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Numerical program integrating motion equation of charged particles from realistic geomagnetic field model, with trajectory calculations for solar cosmic rays
When high-energy charged particles pass through a thin detector, the ionization energy loss in that detector is subject to fluctuations or straggling which must be considered in interpreting the data. Under many conditions, which depend upon the charge and energy of the incident particle and the detector geometry, the ionization energy lost by the particle is significantly different from the energy deposited in the detector. This problem divides naturally into a calculation of the energy loss that results in excitation and low-energy secondary electrons which do not travel far from their production points, and a calculation of energy loss that results in high-energy secondary electrons which can escape from the detector. The first calculation is performed using a modification of the Vavilov energy loss distribution. A cutoff energy is introduced above which all electrons are ignored and energy transferred to low energy particles is assumed to be equivalent to the energy deposited by them. For the second calculation, the trajectory of the primary particle is considered as a source of secondary high-energy electrons. The electrons from this source are transported using Monte Carlo techniques and multiple scattering theory, and the energy deposited by them in the detector is calculated. The results of the two calculations are then combined to predict the energy deposition distribution. The results of these calculations are used to predict the charge resolution of parallel-plate pulse ionization chambers that are being designed to measure the charge spectrum of heavy nuclei in the galactic cosmic-ray flux.
Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(sub lambda) = 110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(sub lambda) turbulent flows.
Mercury is surrounded by a tenuous exosphere in which particles travel on ballistic trajectories under the influence of a combination of gravity and solar radiation pressure. The densities are so small that the surface forms the exobase and particles in the exosphere are more likely to collide with it rather than with each other. For a planet with a more substantial collision-dominated atmosphere, a population of particles that enters from below the exobase supplies the exosphere. In contrast Mercury's exosphere is supplied both by incoming sources including the solar wind (hydrogen and helium), micrometeoroids (dust), meteoroids and cornets, and by particles released from the surface through a variety of processes that include sputtering by solar wind ions, desorption by solar photons and electrons, impacts by micrometeoroids, and thermal desorption of surface materials. These source processes are balanced by loss processes, which include impact with and sticking to the surface, Jeans (or thermal) escape, ionization followed by transport along magnetic field lines, and acceleration by solar radiation pressure to escape velocity. Ground-based attempts to detect an atmosphere around Mercury before Mariner 10 first visited the planet in 1974 were unsuccessful and led only to increasingly tight upper limits, culminating in a limiting value for surface atmospheric pressure of 0.015 Pascal (Pa) determined by Fink et al. (1974).
The present numerical model for neutral or charged dust-particle distribution prediction in P/Halley encompasses the spatial and temporal variations of the plasma parameters and magnetic field. A significant difference is noted between results for neutral dust trajectories and the trajectories of charged dust particles with radii smaller than 0.1 micron. While most of the model and in situ mass spectra were in good agreement, there is a shortage of the lowest-mass model particles, as well as an offset of the total counting rate for two outbound mass spectra. A combination of two Lorentzian particle mass-density functions with a 100:1 ratio for the number of particles with the lower and higher density functions yielded the best agreement.
An idealized two-dimensional model of the distorted electric field configuration, in the limit of a perfectly conducting satellite or satellite ionosphere, has been constructed. This model has been used to trace the adiabatic guiding-center trajectories of energetic protons and electrons across Jupiter's magnetic-field lines, which are taken as rectilinear. The adiabatic trajectories of very low-energy particles (cold-plasma) are thus found to avoid the satellite and escape absorption. In the limit of very high particle energies the adiabatic trajectories are undistorted, and absorption proceeds as if Io were an insulator. The particle absorbing characteristics of an electrically conducting Jovian satellite are found to depend on both the species and the energy of the incident particle, and the satellite's particle-absorbing cross section differs systematically from its geometric cross section.
