Abstract The luminosity of a collision region may be calculated if one understands t he lattice parameters and measures the beam intensities, the transverse and longitudinal emit- tances, and the individual proton and antiproton beam tra- jectories (space and time) through the collision region. This paper explores an attempt to make this calculation using beam instrumentation during Run 1b of the Tev- atron. The instrumentation used is briefly described. The calculations and their uncertainties are compared to lumi- nosities calculated independently by the Collider Experi- ments (CDF and D0).                   1  INTRODUCTION   The primary focus of accelerator instrumentation is on diagnostics in order to identify problems in machine opera- tions. However this same instrumentation may be used to calculate the luminosity of the collision regions assuming that one has knowledge of the lattice. Run 1 of the Te- vatron Collider Program and the availability of on-line analysis tools provided the opportunity to attempt this measurement. Some initial uncertainty regarding the cal- culation of luminosity by the two Collider Detectors (CDF and D0 at the B0 and D0 collision regions respec- tively) provided the motivation. 1.1 Assumptions   The only assumption about the beam is that both pro- ton and antiproton bunches can be described as three di- mensional gaussian distributions, \where Nk is the bunch intensity,skx (s),sky (s),slk , are the transverse and longitudinal bunch sizes, xk (s), yk (s ), are the closed horizontal and vertical orbits, f k is the cog- ging offset (collision offset with respect to s=0), and x, y, s, and ct are the independent transverse, longitudinal and time coordinates (in meters) of the bunch. The superscript k signifies the type beam (p for proton, a for antiproton). Since the proton crossing at s=0 defines ct= 0, f p =0. The gaussian assumption is borne out by measurements from our transverse and longitudinal profile monitors. 1.2 Luminosity   With this form of the beam distribution, the luminosity (with units = (m2 s )-1 ) may be written as   L = hnÚ dx dy ds(2cdt) r p (x , y, s , ct )r a ( x , y, s , - ct ),         x,y,s,ct

with h the rf harmonic number and n the rf frequency. Integrating over x, y, and ct gives the longitudinal lumi- nosity profile,   with l(s) having dimensions   of (m3s)-1. This quantity needs to be summed over the number of colliding bunches.   The transverse beam size st may be written as functions of the lattice parameters b and D (dispersion), the meas- ured values of emittance e t (in rms and unnormalized form), and fractional momentum spread Dp p, Usually the vertical dispersion is so small that it is ne- glected. Since the collision point is in a drift region, and D(s ) = D'(s - s Dmin ) + Dmin   with D' the deriva- tive of the dispersion. Dp p for a relativistic beam can be related to the longitudinal beam size   sl   by where V is the voltage of the rf, g t is the transition g , andEs is the synchronous energy.   Since the transverse beam monitors are (usually) not lo- cated within the collision region, it is necessary to know the lattice well enough to calculate the ratio of in order to use the measured bunch sizes. In addition the location of bmin as well as the dis- persion must be determined.   In order to minimize the beam-beam tune shift in Run 1, electrostatic separators were installed in the Tevatron. These separators give rise to separated helical orbits for the proton and antiproton beams. Another set of electro-

Ý Work supported by the U.S. Deptartment of Energy under contract No. DE-AC02-76CH03000

into the two scope channels). The analysis involves a digi- tal rectification of the BPM signals, and the calculation of proton and antiproton trajectories. Since according to Eq.1 we are only interested in the difference between the proton and antiproton orbits, the absolute systematics should tend to cancel. Unfortunately, the system suffered from proton feed-through into the antiproton signal, thus spoiling the calculation. We plan to add an active feedthrough subtrac- tion in a future update.   In addition the proton and antiproton doublet signals are captured on a single oscilloscope trace for each BPM plate. By determining the zero crossing point for each beam and subtracting, we can calculate the cogging offset. The result of this calculation was a measurement of the offset to bet- ter than 1.5 cm (50 ps).                       3  RESULTS   The program "Luminometer" was written to acquire the instrumentation data every 20 seconds. In addition it read out the luminosities calculated by the Collider detectors from their luminosity monitors. Since the CPM position data was suspect, it was (arbitrarily) assumed that we had head-on collisions, but the cogging offset f   was used. The Flying Wire data were combined with the Sync Lite data and the SBD bunch length to obtain the transverse beam sizes. The lattice parameters were those which were considered as the best estimates (10%). The results are shown in the Figure. This particular store was a 6 (proton) on 1 (antiproton) store. Production luminosity begins at the rise of the D0 Detector plot. This where the beam has already been taken to low beta and scraped in order to lower the detector background. (A programming error in Luminometer prevented the acquisition of CDF data).   The most striking result is that the calculation predicts higher luminosity (50% more) than the detectors observe. The error in the detector luminosity is 5%. The suspicion is that the lattice values are incorrect, although the magni- tude of the error seems to be outside the suspected theo- retical bounds. We are exploring systematic errors in the Flying Wires and Sync Lite. It is also possible that the beams were not making head-on collisions, but this pos- sibility seems remote since the beams are empirically ad- justed to maximize luminosity. The "microstructure" in the calculated plots is due both to the statistical noise in the Sync Lite calculations (every 12 s), and the effect of a simplistic averaging of the current Sync Lite results with older Flying Wire results (flown only every 30 minutes). This gives rise to a step feature whenever fresh Flying Wire data became available. This will be changed in a fu- ture version which will weight the Flying Wire data as a function of elapsed time.

Figure: Operation of Luminometer. The upper traces are those calculated by the on-line program "Luminometer". The lower trace is the D0 Detector Luminosity . See text for more details.                   4  CONCLUSIONS   The results from the Luminometer show much work remains to be done, if we are to achieve the goal of meas- uring luminosity with accelerator instrumentation. We hope to improve the software algorithms (CPM) and ac- tual hardware (Flying Wires and Sync Lite) to give us more confidence in the results. Finally we need to spend a major effort on the attempt to measure the lattice, espe- cially to correlate beam sizes from the measuring instru- ments to the collision regions. We may install a test Fly- ing Wire system in a collision region (before the detectors are installed in Run 2) in order to compare the beam size there and that measured simultaneously at the normal Fly- ing Wire and Sync Lite locations.                       REFERENCES [1] W. Blokland, "Integrating the Commercial Software     package LabVIEW with Fermilab's Accelerator Con-     trol NETwork", ICALEPCS, Chicago, 1995. [2] E.L. Barsotti, Jr., "A Longitudinal Bunch Monitoring     System Using LabVIEW and High-speed Oscillo-     scopes", 1994 Accelerator Instrumentation Workshop,     Vancouver, Canada, 1994, pp. 466-472. [3] W.Blokland, G.Vogel, J.Dey, "A New Flying Wire     System for the Tevatron", this conference (PAC 97). [4] A.A.Hahn, " A Levenberg-Marquardt Least Squares     Fit Algorithm Optimized for LabVIEW". Technical     Note, 1997. [5] A.A.Hahn, "Results from an Imaging Beam Monitor     in the Tevatron using Synchrotron Light",     HEACC'92, pp. 248-250 Int. J. Mod. Phys. A     (Proc.Suppl.) 2B (1993). [6] M.Olson, A.A.Hahn, "Position and Collision Point     Measurement System for Fermilab's Interaction R e-     gions", Seventh Beam Instrumentation Workshop     1996, Argonne, Il. pp. 468-475.