PHASE RETRIEVAL OF COTR SIGNALS FOR THE RECONSTRUCTION OF THREE-DIMENSIONAL MICROBUNCHING

A. Marinelli University of California, Los

Angeles

SLAC April 14th 2011

OUTLINE Transverse structures in high-brightness

electron beams. Phase retrieval from intensity measurements. Application to coherent optical transition

radiation. Experiments at NLCTA

ONE-DIMENSIONAL VS THREE-DIMENSIONAL MICROBUNCHINGMicrobunching is often described as a one-dimensional entity:

€

b(k) =1N

e−ikzn∑ =1N

ρ∫ (x,y,z)e−ikzdxdydz

By integrating over x-y we lose track of any transverse dependence of the density modulation

In many applications it is necessary to keep record of the transverse distribution:

€

b(x,y,kz ) =1N

ρ∫ (x,y,z)e−ikz zdz

B(kx,ky,kz) =1N

ρ∫ (x,y,z)e−ikxx−ikyy−ikz zdz

Microbunching in X-space

Microbunching in K-space

THREE-DIMENSIONAL MICROBUNCHING:LONGITUDINAL SPACE-CHARGE INSTABILITY

Transversely incoherent space-charge fields

Transversely inhomogeneous microbunching

THREE-DIMENSIONAL MICROBUNCHING:ORBITAL ANGULAR MOMENTUM MODES

Helical charge perturbation from harmonic interaction in a helical undulator:

€

ρ ∝ re−

r 2

2w 2−iφ

(to be published on PRL)

OPTICAL REPLICA SYNTHESIZER

Microbunching induced by laser-beam interaction in undulator.

If and

The microbunching distribution is a replica of the beam’s transverse charge distribution.€

Rlaser >> Rbeam

€

llaser >> lbeam

Method for the determination of the three-dimensional structure of ultrashort relativistic electron bunchesGianluca Geloni, Petr Ilinski, Evgeni Saldin, Evgeni Schneidmiller, Mikhail Yurkov

arXiv:0905.1619v1 [physics.optics]

COTR DIAGNOSTIC FOR THREE-DIMENSIONAL MICROBUNCHING

€

b(x,y,k) = e−ikz z∫ ρ (x,y,z)dz

In these applications, it is interesting to reconstruct the transverse structure of the density modulation in amplitude and phase:

Ingredients:

-Narrow bandwidth signal is needed(seeding or bandpass filtering)-Near or far field imaging?

Near field is hard to interpret:1)near field COTR is a convolution between b and the OTR Green’s function.2) Intensity pattern mixes two polarizations!

COTR DIAGNOSTIC FOR THREE-DIMENSIONAL MICROBUNCHING: FAR FIELD IMAGING

dddP

From a single-frequency far-field measurement we can recoverWe are interested in

Phase information on B is needed to recover the signal in x-y space!!

HOW IMPORTANT IS KNOWLEDGE OF PHASE?

€

IFFT(ObamaK e iArg (ObamaK ))=Obama(X,Y )

€

IFFT(McCainK e iArg(McCainK ))= McCain(X,Y)

HOW IMPORTANT IS KNOWLEDGE OF PHASE?

€

IFFT(ObamaK e iArg (McCainK ))≈ McCain(X,Y)

€

IFFT(McCainK e iArg(ObamaK ))≈Obama(X,Y)

Phase carries most of the

information!!

PHASE RETRIEVAL ALGORITHMS Phase information can be recovered by means of

iterative retrieval algorithms.

Apply known amplitude in K-space

Apply constraints in X-space

IFFT

FFT

Generate random phase

The type of constraint that can be applied in X-space depends on the experimental implementation of the method

Customarily used in single molecule imaging experiments to reconstruct three-dimensional molecular structures

SINGLE INTENSITY MEASUREMENT

The constraint in X space is a support constraint:

The signal is equal to 0 outside of a finite domain in X. At each iteration this condition is enforced by the algorithm.Oversampling condition:

Finer sampling in K space gives a stronger constraint in X-space.

Hybrid IO algorithm can be used to speed-up convergence (use feed-back from previous iterations outside the support).

€

δk < 2π /Lsample

J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982) .http://www.opticsinfobase.org/abstract.cfm?URI=ao-21-15-2758

EXAMPLE

Original Signal Retrieved Signal

Note:-Absolute position cannot be retrieved (shifting does not change the amplitude of a signal in frequency domain)

Oversampling ratio

Good convergence after few thousand iterations

€

(2π /Lsample) /δk =10

DOUBLE INTENSITY MEASUREMENTIn the double intensity measurement the phase retrieval is performed on ONE polarization of the COTR field

The constraint in X space is the measured amplitude in the near field zone

The microbunching distribution is recovered by deconvolving the final signal with the OTR Green’s function.

Apply known amplitude in K-space

Apply known amplitude in X-space

IFFT

FFT

Generate random phase

EXAMPLE

-Convergence achieved in few hundred iterations.

-Algorithm capable of retrieving absolute position and transverse phase correlations due to transport elements (R51/R53).

ONGOING EXPERIMENTS AT NLCTA

-Demonstrate feasibility of this technique.

-Microbunching from external seed laser in undulator 1 (echo seed laser at 800 nm).

-Observe COTR at two different locations.

-Performing single intensity measurement, final goal is double intensity.

ONGOING EXPERIMENTS AT NLCTA

-COTR experiment is compatible with current ECHO beamline setup.

Similar operating conditions:

-uncompressed beam (avoid pollution from MBI)-operating energy 120 MeV for laser-beam resonance-seed power and R56 need to be tuned down to avoid overbunching (which is standard operating condition for echo)

COTR represents a new application for the echo laser system.

PRELIMINARY DATA-Single intensity measurement performed in november 2010.

-Microbunching from seeding at 800nm.

-Good signal in the far field zone at 1810 location, but polluted by etalon effect at output window.

-A wedged window will be installed soon.

CONCLUSIONS Reconstruction of the transverse

microbunching structure is important for several applications in beam physics and FELs.

Phase retrieval is a powerful tool, borrowed from a well established research field, that can be used to reconstruct the microbunching distribution in amplitude and phase.

Experiments are currently going on at the NLCTA accelerator to demonstrate the applicability of this technique to COTR imaging.

ACKNOWLEDGEMENTSThis work is the fruit of a big collaboration and

I would like to acknowledge all the people involved:

Jamie Rosenzweig, John Miao, Mike Dunning, Steven Wethersby, Gerard Andonian, Carsten Hast, Dao Xiang, all the NLCTA team, Seedling Zhang, Avi Gover and Gabriel Marcus.

COMPARISONSingle Intensity Measurement

-Easier to measure(requires one camera, no time stamp on images).

-Less sensitive to noise in the signal(double intensity may not converge if noise is too strong due to the data being over-constrained)

Double Intensity Measurement

-Faster convergence of the algorithm (stronger constraints on data):Few seconds to few minuts VS hours

POSSIBLE ISSUES-zero emission on axis:low signal to noise ration close to the far-field axis.

-Analogous to the beam-stopping problem in molecular imaging experiments (center of the detector blinded by unscattered photons)

Possible solutions:-increase oversampling ratio-use of more sophisticated algorithms (e.g. Guided HIO)-Inability to recover pure

orbital angular momentum modes

-interference with small fundamental mode eliminates the ambiguity