A quantitative investigation of the solar modulation of cosmic-ray protons and helium nuclei

The differential energy spectra of cosmic-ray protons and He nuclei have been measured at energies up to 315 MeV/nucleon using balloon- and satellite-borne instruments. These spectra are presented for solar quiet times for the years 1966 through 1970. The data analysis is verified by extensive accelerator calibrations of the detector systems and by calculations and measurements of the production of secondary protons in the atmosphere.

The spectra of protons and He nuclei in this energy range are dominated by the solar modulation of the local interstellar spectra. The transport equation governing this process includes as parameters the solar-wind velocity, V, and a diffusion coefficient, K(r,R), which is assumed to be a scalar function of heliocentric radius, r, and magnetic rigidity, R. The interstellar spectra, j_D, enter as boundary conditions on the solutions to the transport equation. Solutions to the transport equation have been calculated for a broad range of assumed values for K(r,R) and j_D and have been compared with the measured spectra.

It is found that the solutions may be characterized in terms of a dimensionless parameter, ψ(r,R) = ^∞∫_r V dr'/(K(r',R). The amount of modulation is roughly proportional to ψ. At high energies or far from the Sun, where the modulation is weak, the solution is determined primarily by the value of ψ (and the interstellar spectrum) and is not sensitive to the radial dependence of the diffusion coefficient. At low energies and for small r, where the effects of adiabatic deceleration are found to be large, the spectra are largely determined by the radial dependence of the diffusion coefficient and are not very sensitive to the magnitude of ψ or to the interstellar spectra. This lack of sensitivity to j_D implies that the shape of the spectra at Earth cannot be used to determine the interstellar intensities at low energies.

Values of ψ determined from electron data were used to calculate the spectra of protons and He nuclei near Earth. Interstellar spectra of the form j_D α (W - 0.25m)^-2.65 for both protons and He nuclei were found to yield the best fits to the measured spectra for these values of ψ, where W is the total energy and m is the rest energy. A simple model for the diffusion coefficient was used in which the radial and rigidity dependence are separable and K is independent of radius inside a modulation region which has a boundary at a distance D. Good agreement was found between the measured and calculated spectra for the years 1965 through 1968, using typical boundary distances of 2.7 and 6.1 A.U. The proton spectra observed in 1969 and 1970 were flatter than in previous years. This flattening could be explained in part by an increase in D, but also seemed to require that a noticeable fraction of the observed protons at energies as high at 50 to 100 MeV be attributed to quiet-time solar emission. The turnup in the spectra at low energies observed in all years was also attributed to solar emission. The diffusion coefficient used to fit the 1965 spectra is in reasonable agreement with that determined from the power spectra of the interplanetary magnetic field (Jokipii and Coleman, 1968). We find a factor of roughly 3 increase in ψ from 1965 to 1970, corresponding to the roughly order of magnitude decrease in the proton intensity at 250 MeV. The change in ψ might be attributed to a decrease in the diffusion coefficient, or, if the diffusion coefficient is essentially unchanged over that period (Mathews et al., 1971), might be attributed to an increase in the boundary distance, D.

The structure of liquid argon as determined by x-ray diffraction

X-ray diffraction measurements and subsequent data analyses have been carried out on liquid argon at five states in the density range of 0.91 to 1.135 gm/cc and temperature range of 127 to 143°K. Duplicate measurements were made on all states. These data yielded radial distribution and direct correlation functions which were then used to compute the pair potential using the Percus-Yevick equation. The potential minima are in the range of -105 to -120°K and appear to substantiate current theoretical estimates of the effective pair potential in the presence of a weak three-body force.

The data analysis procedure used was new and does not distinguish between the coherent and incoherent absorption factors for the cell scattering which were essentially equal. With this simplification, the argon scattering estimate was compared to the gas scattering estimate on the laboratory frame of reference and the two estimates coincided, indicating the data normalized. The argon scattering on the laboratory frame of reference was examined for the existence of the peaks in the structure factor and the existence of an observable third peak was considered doubtful.

