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NASA NTRS1999

Chain Dynamics in Magnetorheological Suspensions

Magnetorheological (MR) suspensions are composed of colloidal particles which acquire dipole moments when subjected to an external magnetic field. At sufficient field strengths and concentrations, the dipolar particles rapidly aggregate to form long chains. Subsequent lateral cross-linking of the dipolar chains is responsible for a rapid liquid-to-solid-like rheological transition. The unique, magnetically-activated rheological properties of MR suspensions make them ideal for interfacing mechanical systems to electronic controls. Additionally, the ability to experimentally probe colloidal suspensions interacting through tunable anisotropic potentials is of fundamental interest. Our current experimental work has focused on understanding the fluctuations of dipolar chains. It has been proposed by Halsey and Toor (HT) that the strong Landau-Peierls thermal fluctuations of dipolar chains could be responsible for long-range attractions between chains. Such interactions will govern the long-time relaxation of MR suspensions. We have synthesized monodisperse neutrally buoyant MR suspensions by density matching stabilized ferrofluid emulsion droplets with D2O. This allows us to probe the dynamics of the dipolar chains using light scattering without gravitational, interfacial, and polydispersity effects to resolve the short-wavelength dynamics of the dipolar chains. We used diffusing wave spectroscopy to measure these dynamics. The particle displacements at short times that show an independence to the field strength, but at long times exhibit a constrained, sub-diffusive motion that slows as the dipole strength is increased. The experiments are in good qualitative agreement with Brownian dynamics simulations of dipolar chains. Although there have been several important and detailed studies of the structure and interactions in MR suspensions, there has not been conclusive evidence that supports or contradicts the HT model prediction that long-range interactions exist between fluctuating chains of dipolar particles. Resolving this issue would contribute greatly to the understanding of these interesting and important materials. We have begun to test the predictions of the HT model by both examining the dynamics of individual chains and by measuring the forces between dipolar chains directly to accurately and quantitatively assess the interactions that they experience. To do so, we employ optical trapping techniques and video-microscopy to manipulate and observe our samples on the microscopic level. With these techniques, it is possible to observe chains that are fluctuating freely in three-dimensions, independent of interfacial effects. More importantly, we are able to controllably observe the interactions of two chains at various separations to measure the force-distance profile. The techniques also allow us to study the mechanical properties of individual chains and chain clusters. Our work to this point has focused on reversibly-formed dipolar chains due to field induced dipoles where the combination of this chaining, the dipolar forces, and the hydrodynamic interactions that dictate the rheology of the suspensions. One can envision, however, many situations where optical, electronic, or rheological behavior may be optimized with magneto-responsive anisotropic particles. Chains of polarizable particles may have the best properties as they can coil and flex in the absence of a field and stiffen and orient when a field is applied. We have recently demonstrated a synthesis of stable, permanent paramagnetic chains by both covalently and physically linking paramagnetic colloidal particles. The method employed allows us to create monodisperse chains of controlled length. We observed the stability, field-alignment, and rigidity of this new class of materials. The chains may exhibit unique rheological properties in an applied magnetic field over isotropic suspensions of paramagnetic particles. They are also useful rheological models as bead-spring systems. These chains form the basis for our current experiments with optical traps.

Gast, A. P.↗
NASA NTRS1985

Simulations of the mean solar magnetic field during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, the evolution of the photospheric magnetic field during 1976-1984 was computed and the corresponding evolution of the mean line-of-sight field as seen from earth was derived. A good, but imperfect, agreement was obtained between the observed mean field and the field computed for a nominal choice of flux transport parameters. The response of the computed mean field to variations in the transport parameters and the source properties was determined. The results suggest that the mean-field evolution is a random-walk process with dissipation. New eruptions of flux produce the random walk, and together differential rotation, meridional flow, and diffusion provide the dissipation. The net effect of each new source depends on its strength and orientation and on the time elapsed before the next eruption.

