Initial Results from the Tevatron Electron Lens
K. Bishofberger1, G. Kuznetsov2, V. Shiltsev2, X.L. Zhang2
University of California, Los Angeles, CA 90095
Fermi National Accelerator Laboratory, Batavia, IL 60510
2
Abstract. A novel focusing experiment is being conducted on the Tevatron at Fermilab to compensate the beam-beam tune shift. A 10-keV electron beam is generated, sent along the
Tevatron beam pipe, and collected; the antiproton bunches pass through the electron beam and
are defocused through electrical and magnetic interaction with the electron beam. The focusing
force as a function of radius is adjustable, and the passage of the electron beam quickens the settling of plasma waves caused by the interaction. The charge density is fully adjustable, allowing
easy bunch-to-bunch adjustments on a fast, reliable basis. These aspects of the electron lens
concept break through many limitations of other beam control options for future machines.
INTRODUCTION
Circular colliders have improved their performance over the past several decades
by fantastic proportions. Not only do they continually redefine the energy frontier, but
also the luminosity, the average rate of recordable interactions at the collision points,
has escalated over five orders of magnitude in the same time. However, the users of
these colliders with for even more luminosity than what current collider technology
can provide; their searches for ever more elusive particles demands large quantities of
collisions.
However, a significant limit has been reached that makes larger luminosity arduous
to achieve. This barrier is the beam-beam interaction, where each bunch is affected by
the space-charge forces of the colliding bunch; in the Tevatron, antiproton bunches of
several 1010 particles per bunch collide with proton bunches of several 1011 particles
per bunch. This suggests a weak-strong interaction, and the antiprotons will feel large
space-charge forces at the interaction points.
The tune, which is the number of betatron oscillations per revolution, is critical to
beam stability. Resonances occur at all horizontal and vertical tunes vx and v^ that
obey the relation Mvx + Nvy = P for integer M, N, and P. The Tevatron typically
operates with vx = 20.585 and v^ =20.565, squeezed between the 7th and S^-order
resonances, which is simply established via the total focusing strengths of the quadrupoles. Unfortunately, two factors defeat this straightforward scheme.
First, the focusing force at the interaction points is nonlinear, especially for particles with large betatron-oscillation amplitudes. This spreads the distribution of tunes
to a large footprint for each bunch. Second, during normal Tevatron multibunch
operation, each bunch feels long-range forces at crossings with the opposing bunch
train other than the important interaction points. These crossings are called "parasitic"
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
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crossings, and since they are not uniformly positioned throughout the ring, each witness bunch receives a unique tune shift. Again, the antiproton bunches are affected
more drastically than the proton bunches.
The Tevatron Electron Lens (TEL) is a recently installed device that provides another interaction point for the antiproton bunches. However, the bunches interact with
the negative space charge of an electron beam, and the goal is to subtract out the tune
shift induced by the proton bunches. This is what is referred to as beam-beam compensation[l]. The electron beam, discussed in more detail in a later section, can be
adjusted in current for individual bunches, and its radial profile is also adjustable to
decrease the intrabunch tune spread.
Initial successes in shifting the tune using the TEL has been discussed and celebrated among circular collider folk; however, it is largely unnoticed by the plasma lens
community and can provide a possible solution to one of a linear collider's main
concerns: fast steering and focusing feedback loops at the final focus. Groups who
might find TEL work or applications relevant might not know about it. This concern
prompted the current presentation.
DESCRIPTION OF THE TEL APPARATUS
The TEL immerses its electron beam in a longitudinal magnetic field provided by
three separate solenoids. The main solenoid wraps around the Tevatron beam pipe
where the interaction with the antiprotons takes place. Another solenoid surrounds the
gun, and a third surrounds the collector. Together, they produce a 7i-shaped magnetic
field that the low-energy electron beam follows, as Figure 1 illustrates. The gun and
collector are thus out of the path of the Tevatron bunches.
FIGURE 1. A view from above of the TEL apparatus. The gun and collector solenoids are copper
windings, while the main solenoid is superconducting. A new geometry, where the gun and collector
are only 33° off of the main axis, will be implemented early in 2003.
The electron gun is a high-perveance (joP ~ 6) thermionic cathode gun with an oxide-impregnated tungsten cathode heated to roughly 1100°C. The typical cathode-to-
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ground voltage is -10 kV steady, while an intermediate anode is pulsed to 6 or 7 kV
above the cathode. This pulsing drives the electron current. A maximum of about 2.5
A will flow from the cathode, which is 10 mm diameter. The transverse beam profile
is fairly flat, but an additional "profiler" electrode surrounding the cathode can be set
to a more negative potential. This steals electric field lines from the cathode and
decreases the effective beam radius; biasing it enough cuts off all electron current.
