# Run II Luminosity Progress\*

K. Gollwitzer, Fermilab, Batavia, IL 60510, U.S.A.

Abstract

The Fermilab Tevatron Collider Run II program continues at the energy
and luminosity frontier of high energy particle physics. To the collider
experiments CDF and D0, over 3 fb^-1^ of integrated luminosity has been
delivered to each. Upgrades and improvements in the Antiproton Source of
the production and collection of antiprotons have led to increased
number of particles stored in the Recycler. Electron cooling and
associated improvements have help make a brighter antiproton beam at
collisions. Tevatron improvements to handle the increased number of
particles and the beam lifetimes have resulted in an increase in
luminosity.

## Introduction

Run II is part of the Fermilab accelerator based experiment program. The
collider program consists of colliding proton and antiproton beams at
the B0 and D0 collision points within the Tevatron. Each beam is at
980GeV. The layout of the Fermilab accelerator complex associated with
the Run II program is shown in Figure 1.

![](media/image1.wmf){width="3.251388888888889in"
height="2.6055555555555556in"}

Figure 1: Layout of the Fermilab Tevatron Collider accelerator complex.

The process to accelerate protons to collisions is the following:

-   The Crockroft-Walton accelerates H¯ ions to 750 keV

-   The Linac accelerates the ions to 400 MeV

-   The H¯ ions are stripped during multi-turn injection into the
    Booster

-   The Booster accelerates the protons to 8 GeV

-   Protons transferred to the Main Injector are either accelerated to
    120 GeV for antiproton production or to 150 GeV for injection to the
    Tevatron

-   The Tevatron accelerates to 980 GeV

The process to produce, store and accelerate antiprotons to collisions
is the following:

-   The 120 GeV proton beam impinges on a nickel alloy target every 2.4
    sec

-   Downstream of the production target, a collection lens focuses 8 GeV
    secondaries into a transfer line

-   The secondaries are injected into the Debuncher Ring where only
    antiprotons survive the first hundred turns

-   The phase space density is increased by stochastic cooling systems
    before transfer to the Accumulator Ring

-   The Accumulator momentum stacks \~3000 pulses of antiprotons;
    stochastic cooling systems further increase the phase space density

-   The 8 GeV antiprotons are transferred to the Recycler via the Main
    Injector

-   Electron and stochastic cooling increase the phase space density in
    the Recycler

-   After 36 bunches of protons are established in the Tevatron,
    Recycler antiprotons are prepared in 9 injections of 4 bunches

-   Recycler RF manipulations make 9 parcels of antiprotons

-   A parcel is re-formed into 4 bunches and transferred into the Main
    Injector where it is accelerated to 150 GeV for injection into the
    Tevatron

-   The Tevatron accelerates the antiproton and proton beams to 980GeV
    and brings the beams into collision for the CDF and D0 experiments

## Performance

Run II has shown steady progress over the last five years as can be seen
in the peak luminosity and total integrated luminosity shown in Figures
2 and 3. Since PAC 2005, the record peak luminosity has more than
doubled from 127 x 10^30^ cm^-2^sec^-1^ to 292 x 10^30^ cm^-2^sec^-1^.
The total integrated luminosity was less than 1 fb^-1^ two years ago;
recently the total surpassed 3 fb^-1^.

![](media/image2.png){width="3.245833333333333in"
height="2.0444444444444443in"}

Figure 2: Run II history of the peak luminosity.

![](media/image3.png){width="3.2534722222222223in" height="2.0625in"}

Figure 3: Run II history of the integrated luminosity.

## Luminosity Factors

For a proton-antiproton collider, the instantaneous luminosity is

$L = \frac{3\gamma \cdot f_{0}}{\beta \ast} \cdot \frac{N_{p}N_{a}}{(\varepsilon_{p} + \varepsilon_{a})} \cdot F(\beta\text{*,}\varepsilon_{p},\varepsilon_{a},\sigma_{z})$

\(1\)

The major contributors to determining the luminosity are the number of
particles in each bunch (*N*), the transverse emittance of the beams
(*ε*) and transverse beam optics at the interaction point (*β\**). The
quantity and beam quality of the antiprotons available to the Tevatron
Collider are key. In particular, the rate of production is determines
how fast the program is able to recover from any failure that loses
antiprotons.