Sheeley, N. R., Jr.↗
NASA NTRS2002

RHESSI and Trace Observations of the 21 April 2002 X1.5 Flare

Observations of the X1.5 flare on 21 April 2002 are reviewed using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and the Transition Region and Coronal Explorer (TRACE). The major findings are as follows: 1. The 3-25 keV X-rays started 54 mins before the EUV (195 A) emission suggesting that the initial energy release heated plasma directly to 220 MK, well above the 1.6 MK needed to produce the Fe XII (195 A) line. 2. Using coaligned 12-25 keV RHESSI and TRACE images, further evidence is found for the existence of hot (15-20 MK) plasma in the 195 A passband. This hot, diffuse emission is attributed to the presence of the Fe XXIV (192 A) line within the TRACE 195 A passband. 3. The 12-25 keV source centroid moves away from the limb with an apparent velocity of approx. 9.9 km/ s, slowing to approx. 1.7 km/ s after 3 hours, its find altitude being approx. 120 Mm after approx. 12 hours. This suggests that the energy release site moves to higher altitudes in agreement with classical flare models. 4. The 50-100 keV emission correlates well with EUV flare ribbons, suggesting thick-target interactions at the footpoints of the magnetic arcade. The 50-100 keV time profile matches the time derivative of the GOES light curve (Neupert effect), which suggests that the same electrons that produced the thick-target hard X-ray emission also heat the plasma seen in soft X-rays. 5. X-ray footpoint emission has an E(sup -3) spectrum down to approx. 10 keV suggesting a lower electron cutoff energy than previously thought. 6. The hard X-ray (25-200 keV) peaks have FWHM durations of approx. 1 min suggesting a more gradual energy release process than expected. 7. The TRACE images reveal a bright symmetric front propagating away from the main flare site at speeds of greater than or = 120 km/ s. This may be associated with fast CME observed several minutes later by LASCO. 8. Dark sinuous lanes are observed in the TRACE images that extend almost radially from the post-flare loop system. This "fan of spines" becomes visible well into the decay phase of the flare and shows evidence for both lateral and downward motions.

Gallagher, Peter T.↗
NASA NTRS2016

Nongyrotropic Electrons in Guide Field Reconnection

We apply a scalar measure of nongyrotropy to the electron pressure tensor in a 2D particle-in-cell simulation of guide field reconnection and assess the corresponding electron distributions and the forces that account for the nongyrotropy. The scalar measure reveals that the nongyrotropy lies in bands that straddle the electron diffusion region and the separatrices, in the same regions where there are parallel electric fields. Analysis of electron distributions and fields shows that the nongyrotropy along the inflow and outflow separatrices emerges as a result of multiple populations of electrons influenced differently by large and small-scale parallel electric fields and by gradients in the electric field. The relevant parallel electric fields include large-scale potential ramps emanating from the x-line and sub-ion inertial scale bipolar electron holes. Gradients in the perpendicular electric field modify electrons differently depending on their phase, thus producing nongyrotropy. Magnetic flux violation occurs along portions of the separatrices that coincide with the parallel electric fields. An inductive electric field in the electron EB drift frame thus develops, which has the effect of enhancing nongyrotropies already produced by other mechanisms and under certain conditions producing their own nongyrotropy. Particle tracing of electrons from nongyrotropic populations along the inflows and outflows shows that the striated structure of nongyrotropy corresponds to electrons arriving from different source regions. We also show that the relevant parallel electric fields receive important contributions not only from the nongyrotropic portion of the electron pressure tensor but from electron spatial and temporal inertial terms as well.

Parallel Electric Fields↗
NASA NTRS1983

Exit of boundary layer plasma from the distant magnetotail

It is pointed out that the boundary layer plasma must somehow leave the magnetospheric system. It is proposed that the boundary layers on the dawn and dusk flanks are continued into the far magnetotail, becoming joined together far downstream, still on closed magnetic field lines. Within the combined layer there would be a dusk to dawn electric field for antisunward convection (as is the case for the boundary layers on the dawn and dusk flanks nearer to the earth). It is suggested that the boundary layer flow is so massive that the flow itself can generate the right electric field for continued flow. Most of the plasma in the mantle over the polar caps would also be convected out in a similar manner, rather feeding the plasma sheet. There would be a stagnation point inside the magnetotail, with any boundary or mantle plasma diffusing earthward of this point becoming the plasma sheet. It is deduced that no steady state solution is possible.

Heikkila, W. J.↗
NASA NTRS1989

Electron velocity distributions and plasma waves associated with the injection of an electron beam into the ionosphere

An electron beam was injected into earth's ionosphere on August 1, 1985, during the flight of the Space Shuttle Challenger as part of the objectives of the Spacelab 2 mission. In the wake of the Space Shuttle a magnetically aligned sheet of electrons returning from the direction of propagation of the beam was detected with the free-flying Plasma Diagnostics Package. The thickness of this sheet of returning electrons was about 20 m. Large intensifications of broadband electrostatic noise were also observed within this sheet of electrons. A numerical simulation of the interaction of the electron beam with the ambient ionospheric plasmas is employed to show that the electron beam excites electron plasma oscillations and that it is possible for the ion acoustic instability to provide a returning flux of hot electrons by means of quasi-linear diffusion.