Another gun is currently being constructed that provides a more Gaussian beam profile, since the resulting electric field is likely preferential for our goals.
The beam passes from the gun into the beam pipe, which has a smaller acceptance
(\\P -3.2) than the perveance of the gun. Hence, a low-energy, and therefore high
charge-density, beam will not be accepted entirely; a portion of the beam will be
denied access, leaving a beam that has a central depression in its space-charge distribution. However, keeping the electron beam energetic enough preserves the flatness
of the charge distribution.
Another aspect of this system is the high duty cycle. Previous results have tested
the TEL on only one Tevatron bunch, but soon we will pulse for all 36 bunches, separated by 396 nsec). Given the pulser rise time and the dependence on a temporally
constant current, the duty cycle approaches 50%. This implies very high-power supplies with large bandwidth. Since radiation from the Tevatron tends to shorten the
lifetime of electronics near the apparatus, a capacitor-based pulsing scheme was implemented as shown in Figure 2. The power supplies rest far away from the lens itself,
while the cables feeding energy from the capacitors to the gun are purposefully short.
This enables the use of a depressed collector, where the collector sits at a potential just
a little higher than the cathode. The beam then recirculates, and only a small amount
of average power must be provided by the power supply.
Figure 2. Electrical schematic of the TEL. The capacitors and the RF-tube pulser are positioned next to
the lens itself, while the power supplies are removed (represented by inductors) from the radiation
environment.
Since the anode-to-ground capacitance is 40 pF plus that of any cables, the pulser
must push significant currents to pulse the anode quickly. Without space limitations,
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the capacitance could be decrease, and thus the rise time of the pulse could be made
quicker.
Beam Characterization
The main solenoid is typically set to 35 kG, while the gun and collector solenoids
are around 3.8 kG[2]. Since the electron beam is highly magnetized, the beam size
scales with the square root of the field strength. Thus, the beam radius ends up being
about 3.2 mm in the interaction region. Therefore the antiproton bunches, whose
profiles tend to be Gaussian, should have a radius significantly less than that to ensure
equal tune shifts for particles of all betatron amplitudes. The ratio of fields in the main
and gun solenoids can be changed to provide different beam sizes.
The electron beam must also be centered on the antiproton bunches transversely.
This is provided by dipole correctors that are integrated into the main solenoid package. One pair of short dipoles (horizontal and vertical) near the gun establishes the
beginning of the beam at a given location; a second pair extend the length of the main
solenoid to establish the correct angle; a final pair readjusts the beam to send it properly into the collector.
This assumes that the field lines of the main solenoid are straight. Careful mapping
of the field lines concluded that the field lines deviate from a straight line by no more
than 15 um rms horizontally and 50 um rms vertically, which is considerably better
than tolerable limits (around 200 um rms).
Diagnostics
A number of typical diagnostics are used to measure beam properties. Foremost are
BPMs that are positioned in the main solenoid near the gun and near the collector.
These are intended to determine whether the electron beam is centered on the antiprotons. However, these BPMs are required to measure electron, proton, and antiproton
bunches. Currently we switch manually between electronics that select the lower
frequencies of the electron beam (<10 MHz) signal or the higher frequencies (-100
MHz) for the protons and antiprotons. Critical gating is also needed to determine
which bunch is being analyzed. Calibrations of the BPMs show different responses
per plate at these high frequencies, which conforms to our discovery that the greatest
tune shift, found by scanning the dipole correctors over a large range, did not occur at
the position that the BPMs claimed that the electron beam was aligned. A recent
effort to recalibrate the BPMs to provide useful measurements is underway.
The current is monitored in several places. A current transformer set on the wire
feeding the cathode determines the pulse of current leaving the cathode. The BPM
A+B signals are integrated to see the charge flux. Another current transformer by the
collector measures the current being received. Also, the power supply in Figure 2 that
sets the cathode potential from ground is monitored; this should provide negligible
current unless the beam is striking the pipe walls.
The most tenuous measurement in this experiment is the Tevatron tune. This uses
Schottky detectors, which are nondestructive, position-sensitive resonant cavities
tuned to frequencies much higher than the revolution frequency. The passing bunches
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excites multiples of the revolution frequency in the cavities, but statistical fluctuations
in the particle distributions, caused by the average phase advance per revolution,
generates sideband frequency components. By downconverting this signal, a spectrum
analyzer will bear witness to the tune. Not only is the specific tune visible, but peak
amplitudes, peak widths, sidebands, and noise floors are seen and are useful diagnostics as well. A treatise on the interpretation of these elements would fill many
pages[3]; only the central-peak frequency is of interest in this discussion. Monitoring
frequency shifts of this peak while adjusting the TEL is how the focusing strength of
the lens is determined.
