Adiabatic theory of charged particle motion.
Adiabatic theory of charged particle motion, considering first-order effects in radius of gyration and Alfven theory
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Adiabatic theory of charged particle motion, considering first-order effects in radius of gyration and Alfven theory
Particle motions in magnetic fields, as related to charged particle trapping in Van Allen belt
Particle motions in magnetic field, demonstrating existence of adiabatic region in particle phase space for Van Allen belt region
Threshold wind speeds for setting particles into motion on Mars are estimated by evaluating experimentally observed threshold friction velocities and determining the ratio of this velocity to the threshold wind speed at the top of earth's atmospheric boundary layer (ABL). Turning angles between the direction of the wind at the top of the ABL and the wind stress at the surface are also estimated. Detailed consideration is given to the dependence of the threshold wind speed at the top of the ABL on particle diameter, surface pressure, air temperature, atmospheric stability and composition, surface roughness, and interparticle cohesion. The results are applied to interpret a number of phenomena that have been observed on Mars and are attributable to aeolian processes. It is shown that: (1) minimum threshold wind speeds of about 50 to 100 m/sec are required to cause particle motion on Mars under 'favorable' conditions; (2) particle motion should be infrequent and strongly correlated with proximity to small topographical features; (3) in general, particle motion occurs more readily at night than during the day, in winter polar areas than equatorial areas around noon, and for H2O or CO2 ice particles than for silicate particles; and (4) the boundary between saltating and suspendible particles is located at a particle diameter of about 100 microns.
The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.
A flow visualization study using selective dye injection and frame by frame analysis of a movie provided qualitative and quantitative data on the motion of marked fluid particles in a 60 degree artery branch model for simulation of physiological femoral artery flow. Physical flow features observed included jetting of the branch flow into the main lumen during the brief reverse flow period, flow separation along the main lumen wall during the near zero flow phase of diastole when the core flow was in the downstream direction, and inference of flow separation conditions along the wall opposite the branch later in systole at higher branch flow ratios. There were many similarities between dye particle motions in pulsatile flow and the comparative steady flow observations.
First correction to second adiabatic invariant of charged particle motion in magnetic field
In the Young's fringe approach to particle image velocimetry, random particle motions cause loss of fringe visibility by decorrelating the coherent interexposure particle separations responsible for fringe formation. Since the visibility reduction is determined by the random motion through a Fourier transform relation analogous to the Van Cittert Zernike Theorem, it has been proposed that the random motion can be characterized statistically by analyzing fringe visibility distributions in the transform plane. This paper assesses the accuracy of such measurements. In particular, the effects of finite particle population and of correlated random motion are evaluated. The theory applies to diffusive motion, turbulence, and to random motion caused by mean velocity inhomogeneities.
Approximate analytic solutions exist for particle motion in a one-dimensional current sheet with a constant normal magnetic field component. These solutions are tested against precise numerical calculations, and a range of validity of the analytic solutions is inferred. For example, in the geomagnetic tail neutral sheet, for a dawn-dusk electric field of 0.1-1 mV/m, lobe field of 10-40 nT, and sheet thickness of 1000 km, the analytic solutions serve as a good predictor of particle motion when the normal magnetic field component is less than 3 or 4 nT. By using the analytic solutions, initial distribution functions are mapped into final (accelerated) distributions, and the analytic mappings are compared with numerical mappings.
An important phase of laser velocimetry investigations in gas flow fields is an analysis of the particle motion in the gas. The present paper examines three important aspects of particle motion calculations. A comparison of various drag coefficient equations with available experimental sphere drag data is made to determine the relative accuracy of the various empirical expressions available. Then, the most accurate drag coefficient equation is used to determine the limitations of Stokes drag equation for calculating relaxation lengths behind normal shocks, and percent velocity lags in one-dimensional constant velocity gradient regions. Finally, a two-dimensional constant velocity gradient gas flow field is examined to determine the importance of the coupling between the governing equations for the components of particle velocity.
