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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1984

An abrasion-ablation model description of galactic heavy-ion fragmentation

The fragmentation of high-energy galactic heavy ions by nuclear interactions with arbitrary target nuclei is described within the context of a simple abrasion-ablation fragmentation model. The abrasion part of the theory utilizes a quantum-mechanical formalism based upon an optical model potential approximation to the exact nucleus-nucleus multiple-scattering series. Nuclear charge distributions of the excited prefragments are calculated using either a hypergeometric distribution or a method based upon the zero-point oscillations of the giant dipole resonance. The excitation energy of the prefragment is estimated from the geometric clean-cut abrasion-ablation model. The decay probabilities for the various particle emission channels, in the ablation stage of the fragmentation, are obtained from the EVAP-4 Monte Carlo computer program. Elemental production cross sections for 1.88-GeV/nucleon iron colliding with carbon, silver, and lead targets are calculated and compared with experimental data and with the predictions from the semiempirical relations of Silberberg and Tsao.

Townsend, L. W.↗
NASA NTRS2006

Various Ambiguities in Re-constructing Laser Pulse Parameters

We think that mode lock laser pulses are generated by the summation process that take place between the monochromatic EM filed frequencies as if they interact with each other as shown in equation 1. In reality, the pulse generation is a collaborative interaction process between EM fields and various material medium. When we carry out the actual mode lock analysis, we do take into account of interpaly between all the temporal dynamics of the cavity gain medium, cavity round trip time and the response time of the intra cavity element (saturable absorber, Kerr medium, etc.). that really enforces the locking of the phase of the cavity spontaneous emissions. On a conceptual level, this simplistic representation of the mode locking by Eq.1 ignores all these critical physical processes. When we try to analyze a pulsed field, again we start by representing it very much like this equation, even though we can only detect the square modulus of this complex field and loose a lot of phase related information to the detectors quantum whims and their time constants. The key parameters for a light pulse are as follows. Foremost is the (i) carrier frequency, which cannot be described or imagined without its state of undulation expressed as its (ii) phase. Next is our imagined time finite (iii) carrier envelope that provides the temporal boundary of the field amplitude strength of the undulating E-field. The final parameter is the (iv) state of polarization or the unique plane along which the strength of the E-field gradient undulates. None of these filed characteristics are made self-evident to us by the fields themselves. We do not see light. Light does not see light. Light beams pass through each other without altering each others energy distribution unless there are interacting material molecules (dipoles) within the physical volume of superposition of the beams. In contrast, we can sense the material particles. Material particles sense each other and they cannot pass through each other without interacting with (scattering from) each other. Thus the interpretation of the superposition phenomenon of multiple fields on detectors should not be lumped under the mysterious "wave-particle duality" philosophy. The phenomenon of superposition can be understood better when we focus on the actual process experienced by the detecting dipoles when allowed by QM rules, they respond to and sum all the induced stimulations due to all the superposed fields followed by the proportionate energy absorption giving rise to the fringes we observe. We will present various experimental results to illustrate our arguments. Our position is that such detector behavior driven interpretations rather than the generally implied field-field interaction driven explanations, will help us better understand the ultimate nature of light and hence invent better and newer devices and instruments.

Roychoudhuri, Chandrasekhar↗
NASA NTRS1994

A linear method for analyzing lightning field changes

A constrained, least-squares method for analyzing multiple-station measurements of lightning field changes (delta Es) is introduced. Previous methods have attempted to fit the spatial pattern of lightning delta Es using nonlinear models, such as a point charge (Q) or a point dipole (P) model. With the linear method, the delta Es are described not by models but by a general volume charge distribution that is deposited on a large (40 x 40 x 20 cu km) Cartesian grid above the measuring network. A linear system of equations is used to relate the measured delta Es to the charges that are deposited at each grid point. With this approach, the information content of the measurements can be quantified by an eigenanalysis of the covariance matrix of the linear system. Constraints can be used to reduce the infinity of possible solutions to the linear system and also to reduce systematic biases that can be introduced by the method of solution. It is shown that a Landweber iterative method, derived from the general method of steepest descent, can be used to solve the linear system and that the resulting volume charge distributions are generally consistent with computer-simulated charge sources, when these sources are over the measuring network. The Landweber iteration has also provided solutions for natural lightning events that are consistent with Q- and P-model results.

