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Smith-Purcell radiation and picosecond bunch diagnostics. George Doucas and Wade Allison Sub-Dept. of Particle Physics, University of Oxford. Collaborators. University of Oxford (J.H. Mulvey and M. Omori) Univ. of Essex (M.F. Kimmitt)

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## Smith-Purcell radiation and picosecond bunch diagnostics

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**Smith-Purcell radiationand picosecond bunch diagnostics**George Doucas and Wade Allison Sub-Dept. of Particle Physics, University of Oxford**Collaborators**• University of Oxford (J.H. Mulvey and M. Omori) • Univ. of Essex (M.F. Kimmitt) • Dartmouth College (J.E. Walsh+, J.H. Brownell and H.L. Andrews) • ENEA, Frascati (G. Gallerano, A. Doria, E. Giovenale and G. Messina) Support from: Univ. of Oxford, British Council and Royal Society**Outline**• Introduction • Early experiments at Oxford and recent results from Frascati. • The future (higher energy, shorter bunch, more theory at high g). • Summary of where we are now.**First observed in 1953(Phys. Rev. 92, 1069, 1953)**The term is now used todescribe radiation produced from the interaction of a charged particle beam with a periodic structure, such as a grating. Is one aspect of the effect of the electromagnetic field of moving charge, such as transition and diffraction radiation, but with some distinct advantages… 1. Introduction**1. Basicrelationship**q u xo Dispersion relation: nl q l Typically, in the far IR**A reasonably simple theory, capable of predicting behaviour**under various experimental conditions is essential for any application. Not many papers with measured mW’s on the graphs!! Treatment based on assumption that a passing electron induces image charges on the surface of the grating. These are then ‘accelerated’ by the peaks and troughs of the periodic structure. (not the only approach!!) Accelerated charge produces radiation; objective is to find the angular distribution of the emitted intensity I. 2. An elementary calculation**Final relationship, for the case of a single electron, at a**height xoover a grating with period l and overall length Nl, is given by: or Term R2depends on the details of the grating profile; e is the ‘evanescent wavelength’, e~ For high , good coupling is possible even at mm’s distance For a continuous beam of current Ib, the emission is ‘spontaneous’ and the radiated power is given by changing 2pe2 to 2peIb. 2. An elementary calculation**3. Oxford resultsPhys. Rev. Lett., 69 (1992), 1761**First to observe incoherent SP radiation from an essentially continuous, low-density relativistic beam. Limited by range of emission angles accessible and electron beam position jitter. Nevertheless, reasonable agreement with predictions of surface current model of radiation process.**Main motivation was to extend the range of emission angles**accessible by light-collecting system. Confirm theoretical treatment by direct comparison of measured vs. calculated power. Improved experimental set-up and more reliable beam. Work supported by Royal Society. 4. FrascatiPhys. Rev. Sp. Topics-Accel. & Beams 5, 072802, (2002)**4. Frascati-experimental**• Microtron with discreet beam energies, starting at 1.8MeV, up to 5MeV, in steps of 0.8MeV. • Most of the work at 1.8MeV (g=4.52), some at g=10.3 • Bunch length is approx. 15ps, bunch spacing 333ps. • Bunch train duration is approx. 5ms, with an average current of 200mA. Hence, each bunch has about 4.2x108 electrons. • Normalized beam emittance is rather poor (~ 50mm.mrad)**Experimental**• Signal taken to detector through polished copper pipe (3m long) • Detector is InSb electron bolometer, liquid helium cooled. • Note reference point for power calculation.**Data (g=10.3)**• E=4.75MeV, I=120mA, 400 mesh/inch filter in front of detector. • Observed power levels orders of magnitude higher (tens of mW) than those expected from ‘incoherent’ theory. • Spontaneous coherent enhancement of SP.**Coherent enhancement**• For a bunch with Ne electrons: • there is possibility of coherent enhancement, if the ‘coherence integral’ Scoh is not very small • This is the ‘bunch form factor’, which depends on the distribution f (t) of the particles in the time domain.