Numerical studies of the effect of truncation, normalization, the subsidiary peak phenomenon in the radial distribution function, uncertainties in the low angle data relative to errors in the direct correlation function and the distortion phenomenon are presented.

The distortion phenomenon for this experiment explains why the Mikolaj-Pings argon data yielded pair potential well depths from the Percus-Yevick equation that were too shallow and an apparent slope with respect to density that was too steep compared to theoretical estimates.

The data presented for each measurement are: empty cell and cell plus argon intensity, absorption factors, argon intensity, smoothed argon intensity, smoothed argon intensity corrected for distortion, structure factor, radial distribution function, direct correlation function and the pair potential from the Percus-Yevick equation.

Calculation of the current noise spectrum in mesoscopic transport: A quantum master equation approach

Based on our recent work on quantum transport [X. Q. Li , Phys. Rev. B 71, 205304 (2005)], we show how an efficient calculation can be performed for the current noise spectrum. Compared to the classical rate equation or the quantum trajectory method, the proposed approach is capable of tackling both the many-body Coulomb interaction and quantum coherence on an equal footing. The practical applications are illustrated by transport through quantum dots. We find that this alternative approach is in a certain sense simpler and more straightforward than the well-known Landauer-Buttiker scattering matrix theory.

Continuous weak measurement and feedback control of a solid-state charge qubit: A physical unravelling of non-Lindblad master equation

Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of a Lindblad-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback control. In this work, in the context of continuous quantum measurement and feedback control of a solid-state charge qubit, we present a physical unravelling scheme of a non-Lindblad-type master equation. Self-consistency and numerical efficiency are well demonstrated. In particular, the control effect is manifested in the detector noise spectrum, and the effect of measurement voltage is discussed.

Molecular Hydrogen Emission from Protoplanetary Disks: Effects of X-ray Irradiation and Dust Evolution

Detailed models for the density and temperature profiles of gas and dust in protoplanetary disks are constructed by taking into account X-ray and UV irradiation from a central T Tauri star, as well as dust size growth and settling toward the disk midplane. The spatial and size distributions of dust grains are numerically computed by solving the coagulation equation for settling dust particles, with the result that the mass and total surface area of dust grains per unit volume of the gas in the disks are very small, except at the midplane. The H2 level populations and line emission are calculated using the derived physical structure of the disks. X-ray irradiation is the dominant heating source of the gas in the inner disk and in the surface layer, while the UV heating dominates otherwise. If the central star has strong X-ray and weak UV radiation, the H2 level populations are controlled by X-ray pumping, and the X-rayinduced transition lines could be observable. If the UV irradiation is strong, the level populations are controlled by thermal collisions or UV pumping, depending on the dust properties. As the dust particles evolve in the disks, the gas temperature at the disk surface drops because the grain photoelectric heating becomes less efficient. This makes the level populations change from LTE to non-LTE distributions, which results in changes to the line ratios. Our results suggest that dust evolution in protoplanetary disks could be observable through the H2 line ratios. The emission lines are strong from disks irradiated by strong UV and X-rays and possessing small dust grains; such disks will be good targets in which to observe H2 emission.

Cosmic-ray acceleration and escape from supernova remnants

Galactic cosmic-ray (CR) acceleration to the knee in the spectrum at a few PeV is only possible if the magnetic field ahead of a supernova remnant (SNR) shock is strongly amplified by CRs escaping the SNR. A model formulated in terms of the electric charge carried by escaping CRs predicts the maximum CR energy and the energy spectrum of CRs released into the surrounding medium. We find that historical SNRs such as Cas A, Tycho and Kepler may be expanding too slowly to accelerate CRs to the knee at the present time.

