58th ICFA Advanced Beam Dynamics Workshop on High Luminosity Circular e + e Colliders 24-27 October 26, Cockcroft Institute at Daresbury Laboratory, UK Measurement of beam polarisation and beam energy in one device Nickolai Muchnoi Budker INP, Novosibirsk 26 Oct 26 Nickolai Muchnoi ICFA eefact26 26 Oct 26 / 2
Inverse Compton Scattering (ICS) θ ε electron ε = γmc 2 photon ω = hν Scattering parameter: ε, ε, ω ω u = ω ε = θ ε θ ω = ω ε ω = ε ε ε θ ω ; u [, κ], where κ = 4ω ε m 2. Scattering angles: η ω γθ ω = κ u ; κ η ε γθ ε = u u. note that κ.53 for ε = GeV and ω = ev. Nickolai Muchnoi ICFA eefact26 26 Oct 26 2 / 2
LASER BEAM The concept of laser - ICS experiments Here tiny fraction of the beam electrons are scattered on the laser wave DIPOLE MAGNET Compton photons X electron beam Compton electrons with min. energy θ X Δθ X 2 Nickolai Muchnoi ICFA eefact26 26 Oct 26 3 / 2
ICS cross section is sensitive to polarisation { ( dσ = κ( + u) 2 2+ u2 + u +4u κ [ u κ ][ ξ cos(2(ϕ ϕ ))] ) + ( )} u(u + 2)(κ 2u) 2u 2 κ/u + ξ ζ ζ κ 2 ( + u) 3 sin ϕ r κ 2 ( + u) edϕ 2 du, 3 Modified Stokes parameters: ξ and ϕ degree and direction of laser linear polarisation, ξ degree of laser circular polarisation, ζ and ζ longitudinal and transverse electron beam polarisation. Laser beam: ξ 2 + ξ2 =, ξ [, ], ξ [, ]. Electron beam: ζ 2 + ζ2 <, ζ [, ], ζ [, ]. Nickolai Muchnoi ICFA eefact26 26 Oct 26 4 / 2
ICS cross section is sensitive to polarisation dσ/dx(κ=.) dσ/dx(κ=2.) barn / x.25.5.75 x=u/κ Dashed lines illustrate the influence of ξ ζ Nickolai Muchnoi ICFA eefact26 26 Oct 26 5 / 2
Experiments with polarised e ± beams ACO, VEPP-2, SPEAR, DORIS, TRISTAN, VEPP-4, CESR, LEP, HERA... Compton polarimeters usually dealt with scattered photons. At higher electron energies the divergence of γ-beam is small, high energy SR photons appear, etc....... it is reasonable (like ILC) to look at the scattered electrons. Maximum electron scattering angle: max(θ ε ) = 2ω /m. If ω =2.33 ev one has max(θ ε ) µrad. Beam angular spread: σ y = ɛ y /β y max(θ ε ). An example: ɛ y = pm and β y = m gives σ y = µrad. The dimension of scattered electrons angular distribution does not depend on beam energy. Nickolai Muchnoi ICFA eefact26 26 Oct 26 6 / 2
Scattered electrons after a bending dipole An energy of a scattered electron: ε(u) = ε /( + u). This electron will be bent to the angle θ s = c ( + u) Bdl. ε Let η s γθ s = η + uη, where η s and η are the bending angles in units of /γ Note η = Bdl/B c λ c, where B c λ c = mc e.7 3 [T m]. With scattered electron angles defined as { η x (η s η ) = uη + u κ/u cos ϕ η y = one gets the equation: u κ/u sin ϕ (η x uη ) 2 + ηy 2 = u(κ u). Nickolai Muchnoi ICFA eefact26 26 Oct 26 7 / 2
Scattering surface in (η x, η y, u) space, no bend κ=2, η = 2 u - - η x η y Nickolai Muchnoi ICFA eefact26 26 Oct 26 8 / 2
Scattering surface in (η x, η y, u) space, /γ bend κ=2, η = 2 u - 2 - η x 3 η y Nickolai Muchnoi ICFA eefact26 26 Oct 26 9 / 2
Scattering surface in (η x, η y, u) space, /γ bend κ=2, η = 2 u 5 5 - η x 2 η y Nickolai Muchnoi ICFA eefact26 26 Oct 26 / 2
Scattering surface in (η x, η y, u) space, /γ bend 2 κ=2, η = u 5 η 5 2- x η y Nickolai Muchnoi ICFA eefact26 26 Oct 26 / 2
Scattered electrons distribution in η x, η y plane The sizes of ellipse [rad] are: O y = 4ω, O m x = 4ω m + η 2 = θ. O x measurement can be used for calibration of η = Bdl/B c λ c. Nickolai Muchnoi ICFA eefact26 26 Oct 26 2 / 2
LASER BEAM Reminder: the scheme of experiment Here tiny fraction of the beam electrons are scattered on the laser wave DIPOLE MAGNET Compton photons X electron beam Compton electrons with min. energy θ X θ = κ = 4ω E θ m 2 Δθ X 2 Nickolai Muchnoi ICFA eefact26 26 Oct 26 3 / 2
