Diffusive transport of light in a two-dimensional disordered packing of disks: Analytical approach to transport mean free path

Context. Imaging spectroscopy in X-rays with RHESSI provides the possibility to investigate the spatial evolution of X-ray emitting electron distribution and therefore, to study transport effects on energetic electrons during solar flares. Aims. We study the energy dependence of the scattering mean free path of energetic electrons in the solar corona. Methods. We used imaging spectroscopy with RHESSI to study the evolution of energetic electrons distribution in various parts of the magnetic loop during the 2004 May 21 flare. We compared these observations with the radio observations of the gyrosynchrotron radiation of the same flare and with the predictions of a diffusive transport model. Results. X-ray analysis shows a trapping of energetic electrons in the corona and a spectral hardening of the energetic electron distribution between the top of the loop and the footpoints. Coronal trapping of electrons is stronger for radio-emitting electrons than for X-ray-emitting electrons. These observations can be explained by a diffusive transport model. Conclusions. We show that the combination of X-ray and radio diagnostics is a powerful tool to study electron transport in the solar corona in different energy domains. We show that the diffusive transport model can explain our observations, and in the range 25–500 keV, the scattering mean free path of electrons decreases with electron energy. We can estimate for the first time the scattering mean free path dependence on energy in the corona.

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Time-resolved spatial distribution of scattered radiative energy in a two-dimensional cylindrical medium with a large mean free path for scattering

International Journal of Heat and Mass Transfer ◽

10.1016/s0017-9310(00)00306-9 ◽

2001 ◽

Vol 44 (14) ◽

pp. 2611-2619 ◽

Cited By ~ 18

Author(s):

Shang-Hsuang Wu ◽

Chih-Yang Wu

Keyword(s):

Spatial Distribution ◽

Free Path ◽

Mean Free Path ◽

Radiative Energy ◽

Two Dimensional ◽

Time Resolved

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The Parallel Mean Free Path of Heliospheric Cosmic Rays in Composite Slab/Two‐dimensional Geometry. I. The Damping Model of Dynamical Turbulence

The Astrophysical Journal ◽

10.1086/382065 ◽

2004 ◽

Vol 604 (2) ◽

pp. 861-873 ◽

Cited By ~ 35

Author(s):

A. Shalchi ◽

R. Schlickeiser

Keyword(s):

Cosmic Rays ◽

Free Path ◽

Mean Free Path ◽

Two Dimensional ◽

Composite Slab ◽

Damping Model

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Modeling of Phonon Thermal Conductivity of Two Dimensional Nano and Micro Composites in the Longitudinal Direction

Heat Transfer: Volume 1 ◽

10.1115/ht2005-72116 ◽

2005 ◽

Author(s):

Ravi Prasher

Keyword(s):

Thermal Conductivity ◽

Free Path ◽

Longitudinal Direction ◽

Mean Free Path ◽

Two Dimensional ◽

Boltzmann Transport ◽

Host Medium ◽

Alumina Composite ◽

The Mean ◽

Longitudinal Thermal Conductivity

The three important length scales in composites made from nano/micro wires and fibers are: 1) the ratio of inter fiber distance and mean free path of the phonons in the host medium 2) the ratio of the diameter of the fiber or the wire and the mean free path of the phonons in the host medium and 3) the ratio of the diameter of the fiber and the mean free path of phonons in the fiber. Modeling of longitudinal thermal conductivity of two-dimensional nano and micro composites has not been attempted in the literature. This paper develops analytical modeling for the longitudinal thermal conductivity of nano and micro composites by solving the Boltzmann transport equation (BTE) for phonons. The paper shows the scattering of phonons in the host medium by the fiber boundaries play a very important role in deciding the thermal conductivity of nano and micro composites. The model is in good agreement with data on thermal diffusivity of Bismuth Telluride nanowire/ Alumina composite.

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Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100133916 ◽

1990 ◽

Vol 48 (2) ◽

pp. 64-65

Author(s):

L. Reimer ◽

R. Oelgeklaus

Keyword(s):

Fourier Transform ◽

Energy Loss ◽

Electron Energy ◽

Rotational Symmetry ◽

Mean Free Path ◽

Single Scattering ◽

Specimen Thickness ◽

Two Dimensional ◽

Image Position ◽

Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

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