The evolution of luminosity for each store is dependent upon how fast
the beams' emittance increase \[1\]. There are numerous near collisions
of different bunches from each beam \[2\]. These beam-beam effects have
been studied. Each beam is on a helical orbit; there have been efforts
to increase the separation of the orbits during the past few years.

## Antiprotons

At the start of Run II, the Accumulator was the only source of
antiprotons for the Tevatron collider program. The Accumulator had to
balance production rate and the ability to hold onto large antiproton
stacks. The largest Accumulator stack was 250 x 10^10^ antiprotons. The
limitations of stochastic cooling result in the rate of antiproton
production to decrease as the stack size increased.

While the Recycler was being commissioned, some of the Accumulator
antiprotons were diverted to Recycler activities. Once the Recycler
became a viable storage ring, antiprotons were transferred from the
Accumulator to the Recycler before the stacking rate decreased too much.
In this manner, the combination of both rings made it possible to have
up to 350 x 10^10^ antiprotons for the Tevatron program. Combination
shots, where antiprotons from both rings were sent to the Tevatron,
happened between December 2004 and October 2005.

The first evidence of relativistic electron cooling on antiprotons
occurred in July 2005 \[3\]. Figure 4 shows two traces 15 minutes apart
showing the decrease in the antiproton momentum beam spread due to
electron cooling. Two and a half months later, electron cooling was
brought into operations. Soon thereafter, the Recycler became the sole
source of antiprotons for the Tevatron. The Accumulator began to tune
for production rate since stack size would be limited to \<100 x 10^10^
antiprotons. The Recycler is able to provide smaller beam emittance
which increases the luminosity.

![](media/image4.wmf){width="3.2527777777777778in"
height="2.1993055555555556in"}

Figure 4: First demonstration of relativistic electron cooling of
antiprotons.

Figure 5 shows the antiproton intensities in the Accumulator and
Recycler and the Tevatron luminosity for a typical week of operations.
Every 2.4 sec, \~2 x 10^8^ antiprotons from the Debuncher Ring are
transferred to the Accumulator. Momentum stacking occurs for 2-3 hr to
acquire \~50 x 10^10^ antiprotons at which time \~80% are transferred to
the Recycler Ring. Taking into account the overhead of loading the
Tevatron and luminosity lifetime, store duration has a broad
optimization for integrated luminosity around 20 hr. Hence, the Recycler
Ring is nearly emptied once a day for the collider program. Also shown
are gaps in antiproton production and luminosity. There are downtimes
due to failures and studies. Depending upon the length of downtime or
when a failure occurs in the case of losing the Tevatron store, the
number of antiprotons available can be affected.

![](media/image5.wmf){width="6.616666666666666in"
height="4.270833333333333in"}

### Target Station Improvements

The Main Injector slip-stacking process has been able to provide
consistently 8-9 x10^12^ protons on the target. Besides the target
module being subjected to the beam intensities, the Lithium Collection
Lens and Pulsed Magnet need to accommodate the large flux of
secondaries. Whenever one of these components need to be replaced,
antiproton production is stopped for at least 16 hours.

The target material is a nickel alloy and cooling is provided by air
flow. The design of the heat sinks is continually evolving to extend the
life of the target module. A smaller beam spot size improves the yield
however the target degrades quicker. There is a balance between yield
and target lifetime. Recently, the proton beam has been made to "sweep"
a circle during the pulse on the target to distribute the energy
deposition over a larger volume and has been shown to increase the
target lifetime. Currently, there is an operational program to explore
the yield and target degradation as the beam size and sweep radius are
changed.

Historically, Collection Lens failures have two modes: lithium breaches
the electron welded steel body of the lens or the transformer ground
faults due to radiation damage of the kapton insulator. A multiyear
program to improve the Collection Lens design has resulted in a titanium
body which is diffusion bonded. This lens design has been used in
operation for about a year and can be operated at a higher gradient.
More secondaries are focused into the beam line and reach the Debuncher
Ring as the gradient is increased. The transformer has been redesigned
to use an internally water-cooled ceramic insulator and just been put
into operations. The brief operational experience shows that the
transformer and Collection Lens are operating at lower temperatures.

The Pulsed Magnet directs the 8 GeV secondaries into the beam line which
transports beam to the Debuncher Ring. These magnets tended to fail
after \~2 x 10^19^ protons were on target. A collimator was added
between the Collection Lens and the Pulsed Magnet. The current magnet
has seen \>5.5 x 10^19^ protons.

