Showing papers on "Mean free path published in 2010"
TL;DR: In this article, the first experimental study of thermal transport at the nanoscale is reported in the case of a point-like heat source, providing a quantitative description of the transition between the ballistic and diffusive regimes.
Abstract: According to Fourier theory, thermal transport is a diffusive process. However, this cannot be the case at length scales smaller than the mean free path of the energy carriers. The first experimental study of thermal transport at the nanoscale is now reported in the case of a point-like heat source, providing a quantitative description of the transition between the ballistic and diffusive regimes.
330 citations
TL;DR: In this paper, heat conduction and diffusion in silicon nanowires (SiNWs) systematically by using non-equilibrium molecular dynamics was studied and it was found that the thermal conductivity (κ) of SiNWs diverges with the length as, κ √ Lβ, even when the length is up to 1.1μm which is much longer than the phonon mean free path.
225 citations
TL;DR: An elastic-shell-based theory for calculating the thermal conductance of graphene ribbons of arbitrary width w is presented and can be augmented by the phenomenological value of a phonon mean free path to account for scattering and agree well with the reported experimental observations.
Abstract: An elastic-shell-based theory for calculating the thermal conductance of graphene ribbons of arbitrary width w is presented. The analysis of vibrational modes of a continuum thin plate leads to a general equation for ballistic conductance σ. At low temperature, it yields a power law σ ∼ Tβ, where the exponent β varies with the ribbon width w from β = 1 for a narrow ribbon (σ ∼ T, as a four-channel quantum wire) to β = 3/2 (σ ∼ wT3/2) in the limit of wider graphene sheets. The ballistic results can be augmented by the phenomenological value of a phonon mean free path to account for scattering and agree well with the reported experimental observations.
198 citations
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TL;DR: In this article, heat conduction and diffusion in silicon nanowires (SiNWs) were studied using non-equilibrium molecular dynamics and it was found that the thermal conductivity of SiNWs diverges with the length, even when the length is up to 1,100 nm, much longer than the phonon mean free path.
Abstract: We study heat conduction and diffusion in silicon nanowires (SiNWs) systematically by using non-equilibrium molecular dynamics It is found that the thermal conductivity of SiNWs diverges with the length, even when the length is up to 1,100 nm which is much longer than the phonon mean free path Moreover, an anomalous heat diffusion is observed which is believed to be responsible for the length dependent thermal conductivity Our results provide strong evidence that Fourier's law of heat conduction is not valid in low dimensional nanostructures
181 citations
TL;DR: In this paper, the combined effects of solar energetic particle propagation, parallel and perpendicular to the large-scale magnetic field in the solar wind, are investigated using stochastic differential equations.
Abstract: We investigate the combined effects of solar energetic particle propagation, parallel and perpendicular to the large-scale magnetic field in the solar wind. Numerical methods employing stochastic differential equations are used incorporating pitch-angle diffusion, focusing, and pitch-angle-dependent diffusion perpendicular to the magnetic field. We compute spatial distributions of ~100?keV electrons and 4?MeV protons in the inner heliosphere, assuming impulsive injection near the Sun over a limited range of solar longitude and latitude. In addition, spatial distributions and intensity-time profiles for various combinations of the parallel and perpendicular mean free path, with different assumptions for the dependence of ?? on the radial distance and pitch angle, are investigated. We find that realistic results can be obtained when we assume that the perpendicular mean free path scales in the inner heliosphere with the gyroradius of the particles. Step-like decreases of particle intensities as frequently observed in impulsive events at 1?AU can be reproduced for a ratio of ??/?? a few times 10?5.
168 citations
TL;DR: In this paper, an improved version of the nonlinear guiding center theory was employed to compute analytically the perpendicular mean free path of cosmic ray scattering in the direction perpendicular to a mean magnetic field.
Abstract: We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.
98 citations
TL;DR: In this article, the authors considered situations in which the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a maxwellian distribution and proposed a different method to obtain similar results.
Abstract: This paper is devoted to hydrodynamic limits of linear kinetic equations. We consider situations in which the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a maxwellian distribution. A similar problem was addressed in [14] using Fourier transform and it was shown that the long time/small mean free path behavior of the solution of the kinetic equation is described by a fractional diffusion equation. In this paper, we propose a different method to obtain similar results. This method is somewhat reminiscent of the so-called "moments method" which plays an important role in kinetic theory. This new method allows us to consider space dependent collision operators (which could not be treated in [14]). We believe that it also provides the relevant tool to address nonlinear problems.
