A SIMPLE, LOW COST LONGITUDINAL PHASE SPACE DIAGNOSTIC * Kirk Bertsche # , Paul Emma, SLAC, Stanford, CA 94309 USA Oleg Shevchenko, Budker Institute of Nuclear Physics, Novosibirsk, Russia Absract For proper operation of the LCLS [1] x-ray free- electron laser (FEL), and other similar machines, measurement and control of the electron bunch longitudinal phase space is critical. The LCLS accelerator includes two bunch compressor chicanes to magnify the peak current. These magnetic chicanes can generate significant coherent synchrotron radiation (CSR), which can distort the phase space distribution. We propose a diagnostic scheme by exciting a weak skew quadrupole at an energy-chirped, high dispersion point in the first LCLS bunch compressor (BC1) to reconstruct longitudinal phase space on an OTR screen after BC1, allowing a time- resolved characterization of CSR effects. INTRODUCTION To shorten the LCLS electron bunches, the electron beam is linearly energy-chirped, then compressed in two bunch-compressor chicanes (BC1 and BC2). The bend magnets in these chicanes can give rise to coherent synchrotron radiation (CSR), which can add a time- correlated energy spread to the bunch. This energy spread can lead to residual dispersion after the chicane, causing blow-up of the bend-plane emittance and potentially reducing the FEL gain. A transverse RF cavity can be used to streak the bunch vertically [2], time-resolving the CSR effects by measuring the longitudinal phase space directly. But this can be a costly and unavailable diagnostic. Here we present an alternate, simpler method to enable time-resolved electron bunch measurements using a weak skew quadrupole at an energy-chirped, high dispersion point in the bunch compressor beamline. The horizontal beam size at the skew quad should be dominated by the time-correlated energy chirp induced by the off-crest- phased RF system upstream of the compressor. The skew quad then couples the horizontal beam extent into the vertical plane, resulting in a large vertical beam size on a screen after the bend system (after the horizontal dispersion has been fully cancelled), revealing the time coordinate along the bunch. The screen image is then used to time-resolve various horizontal bunch parameters (centroid position, beam size, emittance, etc) along the bunch length, including the temporal distribution. CALCULATIONS Treating the skew quad as a thin lens, the vertical kick angle, y′, of a particle at a horizontal position, x, in the skew quad is given by: y′ = x/f, where f is the focal length of the skew quad, and 1/f = GL/(Bρ), with G as the quadrupole field gradient, L as its magnetic length, and (Bρ) as the standard magnetic rigidity. Also noting that x is dominated by the horizontal dispersion at the quad, η, and the time-correlated rms relative energy spread, σ δ , then: x ≈ ηδ, where δ (≡ ΔE/E) is the relative energy deviation of the particle at position x, and we have: y′ = GLηδ /(Bρ). Here we assume the horizontal beam size at the skew quad is completely dominated by the upstream time-correlated energy chirp, a typical situation in bunch compressors for high brightness electron beams. Now introducing the time-correlated energy chirp as δ = hz (assuming an insignificant uncorrelated energy spread, which is also typical), where h (≈ σ δ /σ z ), is the ratio of rms relative energy spread divided by the rms bunch length prior to compression, and z (= ct) is the bunch length (‘time’) coordinate, we have: y′ = GLηhz/(Bρ). Finally, transporting this vertical kick downstream to the screen where it becomes a vertical position, y (= R 34 y′ = (β q β s ) 1/2 sin(Δψ)), we have: ( 29 ( 29 z B h GL y s q ! " = # $ % % & sin , (1) where β q and β s are the vertical beta functions at the quad and screen, respectively, and Δψ is the vertical betatron phase advance from quad to screen. Similarly, the rms vertical beam size, σ y , on the screen is related to the rms bunch length (upstream of the compressor), including the nominal vertical beam size on the screen with skew quad off (σ y0 = (β s ε) 1/2 ), as: ( 29 ( 29 ( 29 ! ! " # $ $ % & + ’ = 1 sin 2 2 2 2 z q s y B h GL ( ) * + , - * , ( , (2) where ε is the rms vertical beam emittance. From this formulation we can estimate the necessary skew quadrupole gradient and length necessary to dominate the screen (i.e., to render the 2 nd term insignificant). Using the LCLS first bunch compressor (BC1) as an example (see Table 1), and choosing a skew quad bore radius, r, at least 10-times larger than the largest possible chirped horizontal rms beam size in the skew quad (σ x-max ≈ |η max |σ δ-max ≈ (290 mm)(1.7%) ≈ 4.9 mm), then at 250 MeV the skew quad has a maximum pole-tip field of B ≈ 0.3 kG, a pole radius of r ≈ 50 mm, and a length of L ≈ 0.16 m. This produces an 8.6-m focal length, which easily justifies the thin-lens approximation of a 0.16-m long skew quadrupole magnet. ______________________________________________ * Work supported by the U.S. Department of Energy under contract number DE-AC02-76SF00515. # Bertsche@SLAC.Stanford.edu SLAC-PUB-13614 May 2009 Presented at the 2009 Particle Accelerator Conference, 05/04/2009 -- 05/08/2009, Vancouver, Canada