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At least 19 records

Model for Independent Particle Motion

Independent particle model in nuclear physics assumes that the nucleon in the nucleus moves in the average (mean field) potential generated by all other nucleons. This chapter gives a short overview of basic features of the independent particle motion in atomic nuclei and its theoretical realization in the framework of shell models for spherical, deformed, and rotating nuclei as well as in more sophisticated approaches such as microscopic+macroscopic model and density functional theories. Independent particle motion of nucleons leads to global and single-particle consequences. The global ones manifest themselves in the shell structure, and its consequences for the global structure of nuclear landscape, the existence of superheavy nuclei, and the superdeformation at high spin are briefly reviewed. Finally, the latter shows itself in the single-particle properties such as energies, alignments, and densities; their manifestations are illustrated on specific examples.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field

It is pointed out that the conventional Lie transform perturbation theory for the guiding center motion of charged particles in a magnetic field needs to be modified for ordering inconsistency. There are two reasons. First, the ordering difference between the temporal variation of gyrophase and that of the other phase space coordinates needs to be taken into account. Second, it is also important to note that the parametric limit of the derivative of a function is not equivalent to the derivative of the limit function. When these facts are taken into account, the near identity transformation rule for one form related to the Lagrangian is modified. With the modified near identity transformation rule, the drift motion of charged particles can be described in the first order, instead of the second order and beyond through a tedious expansion process as in the conventional formulation. Here, this resolves the discrepancy between the direct and Lie transform treatments in the Lagrangian perturbation theory for charged particle motion in a magnetic field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Estimates of the wind speeds required for particle motion on Mars

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.

Pollack, J. B.↗

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

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.

Stern, D. P.↗

Fluid particle motion and Lagrangian velocities for pulsatile flow through a femoral artery branch model

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.

Cho, Y. I.↗

Young's fringe particle image velocimetry in the presence of random particle motions

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.

Rubinstein, R.↗

Comparison of an analytical approximation for particle motion in a current sheet with precise numerical calculations

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.

Speiser, T. W.↗

Influence of drag coefficient equations on particle motion calculations

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.

Walsh, M. J.↗

Particle motion in the tail current sheet

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.

Speiser, T. W.↗

Experimental determination of the particle motions associated with the low order acoustic modes in enclosures

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.

Byrne, K. P.↗

Charged-particle motion in multidimensional magnetic-field turbulence

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.

Giacalone, J.↗

Charged particle motions in the distended magnetospheres of Jupiter and Saturn

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.

Birmingham, T. J.↗

Quantitative probing of the fast particle motion during the solidification of battery electrodes

Synchrotron x-ray tomography represents one of the most powerful imaging techniques that can visualize the three-dimensional microstructural complexity with a high spatial resolution. To date, however, the temporal resolution of this technique has been handicapped by the intrinsic limitations in the data acquisition speed and the lack of a suitable data processing method. The present study aims to fundamentally resolve this challenge by implementing a data analysis method that is based on differentiating discrete tomography reconstruction from a continuous scan reconstruction. With this methodological development, we capture and quantify the particle motion during the solidification of battery electrodes and reveal the statistics of the dynamically evolving motion in the drying process, which has been challenging to resolve. We discover that the particle motion exhibits a strong dependence on its geometric location within a drying electrode. Our results also imply that the final electrode quality can be controlled by balancing the solvent evaporation rate and the particle mobility in the region close to the drying surface.

25 ENERGY STORAGE↗