[1] It has been suggested that drift loss to the magnetopause can be one of the major loss mechanisms contributing to relativistic electron flux dropouts. In this study, we examine details of relativistic electrons' drift physics to determine the extent to which the drift loss through the magnetopause is important to the total loss of the outer radiation belt. We have numerically computed drift paths of relativistic electrons' guiding center for various pitch angles, various measurement positions, and different solar wind conditions using the Tsyganenko T02 model. We specifically demonstrate how the drift loss effect depends on these various parameters. Most importantly, we present various estimates of relative changes of the omnidirectional flux of 1 MeV electrons between two different solar wind conditions based on a simple form of the directional flux function. For a change of the dynamic pressure from 4 nPa to 10 nPa with a fixed IMF B Z = 0 nT, our estimate indicates that after this increase in pressure, the equatorial omnidirectional flux at midnight near geosynchronous altitude decreases by $56 to $97%, depending on the specific pitch angle dependence of the directional flux. The effect rapidly decreases at regions earthward of geosynchronous orbit and shows a general trend of decrease away from midnight. For a change of the IMF B Z from 0 nT to À15 nT with a fixed dynamic pressure of 4 nPa, the relative decrease of the omnidirectional flux at geosynchronous altitude on the nightside is much smaller than that for the pressure increase, but its effect becomes substantial only beyond geosynchronous orbit. Possibilities exist that our results may change to some extent for a different magnetospheric model than the one used here.
[1] Close to the dayside magnetopause, there is a region of space where each field line has two magnetic field minima, one near each cusp. That region is located around local noon, and extends about 1-2 R e from the magnetopause. Particles that enter this region with equatorial pitch angles sufficiently close to 90°will cross the dayside not along an equatorial path, but along one of the two branches on either side of the equatorial plane. The two branches are joined again past local noon. This process of drift-shell bifurcation (DSB) is nonadiabatic even under static conditions. Two physical mechanisms can cause this nonadiabaticity: one that is operative for nearly all magnetospheric magnetic field configurations and another that depends on a particular combination of north-south and east-west asymmetry in the magnetic field. This paper deals only with the first mechanism. For configurations with north-south and east-west symmetry, DSB changes the second invariant I of the motion by a small amount that is of the order of the gyroradius (the first invariant is intact). For near-equatorial particles (I % 0) the change can be significantly larger. Assuming north-south and dawn-dusk symmetry, we present general theoretical expressions for the second-invariant jump DI, which can be applied to a variety of magnetic field models. The results show that DI is sensitively dependent on the bounce phase of the particle at the bifurcation line. The RMS value of DI over a bounce-phase ensemble increases with decreasing mirror field and with increasing kinetic energy. We verify these results with test-particle simulations using model magnetic fields.
[1] We study trapped energetic particles in the terrestrial magnetosphere undergoing drift shell bifurcation in the magnetic field lacking north-south and east-west symmetry. Drift shell bifurcation occurs near the dayside magnetopause, where, due to the solar wind compression, the field strength has a local maximum near the equatorial plane. As a result, a charged particle may become temporarily trapped in one of the hemispheres while traversing the region. Although this phenomenon has been known for a long time, only recently were the associated second invariant changes quantified for the magnetic field with north-south and east-west symmetry. Here we show that if the magnetic field lacks such symmetry, the effect is more significant. We calculate changes to the second invariant of keV to MeV electrons in Tsyganenko magnetic fields with nonzero interplanetary magnetic field (IMF) B Y component. The changes are on the order of the invariant itself, and thus, this effect is much larger than for the case of symmetric magnetic field (when the particle gyroradius is much less than the magnetospheric scale length). We also quantify the effect for different values of the solar wind dynamic pressure, IMF B Z component, and the Dst index with the Tsyganenko magnetic field T02. We find that Dst has no noticeable role, while larger solar wind ram pressure increases the second invariant changes. We verify our calculations by numerical integration of the guiding center drift equations and discuss properties of different versions of these equations.Citation: Wan, Y., S. Sazykin, R. A. Wolf, and M. K. Öztürk (2010), Drift shell bifurcation near the dayside magnetopause in realistic magnetospheric magnetic fields,
Turbulent blood flow in medical devices contributes to blood trauma, yet the exact mechanism(s) have not been fully elucidated. Local turbulent stresses, viscous stresses, and the rate of dissipation of the turbulent kinetic energy have been proffered as hypotheses to describe and predict blood damage. In this work, simulations of experiments in a Couette flow viscometer and a capillary tube were used to examine extensive properties of the turbulent flow field and to investigate contributing factors for red blood cell hemoglobin release in turbulence by eddy analysis. It was found that hemolysis occurred when dissipative eddies were comparable in size to the red blood cells. The Kolmogorov length scale was used to quantify the size of smaller turbulent eddies, indicating correspondence of hemolysis with number and surface area of eddies smaller than about 10 μm when a k-ε turbulence model is adopted.
I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and present particle trajectories in a dipolar field. I provide twelve computational exercises that can be used as classroom assignments or for self-study. Two of the exercises, drift-shell bifurcation and Speiser orbits, are adapted from active magnetospheric research. The Python code provided in the supplement can be used to replicate the trajectories and can be easily extended for different field geometries.
In this work, contributing factors for red blood cell (RBC) damage in turbulence are investigated by simulating jet flow experiments. Results show that dissipative eddies comparable or smaller in size to the red blood cells cause hemolysis and that hemolysis corresponds to the number and, more importantly, the surface area of eddies that are associated with Kolmogorov length scale (KLS) smaller than about 10 μm. The size distribution of Kolmogorov scale eddies is used to define a turbulent flow extensive property with eddies serving as a means to assess the turbulence effectiveness in damaging cells, and a new hemolysis model is proposed. This empirical model is in agreement with hemolysis results for well-defined systems that exhibit different exposure times and flow conditions, in Couette flow viscometer, capillary tube, and jet flow experiments.
Abstract:Use of laminar flow-derived power law models to predict hemolysis with turbulence remains problematical. Flows in a Couette viscometer and a capillary tube have been simulated to investigate various combinations of Reynolds and/or viscous stresses power law models for hemolysis prediction. A finite volume-based computational method provided Reynolds and viscous stresses so that the effects of area-averaged and time-averaged Reynolds stresses, as well as total, viscous, and wall shear on hemolysis prediction could be assessed. The flow computations were conducted by using Reynolds-Averaged Navier-Stokes models of turbulence (k-ε and k-ω SST) to simulate four different experimental conditions in a capillary tube and seven experimental conditions in a Couette viscometer taken from the literature. Power law models were compared by calculating standard errors between measured hemolysis values and those derived from power law models with data from the simulations. In addition, suitability of Reynolds and viscous stresses was studied by threshold analysis. Results showed there was no evidence of a threshold value for hemolysis in terms of Reynolds and viscous stresses. Therefore, Reynolds and viscous stresses are not good predictors of hemolysis. Of power law models, the Zhang power law model (Artificial Organs, 2011, 35, 1180-1186 gives the lowest error overall for the hemolysis index and Reynolds stress (0.05570), while Giersiepen's model (The International journal of Artificial Organs, 1990, 13, 300-306) yields the highest (6.6658), and intermediate errors are found through use of Heuser's (Biorheology, 1980, 17, 17-24) model (0.3861) and Fraser's (Journal of Biomechanical Engineering, 2012, 134, 081002) model (0.3947).
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