Soft Bend Magnets for SLAC E-166
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1 K.T. McDonald Princeton U. March 25, 2003 Soft Bend Magnets for SLAC E-166 SLAC experiment E-166, a demonstration of undulator-based production of polarized positrons [1], is proposed for the 50-GeV Final-Focus Test Beam (FFTB). The undulator is to be located at the so-called IP1 of an earlier experiment, E-144 [2]. The bend magnets surrounding IP1 of E-144 are shown in Fig. 1, and some parameters related to synchrotron radiation in these magnets are given in Table 1. y [ m ] z [ m ] Figure 1: Layout of bend magnets in the SLAC FFTB in the vicinity of the IP1 of experiment E-144. In experiment E-166 we propose to characterize the polarization of the 10 Mev photons emitted by the undulator in a transmission polarimeter. We also plan to characterize the polarization of positrons produced by conversion of the undulator photons in a thin plate. Synchotron radiation by the electron beam in the magnets surrounding the undulator are a potential source of background in the polarimeters. Hence, we plan to use soft bend magnets next to the undulator to reduce this background. The polarimeters will reside behind a collimator whose aperture has 1-mm diameter, located about 30 m downstream of the undulator. The angular aperture of this collimator is therefore about 33 µrad. 1
2 Table 1: Parameters of magnets considered in the synchrotron radiation calculations. E rad is the total energy radiated by a pulse of GeV electrons into a 30-µrad arc, according to eq. (6). Atten. is the attentuation factor for x-rays of energy E crtical in 15 cm of iron, and E thru is the total energy of the synchrotron radiation photons transmitted thought the iron. Magnet B L E critical E rad Atten. E thru (Gauss) (m) (kev) (MeV) (15 cm Fe) (MeV) Alnico dump magnet Hard soft bends Soft soft bends Earth s magnetic field Final Focus quads 9500 G/26 mm Synchrotron Radiation into a Given Angular Interval A useful result about synchrotron radiation is that the number of photons emitted per unit bend angle of the electron s trajectory is independent of the strength of the bend [3], dn 1.44γα. (1) dθ The spectrum of the radiation is shown in Fig. 2, in terms of the dimensionless variable x = E photon E critical, (2) where the critical energy E critical is related by and B crit is the so-called QED critical field strength, E critical = 3 hc 2 γ3 = 3 ρ bend 2 E γb e, (3) B crit B crit = m2 c 3 e h = gauss. (4) For an electron beam with E e = 50 GeV, the critical energy is given by E critical [kev] = 0.166B[gauss]. (5) The total energy of the synchrotron radiated emitted (per electron) over arc dθ is roughly the number of photons emitted (1) times the critical energy (3), E rad 1.44γαE critical dθ. (6) The total energy radiated by a pulse of GeV electrons into an arc of 30 µrad along the FFTB is listed for various magnets in the column labelled E rad in Table 1. 2
3 1 F ( x) x 1/ x e x Synchrotron Radiation Spectrum x = ω/ω(crit) 1 10 Figure 2: The synchrotron radiation spectral function F (x), where x = E photon /E crit in terms of the critical energy (3). A reasonable analytic approximation is F (x) 1.1x 0.3 e x. 2 Attenuation by the Iron Polarimeter The polarization of the undulator photons will be measured by comparing their transmission through a 15-cm-long (120 g/cm 2 ) iron magnet for fields parallel and antiparallel to the beam. The attenuation of synchrotron radiation photons in this iron magnet can be estimated from Fig. 3, from Figure 3: Photon attenuation length in g/cm 2 for various materials. From 3
4 The attenuation factors for various critical energies are listed in Table 1, and the total energy of synchrotron radiation transmitted through the iron is listed in the column titled E thru. My conclusion is that if the undulator is followed immediately by one of the Alnico dump magnets, the amount of synchrotron radiation after even 15 cm of iron is undesirably high (it would be roughly 1/3 of the energy of the transmitted undulator photons). Hence, we should install at least one soft bend between the undulator and the first Alnico dump magnet. It appears to me that if will be sufficient to use one of the hard soft bends of E-144. Even if operated at nominal full strength corresponding to a critical energy of 75 kev, the attenuation in iron is so strong that there should be not problem using a calorimeter after the iron. Of course, we retain to option to power the hard soft bend to less than full strength, thereby obtaining additional suppression of the synchrotron radiation, should its high-energy tail prove more troublesome. We should, of course, also have a hard soft bend upstream of the undulator to isolate the undulator radiation from the synchrotron radiation in the quads and last bend of the upstream part of the FFTB. 3 Appendix Shown below are numerical calculations [3] of synchrotron radiation of a pulse of electrons of 50 GeV energy γ 10 5 at the Stanford Linear Accelerator Center. While most x-rays are produced in the strongest magnet, the earth s magnetic field gives the greatest contribution of optical photons! 4 References [1] G. Alexander et al., A Two-Stage Proposal to Test Production of Polarized Positrons with the SLAC 50-GeV Beam in the FFTB (revised, Nov. 14, 2002), [2] C. Bamber et al., Studies of nonlinear QED in collisions of 46.6 GeV electrons with intense laser pulses, Phys. Rev. D 60, (1999), mcdonald/e144prd/prd pdf [3] K.T. McDonald, Notes on Synchrotron Radiation (Feb. 10, 1997), mcdonald/examples/synchrad.pdf 4
5 Figure 4: Synchrotron radiation spectra for the magnets in Table 1 and a pulse of GeV electrons. 5
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