64 citations
TL;DR: In this paper, gold-embedded zinc oxide structures are obtained in which the conduction mechanism changes from conduction through oxide and activated tunneling between discontinuous metal islands to metallic conduction in a near-continuous layer, with increase in gold thickness.
Abstract: Gold-embedded zinc oxide structures are obtained in which the conduction mechanism changes from conduction through the oxide and activated tunneling between discontinuous metal islands to metallic conduction through a near-continuous layer, with increase in gold thickness. These structures can show resistivity as low as 5.2×10−5 Ω cm. Optical transmission is elucidated in terms of gold’s absorption due to interband electronic transitions, and free carrier absorption losses combined with limitation of the mean free path in discontinuous nanoparticles. The structures show transmittance, photopic averaged transmittance, and Haacke figure of merit values of 93%, 84%, and 15.1×10−3 Ω−1, respectively.
51 citations
TL;DR: In this paper, the authors used the nonlinear guiding center theory to obtain the perpendicular diffusion coefficient of the cosmic rays and found that the radial mean free path is dominated by the parallel component before 30 AU, after which the perpendicular component becomes important.
Abstract: [1] We calculate the cosmic ray diffusion tensor based on a recently developed model of magnetohydrodynamic (MHD) turbulence in the expanding solar wind. Parameters of this MHD model are tuned by using published observations from Helios, Voyager 2, and Ulysses. We present solutions of two turbulence parameter sets and derive the characteristics of the cosmic ray diffusion tensor for each. We determine the parallel diffusion coefficient of the cosmic rays following the method presented by Bieber et al. (1995). We use the nonlinear guiding center theory to obtain the perpendicular diffusion coefficient of the cosmic rays. We find that (1) the radial mean free path decreases from 1 to 30 AU for both turbulence scenarios; (2) after 30 AU the radial mean free path is nearly constant; (3) the radial mean free path is dominated by the parallel component before 30 AU, after which the perpendicular component becomes important; (4) the rigidity dependence of the parallel mean free path is proportional to P.404 for one turbulence scenario and P.374 for the other at 1 AU from 0.1 to 10 GV, but in the outer heliosphere its dependence steepens above 4 GV; and (5) the rigidity dependence of the perpendicular mean free path is very weak.
50 citations
TL;DR: Based on the Boltzmann transport equation of electrons and taking the scattering effect of electrons in the grain boundary as the boundary conditions of electrons transport in grain, this article presented a theoretical model for the Seebeck coefficient of bulk polycrystalline thermoelectric materials, and applied it to studying the grain size effect on the seebeck coefficient, and discussed the effects of transmissivity, temperature and the mean free path of electrons on the size effect.
Abstract: Based on the Boltzmann transport equation of electrons and taking the scattering effect of electrons in the grain boundary as the boundary conditions of electrons transport in the grain, we presented a theoretical model for the Seebeck coefficient of bulk polycrystalline thermoelectric materials, and applied it to studying the grain size effect on the Seebeck coefficient. Then we discussed the effects of transmissivity, temperature and the mean free path of electrons on the size effect. The results show that the proposed theoretical model is reasonable and effective and the predicted results for the Seebeck coefficient are in good agreement with the experimental data reported in literature. The bulk polycrystalline materials have notable (big) grain size effects on the Seebeck coefficient, and the influences of transmissivity, temperature and the mean free path of electrons on the Seebeck coefficient are also significant.
46 citations
TL;DR: In this paper, thermal and electrical conductivity of 125nm-thick aluminum films were measured as functions of tensile thermo-mechanical strain, using a modified version of the 3-ω technique.
TL;DR: In this paper, an anisotropic Alfvenic turbulence spectrum corresponding to the Goldreich-Sridhar model by employing an enhanced nonlinear guiding center theory is computed for the mean free path of cosmic particles.
Abstract: Perpendicular diffusion coefficients and mean free paths of cosmic particles are computed for an anisotropic Alfvenic turbulence spectrum corresponding to the Goldreich-Sridhar model by employing an enhanced nonlinear guiding center theory. The calculations are important for understanding cosmic ray propagation in the Galaxy and in the solar system. In addition, the knowledge of diffusion coefficients is also useful for modeling charged particles which experience diffusive shock acceleration in supernova remnants and at interplanetary shock waves. To replace the parallel diffusion coefficient in our equation for the perpendicular diffusion coefficient, we employ different models such as quasilinear results and phenomenological models. The results are compared with those derived earlier. We demonstrate that the choice of the turbulence model as well as the choice of the model for the parallel diffusion coefficient has a strong influence on the perpendicular diffusion coefficient.
