Experimental demonstration of colliding-beam-lifetime improvement by electron lenses.
ABSTRACT We report the successful application of space-charge forces of a low-energy electron beam for improvement of particle lifetime determined by beam-beam interaction at a high-energy collider. In our experiments, an electron lens, a novel instrument developed for the beam-beam compensation, was set on a 980-GeV proton bunch at the Fermilab Tevatron proton-antiproton collider. The proton-bunch losses due to its interaction with the antiproton beam were reduced by a factor of 2 when the electron lens was operating. We describe the principle of electron lens operation and present experimental results.
Experimental Demonstration of Colliding Beam
Lifetime Improvement by Electron Lenses
Vladimir Shiltsev, Yuri Alexahin, Vsevolod Kamerdzhiev,
Gennady Kuznetsov, and Xiao-Long Zhang
Fermi National Accelerator Laboratory, PO Box 500, Batavia, IL 60510, USA
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
We report successful application of space-charge forces of a low-energy
electron beam for improvement of particle lifetime determined by beam-beam
interaction in high-energy collider. In our experiments, an electron lens, a novel
instrument developed for the beam-beam compensation, was set on a 980-GeV
proton bunch in the Tevatron proton-antiproton collider. The proton bunch losses due
to its interaction with antiproton beam were reduced by a factor of 2 when the
electron lens was operating. We describe the principle of electron lens operation and
present experimental results.
PACS numbers: 29.27.Bd, 29.20-c, 29.27.Eg, 41.85.Ja
The luminosity of storage ring colliders is limited by the effects of
electromagnetic (EM) interaction of one beam on the particles of the other beam
which leads to a blowup of beam sizes, a loss of beam intensities and unacceptable
background rates in the high energy physics (HEP) detectors. This beam-beam
interaction is parameterized by a dimensionless beam-beam parameter
where r0= e2mc2 denotes the particle’s classical radius, N is the number of particles
in the opposing bunch and ε is its the rms normalized emittance related to transverse
rms beam size σ at the interaction point (IP) as ε =γσ2β∗, γ>>1 is relativistic
gamma factor, is the value at the IP of the beta-function which describes the
focusing properties of the ring’s magnetic lattice (for simplicity here, we consider a
collider with round Gaussian beams). This dimensionless parameter is equal to the
shift of the betatron tune Q
= fβf0 of core particles due to beam-beam forces. (The
tune Qx,y , a key stability parameter, is the number of periods of particle’s horizontal
or vertical oscillations in the focusing lattice in one turn around the ring.) While core
particles undergo a significant tune shift, halo particles with large oscillation
amplitudes experience negligible tune shift. The EM forces drive nonlinear
resonances which can result in instability of particle motion and loss. The beam-
beam limit in modern hadron colliders is at (NIP is the number
of IPs), while it can exceed in high energy e+e- colliders .
02. 0– 01 . 0
1 . 0
Operation with a greater number of bunches allows a proportional increase of
luminosity but requires careful spatial separation of two beams everywhere except at
the main IPs. Long-range (as opposed to head-on) EM interactions of separated
beams are also nonlinear, usually vary from bunch to bunch, and contribute to the
limit on collider performance.
Besides the technique of electron lenses, the subject of this Letter, there are few
beam-beam compensation (BBC) schemes tested experimentally. The 0.8-GeV DCI
storage ring at the Laboratoire de l’Accelerateur Lineaire (Orsay, France) had four
colliding beams – one positron and one electron coming from each direction. Full
space charge and current compensation could be achieved if all the beams had the
same intensities and dimensions, but the observed beam-beam limit was not
significantly different than with just two beams . These results are attributed to
strong coherent beam-beam effects which are characterized by rapid correlated
variations of the beam distributions – see Ref. and references therein. Octupole
magnets were used for compensation of the cubic nonlinearity in the beam-beam
force at the VEPP-4 e+e- collider (Novosibirsk, Russia) . Although a several-fold
reduction of electron halo loss rate was demonstrated at optimal octupole current,
the technique has not found wide application because its efficiency is strongly
dependent on the machine tune. Compensation of the EM fields of separated beams
by placing a current conducting wire at the same distance to the beam as opposite
beam was proposed in . Some 20% reduction of the e+ loss rate due to such a
method was observed at the DAFNE (Frascatti, Italy) . The wire-compensation
technique is less efficient if multiple beam-beam interactions occur at different
distances and betatron phases, and, of course, it is useless for head-on BBC.
