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NASA NTRS2012

Pulsar Pair Cascades in Magnetic Fields with Offset Polar Caps

Neutron star magnetic fields may have polar caps (PC) that are offset from the dipole axis, through field-line sweepback near the light cylinder or non-symmetric currents within the star. The effects of such offsets on electron-positron pair cascades are investigated, using simple models of dipole magnetic fields with small distortions that shift the PCs by different amounts or directions. Using a Monte Carlo pair cascade simulation, we explore the changes in the pair spectrum, multiplicity and energy flux across the PC, as well as the trends in pair flux and pair energy flux with spin-down luminosity, L(sub sd). We also give an estimate of the distribution of heating flux from returning positrons on the PC for different offsets. We find that even modest offsets can produce significant increases in pair multiplicity, especially for pulsars that are near or beyond the pair death lines for centered PCs, primarily because of higher accelerating fields. Pair spectra cover several decades in energy, with the spectral range of millisecond pulsars (MSPs) two orders of magnitude higher than for normal pulsars, and PC offsets allow significant extension of all spectra to lower pair energies. We find that the total PC pair luminosity L(sub pair) is proportional to L(sub sd), with L(sub pair) approximates 10(exp -3) L(sub sd) for normal pulsars and L(sub pair) approximates 10(exp -2) L(sub sd) for MSPs. Remarkably, the total PC heating luminosity for even large offsets increases by less than a factor of two, even though the PC area increases by much larger factors, because most of the heating occurs near the magnetic axis.

Harding, Alice K.↗
NASA NTRS2004

High-Altitude Particle Acceleration and Radiation in Pulsar Slot Gaps

We explore the pulsar slot gap (SG) electrodynamics up to very high altitudes, where for most relatively rapidly rotating pulsars both the standard small-angle approximation and the assumption that the magnetic field lines are ideal stream lines break down. We address the importance of the electrodynamic conditions at the SG boundaries and the occurrence of a steady-state drift of charged particles across the SG field lines at very high altitudes. These boundary conditions and the cross-field particle motion determine the asymptotic behavior of the scalar potential at all radii from the polar cap (PC) to near the light cylinder. As a result, we demonstrate that the steady-state accelerating electric field, E(sub ll), must approach a small and constant value at high altitude above the PC. This E(sub ll) is capable of maintaining electrons moving with high Lorentz factors (approx. a few x 10(exp 7)) and emitting curvature gamma-ray photons up to nearly the light cylinder. By numerical simulations, we show that primary electrons accelerating from the PC surface to high altitude in the SG along the outer edge of the open field region will form caustic emission patterns on the trailing dipole field lines. Acceleration and emission in such an extended SG may form the physical basis of a model that can successfully reproduce some pulsar high-energy light curves.

Muslimov, Alex G.↗
NASA NTRS2022

High-energy Photon Opacity in the Twisted Magnetospheres of Magnetars

Magnetars are neutron stars characterized by strong surface magnetic fields generally exceeding the quantum critical value of 44.1 TG. High-energy photons propagating in their magnetospheres can be attenuated by QED processes like photon splitting and magnetic pair creation. In this paper, we compute the opacities due to photon splitting and pair creation by photons emitted anywhere in the magnetosphere of a magnetar. Axisymmetric, twisted dipole field configurations embedded in the Schwarzschild metric are treated. The paper computes the maximum energies for photon transparency that permit propagation to infinity in curved spacetime. Special emphasis is given to cases where photons are generated along magnetic field loops and/or in polar regions; these cases directly relate to resonant inverse Compton scattering models for the hard X-ray emission from magnetars and Comptonized soft gamma-ray emission from giant flares. We find that increases in magnetospheric twists raise or lower photon opacities, depending on both the emission locale and the competition between field-line straightening and field strength enhancement. Consequently, given the implicit spectral transparency of hard X-ray bursts and persistent "tail" emission of magnetars, photon splitting considerations constrain their emission region locales and the twist angle of the magnetosphere; these constraints can be probed by future soft gamma-ray telescopes such as COSI and AMEGO. The inclusion of twists generally increases the opaque volume of pair creation by photons above its threshold, except when photons are emitted in polar regions and approximately parallel to the field.

radiation mechanisms: non-thermal↗
NASA NTRS1999

"Coulombic Viscosity" In Granular Materials: Planetary and Astrophysical Implications

