1. Free Electron Sources of CoherentRadiation: FREE ELECTRON LASERS
Giuseppe Dattoli
ENEA FRASCATI

2. FAQ Is the The Free Electron “Laser” (FEL) a laser?
Or is it a Klystron-Gyrotron-Carm… ?

3. 1-st-FAQ
Is it a laser?
The relevant active medium is not an atomic or a molecular system
It is provided by a relativitic electron beam moving in a magnetic undulator

4. Is it a problem?

5. Bunching mechanism

6. A Small Hystoric Abuse
Laser physics started with quantum mechanics, (Planck law of "blackbody" radiation)
Such a system absorbs all the incident radiation and emits with a spectrum which only depends on its temperature. A perfectly reflective cavity with a little hole can be considered as a blackbody, its radiated energy resulting from the standing wave or resonant modes of this cavity

7. 1900 Plank Black-Body Theory
energy per unit surface, per unit time, emitted in the frequency interval

8. Wien Law
Wien's displacement law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature

9. A «Two Level System» Any quantum system with two states of energy
With probability B2,1
The excitation of the system to the higher state can result, with a given probability, from the absorption of a photon of suitable energy

10. Spontaneuos Emission
If the system is in the excited state 2, it can decay to the lower state spontaneously, according to the emission of a photon of the same energy as the energy absorbed.
With probability A1,2

11. Stimulated Emission
The decay process may be induced (with a given probability ) probability in the presence of a photon of energy equal to the energy difference between the two states.
With probability B2,1

12. Einstein Coefficients
consider a system of N atoms, among which N1 are in the lower state and N2 in the higher state ( N1 + N2 = N ), in interaction with an electromagnetic field of intensity I . The equilibrium condition of the atomic system- radiation is

13. …So what?
Non equilibrium and stimulated light amplification

14. …So what???
Solution

15. Something is emerging the number of photons remains constant
Population inversion has occurred when N2>N1 accordingly the coefficient α can be interpreted as a gain coefficient per unit length

16. …
Optical Pumping
Cavity Confinement

17. Modelling the evolution inside the optical cavity
n=round trip number

18. Saturation: introduction of non linear effects.
Is=Saturation Intensity

19. Evolution, Intracavity Equilibrium & Output Power.

20. Outcoupled power
The presence of losses allows the intracavity power extraction

21. Efficiency

22. Synchrotron Radiation an old story started before Laser
Radiation emitted by charged particles moving in magnets

23. Free Electron «Laser» (FEL)
A «Relativistic» electron beam is injected inside an «undulator» magnet
the adjective relativistic refers to a particle or a system whose velocity is close to the light velocity

24. Relativistic Kinematics in a nut shell
Ultrarelativitic

25. …
«Newton» equations

26. The Power of a charged beam
Ohm Law
Pump Power

27. Laser Mechanisms A) Spontaneous emission B) Stimulated Emission
C) Absorption
Can we recognize them in FEL devices?

28. 1) Frequency selection
Spontenerous emission a kind of Compton back-Scattering
Weiszecker-Williams approximation

29. Back to Relativistic Equation
Lorenz Force

30. Frequency selection
In inverted systems the wavelength is fixed by the Quantum Jump

31. So what happens for FEL?
Electrons and photons move at different speeds

32. 2-Gain Mechanism
The radiation pulse at the end of the undulator has the structure of a step function

33. …Gain a balance mechanism between emission and absorption.

34. …More In general

35. …
FEL pumping power=Electron beam power

36. …FEL Saturation Intensity.

37. Intracavity growth
Intracavity Intensity builds up from noise to saturation in «n» passes and its growth can be modelled through the equation

38. Wrap up !!!! FEL spontanous emission YES FEL stimulated Emission YES
FEL GAIN YES
FEL saturation intensity YES
FEL pumping power YES
FEL efficiency YES
Is The FEL a laser?
Answer NO!!! What about coherence?

39. Bunching and non linear Harmonic Generation.

40. High-gain «no cavity» .

41. 2-nd (but not last) FAC Is the FEL a …?
Klystron, Gyrotron, CARM or more in General a TWT….

42. Klystron (in a nut shell…)
The key mechanisms that account for klystron gain and RF power generation is the “electron beam modulation”

43. …

44. Catcher Cavity Output Power
Rsho = wall resistance of catcher cavity
RB = beam loading resistance
RL = external load resistance
RSH = effective Shunt resistance
I2 = If = fundamental component of the beam current at the catcher cavity
V2 = fundamental component of the catcher gap voltage
Output power delivered to the catcher and the load is given by

45. May be at the end of nex talk….
Conclusions…
May be at the end of nex talk….