Frank, L. A.↗
NASA NTRS1994

Low-freqency instabilities and the resulting velocity distributions of pickup ions at comet Halley

The interaction between the solar wind and newborn cometary ions is studied using a new analytical theory as well as one- and two-dimensional hybrid simulations. Using the observed parameters upstream of the comet Halley, a detailed study of wave excitation and the resulting particle distributions is presentd. Linear theory as well as simulations show that a variety of modes such as the fast magnetosonic mode, high frequency whistlers and obliquely propagating Alfven ion cyclotron waves can be excited. However, parallel propagating waves are found to be dominant in the wave spectrum and to control the scattering of the pickup ions. Several features of the observed distributions of pickup protons are explained. In particular, it is shown that the observed asymmetric pitch distribution for the pickup protons is due to the small saturation amplitude of the waves for the given parameters. Water group associated waves can lead to energy diffusion and further pitch angle scattering of protons. This effect is most likely to be important in the vicinity of the bow shock of comet Halley where the density of water group ions becomes comparable to that of protons. It is shown that the observed increase in the radius of the proton velocity shell just outside the bow shock can be due to water group waves. The nearby isotropic proton pitch angle distribution observed by Neugebauer et al. (1989) just outside the bow shock may, however, be related to the presence of a rotational discontinuity which has been identified in the magnetic field data. Just outside the bow shock, simulations show that parallel propagating water group waves can steepen with attached whistler wave packets. The steepening process at parallel propagation is a transient effect, in an important contrast to the case of steepening at oblique angles. The smaller beam densitites at comet Halley appears to be the main reason not only why waves at comet Halley have smaller amplitudes but also why oblique, steepening magnetosonic waves have not been detected at comet Halley, whereas they have been seen at comet Giacobini-Zinner. Halley, whereas they have been seen at comet Giacobini-Zinner.

Karimabadi, H.↗
NASA NTRS1993

Correlated variations of UV and radio emissions during an outstanding Jovian auroral event

An exceptional Jovian aurora was detected in the FUV on December 21, 1990, by means of Vilspa and Goddard Space Flight Center (GFSC) International Ultraviolet Explorer (IUE) observations. This event included intensification by a factor of three between December 20 and 21, leading to the brightest aurora identified in the IUE data analyzed, and, in the north, to a shift of the emission peak towards larger longitudes. The Jovian radio emission simultaneously recorded at decameter wavelengths in Nancay also exhibits significant changes, from a weak and short-duration emission on December 20 to a very intense one, lasting several hours, on December 21. Confirmation of this intense radio event is also found in the observations at the University of Florida on December 21. The emissions are identified as right-handed Io-independent 'A' (or 'non Io-A') components from the northern hemisphere. The radio source region deduced from the Nancay observations lies, for both days, close to the UV peak emission, exhibiting in particular a similar shift of the source region toward larger longitudes from one day to the next. A significant broadening of the radio source was also observed and it is shown that on both days, the extent of the radio source closely followed the longitude range for which the UV brightness exceeds a given threshold. The correlated variations, both in intensity and longitude, strongly suggest that a common cause triggered the variation of the UV and radio emissions during this exceptional event. On one hand, the variation of the UV aurora could possibly be interpreted according to the Prange and Elkhamsi (1991) model of diffuse multicomponent auroral precipitation (electron and ion): it would arise from an increase in the precipitation rate of ions together with an inward shift of their precipitation locus from L approximately equal 10 to L approximately equal 6. On the other hand, the analysis of Ulysses observations in the upstream solar wind suggests that a significant disturbance in the solar wind, involving the generation of an interplanetary shock and the presence of a CME have interacted with the Jovian magnetosphere at about the time of the auroral event. Both arguments suggest that we may have observed for the first time a magnetic storm-type interaction in an outer planet magnetosphere, affecting simultaneously several auroral processes. Conversely, the observed relationship between the level of UV auroral activity and the detection of decameter emission (DAM), if it were a typical feature, might argue in favour of a more direct and permanent association between the auroral processes leading to UV and radio aurorae, possibly related to 'discrete-arc'-like activity and electron precipitation.

