Photon Distribution Function Research Articles

Energy exchange processes between electrons and photons in the strong radiation fields encountered in some astrophysical objects. II

On the basis of an analysis of studies made of single-photon Compton interaction between electrons and photons and its importance in the interpretation of the observational data on a number of astrophysical objects (nuclei of Seyfert galaxies, quasars, interstellar masers, the pulsar NP 0532, radio pulsars), three classes of fundamental problems are identified: A,B,C. It is shown that under the physical conditions existing in these astrophysical objects it is also necessary to take into account many-photon Comptonization processes, since the efficiency of these may be appreciably greater than that of the single-photon processes (for example, for the pulsar NP 0532 and for radio pulsars by one and two orders of magnitude). The present paper is devoted to a particular A problem - the relaxation of a nonequilibrium isotropic radiation field interacting with a nonrelativistic nondegenerate equilibrium electron gas through many-photon Compton scatterings. The introduction and use of a new concept, the ''effective photon,'' makes it possible to obtain a kinetic equation that describes the variation in time of the photon distribution function. By a direct calculation of the change in the total entropy of the electron-photon system it is shown that the kinetic equation satisfies Boltzmann's H theorem. Equations thatmore » describe the variation in time of the total exchange energy and the heating and cooling of the electron gas are also obtained.« less

Cooperative atomic interactions in a single-mode laser.

An equation of motion for the reduced density matrix for the field in a single-mode laser is derived when the single- and two-atom interactions are included. An exact steady-state solution for the photon distribution function is presented and some aspects of the photon statistics are discussed.

Exactly solvable three-level two-mode model with multiphoton transitions

The solutions of the equations of motion for the level population and photon number operators are obtained. The characteristic and photon distribution functions, the statistical moments of photon numbers and the correlations of modes are found.

Kinetics of radiation spectrum of multimode laser with fast relaxing active medium

The authors explain that for analyzing the spectrum kinetics of a multimode laser with fast relaxing active medium, the most general assumptions are made regarding the dispersion characteristics of the resonator, the time characteristics of pumping power and energy losses, and the location as well as the dimensions of the active medium. The equations of balance during the transient period revealed, upon analysis, the form of the modal photon distribution function and help reduce the problem from evolution of the spectrum to dynamics of the reference mode. Several special cases of practical importance are also considered such as a low level above the emission threshold and various specific dispersion characteristics of the resonator.

Photon statistics and atomic dynamics in a three-level plus two-mode model

The relations between photon statistical characteristics and atomic level populations are examined rigorously. The characteristic and photon distribution functions are found.

Quantum-chromodynamic corrections to deep-inelastic Compton scattering

Deep-inelastic Compton scattering is a potentially useful source of information concerning the short-distance structure of hadrons. We present here results for several types of corrections to the basic Compton subprocess. Contributions from subprocesses involving photon distribution and fragmentation functions are shown to be small in the high-${p}_{T}$ region in the leading-logarithm approximation. The next-to-leading-order corrections from the subprocesses $\ensuremath{\gamma}q\ensuremath{\rightarrow}\ensuremath{\gamma}\mathrm{qg}$ and $\ensuremath{\gamma}g\ensuremath{\rightarrow}\ensuremath{\gamma}q\overline{q}$ are also calculated and found to be small over a wide rapidity range for large ${p}_{T}$ values. These small corrections suggest that the deep-inelastic Compton process will indeed be a useful reaction to measure.

Double Compton emission in radiation dominated thermal plasmas

view Abstract Citations (106) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Double Compton emission in radiation dominated thermal plasmas Lightman, A. P. Abstract We investigate the process of double Compton (DC) emission and absorption, γ + e ⇔ γ + γ + e. We derive the kinetic equation for this process in a nonrelativistic, thermal plasma and give analytic and detailed numerical solutions of this equation coupled with the Kompaneets equation, which describes redistribution of photons through γ + e → γ + e. The photon distribution function evolves in an approximately self-similar manner. In infinite media, DC achieves a Planck distribution sooner than bremsstrahlung when the ion density satisfies nι < 1030 cm-3 (kT/mc2)11/2. In general, DC will dominate bremsstrahlung as a source of photons in a sufficiently radiation dominated plasma, nγ/nι > 0.1(mc2/kT)5/2. Under the double Compton process, the photon density increases to its equilibrium value almost exponentially in time, on a time scale tDC = τc(π/8α)(mc2/kT)2, where τc = (neσTc)-1 is the ordinary Compton scattering time and α is the fine-structure constant. We also consider the emitted radiation spectrum and time evolution of the double Compton process in a finite medium. The photon number density always adjusts itself so that a finite plasma is just" critical," and this equilibrium solution is stable. A characteristic plasma parameter for the double Compton process under equilibrium conditions is ξDC ≡ (8α/π)τes2 )tes2 (kT/mc2)2, where τes is the electron scattering optical depth. In an effectively thin, DC dominated medium the equilibrium photon density depends exponentially on ξDC. The double Compton process may have applications in high energy astrophysical phenomena and in cosmology, before recombination. Publication: The Astrophysical Journal Pub Date: March 1981 DOI: 10.1086/158716 Bibcode: 1981ApJ...244..392L Keywords: Compton Effect; Cosmic Plasma; Photon Density; Plasma Radiation; Radiative Transfer; Thermal Plasmas; X Ray Spectra; Astrophysics; Bremsstrahlung; Electron Radiation; Gamma Rays; Particle Collisions; Particle Density (Concentration); Plasma Equilibrium; Quantum Statistics; Astrophysics full text sources ADS |