A long-lasting Pc 5 pulsation at the dawn flank of the magnetosphere is studied using particle and field instrumentation from the ISEE 1 and 2 satellites. Electric field and particle modulation signatures were clearer than magnetic field variations, consistent with the satellites' position in latitude near the equatorial node of a fundamental resonance. Pulsation flow velocities along the ISEE 1 trajectory were calculated from particle characteristics using data from several instruments and from electric and magnetic field data. These flow velocities were all consistent with each other, but the velocities derived from plasma and energetic particle observations were a factor of 2.5 larger than velocities derived from the fields data. In contrast to observations of pulsations during magnetic storms, which often involve resonant or gyrating particle behavior, particles at all energies sampled (10 eV to 200 keV) appeared to respond passively to the pulsation throughout most of the period of interest.
A numerical simulation has been made of the 'pinhole effect' which produces the characteristic 'S-shaped' current-voltage curve. A disk-shaped conducting probe immersed in a plasma is modeled using a particle-in-cell (PIC) code. A probe partially covered by a very thin insulating layer is considered, as well as a probe mounted on an insulating disk. The simulation uses a cylindrical particle mover and allows for a variable number of particles in the system. The simulation space grid uses three different mesh sizes, the coarsest being away from the probe and the finest near the probe, in order to accurately calculate the trajectories of the simulation particles contributing the current to the probe and to the surface charge density on the dielectric. The calculation of the electrostatic potential is done self-consistently using successive over-relaxation (SOR). Backscattering and secondary electron emission are included for the case of positive probe voltage.
The nonlocal non-diffusive transport of passive scalars in turbulent magnetohydrodynamic (MHD) convection is investigated using transilient matrices. These matrices describe the probability that a tracer particle beginning at one position in a flow will be advected to another position after some time. A method for the calculation of these matrices from simulation data which involves following the trajectories of passive tracer particles and calculating their transport statistics, is presented. The method is applied to study the transport in several simulations of turbulent, rotating, three dimensional compressible, penetrative MDH convection. Transport coefficients and other diagnostics are used to quantify the transport, which is found to resemble advection more closely than diffusion. Some of the results are found to have direct relevance to other physical problems, such as the light element depletion in sun-type stars. The large kurtosis found for downward moving particles at the base of the convection zone implies several extreme events.
A test particle approach is used to compare gyroresonant pitch angle scattering of energetic electrons by coherent versus incoherent whistler mode waves, for the case in which the coherent wave amplitude is below the nonlinear phase trapping threshold. Wave packets of 400 ms duration propagating along the magnetic field at L = 4 within the plasmasphere are considered, and the wave-induced pitch angle scattering along the propagation path from one hemisphere to the other and the resulting precipitation flux are computed. An incoherent wave spectrum is simulated by random modulation of the wave frequency at intervals of 1 ms, thereby generating signals with nearly constant power spectral density over a bandwidth of 2 kHz centered at 5.5 kHz. The associated pitch angle scattering is compared with that of a monochromatic 5.5-kHz signal of 400 ms duration. Results of the test particle analysis are compared with those expected on the basis of a classical diffusion treatment, and an expression is derived for an effective “diffusion” coefficient for pitch angle scattering by coherent waves. The trajectory followed by a particle when interacting with incoherent waves essentially represents a random walk in velocity space, while for coherent waves the pitch angle of the particle varies in a well-defined manner. In spite of the fact that individual particle scatterings are typically larger for coherent waves, the peak precipitation fluxes induced by incoherent waves are found to be approximately the same as those for coherent waves having the same total power. This results from the fact that incoherent waves interact with particles over a wider range of energies. As a consequence, the energy spectrum and the temporal extent of transient precipitation pulses due to incoherent wave packets are broader than those for equivalent coherent ones.
The findings of the Stardust spacecraft mission returned to earth in January 2006 are discussed. The spacecraft returned two unprecedented and independent extraterrestrial samples: the first sample of a comet and the first samples of contemporary interstellar dust. An important lesson from the cometary Preliminary Examination (PE) was that the Stardust cometary samples in aerogel presented a technical challenge. Captured particles often separate into multiple fragments, intimately mix with aerogel and are typically buried hundreds of microns to millimeters deep in the aerogel collectors. The interstellar dust samples are likely much more challenging since they are expected to be orders of magnitudes smaller in mass, and their fluence is two orders of magnitude smaller than that of the cometary particles. The goal of the Stardust Interstellar Preliminary Examination (ISPE) is to answer several broad questions, including: which features in the interstellar collector aerogel were generated by hypervelocity impact and how much morphological and trajectory information may be gained?; how well resolved are the trajectories of probable interstellar particles from those of interplanetary origin?; and, by comparison to impacts by known particle dimensions in laboratory experiments, what was the mass distribution of the impacting particles? To answer these questions, and others, non-destructive, sequential, non-invasive analyses of interstellar dust candidates extracted from the Stardust interstellar tray will be performed. The total duration of the ISPE will be three years and will differ from the Stardust cometary PE in that data acquisition for the initial characterization stage will be prolonged and will continue simultaneously and parallel with data publications and release of the first samples for further investigation.