TL;DR: Anomalous heat conduction behavior is observed for the first time using non-equilibrium molecular dynamics simulations to obtain the thermal conductivity of thin finite-size silicon nanowires (NWs) in the 001 lattice direction.
Abstract: Anomalous heat conduction behavior is observed for the first time using non-equilibrium molecular dynamics (NEMD) simulations to obtain the thermal conductivity of thin finite-size silicon nanowires (NWs) in the 001 lattice direction. In the series of simulations, the length dependence of thermal conductivity of thin silicon nanowires (NWs) ranging from 6 to 434 nm is analyzed. It is found that a transition occurs in the thermal conductivity versus length curve after the initial convergence trend appears near the mean free path of bulk silicon. Because no experimental measurements of thermal conductivity are available for sub-10 nm diameter silicon NWs, different NEMD methods are used to test and analyze this anomalous thermal behavior of thin Si NWs with different boundary conditions. The underlying mechanism of the observed behavior is inferred from MD simulations with different boundary conditions so that the anomalous behavior is mainly caused by border restriction and boundary scattering of the thin silicon NWs.
TL;DR: In this paper, the phonon transport behavior of normally incident longitudinal acoustic phonon wave packets with wave vectors ranging in magnitude from 2% to 50% of the ⟨100⟩ first Brillouin zone boundary is examined as a function of thin film thickness.
Abstract: The molecular dynamics based phonon wave-packet technique is used to study phonon transport across mass-mismatched fcc thin films. Transport behavior of normally incident longitudinal acoustic phonon wave packets with wave vectors ranging in magnitude from 2% to 50% of the ⟨100⟩ first Brillouin zone boundary is examined as a function of thin film thickness when the phonon mean free path exceeds film thickness. The results indicate that for thin film to bulk solid mass ratios up to a factor of 6, the transmission of energy through the thin film can be well described by treating the thin film as a bulk solid.
TL;DR: In this paper, the authors synthesize seismogram envelopes in the multiple scattering framework, and apply the ordinary MLTWA technique to these synthetic envelopes to generate a suite of energy envelopes as a function of lapse time and distance, for reasonable values of B0, the seismic albedo and Le −1, the extinction length inverse (which are functions of g0 and ηi ).
Abstract: SUMMARY Following the numerical scheme of Yoshimoto we synthesized seismogram envelopes in the multiple scattering framework. We supposed the earth model constituted by a inhomogeneous crust overlying a transparent mantle. In this model velocity is assumed depth-dependent through a continuous function of the depth, v = v(h); Moho discontinuity is approximated by a sharp increase of the velocity around the crust–mantle boundary; inhomogeneity in the crust is parametrized through a depth-dependent scattering coefficient (the inverse of mean free path) g = g0 f (h), with f (h) function of depth, and g0 the scattering coefficient at zero depth; intrinsic attenuation is parametrized in terms of the intrinsic attenuation coefficient, ηi , that is assumed independent of depth. Generating a suite of energy envelopes as a function of lapse time and distance, for reasonable values of B0 , the seismic albedo and Le −1 , the extinction length inverse (which are functions of g0 and ηi ), we span a wide range including most of the measurements done through the world. Then, we apply the ordinary MLTWA technique to these synthetic envelopes. In this application, we assume a constant g and a constant velocity, v = which equals the average of v(h) calculated in the depth range characteristic of the volume encompassed by the scattered waves. In this way, we obtain the estimates of B0, and Le −1 , for a constant half-space. The relationship between the estimates of B0 and Le −1 , obtained assuming half-space, and the correspondent values used in the simulation, results to be well approximated by a second-order polynomial. Then, evaluating the best fit polynomial coefficients, we obtain a correspondence map between attenuation parameters retrieved for a uniform model with those characteristic of a more realistic structure. This map is useful to reinterpret all the couples B0 and Le −1 already calculated through the world in geological structures similar to the one adopted in our simulation. Results show that scattering and intrinsic-attenuation coefficients estimated using MLTWA in the assumption of a uniform half-space are always overestimated.
TL;DR: This paper uses a fractal distribution law for modeling scatterers' sizes distributions and investigates numerically and experimentally how γ is related to the fractal power α, indicating that within the range of γ typically encountered in biological samples, this coefficient is approximately linearly correlated with α.
