1. Fyzika tokamaků1: Úvod, opakování1 Tokamak Physics Jan Mlynář 5. Electromagnetic radiation from tokamaks Introduction, EM waves, cyclotron radiation, bremsstrahlung, power losses, atomic processes, excitation, ionisation and recombination, coronal equilibrium, impurity radiation, plasma regions, gamma radiation

2. Tokamak Physics2 Introduction 5: Electromagnetic radiation Electromagnetic radiation from tokamak plasmas in practice, EM waves cover a very broad energy spectrum Three (or four) major groups of EM radiation depending on its origin: collective EM radiation - plasma waves - turbulences, instabilities radiation of individual plasma particles - cyclotron radiation - bremsstrahlung - ionisation, recombination - excitation, deexcitation radiation due to nuclear reactions radiation due to interaction of fast particles with the vessel

3. Tokamak Physics3 Introduction 5: Electromagnetic radiation refractive index high-energy photons Size of experimental facility ~ meters Lower frequencies  electrostatic or magnetostatic phenomena

4. Tokamak Physics4 Dispersion in plasmas 5: Electromagnetic radiation linearised: Kronecker  Ohm’s law

5. Tokamak Physics5 Cyclotron radiation 5: Electromagnetic radiation !! cyclotron radiation is not a function of (electrons) n = 1, 2, 3 …. Harmonics due to circular orbit & relativistic effects non-zero line width due to imperfect field collisional broadening plasma interactions relativistic effects

6. Tokamak Physics6 Cyclotron radiation 5: Electromagnetic radiation

7. Tokamak Physics7 Cyclotron radiation 5: Electromagnetic radiation POWER LOSSES due to acceleration in an electric field electric dipole momentum cyclotron radiation: losses increase with velocity v electron losses >> ion losses plasma:

8. Tokamak Physics8 Cyclotron radiation 5: Electromagnetic radiation for thermonuclear parameters BUT for  ~ 10 GHz plasma is optically thick, strong re-absorption real power loss negligible & mainly on higher harmonics

9. Tokamak Physics9 Bremsstrahlung 5: Electromagnetic radiation Bremsstrahlung is the main radiation loss channel if H plasma is clean (in reality, line & recombination is worse) time duration of a collision energy loss due to bremsstrahlung

10. Tokamak Physics10 Bremsstrahlung 5: Electromagnetic radiation Maxwellian Kronecker  for cold ions

11. Tokamak Physics11 Bremsstrahlung, Cherenkov radiation 5: Electromagnetic radiation Bremsstrahlung spectrum & suprathermal particles are important ! Cherenkov radiation: Relativistic particles in

12. Tokamak Physics12 Atomic processes 5: Electromagnetic radiation Tokamak plasma: NOT in a global thermal equilibrium, plasma is transparent to radiation Figure: Example of a recombination spectrum General equilibrium condition

13. Tokamak Physics13 Atomic processes 5: Electromagnetic radiation I) Radiative bound – bound ~ line spectrum free – bound : recombination, photoionisation free – free: ~ bremsstrahlung II) Collisional electron impact excitation / deexcitation impact ionisation / 3-body recombination autoionisation / dielectronic recombination

14. Tokamak Physics14 Atomic processes in a plasma 5: Electromagnetic radiation

15. Tokamak Physics15 Coronal equilibrium 5: Electromagnetic radiation only spontaneous radiative emission only collisional excitation & ionisation only collisional ionisation & recombination sources [ s -1 ] sinks [ s -1 ] ionisation states: ionisation recombination

16. Tokamak Physics16 Ionisation and recombination 5: Electromagnetic radiation

17. Tokamak Physics17 Ionisation states 5: Electromagnetic radiation

18. Tokamak Physics18 Ionisation states 5: Electromagnetic radiation

19. Tokamak Physics19 Impurity radiation 5: Electromagnetic radiation Line excitation rate averaged over the Maxwellian Recombination: tabulated Impurities cause increased bremsstrahlung, and – even worse – recombination & line radiation. Tokamak plasmas may help to determine  1i

20. Tokamak Physics20 Power losses, ionisation states 5: Electromagnetic radiation

21. Tokamak Physics21 Limitations of the coronal model 5: Electromagnetic radiation some processes, e.g. autoionisation, prove important particle transport – diffusion of ion states into the centre There are limits of diagnostics – in particular, resolution line broadening & line shifts due to Doppler effect ~ T i ~ v ,v  Line splitting & polarisation due to B & E Zeeman effect Stark effect

22. Tokamak Physics22 Limitations of the coronal model 5: Electromagnetic radiation L I, 10 -6 eV  cm 3 s -1 Carbon cooling rate: Molybden:

23. Tokamak Physics23 Visible radiation 5: Electromagnetic radiation Region without line emission  only bremmstrahlung  measure of Z eff Plasma edge – visible radiation

24. Tokamak Physics24 UV and XUV spectra 5: Electromagnetic radiation Intermediate region – UV, XUV ~ 100 eV

25. Tokamak Physics25 SXR radiation 5: Electromagnetic radiation Tungsten All lines are emitted by tungsten, by Ge-like, Zn-like, Ni-like etc. ionisation states Plasma core – SXR~ keV

26. Tokamak Physics26 SXR from the plasma core 5: Electromagnetic radiation Mo line + suprathermal particles

27. Tokamak Physics27 Radiative cooling 5: Electromagnetic radiation q heat q rad q SOL  rad SOLRadiating edge T max LCFS Poloidal direction !! In a good thermonuclear plasma, radiation losses are low compared to the heat & particle transport !! Radiation losses can be substantial at the edge – GOOD, helps to make the wall power load homogeneous !

28. Tokamak Physics28 Gamma radiation 5: Electromagnetic radiation  photon is a product of a nuclear process (deexcitation of a nucleus) In tokamak plasmas,  s result form nuclear reactions on impurities (see the table in the next slide) ! NOTICE: Lots of X-rays and  s originate in the wall due to fast particles.

29. Tokamak Physics29 Gamma radiation 5: Electromagnetic radiation

30. Tokamak Physics305: Electromagnetic radiation

31. Tokamak Physics315: Electromagnetic radiation