Electron lenses were proposed for compensation of both long-range and head-
on beam-beam effects in the Fermilab’s Tevatron collider (Batavia, USA) . The
lens employs a low energy βe=v/c <<1 beam of electrons which collides with the
high-energy bunches over an extended length Le. Electron space charge forces are
linear at distances smaller than the characteristic beam radius r < ae but scale as 1/r
for r > ae. Correspondingly, such a lens can be used for linear and nonlinear force
compensation depending on the beam-size ratio ae/σ and the current-density
distribution je(r). Main advantages of the electron lens compensation are: a) the
electron beam acts on high-energy beams only through EM forces (no nuclear
interaction), eliminating radiation issues; b) fresh electrons interact with the high-
energy particles each turn, leaving no possibility for coherent instabilities; c) the
electron current profile (and thus the EM field profiles) can easily be changed for
different applications; d) the electron-beam current can be adjusted between each of
the bunches, equalizing the bunch-to-bunch differences and optimizing the
performance of all of the bunches in multi-bunch colliders.
Two Tevatron Electron Lenses (TELs) were built and installed in two different
locations of the Tevatron ring, A11 and F48. Fig.1 depicts a general layout of the
TELs. The TEL and relevant Tevatron parameters are given in Table I. In order to
keep electron beam straight and its distribution unaffected by its own space-charge
and main beam EM fields, the electron beam is immersed in a strong magnetic field
- about 3 kG at the electron-gun cathode and some 30 kG inside the main
superconducting (SC) solenoid. The deviations of the magnetic field lines from a
straight line are less than ±100 μm over the entire length of the SC solenoid. The
electron beam, following the field lines, therefore does not deviate from the straight
Tevatron beam trajectory by more than 20% of the Tevatron beam rms size
σ ≈ 0.5 – 0.7 mm in the location of the TELs.
The electron beam’s transverse alignment on the proton or antiproton bunches
(within 0.2–0.5 mm all along the interaction length) is crucial for successful BBC.
The electron beam steering is done by adjusting currents in superconducting dipole
correctors installed inside the main solenoid cryostat. It was also important that
electron gun generates electron current distribution with wide flat top and smooth
radial edges. Such a distribution is generated in the 7.5-mm radius convex cathode
electron gun with an optimized electrode geometry . The TEL magnetic system
compresses the electron-beam cross-section area in the interaction region by the
(variable from 2 to 30), proportionally increasing the current
density of the electron beam in the interaction region. Most current experiments
have not required more than 0.6 A, though previous tests up to 3.0 A have been
performed. In order to enable operation on a single bunch in the Tevatron with
bunch spacing of 396 ns, the anode voltage, and consequently the beam current, are
modulated with a characteristic on-off time of about 0.6 µs and a repetition rate
equal to the Tevatron revolution frequency of f0= 47.7 kHz by using a HV Marx
pulse generator or a HV RF tube base amplifier. The electron pulse timing jitter is
less than 1 ns and the peak current is stable to better than 1%, so, the TEL operation
does not incur any significant emittance growth. Detailed description of the TEL is
given in Ref.  and references therein.
The high-energy protons are focused by the TEL and experience a positive
betatron tune shift given by :
The tune shift is about the same for most protons in the bunch since
presents results of the measurements of the vertical tune shift dQy of 980-GeV
protons versus electron current in the TEL installed at the A11 location with a
vertical beta-function of
, in good agreement with Eq.(1) using the values
of βe= 0.14 for 5-keV electron energy and for a 0.6-A
beam with an effective radius of about 2 millimeters – see solid line.
mmA 05 /
One of the most detrimental effects of the beam-beam interaction in the
Tevatron is the significant attrition rate of protons due to their interaction with the
antiproton bunches in the main IPs (B0 and D0) and due to numerous long-range
interactions . The effect is especially large at the beginning of the HEP stores
where the positive proton tune shift due to focusing by antiprotons at the main IPs
can reach . Fig. 3 shows a typical distribution of proton loss rates at the
beginning of an HEP store. In the Tevatron, 36 bunches in each beam are arranged in
3 trains of 12 bunches separated by 2.6 µs long abort gaps. Most of the bunches lose
only (4-6)% of their intensity per hour while due to a unique schedule of long range
beam-beam interactions proton bunches #12, 24, and 36 at the end of each bunch
train typically lose about 9%/hr. These losses are a very significant part of the total
luminosity decay rate of about 20% per hour (again, at the beginning of the high
luminosity stores). The losses due to inelastic proton-antiproton interactions at the
two main IPs are much smaller (1.1–1.5%/hr). Fig.3 shows large bunch-to-bunch
variations in the beam-beam induced proton losses within each bunch train but
similar rates for equivalent bunches, e.g. #12, 24, and 36.
