# Tevatron Operational Status and Possible Lessons for the LHC\*

V. Lebedev^\#^, FNAL, Batavia, IL 60510, U.S.A.

Abstract

This paper provides an overview of the Tevatron Run II luminosity
progress and plans, including SC magnet measurements and modeling of
field errors in view of the LHC operation. It also discusses antiproton
production, stacking and cooling.

## Status of the collider

Commissioning of Tevatron Run II began in the spring of 2001 \[1,2,3\]
and was formally finished in the summer of 2003 when we declared that
the collider is operational. That changed an operational attitude to the
studies requiring them to be better focused and organized. Although the
study time was reduced, both peak and integrated luminosities
demonstrated the same steady growth as before culminating in the peak
luminosity of 172∙10^30^ cm^-2^s^-1^ achieved in January 2006 and the
best weekly integrated luminosity of 24.4 pb^-1^ in December 2005 (see
Figures 1 and 2). This progress was a result of many improvements. The
major contributors of the last two years are the commissioning of
Recycler ring \[4\] into collider operations with consecutive
commissioning of electron cooling, and a growth of antiproton production
rate due to slip stacking, aperture improvements in Debuncher and
Accumulator, and improvements of stochastic cooling. That resulted in
the antiproton peak production rate of 2.01∙10^11^ hour^-1^ and the
maximum stack size in Recycler of 4.36∙10^12^.

Three month shutdown in 2006 started one week earlier than scheduled
(March 1) due to a failed Tevatron magnet. Recovery from the shutdown
began in the end of May with first luminosity seen on June 13. Complete
recovery took about 4 weeks.

## Tevatron

The worst problems preventing stable Tevatron operations were addressed
in the first three years of Run II. The last two years resulted in
further operational and engineering improvements aimed at achieving Run
II luminosity goal of 3∙10^32^ cm^-2^s^-1^. In 2003 we found out that
all Tevatron dipoles have coherent skew-quadrupole component \[5\]. It
has been slowly growing since the magnet installation in 1982 due to
compression of thermo-insolating spacers in the support of cold bodies
of SC dipoles. It took 3 years and 3 major shutdowns to finish shimming
for all 772 Tevatron SC dipoles this year. Another persistent problem is
that the Tevatron tunnel is slowly sagging. It forces us to measure and,
if necessary, correct positions and rolls for large number of magnets at
every major shutdown. During 2006 shutdown about 50 quadrupoles we
unrolled. Two additional electrostatic separators and second electron
lens were also installed in this shutdown aiming further improvements in
the machine operation.

![](media/image1.png) Figure 1: Run II luminosity integral (average of
both CDF and D0 detectors).

![](media/image2.png)Figure 2: Run II peak luminosities (average of both
CDF and D0 detectors).

Magnet quenches are the major reason of Tevatron downtime. Operational
changes introduced after collider was commissioned reduced the number of
quenches by a factor of two, resulting in about 8 quenches per month for
the last 3 years and ≈30% of stores ending prematurely. Normally, quench
recovery takes about an hour for mild quenches (magnet temperature
raises to 10-15 K) and multi-hour recovery for major quenches (magnet
temperature raises to \~100 K). But sometimes even a mild quench can
cause a magnet failure resulting in multi-day repair. Table 1 presents
major magnet failures of Tevatron magnets which resulted in significant
downtime. While we were lucky in FY (fiscal year) 2005, when no major
failures happened, three major failures occurred in the first five
months of FY 2006 resulting in 5 weeks downtime and a week earlier start
of 2006 shutdown. Two of these quenches happened due to failed pressure
relief (Kautzky) valves. Considering this a systematic failure, we
replaced the failed part in all of about 1200 valves during 2006
shutdown. One of worst failures happened on Dec. 20, 2003 when a
hardware failure caused a beam loss with consecutive major multi-house
quench with 2/3 of the beam lost in the ring before the beam was
aborted. Magnets and beam collimators had to be repaired. This event was
carefully analyzed and practical recommendations were drawn (see Ref.
\[6\] for details.)

