Emittance Measurement and Correction in the ATF Extraction Line

Transcription

1 Emittance Measurement and Correction in the ATF Extraction Line M. Woodley, J. Turner, M. Ross, J. Nelson, P. Raimondi (SLAC), H. Hayano, K. Kubo, T. Okugi, and the ATF Staff (KEK) 5 th KEK-SLAC International Study Group Meeting (ISG5) February, 2 summary of November 1999 emittance measurements discussion of skew quadrupole "knobs" for emittance correction

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4 EXT line optics checks (R 12, R 34 ) 6 ascii_zh1x_99nov24_1557.data 2 ascii_zv1x_99nov24_167.data R12 (m) -2 o Ψ =364 x R34 (m) S (m) S (m) Note: plot symbols (circles with error bars) are fitted slopes at BPMs; dashed lines are modeled R-matrix elements (SET99NOV24_1357)

5 EXT line skew quadrupole function checks MW3X σ y 2 vs B QK1X (kg) MW3X σ 1 2 vs B QK1X (kg) 7 6 MW3X σ y 2 (µm 2 ) measurement simulation 7 6 MW3X σ 1 2 (µm 2 ) 2 measurement simulation B QK1X (kg) B QK1X (kg) Note: plot symbols (circles with error bars) are measured beam sizes at MW3X; solid lines are parabolic fits to the beam size data; dashed lines are TRANSPORT simulations

6 EXT line dispersion measurement EXT Dispersion Measurement measurement SET99NOV25_ EXT Dispersion Measurement: Diagnostic Section Fit measured fit 1.5 eta x (m) eta x (m) s (m).1.5 EXT Dispersion Measurement measurement SET99NOV25_ s (m).8.6 EXT Dispersion Measurement: Diagnostic Section Fit measured fit.4 eta y (m) eta y (m) s (m) s (m)

7 Estimating beam energy spread in EXT line σ δ

8 Estimating beam jitter in EXT line diagnostic section 4 std= 55.1 um 3 std= 58.9 um 5 std= 56.9 um 4 std= 27.6 um 3 std= 18.2 um 5 std= 43.2 um ML8X X (um) std= 72. um ML9X X (um) std= 31.5 um ML1X X (um) std= 28.4 um ML8X Y (um) std= 7.1 um ML9X Y (um) std= 4.8 um ML1X Y (um) std= 18.1 um ML11X X (um) ML12X X (um) ML13X X (um) ML11X Y (um) ML12X Y (um) ML13X Y (um) Horizontal Vertical

9 Summary of EXT emittance measurement data (November 25, 1999) wire D scan Nscan sigma eta sigma_eta sigma_d jitter sigma tilt angle (measured) (measured) (measured) (corrected) (measured) [um] [deg] [um] [cm] [um] [um] [um] [um] [deg] MWX.x MWX.y MWX MW1X.x MW1X.y MW1X MW2X.x MW2X.y MW2X MW3X.x MW3X.y MW3X MW4X.x MW4X.y MW4X NOTEs: - error values are statistical errors (rms of 3 measurements) - tilt angles are absolute value - eta values estimated via orbit fits to 7-point DR RF frequency scan, propagated to the wire scanners - eta "1" is the projection of eta x and eta y onto the 1 degree wire scan axis - espread = 6.67e-4 for sigma_eta calculation (see T. Okugi measurement of December 15, corresponds to I = 5e9) - spot size contribution for finite size wires is D/4 - jitter values are statistical from 15 1-shot orbit measurements; values quoted are for BPMs nearest to wire scanners