Koshak, William J.↗
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 NTRS1987

Multiple dipole eddies in the Alaska Coastal Current detected with Landsat thematic mapper data

Seventeen dipole eddies, including five large, well-formed ones, three second-generation eddies, and two double eddies, were observed in the Alaska Coastal Current near Kayak Island in one single scene of the Landsat thematic mapper (TM) on April 22, l985. The digital Landsat TM satellite data were computer analyzed to extract details in the near coastal circulation in the northern Gulf of Alaska. Enhancement techniques were applied to the visible and thermal IR bands. The features are evident only in the visible bands because of the ability of these bands to detect the distribution of sediments in the near surface. These eddies did not have a significant thermal signature.The sources of these sediments are the glacial streams found throughout the Gulf of Alaska coast. Eddies of this configuration and frequency have never been observed here previously. However, the oceanographic and meteorological conditions are typical for this time of year. These eddies should be important to the cross-shelf mixing processes in the Alaska Coastal Current and are an indicator that the flow here can be unstable at certain times of the year.

Ahlnas, Kristina↗
NASA NTRS2016

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Xu, Yu-Lin↗
NASA NTRS2006

Noise Radiation from Single and Multiple Rod Configurations

Acoustic measurements were performed on single and multiple rod configurations to study the effect of Reynolds number, surface roughness, freestream turbulence, proximity and wake interference on the radiated noise. The Reynolds number ranged from 3.8 x 10(exp 3) to 10(exp 5). Directivity measurements were performed to determine how well the dipole assumption for the radiation of vortex shedding noise holds for the different model configurations tested. The dependence of the peak Sound Pressure Level on velocity was also examined. Several concepts for the reduction of the noise radiating from cylindrical rods were tested. It was shown that wire wraps and collar distributions could be used to significantly reduce the noise radiating from rods in tandem configurations.

Hutcheson, Florence V.↗
NASA NTRS2003

Distributed magnetic field positioning system using code division multiple access

An apparatus and methods for a magnetic field positioning system use a fundamentally different, and advantageous, signal structure and multiple access method, known as Code Division Multiple Access (CDMA). This signal architecture, when combined with processing methods, leads to advantages over the existing technologies, especially when applied to a system with a large number of magnetic field generators (beacons). Beacons at known positions generate coded magnetic fields, and a magnetic sensor measures a sum field and decomposes it into component fields to determine the sensor position and orientation. The apparatus and methods can have a large `building-sized` coverage area. The system allows for numerous beacons to be distributed throughout an area at a number of different locations. A method to estimate position and attitude, with no prior knowledge, uses dipole fields produced by these beacons in different locations.

Prigge, Eric A.↗
NASA NTRS1993

Microwave emission from a sunspot. I - Implications for the sunspot magnetic structure

The magnetic field strength of a sunspot can be determined from the gyroresonance brightness temperature spectrum by using the property that microwave brightness is limited above a frequency given by an integer-multiple of the gyrofrequency. This concept is used to find the radial distribution of the magnetic field at the coronal base of a sunspot in the active region NOAA 4741. It is shown that the o-mode emission must arise primarily from the second harmonic of the gyrofrequency, and that the third harmonic is responsible for the x-mode emission. An expression is given to describe the radial distribution of magnetic fields at the coronal base of a sunspot. Coronal magnetic fields are found to originate mainly in the photospheric umbral region. Finally, while it is possible to approximate roughly the derived vertical variation of magnetic fields by means of a dipole model, the radial field distribution at coronal heights is determined to be more confined than predicted by this model.

Lee, Jeongwoo W.↗
NASA NTRS2005

Deployable Wide-Aperture Array Antennas

Inexpensive, lightweight array antennas on flexible substrates are under development to satisfy a need for large-aperture antennas that can be stored compactly during transport and deployed to full size in the field. Conceived for use aboard spacecraft, antennas of this type also have potential terrestrial uses . most likely, as means to extend the ranges of cellular telephones in rural settings. Several simple deployment mechanisms are envisioned. One example is shown in the figure, where the deployment mechanism, a springlike material contained in a sleeve around the perimeter of a flexible membrane, is based on a common automobile window shade. The array can be formed of antenna elements that are printed on small sections of semi-flexible laminates, or preferably, elements that are constructed of conducting fabric. Likewise, a distribution network connecting the elements can be created from conventional technologies such as lightweight, flexible coaxial cable and a surface mount power divider, or preferably, from elements formed from conductive fabrics. Conventional technologies may be stitched onto a supporting flexible membrane or contained within pockets that are stitched onto a flexible membrane. Components created from conductive fabrics may be attached by stitching conductive strips to a nonconductive membrane, embroidering conductive threads into a nonconductive membrane, or weaving predetermined patterns directly into the membrane. The deployable antenna may comprise multiple types of antenna elements. For example, thin profile antenna elements above a ground plane, both attached to the supporting flexible membrane, can be used to create a unidirectional boresight radiation pattern. Or, antenna elements without a ground plane, such as bow-tie dipoles, can be attached to the membrane to create a bidirectional array such as that shown in the figure. For either type of antenna element, the dual configuration, i.e., elements formed of slots in a conductive membrane, can also be used. Finally, wide bandwidth antennas or arrays can be formed in which the principal direction of radiation is in the plane of the membrane. For this embodiment, the set of elements on the membrane is arranged to form one or more traveling wave antennas. In this case, a nonconductive form of the perimeter springlike material is required to provide the deploying force.