In the BBC demonstration experiment, we centered and timed the electron
beam of the A11 TEL onto bunch #12 without affecting any other bunches. When
the TEL peak current was increased to Je= 0.6 A, the lifetime τ = N dN /dt
bunch #12 went up to 26.6 hours from about 12 hours - see Fig.4. At the same time,
the lifetime of bunch #36, an equivalent bunch in the third bunch train, remained
low and did not change significantly (at 13.4 hours lifetime). When the TEL current
was turned off for fifteen minutes, the lifetimes of both bunches were, as expected,
nearly identical (16 hours). The TEL was then turned on again, and once again the
lifetime for bunch #12 improved significantly to 43 hours while bunch #36 stayed
poor at 23.5 hours. This experiment demonstrates a factor of two improvement in the
proton lifetime due to compensation of beam-beam effects with the TEL.
The proton lifetime, dominated by beam-beam effects, gradually improves
and reaches roughly 100 hours after 6-8 hours of collisions; this is explained by a
decrease in antiproton population and an increase in antiproton emittance, both
contributing to a reduction of the beam-beam parameter . To study the
effectiveness of BBC later in the store, the TEL was repeatedly turned on and off
every half hour for 16 hours, again on bunch #12. The relative improvement R,
defined as the ratio of the proton lifetime with the TEL and without, is plotted in
Fig.5. The first two data points correspond to
Je= 0.6 A (as is Fig.4 and the above
description), but subsequent points were taken with Je= 0.3 A to observe
dependence of the compensation effect on electron current. The change of the
current resulted in a drop of the relative improvement from R=2.03 to R=1.4. A
gradual decrease in the relative improvement is visible until after about ten hours,
where the ratio reaches 1.0 (no gain in lifetime). At this point, the beam-beam effects
have become very small, providing little to compensate. Similar experiments in
several other stores with initial luminosities ranging from 1.5·1032 cm-2 s-1 to 2.5·1032
cm-2 s-1 repeated these results.
The lifetime improvement due to the TEL can be explained in part by the
positive shift of vertical tune of protons dQy≈0.0015 which makes the detrimental
effects of the 12th order resonance Qy=7/12=0.583 weaker. The average Tevatron
proton tune Qy=0.589 (which is carefully optimized to minimize overall losses) is
just above this resonance, and the bunches at the end of each train, which have
vertical tunes lower by ΔQy=-(0.002-0.003) due to unique pattern of long-range
interactions, are subject to stronger beam-beam effects . The TEL moves those
protons away from the resonance, thus, resulting in significant reduction of the
losses. It is noteworthy, that the TEL operation with Je= 0.6 A resulted in bunch
#12 having one of the lowest loss rates among all bunches, while its tune still
remained lower dQy <|ΔQy|.
In conclusion, we have developed an electron lens - a new instrument for
compensation of beam-beam effects in high-energy colliders. Such a lens
significantly and reliably improves the lifetime of the Tevatron proton bunches. The
observed improvement of the proton lifetime at the beginning of HEP store, when
beam brightness and luminosity are the highest and the beam-beam interaction is the
strongest, has been as large as a factor of two. Ten hours into a store, the beam-beam
effects, and therefore the utility of BBC, decrease significantly. Currently, we
continue to study electron lens effects in further detail and work toward
incorporation of the TELs into the Tevatron collider operation.
The versatility of electron lenses allows their use in many other applications,
also. For example, the TEL installed at F48 location in the Tevatron is routinely used
for removing unwanted DC beam particles out of abort gaps between the bunch
trains . Similar electron lens concepts have been proposed for reduction of a tune
spread in proton-proton or like-charge colliding beams [12,7].
We thank A.Burov, V.Danilov, B.Drendel, D.Finley, R.Hively, A.Klebaner,
S.Kozub, M.Kufer, L.Tkachenko, J.Marriner, V.Parkhomchuk, H.Pfeffer, V.Reva,
A.Seryi, D.Shatilov, N.Solyak, M.Tiunov, A.Valishev, D.Wildman, D.Wolff, and
F.Zimmermann for their help, technical contributions, and fruitful discussions.
Fermilab is operated by Fermi Research Alliance Ltd. under Contract No. DE-
AC02-76CH03000 with the United States Department of Energy.
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TABLE I. Electron Lens and Tevatron Collider parameter list.
Parameter Symbol Value Unit
Tevatron Electron Lens
Tevatron Collider Parameters
βy / βx
Electron beam energy (oper./max)
Peak electron current (oper./max)
Magnetic field in main/gun solenoid
Radii: cathode/e-beam in main solenoid
Radii: cathode radius
e-pulse period/width, “0-to-0”
Effective interaction length
Proton/antiproton beam energy
Proton/antiproton bunch intensity
Emittance proton/antiproton (norm., rms)
Number of bunches/bunch spacing
Beta functions at A11 (F48) TEL
Proton/antiproton head-on tuneshift
36 / 396
max., per IP
Proton/antiproton long-range tuneshift
FIG. 1. Layout of the Tevatron Electron Lens.
FIG.2. Vertical betatron tune shift of 980-GeV proton bunch vs. the peak electron
current in the A11 TEL.