Universal behaviour of shock precursors in the presence of efficient cosmic ray acceleration

The self-consistent interaction between energetic particles and self-generated hydromagnetic waves in a cosmic ray pressure dominated plasma is considered. Using a three-dimensional hybrid magnetohydrodynamics (MHD)-kinetic code, which utilizes a spherical harmonic expansion of the Vlasov-Fokker-Planck equation, high-resolution simulations of the magnetic field growth including feedback on the cosmic rays are carried out. It is found that for shocks with high cosmic ray acceleration efficiency, the magnetic fields become highly disorganized, resulting in near isotropic diffusion, independent of the initial orientation of the ambient magnetic field. The possibility of sub-Bohm diffusion is demonstrated for parallel shocks, while the diffusion coefficient approaches the Bohm limit from below for oblique shocks. This universal behaviour suggests that Bohm diffusion in the root-mean-squared field inferred from observation may provide a realistic estimate for the maximum energy acceleration time-scale in young supernova remnants. Although disordered, the magnetic field is not self-similar suggesting a non-uniform energy-dependent behaviour of the energetic particle transport in the precursor. Possible indirect radiative signatures of cosmic ray driven magnetic field amplification are discussed.

Seismo-acoustic ray model benchmarking against experimental tank data

Acoustic predictions of the recently developed TRACEO ray model, which accounts for bottom shear properties, are benchmarked against tank experimental data from the EPEE-1 and EPEE-2 (Elastic Parabolic Equation Experiment) experiments. Both experiments are representative of signal propagation in a Pekeris-like shallow-water waveguide over a non-flat isotropic elastic bottom, where significant interaction of the signal with the bottom can be expected. The benchmarks show, in particular, that the ray model can be as accurate as a parabolic approximation model benchmarked in similar conditions. The results of benchmarking are important, on one side, as a preliminary experimental validation of the model and, on the other side, demonstrates the reliability of the ray approach for seismo-acoustic applications. (C) 2012 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4734236]

Tracking larval insect movement within soil using high resolution X-ray microtomography

1. In contrast to above-ground insects, comparatively little is known about the behaviour of subterranean insects, due largely to the difficulty of studying them in situ. 2. The movement of newly hatched (neonate) clover root weevil (Sitona lepidus L. Coleoptera: Curculinidae) larvae was studied non-invasively using recently developed high resolution X-ray microtomography. 3. The movement and final position of S. lepidus larvae in the soil was reliably established using X-ray microtomography, when compared with larval positions that were determined by destructively sectioning the soil column. 4. Newly hatched S. lepidus larvae were seen to attack the root rhizobial nodules of their host plant, white clover (Trifolium repens L.). Sitona lepidus larvae travelled between 9 and 27 mm in 9 h at a mean speed of 1.8 mm h(-1). 5. Sitona lepidus larvae did not move through the soil in a linear manner, but changed trajectory in both the lateral and vertical planes.

Simplified estimation of ray-path mirroring height for HF radiowaves reflected from the ionospheric F-region

From Milsom's equations, which describe the geometry of ray-path hops reflected from the ionospheric F-layer, algorithms for the simplified estimation of mirror-reflection height are developed. These allow for hop length and the effects of variations in underlying ionisation (via the ratio of the F2- and E-layer critical frequencies) and F2-layer peak height (via the M(3000)F2-factor). Separate algorithms are presented which are applicable to a range of signal frequencies about the FOT and to propagation at the MUF. The accuracies and complexities of the algorithms are compared with those inherent in the use of a procedure based on an equation developed by Shimazaki.

Trajectory of neutron-neutron-C-18 excited three-body state

The trajectory of the first excited Efimov state is investigated by using a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems. The approach is applied to n-n-C-18, where the n-n virtual energy and the three-body ground state are kept fixed. It is shown that such three-body excited state goes from a bound to a virtual state when the n-C-18 binding energy is increased. Results obtained for the n-C-19 elastic cross-section at low energies also show dominance of an S-matrix pole corresponding to a bound or virtual Efimov state. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths. (C) 2008 Elsevier B.V. All rights reserved.