### Acceptance Improvements

Part of the Run II upgrade plan was to increase the admittance of the
beam line from the Target Station and the Debuncher Ring to 35π mm-mr.
This goal means that a beam (95% normalized) emittance of 325π mm-mr
will be accepted. The upgrade included removal and modifications of
aperture restrictions, motorization of stands of small aperture
components, addition of orbit control (dipole trims and motorization of
quadrupole stands), modification of the lattice to decrease the beam
size in tight apertures, and instrumentation. The admittance has been
increased from 23π mm-mr to nearly the goal. The majority of progress
came with instrumentation commissioning and orbit control studies
performed during Tevatron Magnet replacements in December 2005 and
January 2006. Similar orbit control studies are planned for the
Accumulator to achieve \>10π mm-mr acceptance.

### Cooling Improvements

The Debuncher stochastic cooling systems have to be continually
monitored and adjusted to keep the systems optimized. The gain of each
system is changed throughout the cooling cycle to maximize the kicker
power. There are plans to add two-turn notch filters which would be
switched into the circuit in the middle of the cooling cycle.

The Accumulator stacktail stochastic system does the momentum stacking.
The 2-4 GHz stacktail system is what limits the antiproton stacking
rate. Several on-going upgrades and constant tuning have help to
increase the stacking rate. A summary of changes are the following:

-   Addition of an equalizer which improves the effective bandwidth by
    fixing the phase at band edges and more gain at higher frequencies

-   Radially offset one pickup tank to move one set of pickups away from
    the core orbit

-   Operate the closest set of pickups to the core

-   Change the Accumulator lattice to increase the slip factor and
    better match the phase advances between stochastic cooling systems
    pickups and kickers

    The increase in slip factor and effective bandwidth allows for a
    larger maximum flux through the stacktial system. These changes also
    decreased the amount of power needed to run the stacktail which
    decrease the amount of transverse heating.

    The Accumulator also includes core stochastic cooling systems.
    Improvements have been mainly to the two longitudinal stochastic
    cooling systems operating at 2-4 GHz and 4-8GHz. These two systems
    changed roles of main and helper system in February 2006. Now the
    2-4 GHz is used to transition from the stacktail system to the main
    4-8 GHz core system. The bandwidth of the 4-8 GHz system was nearly
    doubled when the main trunk line was changed from coax cable to
    fiber optic. There are plans to introduce a new equalizer into the
    4-8 GHz system to further increase the bandwidth.

The Recycler stochastic cooling systems have been working well. Electron
cooling is necessary for longitudinal cooling for \>200 x 10^10^
antiprotons. Since the electron cooling has been made operational there
has been effort to understand the cooling rate as a function of beam
position and current \[4\].

![](media/image6.png){width="3.2493055555555554in"
height="2.0388888888888888in"}

Figure 6: Best hour of stacking each day (mA = 10^10^).

![](media/image7.wmf){width="3.248611111111111in"
height="2.9506944444444443in"}

Figure 7: Stacking rate as a function of stack size.

### Summary

Figure 6 shows the best hour of stacking for each day during the past
two years. Figure 7 shows the change in performance of the Accumulator
of the increase in stacking rate as a function of stack size. In
addition, there has been an effort to reduce the amount of time it takes
to transfer antiprotons from Accumulator to the Recycler from about an
hour to \~10 minutes; this means more stacking time per day. The number
of antiprotons collected each week is shown Figure 8.

![](media/image8.wmf){width="3.248611111111111in"
height="2.2041666666666666in"}

Figure 8: Number of Antiprotons produced in a week.

## Other Improvements

The Recycler has changed its working point which improved the lifetime
for large number of antiprotons \[5-6\]. An adaptive Feed Forward RF
correction has been applied in the Recycler \[7\]. Prior to the
correction, there would be a wide range in the intensity of the parcels,
and for bunches within each parcel, sent to the Tevatron. The antiproton
bunch intensities within a store did have variations of \>100% which
leads to large tune shifts and differences in luminosity for each
crossing. With the correction, the antiproton bunches are more uniform
with a variation \<25%.

