INVESTIGATIONS OF THE DISTRIBUTION IN VERY SHORT ELECTRON BUNCHES LONGITUDINAL CHARGE

Transcription

1 INVESTIGATIONS OF THE LONGITUDINAL CHARGE DISTRIBUTION IN VERY SHORT ELECTRON BUNCHES Markus Hüning III. Physikalisches Institut RWTH Aachen IIIa and DESY Invited talk at the DIPAC 2001

2 Methods to obtain the longitudinal Profile of sub-picosecond Bunches Measurements with streak camera * Analysis of coherent radiation spectra * (synchrotron radiation, transition radiation,...) Electro-Optic Sampling / Imaging RF Kicker Cavity * Phase-Space Rotation * Phase-Space Tomography * See DIPAC 99 for topics not highlighted

3 Electro-Optical Sampling Scan the short beam pulse with an even shorter laser pulse: beam pulse laser pulse The interaction of beam and laser can be achieved through the Pockels effect (electro-optical effect) in a nonlinear crystal.

4 Linear Electro-Optic Effect (Pockels Effect) z <001> elliptically polarized E y ZnTe y <010> x <100> (110) An electric field induces birefringence: light (vertically polarized) n z z z y y y n incident linearly polarized light (45 to optical axis) is converted to elliptical polarization, i.e. a fraction of the light is circularly polarized

5 Experimental Setup Ti:Sapphire laser ~ phaselock Φ trigger master clock rf reference detector to gun e - beam pipe ZnTe direct measurement of the co-propagating electrical field nonintercepting

6 Ti:Sapphire laser piezo The Phaselock ~ ω phase locked loop d/dt harmonic photo diode Φ trigger master clock to gun rf reference detector e - beam pipe ZnTe

7 Detection Scheme Ti:Sapphire laser phaselock, ~ photo diode ~E 2 polarizer(90 ) or Φ Wollaston Prism trigger master clock to gun rf reference polarizer λ/4 D 1 D 2 D 1 -D 2 ~ E e - beam pipe ZnTe

8 Experimental Results from FELIX from X. Yan, A.M. MacLeod, W.A. Gillespie, G.M.H. Knippels, D. Oeps, A.F.G. van der Meer, Sub-picosecond electro-optic measurement of relativistic electron pulses

9 The resolution was reported to be 440 fs. The main contribution to the resolution is the timing jitter between Ti:Sapphire laser and electron beam. At 5.3 THz there is an impact of optical phonons inside the ZnTe which cause absorption. The influence of these phonons can be modelled and electrooptic sampling has been demonstrated up to frequencies of 37 THz. (see Q. Wu, X.-C. Zhang: Conference on Lasers and Electro-Optics, Baltimore, postdeadline paper CPD3 (1997))

10 The Step towards Single Shot THz-pulse initial pulse T 0 chirped pulse T C by chirping the laser pulse, i.e. stretching by sorting wavelengths in time, Each time step is marked by the corresponding wavelength Time information can be resolved with a monochromator Resolution is given by τ = T 0 T C

11 Experimental Setup with Cirping Ti:Sapphire laser phaselock beam splitter grid 2 Φ grid 1 mirror or trigger master clock rf reference fibre with dispersion grid ~ to gun CCD beam pipe e - ZnTe possibility to obtain single-shot measurements less sensitive to timing jitter simplified setup when chirping is done with fibre

12 Using the Accelerator RF-System The time-dependend accelerating field in the cavities can be utilized for measuring the longitudinal profile. using a TM110-Mode cavity to induce a time-varying kick in analogy to a streak camera. (See X.J. Wang, Proceedings of PAC 99) measuring the energy distribution at off-crest acceleration. The latter needs some extra effort to disentangle the initial energy spread. Perform a phase-space rotation, needs some special structures in the beam line, E.G. magnetic chicanes. (See K.N. Ricci, T.I. Smith, Phys Rev SP - Accelerators and Beams, Volume 3, ) Perform a phase-space tomography:

13 The Idea of Tomography Given a distribution in 2 dimensions (particle density in phase-space, tissue in human body,...) Take Projections with different angles (Radon Transform) Algorithm to reconstruct original distribution from the projections

14 rf gun 1 st superconducting acceleration module The TESLA Test Facility magnetic chicane 2 nd superconducting acceleration module undulator OTR screen spectrometer dipole

15 rf module Performing the Rotation 0 Phase Space rf module 30 rf module -30 rf module -90 rf module 90 =>impossible to rotate 180!