The term "Coulombic viscosity" is introduced here to define an empirically observed phenomenon from experiments conducted in both microgravity, and in ground-based 1-g conditions. In the latter case, a sand attrition device was employed to test the longevity of aeolian materials by creating two intersecting grain-circulation paths or cells that would lead to most of the grain energy being expended on grain-to-grain collisions (simulating dune systems). In the areas in the device where gravitationally-driven grain-slurries recycled the sand, the slurries moved with a boundary-layer impeded motion down the chamber walls. Excessive electrostatic charging of the grains during these experiments was prevented by the use of an a.c. corona (created by a Tesla coil) through which the grains passed on every cycle. This created both positive and negative ions which neutralized the triboelectrically-generated grain charges. When the corona was switched on, the velocity of the wall-attached slurries increased by a factor of two as approximately determined by direct observation. What appeared to be a freely-flowing slurry of grains impeded only by intergranular mechanical friction, had obviously been significantly retarded in its motion by electrostatic forces between the grains; with the charging reduced, the grains were able to move past one another without a flow "viscosity" imposed by the Coulombic intergranular forces. A similar phenomenon was observed during microgravity experiments aboard Space Shuttle in USML-1 & USML-2 spacelabs where freely-suspended clouds of sand were being investigated for their potential to for-m aggregates. In this environment, the grains were also charged electrostatically (by natural processes prior to flight), but were free from the intervention of gravity in their interactions. The grains were dispersed into dense clouds by bursts of air turbulence and allowed to form aggregates as the ballistic and turbulent motions damped out. During this very brief (30-60 sec) damping period, motion of the grains was observed to be retarded by the electrostatic interactions. The fact that the grains almost instantly formed aggregates was evidence that their ballistic motions had been constrained and redirected by the dipole-dipole interactions that led to filamentary aggregate development. Undoubtedly, the "Coulombic viscosity" of the cloud assisted in damping grain motion so rapidly. The electrostatically-induced grain-cloud viscosity or drag exerted on grain motion, is a complex function of three major parameters: charge magnitude, charge sign, and mean intergranular distance. The above experiments illustrate one particular type of granular behavior. The discussion here will therefore be restricted to drag relationships: (a) between grains that are naturally charged triboelectrically and thus exhibit dipole-dipole attractions between one another even if there are slight net charges present (which can be overwhelmed by dipole coupling at short distances), and (b) between grains that are densely spaced where the intergranular distance varies between zero and some value (usually tens or hundreds of grain diameters) that permits each grain to detect the dipole moment of another grain -- the distance is not so great that other grains appears as neutral electrical "singularities. I. Aeolian transport: During motion of grains in a saltation cloud (on Earth, Mars, or Venus), triboelectric charging must occur as a result of multiple grain contacts, and by friction with the entraining air. A situation might develop that is similar to the one described above in the attrition device: grain motion becoming significantly retarded (reduced flux) as grains find it increasingly difficult to either separate from the surface, or to pass one another without Coulombic retarding forces. A "Coulombic drag" will exist at flux initiation and increase with time to work in direct opposition to the aerodynamic drag that drives the grain motion. It is predicted that this will lead to an increase with time of both the aerodynamic and bed-dilatancy thresholds (3). Because of Paschen discharge effects in the martian atmosphere, the electrostatic charging in a saltation cloud may be partially abated, but this will lead to greater grain mobility, more charging, and thus to a charge-discharge steady state mediated by mechanical interactions. II. Dry colluvial systems: Sand avalanches on dunes, dry debris flows, talus flows, avalanches, and pyroclastic surges are examples of gravity-driven, dense granular flows where rock/grain fragmentation and grain-to-grain interactions cause triboelectrification (sometimes augmented by other electrical charging processes), and where the grain densities of the systems are such that strong dipole-dipole interactions between grains might be expected to be present. Because it is expected that the Coulombic forces between grains will cause a sluggishness or enhanced granular-flow viscosity, the motion of a grain mass will be retarded or damped so that this will assist, ultimately, in terminating the flow. The greatest Coulombic viscosity will be created in the most highly charged systems, which will also be the most energetic. Thus, grain flows have some tendency to be self-limiting by internal energy partitioning; gravitational potential is converted to Coulombic potential, which manifests itself as a drag force between the grains. III. Volcanic eruption plumes and impact ejecta curtains: The violence of these systems leads to powerful electrical charging of particulates. Lightning storms emanating from volcanic plumes are a testimony to the levels of charging. As pyroclastic grains interact forcefully and frequently within eruption plumes, it is reasonable to predict that the internal turbulent motions of the plume will be significantly damped by the Coulombic viscosity exerted by grain charges. Additional information is contained in the original.

