Beam Shape Effects in Non Linear Compton Scattering Signatures of High Intensity QED Daniel Seipt with T. Heinzl and B. Kämpfer Introduction QED vs. classical calculations, Multi Photon radiation Temporal pulse shape and subharmonics Observability of subharmonics Text optional: Institutsname Prof. Dr. Hans Mustermann www.fzd.de Mitglied der Leibniz-Gemeinschaft
High Intensity Lasers & Non linear Effects
ELBE electrons & DRACO laser @ FZD ELBE = Electron Linac with high Brilliance and low Emittance DRACO = Dresden Laser Acceleration Source Compton Scattering Experiments
Compton Scattering: Basics (linear regime) Doppler upshift of optical frequency generates X ray radiation: ELBE DRACO X ray Inverse Compton Scattering Prospects of Compton/Thomson X ray source at FZD observation of harmonic radiation (energy spectrum) study of short pulse effects
Comparison of two possible Descriptions Compton Scattering Thomson Scattering k'=!'n' u,q q' = decay of Volkov electron = laser dressed quasi particle photon momentum k=!n difference: electron recoil no recoil quasi momentum, effective mass
Thomson scattering vs. sqed Compton scattering Recoil expansion of Compton cross section and frequency electron recoil parameter: related to relativistic invariant: relative difference in frequency total cross section
Non linear Compton Scattering Feynman diagrams, (+ crossed diagrams) k' q vs. q' pqed only lowest order sqed effects: harmonic radiation for l = 2,3,... quasi momentum effective electron mass redshift Volkov states Multi Photon Emission
Entangled 2 Photon Radiation production of entangled photon pairs 2 particle decay of Volkov electrons total Compton rate as cutoff for divergences Schützhold (PRL,2008): Unruh radiation only for a0 << 1 (linear) Kinematic separation from 1photon radiation necessary 1 photon radiation as background Matrix Element Emission rate Courtesy Schützhold et.al.
Differential Cross Section circular polarization: angular dependence energy dependence a0= 10 5 a0 = 1 2 1 KN Red shift of Compton edge dead cone (only fundamental harmonic in backscattering direction) (circular) maxima of higher harmonics at larger angles > observation critical a 0,cr :
Non linear Compton Scattering: pqed vs. sqed total emission probability Ug az pqed sqed a in si h N in e Kl l=1 Goldman 2 3 4 Production of harmonics Red shift of Compton edge Reduced total emission probability Now: pulse shape effects
Temporal pulse: Subharmonic Structures plane wave + envelope + circular polarization temporal envelope spectral density in backscattering direction ( µ=0 ): electron current Fourier transformation Deformation of phase w.r.t. proper time Interference > Harmonic Substructures [F. Hartemann, G. Krafft]
Subharmonics # of peaks strongly depends on and T
Transverse beam structure: focus geometry Necessary to minimize transverse effects to observe subharmonics transverse intensity profile (e.g. Gaussian) Ponderomotive Force fixed pulse energy and pulse length i.e. 3J, 25 fs, 40 MeV
Simulation (100TW, 3J, 20fs): small laser focus circular broad spectrum harmonics not visible substructures not visible
Simulation (100TW, 3J, 20fs): large laser focus circular well separated spectral peaks harmonics clearly visible substructures visible
Transverse beam structure: focus geometry Laser pulse Electron bunch parameters What about energy spread and emittance?
Electron beam parameters Include important effects of electron beam phase space: energy spread divergence angle emittance fixed n and n'
Spectral density depends on initial conditions How does spectral density change when changing the scattering geometry?
Scaling Law for spectral density frequency rescaling factor transition function only depends on kinematical quantities (initial values) contains Jacobian (radiation is peaked in direction u ) long laser pulses for, i.e. only change energy exact relation for
Scaling Law for spectral density frequency rescaling factor transition function Remember: only depends on kinematical quantities (initial values) is normalized contains Jacobian (radiationscattered is peakedfrequency in direction u ) long laser pulses for, i.e. only change energy exact relation for
Scaling Law for spectral density frequency rescaling factor transition function only depends on kinematical quantities (initial values) contains Jacobian (radiation is peaked in direction u ) long laser pulses for, i.e. only change energy exact relation for
Warm spectral density Incoherent superposition (test particles, statistical ensemble) Convolution with phase space distribution function Normalized electron phase space distribution functions, e.g. Degradation of spectral density
Warm Spectral Density: Results Comparison between numerical results (Ne= 1000) and scaling
Systematics of Degradation effects energy spread symmetric emittance always lower energy highest energy for head on collisions
Nonlinear regime Replace scaling still perfect,' scaling only for small changes of angles scaling also works in non linear regime for typical electron bunches!!!
Observation of Subpeaks possible? ELBE LWFA proposed Extremely good quality of electron beam required
Summary and Outlook Non linear Compton backscattering Thomson scattering: recoil neglected Temporal envelope: Broadening of spectral peaks and substructures Focus geometry: ponderomotive effects Electron beam parameters: Scaling Law, very low emittance and energy spread needed Possible observation of substructures Entangled 2 photon Radiation
BACKUP
Definition of normalized vector potential amplitude polarization spatial & temporal structure Benefits of this Definition: coincides up to factor with usual definition for plane waves constant value for pulsed fields same value for linear and circular polarization if normalized
Scaling Law for spectral density frequency rescaling factor transition function
Entangled 2 Photon Radiation production of entangled photon pairs 2 particle decay of Volkov electrons total Compton rate cutoff for divergences Schützhold (PRL,2008): Unruh radiation only for a0 << 1 (linear) Kinematic separation from 1photon radiation necessary
Radiation patterns dead cone for circular polarization z x y
Time structure of X ray pulse circular polarization linear polarization spectral broadening: chirp in time domain
Strong Field QED and Volkov States coherent state: matrix elements: Lagrangian: Modification of electron states and electron propagator through background field Furry Picture
Nonlinear Compton Scattering competing diagrams = same harmonic, but higher order in pqed + +... permanent absorption and re emission of laser photons into laser mode (blue) large number of photons in IN state: depletion of photons negligible as classical as possible ) coherent state
Classical Trajectory (plane wave + temporal envelope) constant of motion: light cone variable for strongly resembles structure in exponential of Volkov state quasi momentum effective mass quasi momentum reflects non linear classical motion: drift velocity, figure 8
Strong Field QED and Volkov States non perturbative background field BUT: only plane wave Volkov states: S is classical action of a particle in an electromagnetic wave k
Properties of Volkov Electrons averaging: quasi momentum: effective electron mass: Matrix element for Non linear Compton Scattering: k' q q' I.I. Goldman: contains all harmonics contains interaction with laser field to all orders Decay of Volkov electron
circular linear
Thomson scattering: temporal structure non linear spectral density linear spectral density linear Compton edge: 36,7 kev nonlinear Compton edge: 24,5 kev
Smooth Gaussian Pulse vs. Box Profile Gaussian profile Box profile inherently non linear effect Fourier content of laser pulse, also for Completely different spectral distributions, strong dependence on pulse shape Are substructures observable in experiments? ) Rest of Talk.