Table 1: Failures in Run II

  --------------- ------------- ---------------------------------- --------
  Date            Time lost     Description                        Sector

  29-Apr-01                     Cryostat vacuum leak               D13

  21-May-01                     Helium leak at corrector           F13
                                feed-through                       

  8-Jul-01                      Helium leak on spool               F47

  18-Aug-01                     Helium leak                        F44

  1-Mar-03        12 days       Safety lead ground fault           A13

  5-Dec-03        12 days       Helium leak at corrector           C19
                                feed-through caused by             
                                catastrophic beam loss             

  20-Dec-03       10 days       Cryostat vacuum leak               B14

  15-Mar-04       12 days       Helium leak                        A44

  21-Nov-05       3 weeks       Helium leak caused by stuck        B17
                                Kautzky valve                      

  14-Jan-06       2 weeks       Cryostat vacuum leak (air)         A44

  22-Feb-06       1 week        Helium leak caused by stuck        F47
                                Kautzky valve                      
  --------------- ------------- ---------------------------------- --------

![](media/image3.png){width="3.252083333333333in"
height="2.647222222222222in"}

Figure 3: Distribution of relative normal and skew-quadrupole errors
along the ring for collision optics in units of 10^-3^

Table 2: Relative errors of focusing strength for the interaction region
quadrupoles in units of 10^-3^

+------------+---------+----------+------------+----------+----------+
| NAME       | Inj.    | Low      | NAME       | Inj.     | Low      |
|            |         |          |            |          |          |
|            |         | Beta     |            |          | Beta     |
+------------+---------+----------+------------+----------+----------+
| B0Q3       | 4.34    | -11.18   | D0Q3       | -1.01    | -9.49    |
+------------+---------+----------+------------+----------+----------+
| B0Q2       | 4.62    | -1.87    | D0Q2       | 21.58    | -0.83    |
+------------+---------+----------+------------+----------+----------+
| B0Q3D      | -1.32   | -0.09    | D0Q3F      | 0.77     | 0.24     |
+------------+---------+----------+------------+----------+----------+
| B0Q3F      | -1.37   | -0.47    | D0Q3D      | 0.20     | -1.84    |
+------------+---------+----------+------------+----------+----------+

New BPM system was commissioned at the beginning 2005. It significantly
improved the accuracy of optics measurements and, consequently, led to
better knowledge of linear and non-linear optics of the machine. The
linear part of machine optics model has been built by fitting of large
number of measured differential orbits to the model predictions \[7\].
Although initially the model included the results of magnetic
measurements for all quadrupoles, the beam based measurements yield up
to 2% corrections for quadrupole focusing. Figure 3 presents
corresponding relative values of normal and skew quadrupole components.
The largest fraction of the skew quadrupole component is related to the
skew quadrupole fields of nearby dipoles. We do not know the reason for
so large normal quadrupole component which exceeds the accuracy of the
magnetic measurements by an order of magnitude. These focusing errors
result in about 15% correction for beta-functions and quite strong
coupling which cannot be neglected in any optics or optics related
calculations. Both normal and skew-quadrupole errors depend on beam
energy, further complicating the analysis and optics tuning. Although
the final focus quadrupoles were manufactured and measured a few years
later than other magnets they exhibit similar problems as becomes
evident from Table 2; but their errors affect optics much stronger
because they are located where the beta-functions are large (\~1000 m).
Note that all beam based measurements measure quadrupole strengths
relative to the average dipole strengths determining the beam energy.
This average misbalance is 0.179% at injection and 0.191% at collision
energy. It is not shown in Figure 3.

Success of linear optics measurements inspired us to look for machine
non-linearities. The study aimed to find a sextupole distribution at the
injection energy was carried out in collaboration with CERN \[8\].
Although accuracy of the measurements does not allow us to ascribe
sextupole strength to each magnet, the study pointed out major
contributors. Analysis showed that all of them are related to regular
machine sextupoles and that there is no one or few magnets with large
sextupole components dominating ring non-linearity. That was good news
given the fact that we did not have reliable data on the magnet
non-linearities. Although a full set of magnetic measurements was
carried out for each magnet before its installation in the tunnel, there
is little trust in the measurements of sextupole component. At the time
of the measurements it was unknown that the sextupole component strongly
depends on time due to persistent currents in superconductor (see Ref.
\[9\] and references there). Therefore the time of each measurement in
the magnet hysteresis cycle was not specified and, consequently,
sextupole strength at given time is unknown. Special sextupole circuits
correct time dependent chromaticity of the entire ring but
redistribution of sextupole component along the ring has not been known.