Marshall, J. R.↗
NASA NTRS1994

Properties of acoustic sources in the Sun

The power spectrum of solar acoustic oscillations shows peaks extending out to frequencies much greater than the acoustic cutoff frequency of approximately 5.3 mHz, where waves are no longer trapped. Kumar & Lu (1991) proposed that these peaks arise from the interference of traveling waves which are generated by turbulent convection. According to this model, the frequencies of the peaks in the power spectrum depend on the static structure of the Sun as well as the radial location of the sources. Kumar & Lu used this idea to determine the depth of the acoustic sources. However, they ignored dissipative effects and found that the theoretically computed power spectrum was falling off much more rapidly than the observed spectrum. In this paper, we include the interaction of radiation with acoustic waves in the computation of the power spectrum. We find that the theoretically calculated power spectra, when radiative damping is included are in excellent agreement with the observed power spectra over the entire observed frequency range of 5.3 to 7.5 mHz above the acoustic cutoff frequency. Moreover, by matching the peak frequencies in the observed and theoretical spectra we find the mean depth of acoustic sources to be 140 +/- 60 km below the photosphere. We show that the spectrum of solar turbulence near the top of the solar convection zone is consistent with the Kolmogorov spectrum, and that the observed high frequency power spectrum provides strong evidence that the acoustic sources in the Sun are quadrupolar. The data, in fact, rules out dipole sources as significant contributors to acoustic wave generation in the Sun. The radial extent of the sources is poorly determined and is estimated to be less than about 550 km.

Kumar, Pawan↗
NASA NTRS1995

Average motion, structure and orientation of the distant magnetotail determined from remote sensing of the edge of the plasma sheet boundary layer with E greater than 35 keV ions

We study gradients of the energetic ion intesity observed at the edge of the plasma sheet boundary layer (PSBL) by the energetic ion anisotropy spectrometer (EPAS) on International Sun Earth Explorer 3 (ISEE 3). In particular, we have determined the velocity of the boundary relative to the spacecraft in the direction perpendicular to the tail axis and the angle which the boundary normal makes to the spacecraft spin axis for 1160 PSBL encounters at X(sub GSM) greater than -240 R(sub E). By asuming that, on average, the edge of the PSBL is parallel to the cross-tail current sheet, we are then able to determine a number of properties of the structure, orientation and motion of the deep geomagnetic tail. We conclude the following: (1) Most crossings of the edge of the PSBL are caused by transverse motuion of the entire tail induced by solar wind direction variations, although some are caused by reconfiguration of the tail due to geomagnetic activity. (2) The typical velocity of the PSBL (and hence of the tail) in the direction perpendicular to the tail axis is 50-85 km/s. (3) The average twist of the tail is near zero, with the edge of the PSBL (and by inference the cross-tail current sheet) lying parallel to the ecliptic plane (however, large twists are found in individual events and the distribution of twists is broad, with one standard deviation of approximately 50 deg. (4) The width of the distribution decreases with downtail distance. (5) The variation of the distributions with cross-tail position reveals that this decreas in width is most likely due to the edge of the PSBL being concave, or significantly flared at the tail flanks, in the near-Earth region. (6) During days on which the Interplanetary Magnetic Field (IMF) has 'away' sector structure, the north lobe of the trail is twisted on average towards dawn by 7.0 +/-2.4 deg. (7) During days on which the IMF has 'toward' sector structure, the north lobe is tilted towards duskby 3.8 +/- 2.3. (8) A subset of events for which IMP 8 solar wind data are available show that, for southward IMF BH(sub z) the tail has a mean twist of -12.3 +/- 5.0 deg for IMF B(sub Y) greater than 0 and 5.5 +/- 3.8 deg for IMF B(sub Y) less than 0 (positive twist angles correspond to a tilt of the northern lobe towards dusk). (9) For northward IMF B(sub z) the tail has a twist of -23.9 +/- 5.0 deg for IMF B(sub Y) greater than 0 and 13.4 +/- 6.0 deg for IMF B(sub y) less than 0. Hence the tail appears more twisted on average for the IMF B(sub Z) northward case. (10) The distribution of tail twist is wider for lower levels of geomagnetic activity, indicating that the tail is able to twist more at lower levels of activity. (11) The data set reveals no evident effect of the earth's dipole wobble; tail orientation appears to be controlled by the solar wind and IMF, such that the GSE coordinate system may be appropriate for the study of field and plasma structures in the distant tail region.

Owen, C. J.↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