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

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

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

Is it a problem?

Bunching mechanism

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

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

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

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

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

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

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

…So what? Non equilibrium and stimulated light amplification

…So what??? Solution

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

… Optical Pumping Cavity Confinement

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

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

Evolution, Intracavity Equilibrium & Output Power .

Outcoupled power The presence of losses allows the intracavity power extraction

Efficiency

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

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

Relativistic Kinematics in a nut shell Ultrarelativitic

… «Newton» equations

The Power of a charged beam Ohm Law Pump Power

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

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

Back to Relativistic Equation Lorenz Force

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

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

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

…Gain a balance mechanism between emission and absorption .

…More In general

… FEL pumping power=Electron beam power

…FEL Saturation Intensity .

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

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?

Bunching and non linear Harmonic Generation .

High-gain «no cavity» .

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

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

…

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

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