There has been a significant progress in simulation of the beam-beam
effects for Tevatron \[10\], but further progress required comparison
with experiment and was delayed by absence of accurate bunch-by-bunch
tune measurements. Two tune monitors have been routinely used in
Tevatron. The first one was inherited from Run I. It is based on
resonant circuit built on the capacitance of pickup plates and operates
at \~21 MHz. It has good sensitivity and good tune resolution but it
cannot resolve tunes of separate bunches and can not independently see
protons and antiprotons. Another tune monitor is based on microwave
technology developed for stochastic cooling \[11\]. It operates at 1.7
GHz and can resolve separate bunches. However because of very high
frequency it sees many synchro-betatron modes making tune line much
wider than difference between horizontal and vertical tunes. There is
strong coupling in Tevatron resulting that both horizontal and vertical
modes contribute to the signals of horizontal and vertical monitors.
Consequently, they report a mixture of both tunes making impossible to
determine the real tunes. Recently we started development of another
tune monitor based on a sub-micron resolution BPM and FPGA technology.
After simple analog preprocessing of pickup signal electronics digitizes
each bunch position and records it to memory. Then, FFT is performed for
each bunch turn-by-turn position yielding bunch spectrum and tunes.
Figure 5 presents results of the first tests of such tune monitor. Small
vertical excitation is applied so as to see the signal clearly. It
amplifies beam motion at betatron frequency by about 30 Db. In
accordance with expectations, bunches 1 and 12 have different
frequencies and different amplitudes.

Recently introduced Tevatron tune and orbit feedbacks resulted in more
stable machine operation and minor improvement in the beam lifetime.

![](media/image4.png)

Figure 5: Bunch spectrum (mm per harmonic) for proton bunches 1 and 12
measured with new Schottky monitor. Data are taken during usual Tevatron
store.

## Antiproton production

The success of Run II would not be possible without reliable work of
Booster and Main injector (MI) - two proton synchrotrons used for
injection of protons to Tevatron and antiproton production. In the
spring of 2005, NuMI/MINOS beam operations were included into routine
operation of Tevatron complex. This was achieved by adding 5 additional
Booster batches to the two required for antiproton production. That put
a strong pressure on minimizing beam losses in both Booster and MI. To
address this problem and also increase number of protons on the target a
team of about 20 people was created in the summer of 2005. The group was
divided into four teams charged to improve performance of Booster, MI,
Antiproton source, and instrumentation support.

The major task of the Booster team was to decrease longitudinal
emittance in the Booster. There were a number of improvements, but the
most significant was introduction of longitudinal quadrupole damper
suppressing longitudinal oscillations after transition crossing. The
work resulted in an increase of number of protons from 3.9∙10^12^ to
4.5∙10^12^ with simultaneous decrease of longitudinal emittance from 0.2
to 0.12 eV⋅s.

Presently, MI cycle includes two slip stacked Booster batches \[12\] for
antiproton production and five Booster batches for NuMI. The task of MI
team was to increase beam intensity on the antiproton production target
and minimize beam losses. Improvements in beam loading and longitudinal
matching, optimization of transverse and longitudinal dampers as well as
a few other addressed problems yielded an increase of number of protons
on the target from 6.2∙10^12^ to 7.6∙10^12^ and resulted in the total
number of proton accelerated in one cycle to be \~3∙10^13^.

![](media/image5.png){width="3.2527777777777778in"
height="3.3180555555555555in"}

Figure 6: Historical data for the dependence of antiproton intensity on
the number of protons on the target.

Two additional issues were addressed to maximize the phase density of
antiprotons leaving the target. First, optics of MI-to-target transport
line was redesigned to nullify both dispersions on the target. That
allowed us to reduce the beam size on the target and to exclude its
dependence on the energy spread. Presently, the minimum beam size is
limited by the target damage. Rms size is \~150 μm for normal stacking
and \~220 μm for slip stacking. The second harmful problem was slow
uncontrolled beam position displacements on the target. They were
suppressed by digital damper. Figure 6 presents data showing
improvements in the number of protons on the target and corresponding
increase in number of antiprotons at the end of Debuncher injection
line.

## Antiproton cooling 

Five weeks of downtime spent for Tevatron repairs in FY2006 were lost
for integrating the luminosity but they were exceptionally useful for
studies in other machines resulting in significant improvements for
Antiproton production. This time would be difficult to obtain under
normal operating conditions. Most time consuming was orbit correction to
the centers of quads for Debuncher and AP-2 line, which connects the
target and Debuncher. It was complimented by the redesign of Debuncher
optics aimed to minimize the beam size at places with limited aperture
such as the stochastic cooling tanks, injection septum and extraction
kicker \[13\]. Table 3 presents results of this work. One can see that
the experimentally achieved acceptances are \~10% below design values
and there is a potential for further improvements. Simulations show that
the antiproton yield is proportional to the acceptance and for the
acceptance corresponding to the new optics it should be about 30∙10^-6^
antiprotons/proton. Experimentally achieved value (target to
Accumulator) is 21∙10^-6^. Comparison of measurements and simulations
has shown that there is excessive beam loss in the middle of AP-2 line
and also loss during Debuncher-to-Accumulator transfers. Both of them
require better steering and optics improvements. Recently, additional
vertical correctors were installed in AP-2 line to address the loss in
the line.