On an airless, slowly rotating planetary body like the Moon, ejecta particles from an impact follow simple ballistic trajectories. If gaseous interactions in the fireball are ignored, ejecta particles follow elliptical orbits with the center of the planetary body at one focus until they encounter the surface at the point of reimpact. The partial elliptical orbit of the ejecta particle lies in a plane in inertial (galactic) coordinates. Because of the slow rotation rate (for example, 360 degrees/28 days for the Moon), the intersection of the orbital plane and the surface remains nearly a great circle during the flight time of the ejecta. For this reason, lunar rays, representing concentrations of ejecta with the same azimuth but different velocities and/or ejecta angles, lie essentially along great circles. Ejecta from airless but more rapidly rotating bodies will follow more complicated, curving trajectories when plotted in the coordinate frame of the rotating planet or viewed as rays on the planetary surface. The curvature of trajectories of ejecta particles can be treated as a manifestation of the Coriolis effect, with the particles being accelerated by Coriolis pseudoforces. However, it is more straightforward to calculate the elliptical orbit in inertial space and then determine how far the planet rotates beneath the orbiting ejecta particle before reimpact. The Earth's eastward rotation affects ballistic ejecta in two ways: (1) the eastward velocity component increases the velocity of eastbound ejecta and reduces the velocity of westbound ejecta; and (2) the Earth turns underneath inflight ejecta, so that although the latitude of reimpact is not changed, the longitude is displaced westward, with the displacement increasing as a function of the time the ejecta remains aloft.
Two-phase flow systems play vital roles in the design of some current and anticipated space applications of two-phase systems which include: thermal management systems, transfer line flow in cryogenic storage, space nuclear power facilities, design and operation of thermal bus, life support systems, propulsion systems, In Situ Resource Utilization (ISRU), and space processes for pharmaceutical applications. The design of two-phase flow systems for space applications requires a clear knowledge of the behaviors of the dispersed phase (bubble), its interaction with the continuous phase (liquid) and its effect on heat and mass transfer processes, The need to understand the bubble generation process arises from the fact that for all space applications, the size and distribution of bubbles are extremely crucial for heat and mass transfer control. One important force in two-phase flow systems is the lift force on a bubble or particle in a liquid shear flow. The shear lift is usually overwhelmed by buoyancy in normal gravity, but it becomes an important force in reduced gravity. Since the liquid flow is usually sheared because of the confining wall, the trajectories of bubbles and particles injected into the liquid flow are affected by the shear lift in reduced gravity. A series of experiments are performed to investigate the lift force on a bubble in a liquid shear flow and its effect on the detachment of a bubble from a wall under low gravity conditions. Experiments are executed in a Poiseuille flow in a channel. An air-water system is used in these experiments that are performed in the 2.2 second drop tower. A bubble is injected into the shear flow from a small injector and the shear lift is measured while the bubble is held stationary relative to the fluid. The trajectory of the bubble prior, during and after its detachment from the injector is investigated. The measured shear lift force is calculated from the trajectory of the bubble at the detachment point. These values for the shear lift are then compared with the theoretical predictions from various published works on shear lift in the open literature, which include asymptotic solutions at low bubble Reynolds number, potential flow predictions and numerical studies that deal with intermediate bubble Reynolds numbers.