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11 EXT emittance measurement analysis (4D) Data: 25-NOV-1999 Optics: SET99NOV25_117 Energy: GeV Four Dimensional Phase Space Analysis epsilon_x = 2.132E E-1 epsilon_y = 5.771E E-1 epsilon-b_x = 5.58E E-1 epsilon-b_y = 7.2E E-12 Bmag_x = Bmag_y = E-6 B_cos_x = E-2 B_cos_y = E-2 B_sin_x = B_sin_y = beta_x = E+ beta_y = E+ alfa_x = E+ alfa_y =-6.949E-2 +-.E+ theta_1/deg = E+ theta_2/deg = E+ theta_3/deg = E+ theta_4/deg = E+ tr(cc') = E+ det C = E+ epsilon_1 = 2.124E-9 +-.E+ epsilon_2 = 4.81E E+ beta_x = E+ beta_y = E+ alfa_x = E+ alfa_y = 1.183E-2 +-.E+ -det G+ = 4.5E-3 +-.E+ psi+/deg = E+ det G- = 5.512E-4 +-.E+ psi-/deg = E+ tr(bb') = 9.22E-3 +-.E+ det B =-3.494E-3 +-.E+ beta_x = E+ beta_y = E+ alfa_x = E+ alfa_y = 1.48E-2 +-.E+ B_11 = 5.119E-2 +-.E+ B_12 = 1.61E-2 +-.E+ B_21 = 6.317E-2 +-.E+ B_22 =-4.851E-2 +-.E+ h(x`y) = 5.116E-2 +-.E+ h(x`y`) = 1.6E-2 +-.E+ h(xy) =-6.314E-2 +-.E+ h(xy`) = 4.848E-2 +-.E+ chi^2_x =.E+ chi^2_y =.E+ chi^2_u =.E+ chi^2/dof = 1.4 condition = 2.344E+5 unit angle RMS fit anomaly Tmit/E MWX.E MW1X.E MW2X.E MW3X.E MW4X.E MWX MW1X MW2X MW3X MW4X MWX MW1X MW2X MW3X MW4X beam MWX e e e e e e e e e e e e e e e e-12 monte carlo analysis for 1365 data sets epsilon_x = 2.199E E-1 epsilon_y = 5.653E E-12 epsilon_1 = 2.199E E-1 epsilon_2 = 4.7E E-11

12 Monte carlo simulation of EXT emittance measurement analysis (4D) EXT 4D emittance measurement: Monte Carlo results ε 2 ε 2 ± σε 2 ε y fit to distribution Computed Intrinsic Vertical Emittance (ε 2 ) x 1-11

13 Monte carlo simulation of EXT emittance measurement ("EXT_addwire_5" optics; 5% beam size errors; N sim =5) Uncoupled input beam Coupled input beam (12.8% non-positive σ's) (53.5% non-positive σ's)

14 NLC 4D emittance diagnostic section ("ideal" optics)

15 Monte carlo simulation of NLC 4D emittance measurement ("ideal" optics; 5% beam size errors; N sim =5) Uncoupled input beam (no non-positive σ's) Coupled input beam (42.1% non-positive σ's)

16 EXT line skew correction (before turning on skew quads) 25 2 MW3X sigy 2 VS QD8X K1 p= p1= p2= A= B= C= MW3X sigy 2 /um QD8X K1 /1/m NDF= 8 chisq/n =.323 RMS= 73.4 um 2 26-NOV-1999, Swing Shift Quad-scan vertical emittance measurement (QD8X on MW3X) [NOTE: skew quads OFF] ======================================================= Analysis (statistical errors used; NOT corrected for dispersion): Vertical emittance parameters at upstream end of QD8X [optics: SET99NOV25_1712] energy = GeV emit = 6.531e e-12 m emitn = 1.632e e-8 m emitn*bmag = 1.934e e-8 m bmag = ( 1.) bmag_cos = (.) bmag_sin = (.) beta = m ( 6.965) alpha = ( -.852) chisq/n =.278

17 EXT line skew correction (after turning on skew quads) MW3X sigy 2 VS QD8X K1 p= p1= p2= A= B= C= MW3X sigy 2 /um QD8X K1 /1/m NDF= 8 chisq/n =.359 RMS= 69.3 um 2 26-NOV-1999, Swing Shift Quad-scan vertical emittance measurement (QD8X on MW3X) [NOTE: skew quads ON] ======================================================= Analysis (statistical errors used; NOT corrected for dispersion): Vertical emittance parameters at upstream end of QD8X [optics: SET99NOV25_1712] energy = GeV emit = 5.956e e-12 m emitn = 1.489e e-8 m emitn*bmag = 1.897e e-8 m bmag = ( 1.) bmag_cos = (.) bmag_sin = (.) beta = m ( 6.965) alpha = ( -.852) chisq/n =.378