Theory of particle motion in current sheets is reviewed. For small, approximately constant normal magnetic field, Bz, particles oscillate about the current sheet and 'live' within the sheet for one-half gyroperiod based on Bz. This lifetime replaces the mean collision time in the Lorentzian conductivity and thus gives rise to the concept of an inertial (or gyro-) conductivity. A substorm model by Coroniti utilizes this conductivity to allow reconnection to proceed without anomalous processes, due to wave-particle interactions. Chaotic particle orbits may at times be important to the dynamics, depending on parameters such as particle energy, current sheet thickness, and field line curvature. A current sheet model with neutral line predicts a ridge structure and asymmetries in the distribution function. Ion distributions near the plasma sheet boundary layer, during the CDAW 6 interval, are consistent with the model predictions. In recent studies by Mitchell et al. and Williams et al., the major current carriers during the growth phase of a substorm were found to be adiabatic electrons not more than 1 keV, but just before a current disruption event, the tail current was mainly carried by energetic ions undergoing current sheet oscillation.
A procedure for experimentally determining, in terms of the particle motions, the shapes of the low order acoustic modes in enclosures is described. The procedure is based on finding differentiable functions which approximate the shape functions of the low order acoustic modes when these modes are defined in terms of the acoustic pressure. The differentiable approximating functions are formed from polynomials which are fitted by a least squares procedure to experimentally determined values which define the shapes of the low order acoustic modes in terms of the acoustic pressure. These experimentally determined values are found by a conventional technique in which the transfer functions, which relate the acoustic pressures at an array of points in the enclosure to the volume velocity of a fixed point source, are measured. The gradient of the function which approximates the shape of a particular mode in terms of the acoustic pressure is evaluated to give the mode shape in terms of the particle motion. The procedure was tested by using it to experimentally determine the shapes of the low order acoustic modes in a small rectangular enclosure.
Second term obtained in asymptotic series for second adiabatic invariant of charged particle motion in static magnetic field and found to vanish at mirror points
We present a new analysis of the fundamental physics of charged-particle motion in a turbulent magnetic field using a numerical simulation. The magnetic field fluctuations are taken to be static and to have a power spectrum which is Kolmogorov. The charged particles are treated as test particles. It is shown that when the field turbulence is independent of one coordinate (i.e., k lies in a plane), the motion of these particles across the magnetic field is essentially zero, as required by theory. Consequently, the only motion across the average magnetic field direction that is allowed is that due to field-line random walk. On the other hand, when a fully three-dimensional realization of the turbulence is considered, the particles readily cross the field. Transport coefficients both along and across the ambient magnetic field are computed. This scheme provides a direct computation of the Fokker-Planck coefficients based on the motions of individual particles, and allows for comparison with analytic theory.
Charged particle motion in the guiding center approximation is analyzed for models of the Jovian and Saturnian magnetospheric magnetic fields based on Voyager magnetometer observations. Field lines are traced and exhibit the distention which arises from azimuthally circulating magnetospheric currents. The spatial dependencies of the guiding center bounce period and azimuthal drift rate are investigated for the model fields. Non-dipolar effects in the gradient-curvature drift rate are most important at the equator and affect particles with all mirror latitudes. The effect is a factor of 10-15 for Jupiter with its strong magnetodisc current and 1-2 for Saturn with its more moderate ring current. Limits of adiabaticity, where particle gyroradii become comparable with magnetic scale lengths, are discussed and are shown to occur at quite modest kinetic energies for protons and heavier ions.
Charged particle motion in magnetic radiation shielding fields
Atmospheric acoustic waves transmit energy into the solid Earth through air-to-ground coupling. These waves are recorded by seismic sensors and provide insight into both atmospheric phenomena and subsurface properties. Interpreting these signals is often challenging because they are modulated by subsurface structure and the incidence angle of the acoustic wave. This study examines acoustic--seismic coupling generated by the 2012 Camp Minden Explosion, which was recorded by hundreds of seismoacoustic stations. We apply a novel technique to quantify the seismic particle motion, model coupled waves with a propagator matrix approach, and apply a Bayesian inversion to infer properties of the shallow subsurface. Our analysis reveals that prograde motion is widespread and focused in low shear-wave velocity regions, such as the Mississippi Embayment, and retrograde motion is more common in higher shear-velocity areas. Inversion results at some stations produce plausible subsurface models with strong waveform fits, while inversions at other sites are less successful. These results indicate prograde particle motion in air-to-ground coupled waves is more prevalent than previously recognized and may serve as a diagnostic for shallow velocity structure. Our comprehensive modeling and inversion framework provides a potential method to extract layered near-surface properties from acoustic-seismic coupling observations.
The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.