FPS CalibrationK.Hiller, DESY Zeuthen

Antwerp FPS / VFPS meeting 9/12/2005

• Optics of the beam line is well-defined: HERA Monte Carlo.

• For the nominal beam the there is a unique relation between proton trajectory and momentum at IP.

• At HERA running the proton beam is not at the nominal position.

• For momentum reconstruction the measured proton tracks have to be shifted into the ideal beam line system where the optics is defined

Scattered Proton Trajectory For precise measurement of the proton trajectory a combination of 2 tracking stations is needed “global track parameters”

These “global track parameters” along the ring are uniquely determined by the proton momentum and offset at the IP

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X(Z,E), X’(Z,E) : global track parametersX(0), X’(0) : proton trajectory at IPAX, BX, CX, DX, GX, HX : optical constants

In linear machines, containing only dipols and quadrupoles, X and Y projections are completely decoupled 2 independent energy measurements !!!

Assume X(0) = 0 since under constraint enlarge errors

Calibration of Vertical PotsKinematic range: Kinematic range: 0.1 < Xpom < 0.4 0.1 < Xpom < 0.4

leading proton by Reggeon/Pion exchangeleading proton by Reggeon/Pion exchange no well-defined process for calibration no well-defined process for calibration

use local or global track “hit pattern” for use local or global track “hit pattern” for calibration calibration Local Tracks

Global Tracks

Vertical Calibration Constants 2004

81V at ~ 15 mm90V at ~ 65 mm (detector insert too short poor data)

Calibration of Horizontal Pots

Assume soft, quasi-real photon , compensate by larger errors !!!

Kinematic range: Xpom < 0.05 Diffractive ρ Photoproduction

γ + p γ + p + ρ γ + p + π+ + π-

GeV 0.5/1.5 919.5 p)(

0 )( p)(

0)( p)(

Z

YY

XX

p

pp

pp

Horizontal Calibration Constants 2004

Both detectors ~ 20 +- 5 mm to the proton orbit

Proton Momentum

Vertical Pots:500 < Ep < 600 GeV0 < |t| < 0.3 GeV2

Horizontal Pots:Ep > 880 GeV0.2 < |t| < 1 GeV2

Error Sources

1) real nominal vertex at IP 2) momentum spread at IP (… emittance) 3) spatial detector resolution 4) calibration constants 5) optical constants (negligible !) 6) beam corrections during the proton fill

Error propagation takes into account only 3) + 4) + 6)

To account for remaining sources errors of calibration constants are doubled Since the energy is measured in X and Y projections independently on can control the final errors.

Momentum & Angular ErrorsMomentum & Angular Errors

WhatWhat VerticalVertical HorizontaHorizontall

ΔΔE / GeVE / GeV 5.45.4 3.73.7

ΔΔPx / Px / MeV MeV

77 1111

ΔΔPy / Py / MeVMeV

3838 4343

ΔΔ P PTT22

/GeV/GeV22

0.00150.0015 0.00200.0020

Errors – Main Contributions

WhatWhat VerticalVertical HorizontalHorizontal

Spatial Spatial ResolutioResolutionn

ΔΔX = X = ΔΔYY

~200 ~200 μμmm ΔΔX = X = ΔΔY Y ~200 ~200 μμm m

Energy Energy ErrorError

1.7 GeV1.7 GeV 2.6 GeV2.6 GeV

CalibratioCalibrationn

ΔΔX = 650 X = 650 μμm m

ΔΔY = 540 Y = 540 μμm m

ΔΔX = 660 X = 660 μμm m

ΔΔY = 170 Y = 170 μμm m

Energy Energy ErrorError

5.0 GeV5.0 GeV 2.3 GeV2.3 GeV

Errors - Consistency

WhatWhat VerticalVertical HorizontHorizontalal

RMS RMS 1.21.2 1.31.3

Sigma_1Sigma_1 0.40.4 0.90.9

Sigma_2Sigma_2 1.71.7 2.12.1

RMS: errors 20 - 30% too smallSigma1/2: mixture of too small/large errors

Calibration Status

20041) Survey and geometry JRSU, JR3D: all for 2004 on NDB (no 2004 tunnel survey – use of ad hoc values ….)2) Pot positions JRPP: all on NDB 3) Optical constants JCDX/Y, JCEX/Y : all on NDB4) Calibration constants JCBO: all on NDB

2005 – much more data1) Survey ???? helpful2) Pot positions: done – Spaskov3) Optical constants: ongoing for 2004/5 e-p4) Calibration constants: target H1 meeting

Who needs 2005 calibrated FPS data ?