**Coherent enhancement**• Begins to dominate as the wavelength of the radiation becomes comparable with the bunch length. • Different assumed functions f (t) give verydifferent angular distributions of coherent SP. • Hence, coherent enhancement, not only increases the emitted power but it also provides a clear ‘signature’ of the time profile of the bunch, through a measurement of the angular ( i.e. wavelength) distribution of the radiation.**Coherence & pulse shape**• Sample calculations, based on Frascati conditions (E=4.75MeV) • Beam size was ~1x2mm and beam centroid about 2mm above grating. • Assume pulse length of 16ps. • Assume that 80% of particles are within this nominal length.**Results-analysis**• Same data as before. • Best fit for triangular shape, with 80% of particles inside 16ps. • Shape is slightly asymmetric with respect to reference particle (t=0).**Features**• Simple experimental set-up. • Non-intercepting, valid for any charged particle beam, at almost all energies. • Ample radiated power. • Sensitivity to the bunch length and its harmonics can be optimized by matching it to the grating period. • Measurement of the spectrum of the radiation is facilitated by the natural dispersion of the grating.**The future**• Interest in beam diagnostics for Linear Collider (LC-ABD bid to PPARC) • Knowledge of the bunch longitudinal profile is important (beam-beam interaction) needed by FONT. • Need input from groups that measure beam size, position and backgrounds.**Issues**• Do we understand dependence? new calculations in hand. • Can we make precise predictions of coherent radiation for real bunches, gratings, beam pipe etc? work in hand Can we measure the spectrum at high energies? Questions raised include… • Background radiation help from simulation groups • Test facilities with known short bunches? • Other periodic structures? work in hand • Detector selection, filters etc. need to build up expertise. • Radiation damage??**a. FELIX**• Higher energy (45-50MeV), shorter bunch (1-3ps) • Simpler device, with no rotating mirrors but a series of collimated apertures, to detect simultaneously at a range of angles. • IR detector array preferably pyroelectric • Direct comparison with Electro-Optic technique.**Predictions for tests at FELIX**• If bunch were 3ps ‘triangular’, then.. • Two different beam positions above grating, blue=1mm, red=5mm**b. GeV region**• In parallel with these tests… • New EM field calculations for a high g bunch, passing over a single wire (WA)**I I**z x • A simple model • Start with a fine wire along x-axis (radius 20μm) • A relativistic bunch travels parallel to z, a distance b from the wire (in y) ... then opposing currents I are induced in the wire βc b ... giving a radiated field like quadrupole radiation but compressed into flat disk-shaped lobes with θx~1/γ from the plane perpendicular to the wire**....expanding the calculation to an array of 10 such wires,**300μm pitch ....then the two disks segment into azimuthal lobes around the wire axis eg at λ = 100μm (with exaggerated polar angle): As before the red arrow is the wire direction and the green arrow the beam. Of course generally there is angular dispersion of the radiation by the grating according to wavelength....**λ 200μm**The dependence of the radiation reduction factor on λ for an rms bunch size of 30μm (0.1ps) (m)**Plot of radiated power against bunch size (in m) for**• red λ=100-250μm • green λ=250-600μm z**....and the good news:**• at high γ, the grating to beam separation can be up to ~γ λ without serious loss of radiation flux. No problem! • ....and the bad news: • for maximum flux the width of the grating should be ~γ λ. • ... but it has got to be in the beam pipe! So this effect will be responsible for a substantial reduction in the flux from a grating. • Calculations on these problems and other ideas continue... • We have already learned a lot of things which upon reflection were simply understood • We aim to predict the results of tests quantitatively, depending of course on whether we know the actual bunch length!**Summary**• Coherent SP radiation can be used, in principle, to determine the Fourier transform of the longitudinal profile of finite-length bunches. • Demonstrated (first time ?), using 14ps bunches from Frascati Microtron, at low energies (1.8 and 4.75MeV). • Next runs are at FELIX, then… • Final Focus Test Beam (FFTB) at SLAC (~ 1ps and 30 GeV). is one possibility. • TESLA?

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