18 4D emittance measurement/analysis and correction in the ATF extraction line: conclusions the optics of the extraction line seems well understood, and the skew quads behave predictably it's possible to make good measurements of σ x, σ y, and σ 1 on each of the wire scanners, with reasonable estimates of errors and corrections for dispersion and wire filament size the 4D analysis yields a "believable" result with reasonable χ 2, but monte carlo analysis of the error on the computed intrinsic vertical emittance shows it to be large implementing a skew quad correction based on the 4D analysis has, so far, yielded ambiguous results empirical minimization of the measured projected vertical emittance seems to be a better way to go, but the non-optimal phase advances between the skew quads would make this a time consuming process, unlikely to converge (more or less) orthogonal combinations of the skew quads might be used to speed up the convergence of manual empirical emittance optimization

19 "Irwin Knobs" Coupling Hamiltonian: H= axy+ bxy + cxy + dxy y H, y H y y The "b" knob (the xy' Hamiltonian coefficient) acts like a single skew quadrupole located π/2 in phase upstream of the targeted wire scanner in the y plane and π in phase upstream of the targeted wire scanner in the x plane: ψ x = π ψ y = π/2 effective skew quad wire scanner R = 1 1 R 43 R34 ysq = ksqxsq yw= R34 ysq yw= R k x xsq= yw= R34k x b R k 34 sq sq xw 34 sq sq w The "b" knob couples the horizontal and vertical spot sizes at the targeted wire scanner, generating an x-y tilt there.

20 The "d" knob (the x'y Hamiltonian coefficient) acts like a single skew quadrupole located π/2 in phase upstream of the targeted wire scanner in both x and y planes: ψ x = π/2 ψ y = π/2 effective skew quad wire scanner R R = 21 R 12 R 43 R34 ysq = ksqxsq yw= R 34 ysq yw= R 34 ksqxsq xsq= R 12 xw yw= R 12 R 34 ksqxw d R 12 R 34 k sq The "d" knob acts like SQ3 in the SLC Final Focus, coupling horizontal angular divergence to vertical spot size at the targeted wire scanner. The effects of the "a" and "c" knobs can be similarly derived the x y phase advances from the effective skew quad to the targeted wire scanner will be π π and π/2 π, respectively. a ksq c R k 12 sq

21 "b"-knob simulation (1 of 3)

22 "b"-knob simulation (2 of 3)

23 "b"-knob simulation (3 of 3)

24 "d"-knob simulation (1 of 3)

25 "d"-knob simulation (2 of 3)

26 "d"-knob simulation (3 of 3)

27 Measured x-y tilt angle vs "b"-knob (M. Ross, J. Nelson, December 1999) 15 Tilt angle MW3X vs "b"-knob tilt angle from x y u1 scans (deg) skew quad multi-knob (wrt max)

28 Simulated x-y tilt angle vs "b"-knob 15 1 ATF EXT "b"-knob Simulations (Flight Simulator) measured coupling no coupling tilt MW3X (degree) "b"-knob

29 Emittance correction in the ATF extraction line using Irwin knobs: conclusions except for an overall sign flip (!), the Irwin knobs ("b" and "d") behave as predicted by simulations even though the "a" and "c" Hamiltonian coefficients are not constrained, the knobs appear in simulation to work OK for the beam matrix measured in November 1999, the "b"-knob is the most likely candidate to use to correct the x-y coupling at MW3X "b"-knob scans could allow for more accurate estimates of the x-y tilt of the beam at MW3X the non-optimal phase advances between the skew quads make creation of "a" and "c"-knobs targeted on MW3X impossible (practically zero range); also, the "b" and "d" knobs are not perfect simulations of the Irwin knobs for the measured (coupled) beam of December 1998 show that the "b" and "d"-knobs are ineffective for correcting the coupling modification of the EXT optics in the diagnostic section might be necessary to allow other phases of coupling to be corrected