Abstract: The optical properties within limited volumes of diffusive media can be probed by carrying spatially-resolved measurements of diffused light at short source-detector separation (typically one scattering mean free path). At such distance, analytical models only relying on the absorption and reduced scattering coefficients fail at correctly predicting reflectance and it was demonstrated that adding a third optical coefficient γ improves the description of light propagation conditions near the source. In an attempt to relate the γ coefficient to physical properties of turbid media, this paper uses a fractal distribution law for modeling scatterers’ sizes distributions and investigates numerically and experimentally how γ is related to the fractal power α. The results indicate that within the range of γ typically encountered in biological samples, this coefficient is approximately linearly correlated with α.
TL;DR: The concepts of equivalent scattering area, equivalent scatter reflection area, average scattering coefficient and average scatter reflection coefficient are introduced in order to express all walls' capability of scatter in a room.
Abstract: This paper describes the development of a theoretical framework for quantitatively characterizing sound field diffusion based on scattering coefficient and absorption coefficient of walls. The concepts of equivalent scattering area, equivalent scatter reflection area, average scattering coefficient and average scatter reflection coefficient are introduced in order to express all walls' capability of scatter in a room. Using these concepts and the mean free path, scatter-to-absorption ratio, mean scatter time and diffusion time are defined in order to evaluate degree of diffusion of a space. Furthermore the effect of spatial scattering objects to sound field diffusion is formulated. In addition the time variation of specular and scattered components in a room impulse response is formulated. The verification of these characterization methods was performed with computer simulations based on the sound ray tracing method. The results supported that the ideas presented are basically valid.
TL;DR: In this paper, an individual bismuth nanowire sample, 593nm in diameter and 1.64mm in length, has been successfully grown using a quartz template.
Abstract: An individual bismuth nanowire sample, 593 nm in diameter and 1.64 mm in length, has been successfully grown using a quartz template. The resistivity and the Seebeck coefficient of the nanowire at 300 K were 1.35 μΩ m and −59 μV/K, respectively, similar to those of a bismuth bulk sample. The temperature dependence of the resistivity was found to decrease with temperature from 300 K to 175 K and then increase with further temperature reduction below 175 K. The absolute value of the Seebeck coefficient decreased with temperature from 300 K to 90 K, and the sign of the Seebeck coefficient changed from negative to positive near 90 K. This result indicated that there was a small amount of contamination in the bismuth. The carrier density was estimated from the resistivity and Seebeck coefficient on the basis of limitation of the mean free path and a two-carrier model, and the observed temperature dependences are discussed.
TL;DR: In this article, the authors measured microwave double resonances in a wall-coated Rb vapor cell as a function of additional buffer-gas pressure and found that at intermediate pressures the lineshapes of the microwave resonances become asymmetric with a low-frequency tail.
Abstract: Microwave double resonances were measured in a wall-coated Rb vapor cell as a function of additional buffer-gas pressure. These data were compared with similar measurements in an uncoated cell. It was found that the linewidth in the coated spherical cell of diameter 1.6 cm displays a distinct maximum around 0.2 kPa. This agrees well with theoretical solutions of the diffusion equation, assuming a complex reflection coefficient at the wall. It was also found that at intermediate pressures the lineshapes of the microwave resonances become asymmetric with a low-frequency tail. This agrees with the explanation that where the alkali mean free path is substantially smaller than the average distance between wall collisions at zero pressure, there exist two classes of atoms in the cell. The atoms that get trapped near the walls accumulate much larger phase shifts than those toward the center of the cell. This effect is not seen in the longitudinal relaxation rate, indicating that it is related to a phase-shift effect.
TL;DR: In this article, the authors investigated the acoustic-phonon behavior of Pd-, Pt-, and Zr-based metallic glasses with the combination of inelastic x-ray scattering and ultrasonic (US) measurements.
Abstract: We have investigated acoustic-phonon behavior of Pd-, Pt-, and Zr-based metallic glasses with the combination of inelastic x-ray scattering and ultrasonic (US) measurements. In the dispersion of the longitudinal acoustic modes at small wave number $Q$, the phase velocity of phonon tends to exceed the US velocity with a wavelength of macroscopic scale for Pd- and Pt-based glasses, whereas the former goes close to the latter for Zr-based glasses. Furthermore, in all the cases, the mean free path $L$ of phonon apparently increases steeply at a certain $Q$ value. These phenomena on the acoustic phonon behavior can be qualitatively explained by the elastic-wave-scattering theory with a simple two-phase model.
