1 / 29

Bremsstrahlung

Bremsstrahlung. Rybicki & Lightman Chapter 5. Bremsstrahlung. “Free-free Emission” “Braking” Radiation. Radiation due to acceleration of charged particle by the Coulomb field of another charge. Relevant for (i) Collisions between unlike particles: changing dipole  emission

hei
Download Presentation

Bremsstrahlung

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bremsstrahlung Rybicki & Lightman Chapter 5

  2. Bremsstrahlung “Free-free Emission” “Braking” Radiation Radiation due to acceleration of charged particle by the Coulomb field of another charge. Relevant for (i) Collisions between unlike particles: changing dipole  emission e-e-, p-p interactions have no net dipole moment (ii) e- - ions dominate: acc(e-) > acc(ions) because m(e-) << m(ions) recall P~m-2  ion-ion brems is negligible

  3. Method of Attack: (1) emission from single e- pick rest frame of ion calculate dipole radiation correct for quantum effects (Gaunt factor) (2) Emission from collection of e-  thermal bremsstrahlung or non-thermal bremsstrahlung (3) Relativistic bremsstrahlung (Virtual Quanta)

  4. A qualitative picture

  5. Emission from Single-Speed Electrons e- v Electron moves past ion, assumed to be stationary. b= “impact parameter” b R Ze ion - Suppose the deviation of the e- path is negligible  small-angle scattering The dipole moment is a function of time during the encounter. - Recall that for dipole radiation where is the Fourier Transform of

  6. After some straight-forward algebra, (R&L pp. 156 – 157), one can derive in terms of impact parameter, b.

  7. Now, suppose you have a bunch of electrons, all with the same speed, v, which interact with a bunch of ions.

  8. Let ni = ion density (# ions/vol.) ne = electron density (# electrons / vol) The # of electrons incident on one ion is d/t # e-s /Vol around one ion, in terms of b

  9. So total emission/time/Vol/freq is Again, evaluating the integral is discussed in detail in R&L p. 157-158. We quote the result 

  10. Energy per volume per frequency per time due to bremsstrahlung for electrons, all with same velocity v. Gaunt factors are quantum mechanical corrections  function of e- energy, frequency Gaunt factors are tabulated (more later)

  11. Naturally, in most situations, you never have electrons with just one velocity v. Maxwell-Boltzmann Distribution  Thermal Bremsstrahlung Average the single speed expression for dW/dwdtdV over the Maxwell-Boltzmann distribution with temperature T: The result, with

  12. where In cgs units, we can write the emission coefficient ergs /s /cm3 /Hz Free-free emission coefficient

  13. Integrate over frequency: where In cgs: Ergs sec-1 cm-3

  14. The Gaunt factors - Analytical approximations exist to evaluate them - Tables exist you can look up - For most situations, so just take

  15. Handy table, from Tucker: Radiation Processes in Astrophysics

  16. Important Characteristics of Thermal Bremsstrahlung Emissivity (1) Usually optically thin. Then (2) is ~ constant with hν at low frequencies (3) falls of exponentially at

  17. Examples: Important in hot plasmas where the gas is mostly ionized, so that bound-free emission can be neglected. T (oK) Obs. of

  18. Bremsstrahlung (free-free) absorption Brems emission photon e- e- ion photon Inverse Bremss. free-free abs. e- collateral Recall the emission coefficient, jν, is related to the absorption coefficient αν for a thermal gas: is isotropic, so and thus in cgs:

  19. Important Characteristics of (1) (e.g. X-rays) Because of term, is very small unless ne is very large. in X-rays, thermal bremsstrahlung emission can be treated as optically thin (except in stellar interiors)

  20. (2) e.g. Radio: Rayleigh Jeans holds Absorption can be important, even for low ne in the radio regime.

  21. From Bradt’s book: BB spectrum is optically thick limit of Thermal Bremss.

  22. HII Regions, showing free-free absorption in their radio spectra:

  23. Spherical source of X-rays, radius R distance L=10 kpc flux F= 10 -8 erg cm-2 s-1 R&L Problem 5.2 (a) What is T? Assume optically thin, thermal bremsstrahlung. Turn-over in the spectrum at log hν (keV) ~ 2

  24. (b) Assume the cloud is in hydrostatic equilibrium around a central mass, M. Find M, and the density of the cloud, ρ Vol. emission coeff. Vol. 1/r2

  25. - Since T=109 K, the gas is completely ionized - Assume it is pure hydrogen, so ni = ne, then ρ=mass density, g/cm3 Z=1 since pure hydrogen (1)

  26. - Hydrostatic equilibrium  another constraint upon ρ, R Virial Theorem: For T=109 K (2) - Eqn (1) & (2)  Substituting L=10 kpc, F=10-8 erg cm-2 s-1

More Related