QCD predictions for the distribution functions of the photon using Altarelli-Parisi type equations

In a leading approximation, the distribution functions of the photon are investigated using Altarelli-Parisi type equations including point-like and hadron-like components. Using a new method to make a Mellin transformation, the full inhomogeneous equation is solved numerically. The point-like and hadron-like parts of photon distribution function are discussed separately. The point-like part has a form ƒ(x, t) In Q 2 , where t = In Q 2. Analytic expressions for the photon distribution functions near x = 1 and x = 0 are also given. These results are compared with others which have been given using other methods.

Tests of quantum chromodynamics in two-photon collisions and high-pTphoton production

We use the diagrammatic approach to scale breaking to rederive the results of the renormalization-group approach to two-photon, ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}$, collisions, where one of the photons is highly virtual and the other nearly real. In an axial gauge only ladder diagrams contribute to leading-logarithmic accuracy. When interpreted in terms of the quark distribution of the real photon we obtain the result ${G}_{\frac{q}{\ensuremath{\gamma}}}({q}^{2},x)=[\frac{\ensuremath{\alpha}}{{\ensuremath{\alpha}}_{s}({q}^{2})}]{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}_{q}(x)+O(1)$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}_{q}(x)$ is an exactly calculable scaling function. By virtue of the fact that only ladder diagrams contribute in leading-logarithmic accuracy for this and other short-distance photon-target probes, we find that this form for ${G}_{\frac{q}{\ensuremath{\gamma}}}$ can be employed (to leading-logarithmic accuracy) in any short-distance application involving a photon target. We give a summary of these additional applications with emphasis on high-transverse-momentum phenomena. We present also estimates of the vector-dominance background to the pointlike component of the photon distribution function. In addition we present a convenient summary of leading-logarithmic quantum-chromodynamic corrections including dominant $x\ensuremath{\rightarrow}1$ behaviors.

Antibunching: more than one kind in two-photon absorption

Properties of the second moment of the photon distribution and intensity autocorrelation function are examined in a system undergoing only two-photon transitions. These properties are interpreted in terms of two kinds of antibunching, strict and temporal. It is shown that antibunching is a richer class of phenomena than usually supposed and that temporal antibunching may be easier to observe than the strict antibunching usually considered.

Effect of relaxation parameters on the quantum theory of a detuned laser with inhomogeneous broadening

The results of the quantum theory of a laser given by Riska and Stenholm (see ibid., vol.3, p.536 (1970)) for the case of inhomogeneous broadening and detuning are re-derived by avoiding the Doppler limit approximation to show the exact influence of relaxation parameters on the theory. The threshold condition is seen to be dependent on gamma ab/ku where gamma ab is the relaxation parameter and ku the Doppler parameter. Its value is found to be higher than earlier results. It is noted that the photon distribution function at resonance is much closer to the corresponding distribution obtained from exact calculations for the tuned case. The photon number at the peak of the distribution curve is much lower than earlier values for comparable situations.

Nonlinear stability of spin-flip excitations

A rather complete discussion of the nonlinear electrodynamic behavior of a negative-temperature spin system is presented. The method presented here is based on a coupled set of master equations, one describing the time evolution of the photon (i.e., the spin-flip excitation) distribution function and the other describing the time evolution of the particle distribution function. It is found that the initially unstable (i.e., growing) sping-flip excitations grow to such a large amplitude that their nonlinear reaction on the particle distribution function becomes important. It is then shown that the initially totally inverted two-level spin system evolves rapidly (through this nonlinear photon-particle coupling) towards a quasilinear steady state where the populations of the spin-up and the spin-down states are equal to each other. Explicit expressions for the time taken to reach this quasilinear steady state and the energy in the spin-flip excitations at this state are also presented.