Fink, Patrick W.↗
NASA NTRS2003

Chandra X-Ray Observatory Observations of the Globular Cluster M28 and its Milisecond Pulsar PSR B1821-24

We report here the results of the first Chandra X-Ray Observatory observations of the globular cluster M28 (NGC 6626). We detect 46 X-ray sources, of which 12 lie within 1 core radius of the center. We show that the apparently extended X-ray core emission seen with the ROSAT HRI is due to the superposition of multiple discrete sources, for which we determine the X-ray luminosity function down to a limit of about 6 x 10(exp 30) ergs/s. We measure the radial distribution of the X-ray sources and fit it to a King profile finding a core radius of r(sub c,X) approx. = 5 11". We measure for the first time the unconfused phase-averaged X-ray spectrum of the 3.05 ms pulsar B1821-24 and find that it is best described by a power law with photon index Gamma approx. = 1.2. We find marginal evidence of an emission line centered at 3.3 keV in the pulsar spectrum, which could be interpreted as cyclotron emission from a corona above the pulsar s polar cap if the magnetic field is strongly different from a centered dipole. The unabsorbed pulsar flux in the 0.1 - 8.0 keV band is approx. = 3.5 x 10(exp -13) ergs/s sq cm. We present spectral analyses of the five brightest unidentified sources. Based on the spectral parameters of the brightest of these sources, we suggest that it is a transiently accreting neutron star in a low-mass X-ray binary, in quiescence. Fitting its spectrum with a hydrogen neutron star atmosphere model yields the effective temperature T(sub eff, sup infinity) = 90(sup +30, sub -10) eV and the radius R(sub NS, sup infinity) = 14.5(sup +6.9, sub -3.8) km. In addition to the resolved sources, we detect fainter, unresolved X-ray emission from the central core. Using the Chandra-derived positions, we also report on the result of searching archival Hubble Space Telescope data for possible optical counterparts.

Becker, Werner↗
NASA NTRS2005

Deep Interior Mission: Imaging the Interior of Near-Earth Asteroids Using Radio Reflection Tomography

Near-Earth asteroids are important exploration targets since they provide clues to the evolution of the solar system. They are also of interest since they present a clear danger to Earth. Our mission objective is to image the internal structure of two NEOs using radio reflection tomography (RRT) in order to explore the record of asteroid origin and impact evolution, and to test the fundamental hypothesis that some NEOs are rubble piles rather than consolidated bodies. Our mission s RRT technique is analogous to doing a CAT scan of the asteroid from orbit. Closely sampled radar echoes are processed to yield volumetric maps of mechanical and compositional boundaries, and to measure interior material dielectric properties. The RRT instrument is a radar that operates at 5 and 15 MHz with two 30-m (tip-to-tip) dipole antennas that are used in a cross-dipole configuration. The radar transmitter and receiver electronics have heritage from JPL's MARSIS contribution to Mars Express, and the antenna is similar to systems used in IMAGE and LACE missions. The 5-MHz channel is designed to penetrate greater than 1 km of basaltic rock, and 15-MHz penetrates a few hundred meters or more. In addition to RRT volumetric imaging, we use redundant color cameras to explore the surface expressions of unit boundaries, in order to relate interior radar imaging to what is observable from spacecraft imaging and from Earth. The camera also yields stereo color imaging for geology and RRT-related compositional analysis. Gravity and high fidelity geodesy are used to explore how interior structure is expressed in shape, density, mass distribution and spin. Ion thruster propulsion is utilized by Deep Interior to enable tomographic radar mapping of multiple asteroids. Within the Discovery AO scheduling parameters we identify two targets, S-type 1999 ND43 (approximately 500 m diameter) and V-type 3908 Nyx (approximately 1 km), asteroids whose compositions bracket the diversity of solar system materials that we are likely to encounter, from undifferentiated to highly evolved. The 5-15 MHz radar is capable of probing more primitive bodies (e.g. comets or C-types) that may be available given other launch schedules. 5 MHz radar easily penetrates, with the required SNR , greater than 1 km of basalt (a good analog for Nyx). Basalt has a greater loss tangent than expected for most asteroids, although iron-rich M-types are probably not appropriate targets. 15 MHz radar penetrates the outer approximately 100 m of rocky 1 km asteroids and the deep interiors of comets. Laboratory studies of the most common NE0 materials expected (S-, C- and V-type meteorite analogs) will commence in 2005.