Prange, R.↗
NASA NTRS1984

The effect of convection upon charged particle transport in random magnetic fields

In a coordinate system moving with the plasma and random magnetic fields of a wind that blows with constant velocity in the direction of the guiding field, transport of energetic particles is described by a Boltzmann equation which is similar to the one that describes unconvected transport. Although this formulation is mathematically identical to that developed by Luhmann, which refers to the system where the guiding field is static, there are both practical and fundamental reasons to adopt the new approach. It leads to first-order approximate transport equations which are similar to those that apply in the absence of convection. However, these equations are more general than Parker's description of diffusion and convection, for they describe the coherent modes of transport that appear when the mean free path is large compared to the scale length for spatial variations of the guiding field, and they are valid for arbitrary wind velocity. The latter characteristic opens up new possibilities for analyzing particle transport in relativistic flows seen in some astronomical objects.

Earl, J. A.↗
NASA NTRS1991

Multifrequency VLA observations of PKS 0745 - 191 - The archetypal 'cooling flow' radio source?

Ninety-, 20-, 6- and 2-cm VLA observations of the high-radio-luminosity cooling-flow radio source PKS 0745 - 191 are presented. The radio source was found to have a core with a very steep spectrum (alpha is approximately -1.5) and diffuse emission with an even steeper spectrum (alpha is approximately -1.5 to -2.3) without clear indications of the jets, hotspots, or double lobes found in the other radio sources of comparable luminosity. It is inferred that the energy to power the radio source comes from the central engine, but the source's structure may be heavily influenced by the past history of the galaxy and the inflowing intracluster medium. It is shown that, while the radio source is energetically unimportant for the cluster as a whole, it is important on the scale of the cooling flow. The mere existence of cosmic rays and magnetic fields within a substantial fraction of the volume inside the cooling radius has important consequences for cooling-flow models.

Baum, S. A.↗
NASA NTRS1986

Multiple star formation and the dynamical evolution of B335

The detection of a second high-velocity bipolar flow in the dark cloud B335 located in the diffuse envelope to the east of the core is reported. This flow has the same orientation as the first one. The visual extinction in the region between the redshifted and blueshifted lobes is less than or about 1 mag and is not coincident with a condensation. The flow is not associated with any known infrared source in the IRAS catalog. The new flow is about three times older than the first, and its energetics are somewhat smaller. The flows are aligned not only with each other but also with the long axis of the structure of B335 as outlined by CO maps, suggesting that magnetic fields have a role in guiding the flow. From the presence of multiple flows and the structure of the envelope, it is concluded that B335 is at the end of its starbearing life, rather than a young cloud beginning star formation, as previously supposed.

Langer, W. D.↗
NASA NTRS1983

13C and 1H NMR (Nuclear Magnetic Resonance) studies of solid polyolefines

The basis of H-1 and C-13 high-resolution NMR investigations of solid polymers is outlined. The C-13 NMR spectra of solid syndiotactic and isotactic polypropene are discussed and their interpretation in terms of conformation and chain-packing effects are reviewed. The effects of decreasing temperature on the C-13 high-resolution spectrum of an annealed sample of isotactic polypropene is described and interpreted in terms of the crystal structure. The question of the proportion of the sample giving rise to C-13 signals is addressed and some results reported. The main cause for observing only part of the total sample is shown to be the H-1 rotating frame spin-lattice relaxation behavior. The H-1 spin-lattice relaxation and spectral characteristics of a number of polyolefin samples are summarized and the role of spin-diffusion discussed.

Cudby, M. E. A.↗
NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗
NASA NTRS1983

Electrostatic discharges in Saturn's B-ring

The Voyager observations of electrical discharges in Saturn's rings strongly support earlier speculations on the role played by electrostatics, magnetic fields, and lightning phenomena in the primitive solar system. They also suggest conditions then by direct analogy rather than by extrapolating backwards through time from conditions now. The observed discharges show a pronounced 10h periodicity, which suggests a source in Keplerian orbit at 1.80 + or - 0.01 Saturn radii. In that region, the B ring is thicker than optical depth 1.8 for about 5,000 km. At 1.805 + or - 0.001 Saturn radii, however, the ring is virtually transparent for a gap of width 200 m. It is concluded that a small satellite orbits Saturn at that radius and clears the gap. The gap edges must prevent diffusive filling of the gap by fine material which is especially abundant at this position in the rings and would otherwise destroy the gap in minutes. The discharges represent the satellite's interaction with the outer edge of the gap. Spoke formation may involve the interaction of ring material in the vicinity of the gap.

