Effect of correlations on the thermal equilibrium and normal modes of a non-neutral plasma

1996 ◽  
Vol 53 (5) ◽  
pp. 5268-5290 ◽  
Author(s):  
Daniel H. E. Dubin
Keyword(s):  
Thermal Equilibrium ◽  
Normal Modes ◽  
Neutral Plasma

On the Wave Speed of Thermal Radiation Inside and Near the Boundary of an Absorbing Material

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Bair V. Budaev ◽  
David B. Bogy
Keyword(s):  
Refractive Index ◽  
Thermal Radiation ◽  
Thermal Equilibrium ◽  
Wave Speed ◽  
Normal Modes ◽  
Absorbing Medium ◽  
Absorbing Material ◽  
Absorbing Media ◽  
Planck’S Law ◽  
Complex Valued

Abstract Planck's law describes thermal radiation into vacuum from a black body in thermal equilibrium. This law can be easily adapted to describe radiation into a transparent medium with a constant refractive index, and it admits a less trivial extension to radiation into a transparent medium with a nonconstant refractive index. However, this law cannot be straightforwardly generalized to describe thermal radiation into absorbing media and, in particular, to describe thermally exited electromagnetic fields inside the radiating body itself. We first analyze Planck's law and show why it cannot be straightforwardly extended to radiation into an absorbing medium. The derivation of this law relies on the assumption that a radiated field admits decomposition into normal modes, which cannot exist in absorbing media that are characterized by a complex-valued refractive index n=n′+in″, whose imaginary part describes the rate of energy dissipation. Correspondingly, the speed of electromagnetic waves in absorbing media c=c0/n, where c0 is the speed of light in vacuum, is also complex-valued, which suggests that the conventional concept of a complex valued wave speed is not suitable for modeling thermal radiation. We demonstrate that complex-valued wave speeds adequately describe waves that carry signals, such as radio waves and laser beams. Such waves decay because they pass some of their energy to the medium. The energy absorbed by the medium is eventually reradiated, but in studies focused on the transmission of signals, the reradiated fields are ignored as noise. In order to study thermal radiation in an absorbing material, one must treat the material and the radiation together as a closed system. The energy in such a system is conserved, and its distribution between the material and radiation does not change in time. This radiation admits decomposition into normal modes, which makes it possible to extend Planck's law to radiation into absorbing materials. This paper proposes a model of thermal radiation in an absorbing medium as a closed, energy conserving system. The radiation field has normal modes that correspond to an effective speed of wave propagation. Assuming that an absorbing material and the radiation in it are in thermal equilibrium, we show that deep inside the material, the average speed of photons is given by a frequency and temperature-dependent expression c∗=c0/(1+e−ℏω/κT). While this result is independent of the material, we further show that close to the boundary of the medium, the speed of thermal radiation depends in a complex way on the refractive index and the extinction coefficient of the material, as well as the direction of propagation and the distance from the material's surface.

scholarly journals Thermal equilibrium of non-neutral plasma in dipole magnetic field

2015 ◽  
Vol 22 (4) ◽  
pp. 042508 ◽  
Author(s):  
N. Sato ◽  
N. Kasaoka ◽  
Z. Yoshida
Keyword(s):  
Magnetic Field ◽  
Thermal Equilibrium ◽  
Dipole Magnetic Field ◽  
Neutral Plasma

Temperature Rise Times in Pneumatic Tires

1976 ◽  
Vol 4 (3) ◽  
pp. 181-189 ◽  
Author(s):  
S. K. Clark
Keyword(s):  
Heat Transfer ◽  
Thermal Properties ◽  
Temperature Rise ◽  
Thermal Equilibrium ◽  
Transfer Coefficients ◽  
Pneumatic Tire ◽  
Heat Transfer Coefficients ◽  
Idealized Model ◽  
Pneumatic Tires

Abstract An idealized model is proposed for heating of a pneumatic tire. A solution is obtained for the temperature rise of such a model. Using known thermal properties of rubber and known heat transfer coefficients, the time to reach thermal equilibrium is estimated.

Thermodynamic Stability of Hexagonal and Rhombohedral Bn at Cvd Conditions from Van der Waals Corrected First Principles Calculations

2019 ◽  
Author(s):  
Henrik Pedersen ◽  
Björn Alling ◽  
Hans Högberg ◽  
Annop Ektarawong
Keyword(s):  
Thin Films ◽  
Thermodynamic Stability ◽  
First Principles ◽  
Thermal Equilibrium ◽  
Density Functional ◽  
Van Der Waals ◽  
Chemical Vapor ◽  
First Principles Calculations ◽  
Functional Theory ◽  
The Stability

Thin films of boron nitride (BN), particularly the sp<sup>2</sup>-hybridized polytypes hexagonal BN (h-BN) and rhombohedral BN (r-BN) are interesting for several electronic applications given band gaps in the UV. They are typically deposited close to thermal equilibrium by chemical vapor deposition (CVD) at temperatures and pressures in the regions 1400-1800 K and 1000-10000 Pa, respectively. In this letter, we use van der Waals corrected density functional theory and thermodynamic stability calculations to determine the stability of r-BN and compare it to that of h-BN as well as to cubic BN and wurtzitic BN. We find that r-BN is the stable sp<sup>2</sup>-hybridized phase at CVD conditions, while h-BN is metastable. Thus, our calculations suggest that thin films of h-BN must be deposited far from thermal equilibrium.

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