Radiative transfer
Under radiation transport mean the description of the propagation of radiation (usually light Electromagnetic radiation as an example ) through a medium. Radiation transport plays an essential role especially in areas of astrophysics. So based the theory of stellar atmospheres, the formation of the stellar spectra, or the formation of interstellar line spectra to radiative transfer. Further radiation transport is also the understanding of spectroscopy in many other physical (for example, for analysis of plasma physics ) and technical (at different non-thermal light sources, for example ) areas required. A major role is played by the radiative transfer for the greenhouse effect of the earth's atmosphere.
- 7.1 Detailed literature and sources
The process
When electromagnetic radiation propagates through a medium (whether in the photon - viewing or field observation ), it is of the medium ( in particular, its atoms and ions) absorbed, scattered, or may leave the medium. These processes and the description of these processes is called radiative transfer. In this process, the radiation of different wavelengths according to the properties of the medium (in particular, the atoms and ions) affects different. Goal of a radiative transfer calculation is the light output to calculate (either as a whole or individual spectral range ) and the radiation field inside the medium; either predict a spectrum, or to draw conclusions to win on the composition of the medium.
Radiative transfer calculations in the real sense take into account the effects of radiation on the medium is limited. For example, the energy deposition is in the medium ( ie, its warming) by absorption in radiative transfer explicitly as little treatment as the cooling at the prevailing emission from the medium. If you use no other physical laws to einzubeschließen these effects, it is assumed that other processes (eg convection or conduction ) keep the temperature structure in the medium still constant. A physically more complete simulation therefore includes not only energy conservation and other laws of physics radiation transport as a part of the broader model.
The radiative transfer equation
The foundation of radiation transport is the radiative transfer equation. It links the radiance L of the absorption coefficient, the scattering coefficient and the emission power of j on the passing materials. The absorption and scattering coefficients as well as the emission power depends on, inter alia, upon the density and temperature of the material. In astrophysics, as in the following equations, however, the radiation density L is usually referred to with specific intensity I.
In a simple one-dimensional, time-independent form, it is:
In a very general form, it is along the direction
Since the emission performance of the material is partly caused by scattering, and because the variation in turn is an integral over the specific intensity to be calculated, the radiative transfer equation is an integro-differential equation.
It is usual to postulate the radiative transfer equation or derive either from a Boltzmann transport formalism for photons. Ultimately, however, then has to be postulated that photon transport can be described by the Boltzmann equation. Alternatively, one can derive the time-independent radiative transfer equation from the Maxwell equations, if one takes advantage of the microphysical properties of arbitrarily shaped and arbitrarily oriented, as well as independent scatterers.
Solution of the radiative transport equation
Analytically can indeed be called a formal solution of the radiative transfer equation specify. This is but ausformulierbar only for special cases in a real, workable solution.
The numerical solution of the radiative transfer equation is iA very expensive. The most modern and most stable method is the so-called " Accelerated Lambda Iteration ". Mathematically, this corresponds to a Gauss - Seidel method. For three-dimensional systems and easy absorption properties can the radiative transfer problem with Monte Carlo simulations to solve. A specially proven in engineering methods for three-dimensional systems with arbitrary properties is originally developed for the solution of the Boltzmann equation Discrete ordinates method.
Limiting cases
- For monochromatic light, and a non-self -emitting medium, the solution of the one-dimensional radiative transfer equation becomes the Lambert- Beer law.
- In the interior of stars, the so-called diffusion approximation is valid for the radiative transfer. With their help, can then be expressed as the integrated luminosity of the radiation density.
- For three-dimensional arrays also provide specific raytracing algorithms (see volume rendering or volume scattering ) an approximate solution of the radiative transfer problem dar.