TUNE SHIFT AND FOCUSING STRENGTH
Theoretical Analysis
By analyzing the focusing force of an electron beam on a passing test charge, we
can easily calculate the expected focal length and tune shift of the TEL. We will
assume the test charge is offset from the electron-beam center by b, and since the
incident bunch for the TEL will be antiprotons, the momentum kick will be outward,
that is, defocusing. The currents are opposed, so the magnetic kick supplements the
electrical kick.
Given a uniform electron beam of radius Re and length L, we can show that the
force felt by an ultra-relativistic particle due to the electric and magnetic fields is
Since the electron beam is moving at some speed (3ec in the lab frame, the force due to
the magnetic field is (3e times the electric force. The total momentum imparted to the
antiproton is simply A/?± =FxL/c. Knowing the total antiproton momentum, we can
show that the focal length of the lens is
* =- .=
A/7
(l+p c ) 2rpIL
where rp is the classical proton radius and y is E/E0 for the antiprotons. For a uniform
current profile of the electron beam, the focal length is independent of the incoming
particle's position.
For circular machines, the tune shift is a more vital parameter and is found immediately [4] from the focal length:
I B
B ( 1 + B ) rJL
A vx = — . • " . = —*-*• - i—S-£* - —E—
471 /
271
pe
ecR*y
825
(2)
()
where (3x is the horizontal beta function. The vertical tune shift is similarly based on
the vertical beta function. Table 1 lists the relevant parameters of the TEL.
Using
these values, we can calculate a focal length of 1414 m or a tune shift of 5.72 xlO~ 3 .
Of course, the TEL parameters are mostly quite adjustable, and the current is designed
to change for each antiproton bunch in the bunch train. The next section will illustrate
current ramping.
TABLE 1. Relevant TEL Parameters.
antiproton bunch parameters
..........................................................
.................___.™........._™...
horizontal beta function
101.67 m
vertical beta function
30.89 m
electron beam parameters
energy, typical
10 keV
maximum current
2.5 A
radius, typical
1.6 mm
interaction length
2.05
m
electron density, typical
3.3xKT
Experimental Results
The design of the lens is to shift the tune of the antiprotons, but since antiprotons
are a rare commodity, experiments so far have relied on proton bunches. The charge
is opposite that of the antiprotons, but the flow of current is the same. Therefore, we
expect the electrical force to be focusing and the magnetic defocusing. Using a negative (3e in Equations 1 and 2 will predict the correct tune shift. For the results shown
here of the proton tune shift, multiplying by -(l + P e )/(l- PJ--1.5 will give the
equivalent antiproton tune shift.
A typical scope trace of the current leaving the cathode is shown on the left side of
Figure 3. Also displayed is the current returning via the collector. The rise time
reflects the ramping of the anode by the pulse modulator, which is an RF-tube amplifier design. This enables us to provide arbitrary waveforms to allow different currents
for each bunch. The right side of Figure 3 again shows a typical pulse of cathode
current, but the second trace shows the raw signal from a BPM plate. This signal is
the derivative of the passing current, on top of which is a small blip of current indicating when a proton bunch passed through.
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200:mA/div:
200 nsec/div
cathode
current
FIGURE 3. Typical scope traces of electron beam. The left trace shows current leaving the cathode
and entering the collector; the right trace shows another cathode current and the raw voltage (arbitrary
units) on a BPM plate. The spike on the BPM signal about 650 nsec after the start of the pulse is the
passage of the proton bunch.
As discussed in the previous section, results must be taken from tune-shift measurements known as Schottky spectra. A representative scan is shown in Figure 4.
Two proton bunches were injected into the Tevatron, one of which interacted with the
TEL. The other one shows an unperturbed horizontal tune of 0.5834 (only the fractional tune is discussed; in fact the total tune is 20.5834), but the TEL pushed the first
to a higher tune of 0.5899.
.53
.53S
.583
.534
.536
.537
.533
.59
.591
. 59S
.594
horizontal tune
FIGURE 4. Output from a horizontal Schottky detector. The untouched bunch's tune distribution is
on the left side, while the TEL increased the tune of the second, pushing its distribution to the right.
The best measurable tune shift due to the TEL so far is 0.0082 on protons, which
corresponds to 0.0123 for antiprotons, or a focal length of 658 m. This is slightly
stronger than theory predicts, and current efforts are attempting to explore these differences. The effect of the electron beam in the bends may be contributing more than
we originally anticipated, or ions might be gathering on the cathode during the pulse,
making the measured current less than the actual current is.
