isotropic

Examples of isotropic in the following topics:

• Emission

  • If the emitter is isotropic or the emitters are randomly oriented then the total power emitted per unit volume and unit frequency is
  • Often the emission is isotropic and it is convenient to define the emissivity of the material per unit mass
  • $\epsilon_\nu$ is simply related to $j_\nu$ for an isotropic emitter

• Flux

  • For example, if you have an isotropic source, the flux is constant across a spherical surface centered on the source, so you find that

• Eddington Approximation

  • In this region, the radiation field is nearly isotropic, but it need not be close to a blackbody distribution.
  • Because the intensity is close to isotropic we can approximate it by
  • which we found earlier to hold for strictly isotropic radiation fields.
  • The source function $S_\nu$ is isotropic, so let's average the radiative transfer equation over direction to yield

• Volume Expansion

  • Such substances that expand in all directions are called isotropic.
  • For isotropic materials, the area and linear coefficients may be calculated from the volumetric coefficient (discussed below).
  • For isotropic material, and for small expansions, the linear thermal expansion coefficient is one third the volumetric coefficient.

• A Physical Aside: Intensity and Flux

• Energy Density

  • But let's assume that the radiation field is isotropic, so $I = J$ for all directions, we get

• Inverse Compton Scattering

  • If we assume that the photon distribution is isotropic, the angle $\langle \cos\theta \rangle = 0$.

• Dipole Approximation

  • The factor of threes arise because we assume that the radiation is isotropic so the value of $E_x^2$ is typically one third of $E^2$ .

• Inverse Compton Spectra - Single Scattering

  • Let's suppose that we have an isotropic distribution of photons of a single energy $E_0$ and a beam of electrons traveling along the $x$-axis with energy $\gamma m c^2$ and density $N$.
  • Let's assume that there are many beams isotropically distributed, so we need to find the mean value of $j(E_f,\mu_f)$ over angle,
  • To be more precise, we could have relaxed the assumption that the scattering is isotropic and we would have found

• Relation to the flux