Primeval Adiabatic Perturbation in an Expanding Universe

view Abstract Citations (1093) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Primeval Adiabatic Perturbation in an Expanding Universe Peebles, P. J. E. ; Yu, J. T. Abstract The general qualitative behavior of linear, first-order density perturbations in a Friedmann-Lemaitre cosmological model with radiation and matter has been known for some time in the various limiting situations. An exact quantitative calculation which traces tbe entire history of the density fluctuations is lacking because the usual approximations of a very short photon mean free path before plasma recombination, and a very long mean free path after, are inadequate. We present here results of the direct integration of the collision equation of the photon distribution function, which enable us to treat in detail the complicated regime of plasma recombination. Starting from an assumed initial power spectrum well before recombination, we obtain a final spectrum of density perturbations after recombination. The calculations are carried out for several general-relativity models and one scalar-tensor model. One can identify two characteristic masses in the final power spectrum: one is the mass within the Hubble radius ct at recombination, and the other results from the linear dissipation of the perturbations prior to recombination. Conceivably the first of these numbers is associated with the great rich clusters of galaxies, the second with the large galaxies. We compute also the expected residual irregularity in the radiation from the primeval fireball. If we assume that (1) the rich clusters formed from an initially adiabatic perturbation and (2) the fireball radiation has not been seriously perturbed after the epoch of recombination of the primeval plasma, then with an angular resolution of t minute of arc the rms fluctuation in antenna temperature should be at least T7T = 0.00015. Publication: The Astrophysical Journal Pub Date: December 1970 DOI: 10.1086/150713 Bibcode: 1970ApJ...162..815P full text sources ADS |

Approach to Radiative Equilibrium of Free Electrons through Čerenkov Emission and Absorption

The approach to radiative equilibrium of a system of free electrons in a background medium whose index of refraction is larger than unity is studied in the light of the basic principles of elementary nonrelativistic quantum theory. It is shown that the radiative equilibrium arises as a consequence of a balance between Čerenkov emission (spontaneous plus the induced emission) and absorption of photons by the uniformly moving electrons. A coupled pair of equations, one describing the time evolution of the photon distribution function and the other describing the time evolution of the electron distribution function, is thus derived. The equation for the time rate of change of the electron distribution function reduces, in the classical limit, to a Fokker-Planck equation.

Radiative Transfer in Dispersive Media

The equation of radiative transfer in a dispersive medium is derived from the equation of continuity for the photon distribution function. The properties of the medium are allowed to depend upon both position and time

Equation of motion for the photon distribution function derived from the laser masterequation

From the complete laser masterequation for atoms and field, an equation of motion for the fiels distribution function is derived, which differs from the semiclassical Fokker-Planck equation [1.2] by second order time derivatives. The solutions of both equations are compared.

Determination of the photon distribution function in vacuo for the case of multiple reflections at a boundary

Determination of the photon distribution function in vacuo for the case of multiple reflections at a boundary

Radiative Equilibrium of a Free-Electron Gas in a Uniform Magnetic Field

In this paper the subject of radiative equilibrium of a free-electron gas in a uniform magnetic field is studied on the basis of Landau's quantized particle motion of the electrons and the "Golden Rule" of time-dependent perturbation theory. The analysis presented here is somewhat analogous to the quantum theory of blackbody radiation. It is shown that the radiative equilibrium between electrons and their radiation field arises as a consequence of a balance between the two competing processes: photon emission (spontaneous plus induced or stimulated emission) and photon absorption. A coupled set of equations, one describing the time evolution of the photon distribution function and the other describing the time evolution of the electron distribution function, is thus derived. A simple closed-form solution of the equation for the time rate of change of the photon distribution function is presented for situations where absorption exceeeds the stimulated emission. This solution yields equations for the steady-state photon number density and the radiative relaxation time. It is shown that the steady-state photon number density is the familiar distribution function corresponding to Bose-Einstein statistics for "complete thermodynamic equilibrium." The conditions for the existence of overstabilities near the cyclotron frequency and its harmonics are also discussed. The equation for the time rate of change of the electron distribution function reduces, in the classical limit, to a Fokker-Planck equation in which there appear the usual "diffusion" and "dynamical friction" terms. In the classical limit, it is shown that this coupled set of equations (one describing the time evolution of the electromagnetic energy density and the other describing the time evolution of the electron distribution function) is self-consistent, by proving that the average rate of loss of $z$ momentum of the electrons as predicted by one equation is equal to the average rate of gain of $z$ momentum of their radiation field as predicted by the other equation. The $z$ axis is chosen to be along the uniform magnetic field.

Photon Emission from Irradiated Dielectric Slabs

In this paper a simple derivation is given of the distribution of photons emitted when an energetic charged particle passes through a thin layer of dielectric material. This derivation emphasizes the individual microscopic events which occur during such a process. The distribution function is shown to agree with that obtainable from the transition radiation theory of Frank and Ginzburg and from the plasmon decay theory of Ferrell for the case of a thin foil. The special case of a double foil bounded by vacuum is considered in detail, and a general formula is found for the photon distribution function. An approximation analogous to that of Born's in quantum mechanics is developed to treat the case of a general composite foil whose thickness is small compared with λ but which may be large compared with vλ/c, where λ is the wavelength of the light emitted and v is the speed of the charged particle.