Table 3: Improvements of Debuncher acceptances

+------+--------------+---------------+---------------+---------------+
|      | Initial      | Initial,      | New design    | Present       |
|      | design mm    | measured      |               | measured      |
|      | mrad         |               | mm mrad       |               |
|      |              | mm mrad       |               | mm mrad       |
+------+--------------+---------------+---------------+---------------+
| *ε   | 34           | 30            | 40.5          | 35.3          |
| ~x~* |              |               |               |               |
+------+--------------+---------------+---------------+---------------+
| *ε   | 31           | 25            | 37.5          | 34.6          |
| ~y~* |              |               |               |               |
+------+--------------+---------------+---------------+---------------+

The growth of the stacking rate would not be possible without
improvements in the stochastic cooling. First, we introduced gain ramps
for Debuncher cooling. The ramps increase the gain for transverse
systems and decrease it for the longitudinal ones maximizing cooling
power for Debuncher cooling cycle of \~2.5 s. Second, we redistributed
gains in the longitudinal core cooling system in Accumulator.
Historically, main cooling was supplied by 2-4 GHz system while 4-8 GHz
system was considered auxilliary. Using 4-8 GHz system as a main system
and the 2-4 GHz as a helper we improved performance for the core cooling
system. That suppressed the inverse particle flux from the core to the
stack and resulted in faster stacking. Figure 7 presents historical data
for the dependence of stacking rate on the stack size demonstrating
steady growth for last two years.

As one can see in Figure 7 the stacking rate is decreasing with stack
size and comes to zero for about 2.5∙10^12^ antiprotons. Before Recycler
was commissioned we usually stacked \~1.5∙10^12^ antiprotons every 25-30
hours to fill the collider. With Recycler being operational we could
split the stack between Recycler and Accumulator so that the collider
would be filled from both machines -- so called mixed mode operation.
That allowed us to increase the total number of Antiprotons available
for the collider fill to (2-2.5)∙10^12^. But the phase density in both
machines was not high. Just as in the Accumulator, the efficiency of
Recycler stochastic cooling has been decreasing with stack size limiting
the Recycler stack to \~1.5∙10^12^. Successful commissioning of electron
cooling in the fall of 2005 addressed this problem \[4, 14\]. Gradual
transition from the mixed mode operation to the Recycler only shots was
carried out in the second half of 2005 (see Figure 8) and resulted in
the record number of antiprotons available for the shot of 4.36∙10^12^.

![](media/image6.png){width="3.254166666666667in"
height="3.2493055555555554in"}

Figure 7: Historical data for the dependence of stacking rate on the
stack size.

Main advantage of the electron cooling is that its efficiency does not
depend on number of antiprotons. But deeper cooling makes the antiproton
beam less stable. The first problem we encountered was the transverse
resistive wall instability. It was suppressed by digital wideband damper
with \~25 MHz bandwidth upgraded to \~90 MHz during 2006 shutdown
\[15\]. That allowed us to increase the phase density by a factor of 2.
Further increase of the phase density was limited by growth of tails in
the bunch distribution with consecutive lifetime degradation.
Measurements show that this loss is not accompanied by measurable dipole
beam motion. That basically excludes dipole instabilities. The entire
set of experimental data is quite controversial leaving us with a wide
range of speculations. Three mechanisms were discussed. The first one is
related to the development of transverse quadrupole instability due to
interaction of antiproton beam with the electron beam \[16\]. Another
possibility is storing electrons in the electron cooler with consecutive
excitation of $e\overline{p}$-instability. There is also a possibility
that the non-linear field of cold antiproton beam drives non-linear
resonances for halo particles. We are discussing a set of experiments
allowing us to find out the reason of particle loss and possible ways to
mitigate it.

![](media/image7.png){width="3.245138888888889in"
height="2.0256944444444445in"}

Figure 8: Changes in number of antiprotons available in Recycler for
collider shots.

## PLANs for the future

Present DoE guidance is that Fermilab will operate the collider to the
end of 2009 when LHC is expected to be fully operational. The design
plan anticipates that by this time we will achieve the peak luminosity
of 3∙10^32^ cm^-2^s^-1^ and the total Run II luminosity integral of \~7
fb^-1^. To achieve this we need to double the peak luminosity and the
luminosity integral per week. That is a challenging task. For last three
years we were able to follow the design plan and it supports our
confidence that we can continue this trend in the future.

