Tables for determining reduction of energy and intensity of X-rays and gamma-rays at various scattering angles in small thickness of matter
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One of the critical issues for the US space program is fire safety of the space station and future launch vehicles. A detailed understanding of the scattering signatures of particulate is essential for the development of a false alarm free fire detection system. This paper describes advanced optical instrumentation developed and applied for fire detection. The system is being designed to determine four important physical properties of disperse fractal aggregates and particulates including size distribution, number density, refractive indices, and fractal dimension. Combustion generated particulate are the primary detection target; however, in order to discriminate from other particulate, non-combustion generated particles should also be characterized. The angular scattering signature is measured and analyzed using two photon optical laser scattering. The Rayleigh-Debye-Gans (R-D-G) scattering theory for disperse fractal aggregates is utilized. The system consists of a pulsed laser module, detection module and data acquisition system and software to analyze the signals. The theory and applications are described.
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The complete radiation field including polarization is calculated for a model of the real atmosphere by the matrix operator method. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0; 0.15 0.90) and five solar zenith angles. Scattering and absorption by molecules (including ozone) and by aerosols are taken into account together with the variation of the number density of these substances with height. All results are calculated for both a normal aerosol number and a distribution which is one-third of the normal amount at all heights. The calculated values show general qualitative agreement with the available experimental measurements. The position of the neutral points of the polarization in the principal plane is a sensitive indicator of the characteristics of the aerosol particles in the atmosphere, since it depends on the sign and value of the single scattered polarization for scattering angles around 20 deg and 160 deg for transmitted and reflected photons respectively.
The modified Harris field model is used to investigate the process of pitch angle scattering by a current sheet. The relationship between the incoming asymptotic pitch angle alpha(in) and the outgoing asymptotic pitch angle alpha(out) is studied from first principles by numerically integrating the equation of motion. Evidence that charged particles undergo chaotic scattering by the current sheet is found. For fixed alpha(in), it is shown that alpha(out) exhibits sensitive dependence on the energy parameter in certain energy ranges. For a fixed energy parameter value in the same energy ranges, alpha(out) sensitively depends on alpha(in). For other energy values, alpha(out) does not show sensitive dependence on alpha(in) for most phase angles. A distribution of alpha(in) is mapped from the asymptotic region to the midplane, and it is found that the resulting particle distribution should have beam structures with well-collimated pitch angles near each resonance energy value. Implications for the particle distribution functions in the earth's magnetotail are discussed.
Solar energetic particles (SEPs) are high-energy particles originating from the Sun that pose potential risks to space missions, especially those outside Earth's protective magnetosphere. Understanding their behavior within the heliosphere and Earth's magnetosphere is vital for the safety and functionality of space exploration. The study focuses on how the pitch angle scattering, the angle change between a particle's velocity and the magnetic field due to interactions with magnetic irregularities, impacts the decay phase of SEP events. By solving the focused transport equation, the study models the transport of SEPs along magnetic field lines, extending these lines up to 5 AU (Astronomical Units) to understand their behavior even beyond the typical proximity to the Sun. Incorporating the effects of pitch angle scattering at such vast distances is crucial for understanding the decay dynamics of a SEP event. This modeling of SEPs is integrated with simulations of other vital space phenomena: the solar wind, interplanetary magnetic field, and Alfven wave turbulence. This presentation covers the modeling approach used in this research and the role of pitch angle scattering at various heliocentric distances on the dynamics of the SEP events' decay phase.
Low angle light scattering diffraction patterns of ionotropic gels, formed by Ca ion diffusion into polygalacturonate solution, indicating organized structures
Absolute differential elastic scattering cross sections measured with the 3-m, high resolution, time-of-flight spectrometer are presented for 54.9eV positrons incident on He. Five point moving average differential cross sections are plotted against average scattering angles which range from 14 to 36 deg. Also the averages of five differential cross sections which have adjacent values of scattering angle are plotted versus the corresponding averages of the scattering angles. The curve fitted to these data is shaped like the theoretical curve but has its minimum and its maximum at scattering angles that are about 4 deg higher and 15 deg lower respectively than predicted by theory.
The various definitions of albedo used in planetary astronomy are reviewed. In particular, the Bond albedo, which refers only to the reflected and refracted components, is not applicable to small particles or highly irregular particles, where diffraction is not restricted to a well-defined lobe at small scattering angles. Measured scattering functions for irregular particles are presented in a normalized form and are applied to the case of zodiacal light.
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.
The theory and measurement of angle-resolved scatter are described. Values of rms roughness that were obtained by using this technique to characterize four different materials are compared with values that were obtained by using a total integrated scatter measuring instrument, an optical profiler, and a mechanical profiler. The spatial frequency bandwidths and modulation transfer functions of the four instruments are different, and results are described in light of these differences.
Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.
Instrumentation and data interpretation method for particle size determination by low-angle light scattering
Expressions are given for the drag due to Coulomb collisions on a charged dust grain moving through a plasma. The commonly used Chandrasekhar (1943) result does not include large scattering angles or plasma collective effects. An equation given by Morfill et al. (1980) which does include large scattering angles, is limited to one-dimensional plasma particle motion and can give at least an order of magnitude too much drag. This paper also makes use of an analogy between the drag problem and problems in electrostatics. This analogy permits generalization to any isotropic plasma of an observation made by Chandrasekhar for a Maxwellian, namely, that the drag is independent of the presence or absence of plasma particles moving faster than the grain. Finally, the contribution of plasma collective effects to the drag is studied with the inclusion of large scattering angles.
This study addresses the question whether 1D radiative transfer theory describes well the angular distribution of shortwave cloud reflection. The statistical analysis of a large set of MODIS observations indicates that in oblique backward scattering directions, cloud reflection is stronger than 1D theory would predict. After considering a variety of possible causes, the paper concludes that the most likely reason for the increase lies in 3D radiative interactions. The results' main implication is that cloud optical depths retrieved at back scattering view angles larger than about 50 degrees tend to be overestimated and should be used only with great caution.
Landau resonance and cyclotron resonance of coherent whistler mode waves and energetic electrons are explored for magnetoplasmas with appreciable gradients in the plasma density and magnetic field strength. It is shown that in the topside ionosphere of the earth near the ion transition height the gradients in plasma density and magnetic field strength along a magnetic field line may match in a way which enhances both Landau and cyclotron interactions between waves and electrons at the loss cone pitch angle. The pitch angle scattering induced by a signal from a ground-based VLF transmitter in the ionosphere above the transmitter has been estimated and compared to the pitch angle scattering induced by naturally occurring ELF hiss through cyclotron resonance. It is found that the expected scattering due to plasmapheric hiss is an order of magnitude larger than that due to Landau resonance in the topside ionosphere. Pitch angle scattering due to cyclotron resonance in the topside ionosphere, however, may be larger by a factor of 2. It is suggested that the 'fast Trimpi' effect may be caused by a cyclotron resonance interaction in the topside ionosphere.