Safaeinili, A.↗
NASA NTRS2003

Chandra X-Ray Observatory Observations of the Globular Cluster M28 and its Millisecond Pulsar PSR B1821-24

We report here the results of the first Chandra X-Ray Observatory observations of the globular cluster M28 (NGC 6626). We detect 46 X-ray sources of which 12 lie within one core radius of the center. We show that the apparently extended X-ray core emission seen with the ROSAT HRI is due to the superposition of multiple discrete sources for which we determine the X-ray luminosity function down to a limit of about 6 x 10(exp 30) erg/s. We measure the radial distribution of the X-ray sources and fit it to a King profile finding a core radius of r(sub c,x) approx. 11 sec. We obtain the best-fit mass of the X-ray sources to be M(sub x) approx. 1.9 solar masses. We measure for the first time the unconfused phase-averaged X-ray spectrum of the 3.05-ms pulsar B1821-24 and find it best described by a power law with photon-index Gamma approx. equal to 1.2. We find marginal evidence of an emission line centered at 3.3 kev in the pulsar spectrum, which could be interpreted as cyclotron emission from a corona above the pulsar's polar cap if the the magnetic field is strongly different from a centered dipole. The unabsorbed pulsar flux in the 0.5-8.0 keV band is approx. 3.5 x 10(exp -13) ergs/s/sq cm. We present spectral analyses of the 5 brightest unidentified sources. Based on the spectral parameters of the brightest of these sources, we suggest that it is a transiently accreting neutron star in a low-mass X-ray binary, in quiescence. Fitting its spectrum with a hydrogen neutron star atmosphere model yields the effective temperature T(sup infinity)(sub eff) = 90(sup +30)(sub -10) eV and the radius R(sup infinity)(sub NS) = 14.5(sup +6.9)(sub -3.8) km. In addition to the resolved sources, we detect fainter, unresolved X-ray emission from the central core. Using the Chandra-derived positions, we also present a preliminary report on the result of searching archival Hubble Space Telescope data for possible optical counterparts.

Becker, Werner↗
NASA NTRS2002

A New Method for Estimating the Single Scattering Phase Functions of Regolith Grains

Hapke's photometric model has been widely used in solar system remote sensing applications for nearly two decades. Recently, Hapke extended his model to describe the coherent-backscatter opposition effect and multiple-scattering by particles with anisotropic single particle phase functions (SPPF's). A practical difficulty for retrieving Hapke's model parameters from typical planet, satellite, and asteroid photometry data sets is that the model employs a large number of adjustable parameters (at least eight) that can be reliably constrained only for a small number of planetary data sets in which both disk-resolved and whole-disk observations are available from opposition to very large phase angles. The present work aims to reduce the number of adjustable parameters and preserve (or even enhance) the model's accuracy and usefulness by expressing Hapke's parameters in terms of more fundamental physical properties on which they mutually depend. The most difficult part of this task, described here, is to develop a simple method for computing the effective SPPF for structurally complex regolith grains from optical constants, grain-size distribution, and average regolith porosity. The development of light-scattering models for irregularly shaped particles is a large, complex subject and many sophisticated methods, such as Discrete Dipole Approximation (DDA) and Monte-Carlo simulations, have been explored elsewhere. Many of these methods are computationally intensive and probably impractical for routine substitution in Hapke's model. Here, progress is reported in developing a practical, semi-empirical method for estimating the directional scattering behavior (i.e. SPPF) of irregular regolith grains. The method employs Optical Transfer Function (OTF) techniques to model how the structural complexity of regolith particles broaden and attenuate the angular distribution of scattered light relative to that expected from ideal spherical particles of equivalent size and composition.

Helfenstein, P.↗
NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