A thermoporometry and small-angle x-ray scattering study of wet silica sonogels as the pore volume fraction is varied

Silica sonogels with different porosities were prepared by acid sono-hydrolysis of tetraethoxysilane. Wet sonogels were studied using small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC shows a broad thermal peak below the normal water melting point associated with the melting of confined ice nanocrystals, or nanoporosity. The nanopore size distribution was determined from the Gibbs-Thomson equation. As the porosity is increased, a second sharp DSC thermal peak with onset temperature at the water melting point is apparent, which was associated with the melting of ice macrocrystals, or macroporosity. The DSC result could be causing misinterpretation of the macroporosity because water may not be exactly confined in very feeble silica network regions in sonogels with high porosity. The structure of the wet gels can be described fairly well as mutually self-similar mass fractal structures with characteristic length. increasing from similar to 1.8 to similar to 5.4 nm and mass fractal dimension D diminishing discretely from similar to 2.6 to similar to 2.3 as the porosity increases in the range studied. More specifically, such a structure could be described using a two-parameter correlation function gamma(r) similar to r(D-3) exp(-r/xi), which is limited at larger scale by the cut-off distance xi but without a well-defined small scale cut-off distance, at least up to the maximum angular domain probed using SAXS in the present study.

Mass fractal characteristics of wet sonogels as determined by small-angle x-ray scattering and differential scanning calorimetry

Low density silica sonogels were prepared from acid sonohydrolysis of tetraethoxysilane. Wet gels were studied by small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC tests were carried out under a heating rate of 2 degrees C/min from -120 degrees C up to 30 degrees C. Aerogels were obtained by CO(2) supercritical extraction and characterized by nitrogen adsorption and SAXS. The DSC thermogram displays two distinct endothermic peaks. The first, a broad peak extending from about -80 degrees C up to practically 0 degrees C, was associated to the melting of ice nanocrystals with a crystal size distribution with pore diameter ranging from 1 or 2 nm up to about 60 nm, as estimated from Thomson's equation. The second, a sharp peak with onset temperature close to 0 degrees C, was attributed to the melting of macroscopic crystals. The DSC incremental nanopore volume distribution is in reasonable agreement with the incremental pore volume distribution of the aerogel as determined from nitrogen adsorption. No macroporosity was detected by nitrogen adsorption, probably because the adsorption method applies stress on the sample during measurement, leading to a underestimation of pore volume, or because often positive curvature of the solid surface is in aerogels, making the nitrogen condensation more difficult. According to the SAXS results, the solid network of the wet gels behaves as a mass fractal structure with mass fractal dimension D=2.20 +/- 0.01 in a characteristic length scale below xi=7.9 +/- 0.1 nm. The mass fractal characteristics of the wet gels have also been probed from DSC data by means of an earlier applied modeling for generation of a mass fractal from the incremental pore volume distribution curves. The results are shown to be in interesting agreement with the results from SAXS.

Comparative study using small-angle x-ray scattering and nitrogen adsorption in the characterization of silica xerogels and aerogels

A comparative study using small-angle x-ray scattering (SAXS) and nitrogen adsorption has been carried out in the structural characterization of silica xerogels and aerogels, obtained from tetraethoxysilane sonohydrolysis. The specific surface and the mean pore size as measured by both the techniques were found to be in notable agreement in all cases for aerogels and xerogels. According to the SAXS data, aerogels at 500 °C exhibit a mass fractal structure with fractal dimension D∼2.4 in the range between the correlation length ξ∼5.3 nm and a∼0.75 nm. An experimental method to probe the mass fractal structure of aerogels from exclusively nitrogen adsorption isotherms has been presented. For aerogels at 500 °C, we have found D∼2.4 in the range between the pore width 2rξ∼33 nm and 2ra∼4.5 nm, which is in notable agreement with the SAXS results (D ∼2.4, ξ∼5.3 nm, a∼0.75 nm) if we assign the pore width 2r probed by the Kelvin equation in the adsorption method to the Bragg distance 2π/q associated to the correlation length 1/q probed by SAXS.