Bernhard, Axel

Braun, Nils

Peiffer, Peter

Rodríguez, Verónica Afonso

Rossmanith, Robert

Scheer, Michael

Widmann, Christina

English

KITopen

 Erratum: Radiation emitted by transverse-gradient undulators[Phys. Rev. Accel. Beams 19, 090704 (2016)]Axel Bernhard , Nils Braun, Verónica Afonso Rodríguez, Peter Peiffer,Robert Rossmanith, Christina Widmann, and Michael Scheer(Received 28 August 2020; published 28 September 2020)DOI: 10.1103/PhysRevAccelBeams.23.099901In the figures showing comparisons of on-axis photon flux per unit solid angle were labeled incorrectly. The dimensionsshould have read 1=ðs rad2 0.1% bwÞ instead of 1=ðsmrad2 0.1% bwÞ. Consequently, the numbers shown in these figureswere too large by a factor of 106.−2−1012110115120125130(a)Dispersive displacement x [mm]E [MeV]−2−1012(b)−2−1012(c)−2−1012110115120125130(d)E [MeV]1x1032x1033x1034x1035x103−0.2 0.0 0.2on−axis photon flux per unit solid angle [1/(s mrad2 0.1% bw)]/ 110 115 120 125 130Electron energy E [MeV]1x1032x1033x1034x1035x1031x1032x1033x1034x1035x1031x1032x1033x1034x1035x103−0.05 0.00 0.05/FIG. 5. Basic proof of the TGU concept: Electron energy dispersion and resulting radiation spectra for an electron energy band ofΔE ¼ 120 MeV 10% for the cases (a) planar undulator with K ¼ 1.07, (b) ideal linear TGU with K0 ¼ 1.07 and α ¼ 139.7 m−1 andlinear dispersion (Eq. (4) of the original article), (c) the same with nonlinear dispersion according to Eq. (12) of the original article,(d) idealized cylindric SCTGU with optimized dispersion. For all cases a beam current of 10 pA, equally distributed over the 21monoenergetic zero-emittance beamlets, is assumed.Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s) and the published articles title, journal citation, and DOI.PHYSICAL REVIEW ACCELERATORS AND BEAMS 23, 099901(E) (2020)2469-9888=20=23(9)=099901(4) 099901-1 Published by the American Physical SocietyFigures 5, 6, 7, 8, 11, 12, and 15 show the revised plots in now correct units of 1=ðsmrad2 0.1% bwÞ. Since ourarguments rely on comparisons of the quantities displayed in each of these plots, and all quantities which we compare toeach other have to be corrected by the same factor, the conclusions of our article are not affected by this correction andremain unchanged.−0.8−0.6−0.4−0.20.00.2(a)electron trajectory (x(z)−x ) [mm]−0.8−0.6−0.4−0.20.00.2(b)−0.8−0.6−0.4−0.20.00.2(c)−0.8−0.6−0.4−0.20.00.2−0 −0 0 0 0(d)x [mm]1x1032x1033x1034x1035x103on−axis photon flux per unit solid angle [1/(s mrad2 0.1% bw)] 110 115 120 125 130Electron energy E [MeV]1x1032x1033x1034x1035x1031x1032x1033x1034x1035x1031x1032x1033x1034x1035x103−0.05 0.00 0.05/FIG. 6. The effect of the ponderomotive particle drift in TGUs: (a) linear TGU without trajectory correction and (b) with correction,(c) cylindric SCTGU without trajectory correction and (d) with correction.−2−1012110 115 120 125 130Disp. displacement x [mm]E [MeV]100 periods out of infinite TGU100−period TGU, matched1x1032x1033x1034x1035x103−0.02 0.00 0.02ph. flux density [1/(s mrad2 0.1% bw)]/infinite TGU1x1032x1033x1034x1035x103−0.02 0.00 0.02/matched finite TGU 110 115 120 125 130electron energy [MeV]FIG. 7. Comparison of the required dispersion and the resulting radiation spectra (assuming zero-emittance beamlets) between thecase of 100 periods out of an infinitely long SCTGU and the case of a finite 100-period SCTGU with matching periods. See the text fordetails.AXEL BERNHARD et al. PHYS. REV. ACCEL. BEAMS 23, 099901 (2020)099901-2−2−1012110 115 120 125 130Disp. displacement x [mm]E [MeV]observation at infinite distanceobservation at 2 m distance12345−0.02 0.00 0.02x 103ph. flux density [1/(s mrad2 0.1% bw)]/infinite12345−0.02 0.00 0.02x 103/close 110 115 120 125 130electron energy [MeV]FIG. 8. Comparison of the optimized spectral dispersion of the electron beam and resulting radiation spectra for an observation pointin infinite and 2 m distance, respectively.−0.5 0 0.5−0.4 0.0 0.4x’ [mrad]x [mm]−0.4 0.0 0.4x [mm]−0.4 0.0 0.4x [mm]−0.50.00.5−0.4 0.0 0.4z = −50uy’ [mrad]y [mm]−0.4 0.0 0.4z = 0uy [mm]−0.4 0.0 0.4z = +50uy [mm]−1.5−1−0.5 0 0.5 1 1.5( peak− 0)/ 0 [%]1x1032x1033x1034x1035x103−2.0 0.0 2.0phot. flux density [1/(s mrad2 0.1% bw)](−0)/0 [%]x = 10 nm radx = 1 nm radx = 0FIG. 11. Left: phase space distribution in x and y of a 120 MeVelectron bunch at the entrance, center and exit of the idealized cylindricTGU. The electron bunch parameters were chosen as βwaistx ¼ 0.5 m, βy ¼ 0.7 m ¼ const and the geometric emittanceϵx ¼ ϵy ¼ 10−8 m rad. The color scale refers to the relative deviation of the peak energy of the radiation emitted by the respectiveparticle with respect to that of the reference particle. Right: incoherently added radiation spectrum emitted by the particle bunch as awhole for different values of ϵx;y, observed at infinite distance.1x1032x1033x103−2  0  2phot. flux density [1/(s mrad2 0.1% bw)](−0)/0 [%]xwaist = 0.2 mxwaist = 0.5 mFIG. 12. Incoherently added radiation spectra emitted by particle bunches with E ¼ 120 MeV, ϵx ¼ 10−8 m rad for two differentchoices of βwaistx , observed at 105 m distance.ERRATUM: RADIATION EMITTED BY … PHYS. REV. ACCEL. BEAMS 23, 099901 (2020)099901-3The authors would like to thank the attentive PRAB reader who advised us of our mistake.5x1031x104 140  145  150  155  160phot. flux density [1/(s mrad2 0.1% bw)] [nm]zero emittance, inf. distance(a)(b)planar undulatorFIG. 15. Radiation spectra expected for the real SCTGU-P40 with finite beam emittance and observation at 2 m distance with (a) aphoton optics for a parallel beam (zero angular acceptance) and (b) a point detector. The corresponding zero-emittance and planarundulator spectra in forward direction (parallel beam) are added for comparison. For the undulator and beam parameters refer to Table IIof the original article.AXEL BERNHARD et al. PHYS. REV. ACCEL. BEAMS 23, 099901 (2020)099901-4

Erratum: Radiation emitted by transverse-gradient undulators [Phys. Rev. Accel. Beams 19, 090704 (2016)]

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Erratum: Radiation emitted by transverse-gradient undulators [Phys. Rev. Accel. Beams 19, 090704 (2016)]

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