ILC note LC-M-22- A Transverse Polarimeter for a Linear Collider of 25 GeV e Beam Energy Itai Ben Mordechai and Gideon Alexander For the detection of the scattered electrons we consider only a position measurement using a Silicon pixel detector placed at a distance of 37.95 m from the Compton IP. The active dimension of the detector is 2 2 mm 2. The size of the pixels cell taken is 5 4 µm 2 similar to the one used in the ATLAS detector [9]. This scheme yields an approximate two dimensional resolution of 4.4 5.5 µm 2 [] with a data read-out rate of 6 Mb/sec. Nickolai Muchnoi ICFA eefact26 26 Oct 26 4 / 2
Fitting the distribution of scattered electrons U - unpolarised cross section L - longitudinal electron polarisation T - transverse electron polarisation 2 5 5 3 2 - -2-3 2 - -2 - - y - y x - x x - - The x, y distribution of scattered electrons is the convolution of a) cross section f(x, y) = U + ξ (ζ L + ζ T ) and b) transverse distributions (σ x, σ y ) of electrons in the beam. y Nickolai Muchnoi ICFA eefact26 26 Oct 26 5 / 2
Fitting the distribution of scattered electrons x-bins [ : 2] 5 y-bins [ 2 : 2] Fit range η x = [2, 2]. MC: γ θ = 3.26 5 = 63. Fit result: θ = X 2 X = (63.2 ±.8) (. ±.5) Nickolai Muchnoi ICFA eefact26 26 Oct 26 6 / 2
Two arcs in a dipole of length L R e L θ R Δθ ΔX Note that R min = R /( + κ). S, R black arc length & radius, S, R min red arc length & radius. [ ] L S = 2R arcsin and 2R [ ] L2 + X 2 S = 2R min arcsin 2R min, where X = R 2 min [ LRmin 2R ] 2 [ Rmin 2 L LR ] 2 min. 2R Nickolai Muchnoi ICFA eefact26 26 Oct 26 7 / 2
Spectrometer: general consideration 2 m L 2 m ΔX θ Δθ Let κ =.53 (E = GeV, ω = ev): θ θ L X S/S D mrad mrad m mm mm.53 3.83 2.59 7 46 2 3.6 7.65.4 6 92.53 5.9 2.59 7 46 2 3.6 5 3.83.4 6 92 Therefore: D a) S/S κθ b) X κθ L c) D κθ L arm The best case: a) small κθ; b) short dipole; c) long arm. Nickolai Muchnoi ICFA eefact26 26 Oct 26 8 / 2
The penultimate slide Initial conditions: Inverse Compton scattering of laser radiation is a currently available reliable method for beam polarisation and energy determination. 2 The future high energy lepton colliders require polarised beams and polarimetry, inter alia for application of resonant depolarisation technique for precise beam energy calibration at circular machines. Conclusions: Analysis of 2D-distribution of ICS electrons allows to measure beam polarisation degree and direction as well as to provide a unique way for accurate calibration of the Bdl exactly along a beam trajectory in a conventional magnetic spectrometer. Such a spectrometer was installed at LEP and no doubt it should be implemented at future high-energy colliders, either linear or circular. 2 The proposed approach has no limitations in beam energy, the only thing it requires is a small value of vertical emittance of the electron beam. So now it s a good time to start the proof-of-principle project at one of the existing low-emittance facilities. 3 Another subject for further studies should be a possibility to measure the position of backscattered photons with high accuracy. This seems to be not an easy task, but it allows to build the completely independent beam energy measurement approach for arbitrary beam energies. Nickolai Muchnoi ICFA eefact26 26 Oct 26 9 / 2
The End THANK YOU! Special thanks to the conference organizers for the invitation and warm welcome! Nickolai Muchnoi ICFA eefact26 26 Oct 26 2 / 2
Another example More statistics, another κ, longitudinal polarization %, 5 accuracy in X 2 measurement, etc. Nickolai Muchnoi ICFA eefact26 26 Oct 26 2 / 2
Photon detector? The task is to measure accurately the centre of gravity in a narrow spatial distribution of high energy photons. Can have up to photons/bunch with some simple laser source Nickolai Muchnoi ICFA eefact26 26 Oct 26 2 / 2