The upper critical magnetic field of lead as a function of the mean free path of the electrons

1971 ◽  
Vol 242 (1) ◽  
pp. 31-44 ◽  
Author(s):  
R. Koepke ◽  
G. Bergmann
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Mean Free Path ◽  
Critical Magnetic Field ◽  
Upper Critical Magnetic Field ◽  
The Mean

scholarly journals The diffusion and mobility of ions in a magnetic field

1912 ◽  
Vol 86 (590) ◽  
pp. 571-577 ◽  
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Magnetic Force ◽  
Mean Free Path ◽  
Electric Force ◽  
Mobility Of Ions ◽  
The Mean ◽  
The Magnetic Field

1. When the motion of ions in a gas takes place in a magnetic field the rates of diffusion and the velocities due to an electric force may be determined by methods similar to those given in a previous paper. The effect of the magnetic field may be determined by considering the motion of each ion between collisions with molecules. The magnetic force causes the ions to be deflected in their free paths, and when no electric force is acting the paths are spirals, the axes being along the direction of the magnetic force. If H be the intensity of the magnetic field, e the charge, and m the mass of an ion, then the radius r of the spiral is mv /He, v being the velocity in the direction perpendicular to H. The distance that the ion travels in the interval between two collisions in a direction normal to the magnetic force is a chord of the circle of radius r . The average lengths of these chords may be reduced to any fraction of the projection of the mean free path in the direction of the magnetic force, so that the rate of diffusion of ions in the directions perpendicular to the magnetic force is less than the rate of diffusion in the direction of the force.

The conductivity of thin wires in a magnetic field

1950 ◽  
Vol 202 (1070) ◽  
pp. 378-394 ◽  
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Bulk Material ◽  
Mean Free Path ◽  
Electron Theory ◽  
Conduction Electrons ◽  
Thin Wires ◽  
The Mean ◽  
The Magnetic Field ◽  
Theory And Experiment

A thin film or wire of metal has a lower electrical conductivity than the bulk material if the thickness is comparable with or smaller than the electronic mean free path. Previous workers have obtained expressions for the magnitude of the effect by integrating the Boltzmann equation and imposing the appropriate boundary conditions. The problem is re-examined from a kinetic theory standpoint, and it is shown that the same expressions are obtained by this method, usually rather more simply, while the physical picture is considerably clarified. The method is applied to an evaluation of the conductivity of a thin wire with a magnetic field along the axis, and it is found that the resistivity should decrease as the magnetic field is increased; it should be possible to derive the mean free path and velocity of the conduction electrons by comparison of theory and experiment. The theory has been confirmed by experimental measurements on sodium; estimates of electronic velocity and mean free path are obtained which are in fair agreement with the values given by the free-electron theory.

scholarly journals Departure from MHD prescriptions in shock formation over a guiding magnetic field

2017 ◽  
Vol 35 (3) ◽  
pp. 513-519 ◽  
Author(s):  
A. Bret ◽  
A. Pe'er ◽  
L. Sironi ◽  
M.E. Dieckmann ◽  
R. Narayan
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Mean Free Path ◽  
Distribution Functions ◽  
Shock Formation ◽  
Physical Analysis ◽  
Particle In Cell ◽  
The Mean ◽  
Collective Plasma ◽  
Aligned Magnetic Field

AbstractIn plasmas where the mean-free-path is much larger than the size of the system, shock waves can arise with a front much shorter than the mean-free-path. These so-called “collisionless shocks” are mediated by collective plasma interactions. Studies conducted so far on these shocks found that although binary collisions are absent, the distribution functions are thermalized downstream by scattering on the fields, so that magnetohydrodynamics prescriptions may apply. Here we show a clear departure from this pattern in the case of Weibel shocks forming over a flow-aligned magnetic field. A micro-physical analysis of the particle motion in the Weibel filaments shows how they become unable to trap the flow in the presence of too strong a field, inhibiting the mechanism of shock formation. Particle-in-cell simulations confirm these results.

scholarly journals Model Images of Radio Halos Around Supernova Remnants

1994 ◽  
Vol 142 ◽  
pp. 845-856
Author(s):  
Stephen P. Reynolds
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Free Path ◽  
Supernova Remnants ◽  
Mean Free Path ◽  
Relativistic Electrons ◽  
Radiation Mechanisms ◽  
Model Calculations ◽  
Aspect Angle ◽  
The Mean

AbstractI present model calculations of profiles and two-dimensional images of the radio synchrotron emission of young supernova remnants, concentrating on observable effects of relativistic electrons diffusing upstream of the shock wave. If the preshock electron scattering mean free path is sufficiently long, observable synchrotron halos outside the bulk of the radio emission can potentially result; their absence can constrain the mean free path from above. If scattering is primarily due, as expected, to Alfvén waves with amplitude δB, the halo is expected to extend a distance of order rg c(δB/B)−2 /vs beyond the shock, where rg is the gyroradius of the electrons emitting at the observed frequency, B is the upstream magnetic field strength, vs is the shock velocity, and the amplitude δB refers to waves with wavelength comparable to rg , of order 1013 cm for typical supernova-remnant parameters. However, the detailed geometry of the halo varies with the assumptions about particle acceleration in the shock wave. I present an atlas of model profiles and images as a function of preshock diffusion length, of aspect angle between the magnetic field and the line of sight, and of other relevant parameters.Subject headings: radiation mechanisms: miscellaneous — shock waves — supernova remnants

scholarly journals Ballistic Heat Transport in Nanocomposite: The Role of the Shape and Interconnection of Nanoinclusions

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1982
Author(s):  
Paul Desmarchelier ◽  
Alice Carré ◽  
Konstantinos Termentzidis ◽  
Anne Tanguy
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Free Path ◽  
Mean Free Path ◽  
Strong Increase ◽  
Moderate Increase ◽  
Energy Propagation ◽  
The Mean ◽  
Dynamics Simulations

In this article, the effect on the vibrational and thermal properties of gradually interconnected nanoinclusions embedded in an amorphous silicon matrix is studied using molecular dynamics simulations. The nanoinclusion arrangement ranges from an aligned sphere array to an interconnected mesh of nanowires. Wave-packet simulations scanning different polarizations and frequencies reveal that the interconnection of the nanoinclusions at constant volume fraction induces a strong increase of the mean free path of high frequency phonons, but does not affect the energy diffusivity. The mean free path and energy diffusivity are then used to estimate the thermal conductivity, showing an enhancement of the effective thermal conductivity due to the existence of crystalline structural interconnections. This enhancement is dominated by the ballistic transport of phonons. Equilibrium molecular dynamics simulations confirm the tendency, although less markedly. This leads to the observation that coherent energy propagation with a moderate increase of the thermal conductivity is possible. These findings could be useful for energy harvesting applications, thermal management or for mechanical information processing.

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