The NAIRAS(Nowcast of Aerospace Ionizing RAdiation system) model was initially developed for fast computation of GCR and SEP events in the Earth's atmosphere. It was recently improved for computing the effects of trapped particles and its domain of validity was extended to the near space environments, which notably includes the international space station (ISS). To validate the new capabilities of the model, we compared its outputs with some measurements made in the ISS. Historical data contained several SEP events while newer measurements made with the ARMAS instrument flying in the experience bay of KIBO show the influence of trapped particles and GCR over the total dose received.
The access of charged particles to the earth from space through the geomagnetic field has been of interest since the discovery of the cosmic radiation. The early cosmic ray measurements found that cosmic ray intensity was ordered by the magnetic latitude and the concept of cutoff rigidity was developed. The pioneering work of Stoermer resulted in the theory of particle motion in the geomagnetic field, but the fundamental mathematical equations developed have 'no solution in closed form'. This difficulty has forced researchers to use the 'brute force' technique of numerical integration of individual trajectories to ascertain the behavior of trajectory families or groups. This requires that many of the trajectories must be traced in order to determine what energy (or rigidity) a charged particle must have to penetrate the magnetic field and arrive at a specified position. It turned out the cutoff rigidity was not a simple quantity but had many unanticipated complexities that required many hundreds if not thousands of individual trajectory calculations to solve. The accurate calculation of particle trajectories in the earth's magnetic field is a fundamental problem that limited the efficient utilization of cosmic ray measurements during the early years of cosmic ray research. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable, and magnetic field models of increasing accuracy and complexity have been utilized. This report is documentation of a general FORTRAN computer program to trace the trajectory of a charged particle of a specified rigidity from a specified position and direction through a model of the geomagnetic field.
A method and model of predicting particle-surface interactions with a surface, such as the surface of a spacecraft. The method includes the steps of: determining a trajectory path of a plurality of moving particles; predicting whether any of the moving particles will intersect a surface; predicting whether any of the particles will be captured by the surface and/or; predicting a reflected trajectory and velocity of particles reflected from the surface.
Ionization of cometary neutral molecules produces ions which are picked up by the solar wind. The cometary ion pickup process for comet Giacobini-Zinner is studied in two ways: (1) with a test particle method in which trajectories are numerically calculated for several thousand ions whose initial locations were chosen randomly with probability proportional to the neutral density and (2) with a quasi-linear diffusion model. The cometary ion distribution function was calculated with the test particle model at several locations upstream of the bow shock and for several types of magnetic fluctuations (or waves). These waves were allowed to propagate in both directions along the magnetic field at the Alfven speed. Both pitch angle scattering and energy diffusion are evident in the derived ion distributions. The monochromatic waves result in less ion acceleration than turbulent fluctuations with about the same amplitude. The calculated ion distribution functions are in reasonable agreement with the distributions measured in the vicinity of comet Giacobini-Zinner in 1985 by particle detectors on the ICE spacecraft when the ratio of power in sunward propagating Alfven waves to the power in antisunward propagating waves is assumed to lie between about 20% and 50%. However, the quasi-linear diffusion model results agree best with the measured distribution functions when the power ratio is only about 3 percent.
Space weather can be defined as the total ensemble of radiation in space, as well as on the surface of moons and asteroids. It consists of electromagnetic, charged-particle, and neutral particle radiation. The fundamental goal behind this NIAC Phase I research is to investigate methods of generating a static electric-field potential phi(x, y, z) in the volume above and around a "safe" or protected area on the lunar surface so that trajectories of harmful charged particle radiation are modified (deflected or reflected), thus creating a shadow over that region. Since the charged particles are not neutralized but merely redirected, there will be areas outside of the shadowed protected region that will have a higher flux concentration of radiation. One of the fundamental limitations of the static electric (electrostatic)-field approach to radiation shielding is that complete shadowing is accomplished only by complete reflection, which can only occur for shield voltages greater than or equal to the kinetic energy (in electron volts) of the incoming charged particles. Just as habitats on Earth are protected from severe weather events and conditions, such as extreme temperatures, high winds, and UV radiation, using multiple methods of shielding protection from severe space weather will undoubtedly require multiple strategies. The electrostatic shield concept may be one of many methods employed to protect astronaut habitats on the lunar surface from some of the harmful effects of space weather.