Planck radiation model

The experimental results were analyzed using an integrated approach. To obtain the temporal evolution of the temperature and the density profiles of the bulk plasma, the experimental hot-electron temperature was used as an initial condition for the 1D-FP code [26]. The number of hot electrons in the distribution function were adjusted according to the assumed laser absorption. The FP code is coupled to the 1-D radiation hydrodynamic simulation ILESTA [27]. The electron (or ion) heating rate from hot electrons is first calculated by the Fokker-Planck transport model and is then added to the energy equation for the electrons (or ions) in ILESTA-1D. Results were then used to drive an atomic kinetics package [28] to obtain the temporal evolution of the Ka lines from partially ionized Cl ions. 

In 1900, Max Planck (1858-1947) discovered a formula (now often called the Planck radiation law) that modeled curves like those shown in Figure 24-21 nearly perfectly. He followed this discoveiy by developing a theory that made two bold assumptions regarding the oscillating atoms or molecules in blackbody radiators. He assumed (1) that these species could have only discrete energies and (2) that they could absorb or emit energy in discrete units, or quanta. These assumptions, which are implicit in Equation 24-3, laid the foundation for the development of quantum theory and eventually won him the Nobel Prize in Physics in 1918. 

The Bose-Einstein distribution (1.162) may be considered to recover the Planck law of black body radiation, i.e., the photon radiation modeling, by considering the following peculiarities ... 

Using Bohr s model, one could calculate the energy difference between orbits of an electron in a hydrogen atom with Planck s equation. In the example of a system with only two possible orbits, the equation of the emitted radiation as the electron went from a higher energy state 2 to a lower one j would be - E = hf, where h is Planck s constant and/is the frequency of the emitted radiation. 

In order to understand these observations it is necessary to resort to quantum mechanics, based on Planck s postulate that energy is quantized in units of E = hv and the Bohr frequency condition that requires an exact match between level spacings and the frequency of emitted radiation, hv = Eupper — Ei0wer. The mathematical models are comparatively simple and in all cases appropriate energy levels can be obtained from one-dimensional wave equations. 

With a nonzero rest mass one would at a first glance expect a photon gas to have three degrees of freedom two transverse and one longitudinal. This would alter Planck s radiation law by a factor of, in contradiction with experience [20]. A detailed analysis based on the Proca equation shows, however, that the B3 spin field cannot be involved in a process of light absorbtion [5]. This is also made plausible by the present model of Sections VII and VIII, where the spin field is carried away by the pilot field. As a result, Planck s law is recovered in all practical cases [20]. In this connection it has also to be observed that transverse photons cannot penetrate the walls of a cavity, whereas this is the case for longitudinal photons which would then not contribute to the thermal equilibrium [43]. 

Figure 16.8. Relic density of gravitationally-produced WIMPZILLAs as a function of their mass Mx Hi is the Hubble parameter at the end of inflation, 1 i, is the reheating temperature, and Mpi 3 x 1019 GeV is the Planck mass. The dashed and solid lines correspond to inflationary models that smoothly end into a radiation or matter dominated epoch, respectively. The dotted line is a thermal distribution at the temperature indicated. Outside the thermalization region WIMPZILLAs cannot reach thermal equilibrium. (Figure from Chung, Kolb Riotto (1998).)...

Planck s constant was discovered as part of the solution to a nineteenth century conundrum in physics, known as the black-body problem. The challenge was to model the wavelength distribution of radiation emitted through the aperture in a closed cavity at various temperatures6. The standard equations of statistical thermodynamics failed to produce the observed spectrum, unless it was assumed that the energy of radiation with frequency v was an integral multiple of an elementary energy quantum hv. 

Niels Bohr incorporated Planck s quantum concept into Rutherford s model of the atom in 1913 to explain the discrete frequencies of radiation emitted and absorbed by atoms with one electron (H, He+, and Li2+). This electron is attracted to the positive nucleus and is closest to the nucleus at the ground state of the atom. When the electron absorbs energy, it moves into an orbit further from the nucleus and the atom is said to be in an electronically excited state. If sufficient energy is absorbed, the electron separates from the nucleus entirely, and the atom is ionized ... 

The story of the evolution of physics in the twentieth century is the story of the elaboration and acceptance of a wave-mechanical conception of the primary nature of matter. No model of matter can fail to take into account that contemporary physics has recaptured a Pythagorean intuition too long forgotten by the followers of the commonsense physics of Newton. Common sense is gone from physics Planck banished it when he discovered the discrete nature of radiation, and Heisenberg s Principle of Uncertainty made a return to the notion of simple location forever impossible. Our own theory is thoroughly kymatic, or wavelike. 

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