Another likely candidate is that the profile of the beam is not as flat as expected. A
normalized (95%) emittance of the protons in the Tevatron currently stays around 2071
um, which implies half of the particles oscillate around the central orbit with an amplitude of less than 0.7 mm. Therefore, an electron beam with a higher charge density
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in the center than along the outer rim would shift most of the bunch's tune more than
the simple theory above predicts.
However, Figure 5 is a profile measurement of the electron beam, which indicates
that the charge density is slightly depressed in the center. Finding the largest tune
shift consists of scanning the electron beam (using the dipole correctors) over different
areas, so it is likely that the beam was not centered around the bunch producing a
larger tune shift. It should be noted that plotting the tune shift as a function of electron
beam current produced an expectedly jejune line.____
radial position [cm]
FIGURE 5. Profile scan of the electron beam. The wire profile technique intercepts the beam along a
whole line, thereby needing deconvolution before the radial profile can be viewed.
Until recently, turning on the TEL decreased the lifetime of the Tevatron bunches
significantly. Steering the electron beam played an important role in the lifetime, but
keeping the lifetime near the original one proved impossible. At the time of this writing, we have just completed a tune scan, where we measured the lifetime of bunches,
with the TEL running, at many different horizontal and vertical tunes. Several regions
of working points emerged that seem to have dramatically larger lifetimes (over 30
hours). Further studies will be conducted using these Tevatron tunes.
Assessment, Advantages, and Applications
A number of features of the TEL provide solutions to many problems faced by
other beam control concepts. The first is that the electron beam refreshes itself within
35 nsec, and increasing the beam energy or shortening (staging) the interaction length
can significantly decrease this recovery time.
However, that assumes that the electron beam is affected by the antiprotons.
Transversely, the solenoid field holds the electrons in place, but longitudinal effects
are not yet fully understood. We do not see any drastic effects, but plasma waves
propagating in both directions could occur. The many transverse instabilities observed
in various plasma lens experiments are quelled by the magnetic field.
Not only is the space-charge force available without driving a plasma initially, but
it is malleable to an arbitrary radial distribution. In several months a modified electron
gun with a more rounded profile will be installed in order to produce a continuous tune
shift as a function of oscillation amplitude. Other applications (positron focusing in
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B-factories) could desire inverted profiles[5]; this is a distinct advantage over other
beam control schemes.
The TEL has recently found another use. The Tevatron currently leaks protons and
antiprotons out of the buckets, and the resulting "DC beam" builds in intensity over a
given store. This undesired beam produces background noise in the detectors, and,
when the store is finished and is being dumped, will get kicked suddenly into one area
of the beam pipe, quenching Tevatron magnets and causing hours of wasted time. The
TEL is often used to clear this beam. It is pulsed between bunches and is purposefully
offset transversely; protons caught in the TEL influence are kicked out of the orbit.
Before building in intensity to annoy the detector and cause a quench, the DC beam is
drained as it develops.
In addition to these uses, electron lenses could be used for space-charge compensation in low-energy boosters[6]; cleaning, stabilizing, dumping, and shaping higherenergy beams; compensation of wakefields and bunch-to-bunch focus jitter in LC
beams, slow extraction from particular bunches [7]; increasing transverse impedance
and TMCI studies.
ACKNOWLEDGMENTS
We thank all of the Tevatron group and Beams Division at Fermilab for their undying enthusiasm and patience. Previous members of our group are N. Solyak and Y.
Alexahin, whose efforts enabled us to have so much progress. Designing the magnets
and successfully squeezing a whole physics experiment in the already congested
Tevatron tunnel are S. Kozub, V. Sytnik, and L. Tkachenko at BINP in Protvino.
Tireless efforts made by G. Saewert, H. Pfeffer, D. Wildman, A. Semenov, and a host
of other engineers, physicists, and technicians have fulfilled so many large and small
needs (half of which we are not even aware) that we must offer sincere appreciation
and acknowledgements.
REFERENCES
1. Shiltsev, V. and Finley, D., Fermilab Technical Memo TM-2008 (1997).
2. Bishofberger, K. et al., Proceedings of the 2001 Particle Accelerator Conference, pp. 3406-3408
(2001).
3. Koziol, W., Proceedings of the 1998 European Particle Accelerator Conference, pp. 164-168
(1998).
4. Edwards, D.A. and Syphers, M.J., An Introduction to the Physics of High Energy Accelerators,
John Wiley, New York, 1993, pp. 94-95.
5. Shiltsev, V., Proceedings of the 23rd ICFA Beam Dynamics Workshop on High-Luminosity e+e~
Colliders (2001).
6. Burov, A.V. etal., Proceedings Proceedings of the 2001 Particle Accelerator Conference, pp. 28962898 (2001).
7. Shiltsev, V. and Marriner, J., Proceedings of the 2001 Particle Accelerator Conference, pp. 14681469 (2001).
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