Table 1: Run II records

  --------------------------- -------------- ------------- -------------------
  **Record**                  **Pre-2006**   **Current**   **Units**

  Antiprotons Stacking Rate   17.5           23.1          10^10^/hr

  Antiprotons produced in one 1710           2810          10^10^
  week                                                     

  Antiprotons in Recycler     325            465           10^10^

  Peak Instantaneous          180            292           10^30^cm^-2^s^-1^
  Luminosity                                               

  Weekly Integrated           25             45            pb^-1^
  Luminosity                                               

  Monthly Integrated          85             167           pb^-1^
  Luminosity                                               
  --------------------------- -------------- ------------- -------------------

Tevatron efforts have been to measure, understand and mitigate the
effects of beam-beam interactions; those efforts are presented by others
at this conference \[8-11\]. The optics was change to decrease *β\**
\[12-13\]. About the same time that the Recycler became the only source
of antiprotons for the Tevatron. The optics change and Recycler only
operation occurred in October 2005 and the peak luminosity increase can
be seen in Figure 2.

There have been small improvements to the antiproton transfer
efficiencies and Main Injector coalescing process \[14\]. There has been
work to improve the reliability of the storage rings and Tevatron.

## Summary

Since the last Particle Accelerator Conference in 2005, there has been
enormous progress made in Run II. Table 1 shows a comparison of records
prior to 2006 and current. The integrated luminosity has increased
significantly mostly due to a larger number of antiprotons being
available. The antiproton production rates are the result of the Run II
upgrade program, bringing into operation the Recycler with electron
cooling and attacking reliability issues so that downtime is infrequent
and minimal.

Work continues on further increasing the antiproton stacking rate in the
Accumulator. Both the Recycler and Tevatron have projects to handle the
increase in number of antiprotons expected to circulate in each ring.
Both rings will have new challenges in either cooling or beam-beam
effects. The Run II program expects to easily provide 4 fb^-1^ over the
next two years.

##  References

\[1\] R. Moore, "Review of Recent Tevatron Operations," PAC'07,
Albuquerque, June 2007, TUOCKI01.

\[2\] Y. Alexahin, "Optimization of the Helical Orbits in the Tevatron,"
PAC'07, Albuquerque, June 2007, FRPMS006.

\[3\] S. Nagaitsev et al., "Antiproton Cooling in the Fermilab Recycler
Ring," Beam Cooling and Related Topics, International Workshop on Beam
Cooling and related Topics -- COOL05, Galena IL, USA, September 2005, p.
39.

\[4\] L. Prost and A.V. Shemyakin, "Electron Cooling Rates
Characterization at Fermilab's Recycler," PAC'07, Albuquerque, June
2007, TUPAS030.

\[5\] A. Burov and V. Lebedev, "Instabilities of Cooled Antiproton Beam
in the Fermilab Recycler Ring," PAC'07, Albuquerque, June 2007, WEYC01.

\[6\] B. Chase et al., "Longitudinal Momentum Mining of Antiprotons at
the Fermilab Recycler: Past, Present, and Future," PAC'07, Albuquerque,
June 2007, WEOCKI04.

\[7\] M. Hu et al., "Uniform Longitudinal Beam Profiles in the Fermilab
Recycler Using Adaptive RF Correction," PAC'07, Albuquerque, June 2007,
MOPAS011.

\[8\] A. Valishev et al., "Observations and Modeling of Beam-Beam
Effects at the Tevatron," PAC'07, Albuquerque, June 2007, TUOCKI03.

\[9\] V. Shiltsev et al., "Experimental Demonstration of Beam-Beam
Compensation and Prospects for the LHC," PAC'07, Albuquerque, June 2007,
TUOCKI04.

\[10\] V. Kamerdzhiev, "Experimental and Simulation Studies of Beam-Beam
Compensation with Tevatron Electron Lenses," PAC'07, Albuquerque, June
2007, TUPAS024.

\[11\] E. Stern and A. Valishev, "Simulation of Coherent Beam-Beam
Effects in the Presence of Impedance," PAC'07, Albuquerque, June 2007,
FRPMS012.

\[12\] M.J. Syphers and R. Miyamoto, "Direct Measurements of Beta-star
in the Tevatron," PAC'07, Albuquerque, June 2007, THPAN115.

\[13\] A. Valishev, "Correction of Second Order Chromaticity at
Tevatron," PAC'07, Albuquerque, June 2007, FRPMS015.

\[14\] C. Bhat, "Anti-Buckets at Fermilab Recycler for Antiprotons
Stacking and Unstacking," PAC'07, Albuquerque, June 2007, TUPAS008.