16 Conventional Tomography: simulated Most of the well known algorithms for tomography strongly require full rotation (180 ) of the object in question. Otherwise severe artefacts have to be expected and the achievable resolution is bad.

17 rf module Performing the Rotation 0 Phase Space rf module 30 rf module -30 rf module -90 rf module 90 =>Combine Projections!

18 Find the Phase-Space Distribution Dividing of the phase-space: G JM G 2M G J1 G 11 s G 1M G f ( x, y) Let be the density function in phase-space. The projections onto the energy axis are s jm + 1 G jm = ds dt f( scos( θ j ) t sin( θ j ), scos( θ j ) + t sin( θ j )) θ j s jm = jth rotation angle s = energy t = time

19 How to suppress the Artefacts? Given the projections onto the energy axis: s jm + 1 G jm = ds dt f( scos( θ j ) t sin( θ j ), scos( θ j ) + t sin( θ j )) θ j s jm = jth rotation angle s = energy t = time Define entropy of the phase-space distribution: η( f ) = dx dy f( x, y) log[ f( x, y)a] (2) There are many distributions f which deliver good agreement with the projection data, but the one with the η( f ) maximal is the most probable solution. find f which meets condition (1) and maximizes (2) details in: Computer Graphics and Image Processing 10, (1979), G. Minerbo, MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data -> The solution does not need the calculation of logarithms or exponentials. -> It is an recursive algorithm. (1)

20 Achievable Resolution When two spots in phase-space can be distinguished? Let y = 0 x x = 0 σ t, σ E be the sigma in time resp energy. y = 0.5 x x = 0 y = 1 x x = 0 The sheering is written as E a t Then the projection on energy is broadened by Impossible to separate projections in the same way as original peaks! get along with 2σ separation in projection when original was 3σ. = 2 σ' E σ E + a 2 2 = σ t Then the achievable resolution can be calculated: 2 σ t = σ E 5a

21 In the Case of TESLA Test Facility When accelerating off-crest, an offset in time induces a change of energy: ω 0 Assume phaseshift θ = +/- 45, E = te 0 ω 0 sinθ = 2π 1.3GHz, E 0 100MeV a E = keV ps t β-function at spectrometer target <0.5m, Dispersion 1m, total Energy 200 MeV, norm Emittance 3πmm mrad (slice) σ x = βε 150µm σ E 30keV From previous calculation 2 σ t = σ E 5a In case of TTF (nominal operation) σ t =50 fs, total separation can be assumed for 3σ t = 150 fs.

22 Contribution of Reconstruction Algorithm: t =90 fs t=150 fs No reduction of resolution due to reconstruction algorithm!

23 The Bunches of TESLA Test Facility One result from longitudinal tomography at the TTF E [MeV] Population [arb units] 80 Population [arb units] Time [ps]

24 1 0.8 Charge Distribution (Current) [normalized] time [ps]

25 Conclusion Diagnostics for bunch length measurement is being developed aiming for resolutions in the vincinity 100 fs. Promising techniques are electro-optic sampling / imaging measuring the electrical field of the electron bunches - potential for resolution has to be explored - opportunity for single-bunch diagnostics - possibility to measure wakefields inside the accelerator longitudinal phase-space tomography - resolution depending on setting of accelerator - reconstruction of the two dimensional longitudinal phase space - possibility to measure effects of wakefields, coherent synchrotron radiation, etc directly on the beam itself