The antiproton production is a cornerstone of further luminosity growth.
By the next summer we expect to increase the present peak antiproton
production rate from 20∙10^10^ to 30∙10^10^ antiprotons per hour. The
following upgrades are planned. First, better steering and optics
corrections should yield acceptance increase in AP2 line and Debuncher
resulting in 10-30% gain in antiproton yield. Second, replacement of RF
tubes in Debuncher and the lithium lens upgrade should yield another
10-20% gain. Third, this growth needs to be supported by improved
performance of stochastic cooling in Debuncher and Accumulator. Modeling
and simulations show that with a few comparatively inexpensive hardware
upgrades like gain correction and installation of additional notch
filters it should support fluxes up to 35-40∙10^10^ hour^-1^.

Presently, total loss of antiprotons at beam transfers
(Debuncher-to-Accumulator, Accumulator-to Recycler) and coalescing of
antiproton bunches in Debuncher is in the range \~15-25%. At least half
of this loss can be recovered with better machine tuning. Decreasing the
Accumulator-to-Recycler transfer time from present 45 minutes to 15
minutes will increase the amount of antiprotons by additional \~15%. The
maximum stack size of 436∙10^10^ achieved in Recycler is already close
to the Run II goal of 600∙10^10^. Planned improvements of beam stability
in Recycler should be adequate in achieving the final goal.

We already observe problems with beam-beam effects from antiprotons to
protons. It is expected to be worse with further antiproton intensity
increase. To alleviate problems with beam-beam effects we plan to change
the working tune of the collider so that larger tune space would be
available. Two working points have been discussed. The first one is
located just above half integer resonance (like in KEKB collider), and
the second one is near 2/3 resonance (like in SPS collider). Our present
preference is with the first choice, but approaching closer to
half-integer resonance amplifies chromaticity of beta-functions and,
consequently, reduces momentum aperture to unacceptable level, if this
chromaticity is not compensated. During the last shutdown Tevatron
sextupoles were rearranged and new sextupole circuits were formed to
control this chromaticity. Simulations show significant mitigation of
beam-beam effects at the new working point if the beta-function
chromaticity is suppressed. That also should allow us to increase the
proton intensity by \~10%.

## References

\[1\] V. Lebedev, PAC'03, Portland, May 2003, p. 29.

\[2\] V. Shiltsev, EPAC'04, Lucerne, July 2004, p. 239.

\[3\] P. Bauer, *et. al*, PAC'05, Knoxville, May 2005, p.54.

\[4\] S. Nagaitsev, "Fermilab Recycler Performance with a Dual Cooling
System, This conference.

\[5\] V. Lebedev, *et. al*, Proc. of the 8th Intern. Computa-tional
Accelerator Phys. Conf. (ICAP'04), June 2004; NIM-A, 558, No.1, Oct.
2005, p.299; M. Syphers -- private communications, 2003.

\[6\] N. Mokhov, *et. al*, "Beam-induced damage to the Tevatron
components and what has been done about it," ICFA-HB2006, Tsukuba, May
29-June 2, 2006, [http://indico.kek.jp](http://indico.kek.jp/).

\[7\] A. Valishev, *et. al*, "Progress with Collision Optics of the
Fermilab Tevatron Collider," This conference.

\[8\] F. Schmidt, et. al, "Measurement and Correction of the 3rd Order
Resonance in the Tevatron," This conference.

\[9\] G. Velev, *et. at*, "New Measurements of Sextupole Field Decay and
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\[10\] A. Valishev, *et. al*, PAC'05, Knoxville, May 2005, p. 4117.

\[11\] A. Jansson, *et. al*, EPAC'04, Lucerne, July 2004, p. 239.

\[12\] K. Koba, *et.al*, PAC'03, Portland, May 2003, p.1736.

\[13\] V. Nagaslaev, *et. al*, "Measurement and Optimization of the
Lattice Functions in the Debuncher Ring at Fermilab," This conference.

\[14\] A. Shemyakin, *et. al*, "Performance of Fermilab\'s 4.3 MeV
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\[15\] A. Burov, *et. al*, "Suppression of Beam Transverse Microwave
Instability by a Digital Damper," This conference.

\[16\] A. Burov, *et. al*, "Transverse electron-antiproton instability
in the recycler ring," ICFA-HB2006, Tsukuba, May 29-June 2, 2006,
[http://indico.kek.jp](http://indico.kek.jp/).