TL;DR: In this paper, the influence of the polarization state and the dissipation range spectral steepening of slab plasma waves on the scattering mean free path of single-charged cosmic-ray particles is investigated in a turbulence model, where the crucial scattering of cosmicray particles with small pitch-angle cosines is caused by resonant cyclotron interactions with slab plasma waves.
Abstract: The influence of the polarization state and the dissipation range spectral steepening of slab plasma waves on the scattering mean free path of single-charged cosmic-ray particles is investigated in a turbulence model, where the crucial scattering of cosmic-ray particles with small pitch-angle cosines is caused by resonant cyclotron interactions with slab plasma waves. Analytical expressions for the mean free path of protons, antiprotons, negatrons, and positrons are derived for the case of constant frequency-independent magnetic helicity values ? and different values of the dissipation range spectral index k for characteristic interplanetary and interstellar plasma conditions. The positron mean free path is not affected by the dissipation range spectral index k as these particles can only cyclotron-resonate for rigidity values larger than R 0 = mpc = 938?MV. Proton and antiproton mean free paths are only slightly affected by the dissipation range spectral index k at small rigidities R < R 0. The negatron mean free path is severely affected by the dissipation range spectral index k at rigidities smaller than R 0. At high rigidities R R 0, all particle species approach the same power-law dependence R 2?s determined by the inertial range spectral index s = 5/3. The magnetic helicity value ? affects the value of the mean free path. At all rigidities, the ratio of the antiproton to proton mean free paths equals the constant (1 + ?)/(1 ? ?), which also agrees with the ratio of the negatron to the proton and positron mean free paths at relativistic rigidities. At relativistic rigidities the positron and proton mean free paths agree, as do the negatron and antiproton mean free paths.
TL;DR: The temperature and defect density dependences of the Transition field point to vortex pinning mediated by fluctuations in the quasiparticle mean free path reveal the mechanism of the transition in the absence of complicating factors such as layeredness or thermal fluctuations.
Abstract: The field-driven transition from an ordered Bragg glass to a disordered vortex phase in singlecrystalline MgB2 is tuned by an increasing density of point defects, introduced by electron irradiation. The discontinuity observed in magnetization attests to the first-order nature of the transition. The temperature and defect density dependences of the transition field point to vortex pinning mediated by fluctuations in the quasiparticle mean free path, and reveal the mechanism of the transition in the absence of complicating factors such as layeredness or thermal fluctuations.
TL;DR: In this article, the carrier statistics in carbon nanotubes with nonparabolic energy spectrum were studied in order to predict the ultimate (intrinsic) drift velocity as a function of temperature, concentration, and chirality.
Abstract: The carrier statistics in carbon nanotubes (CNTs) with nonparabolic energy spectrum is studied in order to predict the ultimate (intrinsic) drift velocity as a function of temperature, concentration, and chirality. The extremely high mobilities in CNTs do not necessarily lead to higher saturation velocity that is limited to the intrinsic velocity calculated using Arora's formalism [V. K. Arora, Current Nanoscience 5, 227(2009)]. The ballistic nature of the mobility when CNT length is smaller than the scattering-limited mean free path is delineated. The results are of enormous importance in extracting carrier transport properties from a variety of experiments performed on CNTs.
TL;DR: In this article, a simple approximate model is proposed to predict boundary/interface scattering phonon mean free path (MFP) and thermal conductivity of nanowire heterostructures (NWHSs) based on Casimir formalism.
Abstract: Boundary scattering phonon mean free path (MFP) is an important parameter for thermal conductivity calculation of nanocomposites. In this work, a simple approximate model is proposed to predict boundary/interface scattering MFP and thermal conductivity of nanowire heterostructures (NWHSs) based on Casimir formalism. Calculated thermal conductivities of Si tubular nanowires and Si/Ge NWHSs agree well with the numerical and analytical solutions of Boltzmann transport equation. It is demonstrated that core/shell layer thickness plays a significant role on tuning NWHS thermal conductivity. The results indicate the approximate model of thermal conductivity can be used for quickly evaluating the thermal behavior of nanocomposites.
TL;DR: In this article, an experimental study of the light emission from dye-doped polymer random media dispersed with TiO2 particles of various sizes, shapes, and structures is presented.
