Quantum Effects in Compton Backscattering R Bonifacio Outline

Quantum Effects in Compton Backscattering R. Bonifacio

Outline 1. Compton Red-Shift 2. Novel Quantum Statistical Model 3. Classical and Quantum Limit 4. Implications for ELI-NP: Q. C. S.

Introduction Conceptual design : Compton back-scattering High power laser + relativistic e-beam Backscattered field Laser “wiggler” l. L lr

Compton backscattering shift Electron rest frame: (1) Lab frame: (2) Compton shift parameter: ELI-NP Å

Spontaneous Emission : Quantum Model Spontaneous emission – Why? – random emission of photons leads to growth of energy spread spontaneous emission is a random process - after a distance z through wiggler, different electrons emit different numbers of photons - different number of recoils = momentum/energy spread

Spontaneous Emission Models Previous models (Saldin, Madey) predict diffusive growth of energy spread due to spontaneous emission i. e. Our model – can use Poisson process argument or physical argument

Spontaneous Emission Models Physical argument – consider ensemble described by distribution function will be increased by electrons with momentum p+hk emitting photons will be decreased by electrons with momentum p emitting photons

Spontaneous Emission Models Where R = spontaneous rate of emission of photons From Jackson (a 0 << 1) a = fine structure constant = 1/137

Spontaneous Emission Models can be expressed in terms of the emitted number of photons, N, using the change of variable so which is the master equation for a Poisson process with solution Quantum Coherence where so

Quantum Recoil Parameter We define classical and quantum regimes The parameter we use to identify the different regimes is the “quantum recoil parameter” : Classical regime : Quantum effects

Spontaneous Emission Models In scaled notation : where: and , so: Note that when : (Saldin et al. ) Drift Diffusion

Spontaneous Emission Model – Momentum Evolution Classical limit : Model produces diffusive growth of spread in classical limit – results of Saldin & Madey can also be recovered analytically

Spontaneous Emission Models Quantum limit : Momentum distribution is a series of discrete lines separated by i. e. in unscaled units spacing is ħk.

Spontaneous Emission Model – Momentum Evolution Quantum limit with large initial spread: Initial momentum spread > spacing between momentum levels Discreteness of momentum states is lost

Condition for Discrete Lines I ) Compton Shift negligible if II ) Discrete lines if I ) and II ) compatible if ELI-NP: Å

Conclusions Continuous Classical drift-diffusion process Discrete Lines Centered on Poisson distribution ELI: NP if NOVEL QUANTUM EFFECT OBSERVABLE Quantum Compton Source Q. C. S. G. Robb and R. Bonifacio, EPL 94 34002 (2011)

Coherent and Spontaneous Emission Coherent Spontaneous emission parameter For sufficiently large b, spontaneous emission kills FEL gain if