), the shear tensor of the flow, and the acceleration of the flow, and a fourth shock pre-heating mechanism associated with the cross-shock electric field, to determine which pre-heating mechanism contributes the most to injecting shock pre-heated source particles into the first-order Fermi acceleration process. The effects of variations in traveling shock conditions, such as increasing shock obliquity and shock slowdown, and variations in the SEP source with increasing shock distance from the Sun on the coupled processes of shock pre-heating, injection, and first-order Fermi acceleration are analyzed. Besides the finding that the cross-shock acceleration of the solar wind flow yields the dominant shock pre-heating mechanism at high shock speeds, we find that first-order Fermi acceleration at fast traveling shocks differs in a number of respects from the predictions and assumptions of standard steady-state diffusive shock acceleration theory as is discussed below.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

THE TRANSPORT OF LOW-FREQUENCY TURBULENCE IN ASTROPHYSICAL FLOWS. I. GOVERNING EQUATIONS

Numerous problems in space physics and astrophysics require a detailed understanding of the transport and dissipation of low-frequency turbulence in an expanding magnetized flow. We employ a scale-separated decomposition of the incompressible MHD equations (based on an Elssaesser description) and develop a moment hierarchy to describe the transport of the total energy density in fluctuations, the cross-helicity, the energy difference, and correlation lengths corresponding to forward- and backward-propagating modes and to the energy difference. The dissipation terms for the various transport equations are derived. One-point closure schemes are utilized. The technical elements of this work that distinguish it from previous studies are (1) the inclusion of the large-scale background inhomogeneous Alfvenic velocity V{sub A} at a level of detail greater than before, (2) the introduction of a tractable slow timescale closure to eliminate high-frequency interference terms that is likely to prove a useful approximation for practical problems related to the transport of turbulence in an inhomogeneous flow such as the solar wind or solar corona, and finally, (3) we develop a simplified phenomenology for the energy difference or equivalently residual energy that may be useful for practical applications. This yields a coupled system of six equations that describes the transport of turbulence in inhomogeneous sub-Alfvenic and super-Alfvenic flows. The turbulence transport equations are quasi-linear in their spatial evolution operators and nonlinear in the dissipation terms, making the model equations relatively tractable to analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2010

Modified Burgers' equation resulting from a hydrodynamic model of shock waves with reflected particles

Ion reflection at perpendicular, collisionless shock waves is treated in a simple gas dynamical context. The effect of pickup ions reflected by the cross-shock potential and their subsequent energization in the motional electric field is included through the introduction of source terms in the basic inviscid fluid equations. From a weak source description, a Burgers' equation is derived modified by the addition of a quadratically nonlinear term. The construction of Burgers' equation demonstrates explicitly that particle reflection is a dissipation mechanism for collisionless shocks. Numerical solutions for the modified Burgers' equation (MBE) are presented. From these solutions it is implied that the dissipative term of the MBE is associated with the length scale of the shock foot, while the additional term is associated with the shock ramp. The general physical model is discussed in terms of the reflection and energization of pickup ions at outer heliospheric perpendicular shocks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

ALFVEN SIMPLE WAVES: EULER POTENTIALS AND MAGNETIC HELICITY

The magnetic helicity characteristics of fully nonlinear, multi-dimensional Alfven simple waves are investigated, by using relative helicity formulae and also by using an approach involving poloidal and toroidal decomposition of the magnetic field and magnetic vector potential. Different methods to calculate the magnetic vector potential are used, including the homotopy and Biot-Savart formulae. Two basic Alfven modes are identified: (1) the plane one-dimensional Alfven simple wave given in standard texts, in which the Alfven wave propagates along the z-axis with wave phase {psi} = k{sub 0}(z - {lambda}t), where k{sub 0} is the wave number and {lambda} is the group velocity of the wave and (2) the generalized Barnes simple Alfven wave in which the wave normal n moves in a circle in the xy-plane perpendicular to the mean field, which is directed along the z-axis. The plane Alfven wave (1) is analogous to the slab Alfven mode and the generalized Barnes solution (2) is analogous to the two-dimensional mode in Alfvenic, incompressible turbulence. The helicity characteristics of these two basic Alfven modes are distinct. The helicity characteristics of more general multi-dimensional simple Alfven waves are also investigated. Applications to nonlinear Alfvenic fluctuations and structures observed in the solar wind are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