Warwick, J. W.↗
NASA NTRS1995

Heat flux and viscosity of ions in the collisionless solar wind

Between 1 and 2 solar radii, the Coulomb-collision mean free path for thermal ions exceeds the scale height of the solar atmosphere. The expanding solar plasma becomes collisionless and the kinetics of the solar wind are no longer dominated by thermalizing collisions. The usual Braginskii-type expressions for solar wind ion heat flux and viscosity are no longer valid. However, another microscale still exists in the solar wind, dictated by the gyro-radius of ions in the turbulent embedded solar wind magnetic field. Wave-particle interactions will act to isotropize (but not thermalize) particle distributions, and the relevant microscale for this process is the ion gyro-radius. The ion distribution can be modelled as undergoing isotropizing 'collisions,' with the relevant mean free path scaling with gyro-radius. Here, the author presents the heat flux and viscosity expected for solar wind protons which are relaxing to isotropy on a microscale that scales with gyro-radius. The collisionless viscosity and heat flux have a functional dependence different than their collisional analogs. The collisional expressions for ion viscosity and heat flux drastically overestimate the efficiency of diffusive energy and momentum transport actually operative in the solar wind.

Williams, L. L.↗
NASA NTRS2016

Investigating Global Ion and Neutral Atom Populations with IBEX and Voyager

The main objective of this project was to investigate pickup ion (PUI) production in the solar wind and heliosheath (the region between the termination shock and the heliopause) and compute the distributed energetic neutral atom fluxes throughout the helioshpere. The simulations were constrained by comparing the model output against observations from Ulysses, New Horizons, Voyager 1 and 2, and IBEX space probes. As evidenced by the number of peer reviewed journal publications resulting from the project (13 plus three submitted) and their citation rate (156 citations over three years), the project has made a lasting contribution to the field. The outcome is a significant improvement of our understanding of the pickup ion production and distribution in the distant heliosphere. The team has accomplished the entire set of tasks A-H set forth in the proposal. Namely, the transport modeling framework has been augmented with two populations of pickup ions (PUIs), the boundary conditions for the plasma and interstellar neutral hydrogen were verified against Ulysses and New Horizons PUI and an optimal set of velocity diffusion parameters established. The multi-component fluxes of PUIs were computed and isotropic velocity distributions generated for each cell in the computer simulation that covered the heliosphere from 1.5 AU to the heliopause. The distributions were carefully compared with in situ measurements at 3 AU (Ulysses), 12 AU (New Horizons), and 80-90 AU (Voyager 1 and 2) as well as those inferred from ENA fluxes measured by Cassini and IBEX (Wu et al., 2016). Some examples of modeldata comparison are shown in Figure 1. We have used coupled MHD-plasma and kinetic-neutral code to investigate the likely range of plasma and magnetic field parameters in the local interstellar medium (LISM), based on the assumption that the shape of the IBEX ribbon could be used to determine the orientation of the interstellar magnetic field. While the magnetic field is believed to be oriented toward the center of the ribbon, constraining its strength requires comparing the model-predicted angular diameter and circularity of the ribbon with the observations. The study, published in Heerikhuisen et al. (2014), found that the most likely range for the LISM magnetic field strength is between 0.2 and 0.3 nT, which is less than previously thought. Figure 2 shows the IBEX data (left) and compares it to the simulation with a 0.2 nT interstellar magnetic field (center) and a 0.4 nT (right).

Florinski, Vladimir↗
NASA NTRS1999

Non-Equilibrium Superconductivity and Magnetic Pair Breaking in Perovskite Half-Metallic Ferromagnet-Insulator-Superconductor (F-I-S) Heterostructures

The effect of spin-polarized quasiparticle currents on the critical current density (J-c) of cuprate superconductors is studied in perovskite F-I-S heterostructures as a function of insulator thickness and of underlying magnetic materials. A pulsed current technique is employed to minimize extraneous Joule heating on the superconductor. At temperatures near T-c, F-I-S samples with insulator thicknesses\1e2nm show precipitous decrease in J_c as current injection (I_m) is increased. In contrast, J_c in a controlled sample with a substituted non-magnetic material (N-I-S) exhibit no dependence on I_m. Similarly, a F-I-S sample with a 10 mn insulating barrier also show little J_c effect versus I_m. At low temperatures with I_m = 0, significant suppression of J-c is observed only in the thin barrier F-I-S samples, although T_c and the normal-state resistivity of all samples are comparable. These phenomena can be attributed to the Cooper pair breaking induced by externally-injected and internally-reflected spin-polarized quasiparticle currents. We estimate an order of magnitude range for the spin diffusion length of 100 nm to 100\ mum.

Fu, C.-C.↗
NASA NTRS1987

Gyroresonant pitch angle scattering by coherent and incoherent whistler mode waves in the magnetosphere

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.

Umran S Inan↗