Abstract: We present an experimental study of the light emission from dye-doped polymer random media dispersed with TiO2 particles of various sizes, shapes, and structures. Random lasing with nonresonant feedback, similar to that for spherically shaped particles that are used for conventional random lasers, is observed for almost all types of particles and aggregates. The efficiency of random lasing for each medium is analyzed using the relationship between the emission spectrum and the transport mean free path (TMFP), which is measured by enhanced backscattering experiments. Results show that the peak emission intensity depends strongly on the particle shape and structure, whereas the spectral linewidth is governed by the TMFP.
TL;DR: In this article, the authors investigated the kinetics of a coma, consisting of water vapor plasma and ice grains, illuminated by solar radiation and found that the photoelectric emission of electrons from ice grains strongly affects the composition of the coma.
Abstract: This paper presents an investigation of the kinetics of a coma, consisting of water vapor plasma and ice grains, illuminated by solar radiation. The photoelectric emission of electrons from ice grains strongly affects the composition of the coma. In deference to the recent emphasis on the character of openness of a complex plasma system, the investigation is based on the balance of the number density of the constituent species and energy of electrons and ions, and the charge neutrality. Accretion of electrons and ionic species by the ice particles, ionization of neutral species by solar radiation, the recombination of electrons and ions, the collisions between electrons, ions and neutral species, charge exchange between atomic ions and neutral molecules and photoelectric emission of electrons by ice grains have been considered in this study; further, the energy exchange associated with these processes has also been taken into account. An interesting conclusion, that the maximum charging of ice particles occurs for an optimum value of number density of ice particles, has been obtained; opposite charging of grains of different sizes has also been predicted in certain conditions. The validity of the theoretical model on the basis of the mean free path of electrons being less than the dimensions of the coma has also been discussed.
TL;DR: In this paper, the PARASOL-1D simulation was used to determine four kinetic factors commonly needed in fluid codes: the electron and ion heat flux limiting factors, αe and αi, the ion adiabatic index, γA, and the ion temperature anisotropy, T∥/T⊥.
Abstract: Fluid models are not generally applicable to fusion edge plasmas without external provision of kinetic factors: closure parameters and boundary conditions inside the sheath region. We explain the PARASOL-1D simulation, a particle-in-cell code with a binary collision Monte-Carlo model, and use it to determine four kinetic factors commonly needed in fluid codes. These are the electron and ion heat flux limiting factors, αe and αi, the ion adiabatic index, γA, and the electron and ion temperature anisotropy, T∥/T⊥. We survey these factors over a wide range of collisionalities and find that, as predicted, the conductive heat flux is accurately described by the Spitzer-Harm expression in the collisional limit and asymptotes to a constant value in the collisionless limit. However, unique behavior occurs in the weakly collisional regime when the ratio of the mean free path to connection length is 0.1 < λmfp/L∥< 10, when the SOL is between the conduction- and sheath-limited regimes. We find that αe can peak, becoming larger than the collisionless limit, γA is less than unity, and only the ions are anisotropic. The effects of electron energy radiation and Langevin heating are explored. Finally, the strong deviations of the energy distribution function from Maxwellian in the weakly collisional and collisionless regimes are explained.
TL;DR: In this paper, the effect of nucleon mean free path on differential cross sections of tritium-emission spectra for (p, 3H) reactions on 27Al, 54, 56Fe, 89Y, 120Sn, 197Au, 208Pb and 209Bi induced by 62 MeV protons in the pre-equilibrium reaction mechanisms were carried out by using the geometry dependent hybrid model.
Abstract: This study aims on the effect of nucleon mean free path on differential cross sections of tritium-emission spectra for (p, 3H) reactions on 27Al, 54, 56Fe, 89Y, 120Sn, 197Au, 208Pb and 209Bi induced by 62 MeV protons in the pre-equilibrium reaction mechanisms. The pre-equilibrium calculations were carried out by using the geometry dependent hybrid model. The calculated results are compared with experimental data existing in literature and found to be in good agreement. Furthermore, using different multiplication factor for the mean free path in the calculation changes the differential cross sections of tritium emission spectra.
TL;DR: In this paper, an analytic continuation to arbitrary complex frequencies of the complex optical and ac conductivity of a homogeneous superconductor with an arbitrary mean free path was presented, which is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type I superconducting bodies.
Abstract: We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and ac conductivity of a homogeneous superconductor with an arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers–Kronig transforms. A number of applications illustrate its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.