AN ENERGY RECOVERY ELECTRON LINAC-ON-PROTON RINGCOLLIDER
L. Merminga, G. A. Krafft, Jefferson Lab, Newport News, VA 23606, USA
V. A. Lebedev, FNAL, Batavia, IL 60510, USA

Abstract
Electron-proton colliders with center of mass energies
33
between 14 GeV and 30 GeV and luminosities at the 10
level have been proposed recently as a means forstudying hadronic structure [1]. Electron beampolarization appears to be crucial for the majority ofexperiments. Two accelerator design scenarios have been
examined in detail: colliding rings [2] and recirculating
linac-on-ring [3]. Although the linac-on-ring scenario is
not as well understood as the ring-ring scenario,
comparable luminosities appear feasible, while the linacon-ring option presents a significant advantage with spin
manipulations. Rf power and beam dump requirements
make the linac-on-ring option viable only if the electron
linac recovers the beam energy, a technology
demonstrated at Jefferson Lab’s IR FEL, with cw current
up to 5 mA and beam energy up to 50 MeV [4]. We begin
with a brief overview of the Jefferson Lab energy
recovery FEL and summarize the benefits of energy
recovery. The feasibility of an energy recovery linac–ringcollider is investigated and two conceptual point designs
are shown. Luminosity projections for the linac–ringscenario based on fundamental limitations are presented.
Accelerator physics issues are discussed and we conclude
with a list of required R&D for the realization of such adesign.

recirculated through two isochronous, achromatic bends
separated by a quadrupole transport line, back through the
cryomodule in the decelerating rf phase and dumped at
the injection energy of ~10 MeV. The benefits of energy
recovery are:
1. The required rf power becomes nearly independentof beam current.
2. The overall system efficiency is increased.
3. The electron beam power to be disposed of at thebeam dumps is reduced by the ratio of the final toinjected energy.
4. The induced radioactivity (and therefore theshielding problem) is reduced, if the beam is dumped
below the neutron production threshold.

2 CONCEPTUAL DESIGNSNext we present the reasoning that allows us to develop a
self-consistent set of parameters for an electron linac–
proton ring collider. Here we consider only the case of 50
GeV protons colliding with 5 GeV electrons. Conceptual
designs at different energies [3], and a design based on
the existing RHIC storage ring [8] have also been
explored. A schematic representation of the electronproton collider is shown in Figure 1.

1 ENERGY RECOVERY LINACS
Energy recovery is the process by which the energy
invested in accelerating a beam is returned to the rf
cavities by decelerating the beam. To date, energy
recovery has been realized in a number of different ways[5], [6], [7].
Same-cell energy recovery with cw current up to 5 mA
and energy up to 50 MeV has been demonstrated at
Jefferson Lab’s (JLab) IR FEL and it is used routinely forthe operation of the FEL as a User Facility [4].
Microbunches with an rms bunch length of ~20 psec are
produced in a DC photocathode gun and accelerated to
320 kV. The bunches are compressed by a copper
buncher cavity operating at 1497 MHz. They passthrough a pair of superconducting rf (srf) cavities
operating at an average gradient of 10 MV/m. The output
beam at ~10 MeV is injected into an 8-cavity srf
cryomodule where it is accelerated up to ~48 MeV. The
beam then passes through the wiggler. Afterward it is

Figure 1. Schematic layout of the electron linac – proton
ring collider.
The linac technology assumed here uses TESLA-stylecavities, with shunt impedance R/Q=1036 Ohms per
cavity and cavity length equal to 1.038m. The residual
11
resistance is ~3 nΩ, equivalent to a Q of ~10 .
Considering demonstrated performance from a number of10
manufacturers, we will assume Q0 of 1x10 at 2K andaccelerating gradient of 20MV/m. At these values therefrigeration power is 40 W/cavity. Thus a 5 GeV linac
will require 250 cavities with dissipation due to dynamic
losses of 10 kW. Two point designs will be explored. In
design 1 both the Laslett and beam-beam tuneshifts willremain below the rather conservative and generally
agreed upon value of 0.004. To arrive at a self-consistent
set of parameters and a luminosity estimate the reasoningproceeds as follows. We first set the electron beam size at
the IP based on projected electron source performance.
Then the proton beam parameters are set at the Laslett
tuneshift limit. The maximum number of electrons per
bunch is determined at the beam-beam tuneshift limit of
the protons. Finally effects that influence the choice ofthe bunch collision frequency are discussed and a choice
is made.
An rms normalized emittance of 60 µm for electrons at abunch charge of 1.75 nC is assumed, yielding a geometricemittance of 6 nm at the interaction point (IP) at 5 GeV.
For a beta function of 10 cm the rms electron beam sizeat the IP is 25 µm. (Round beams are assumed forelectrons and protons, not necessarily equal.)
In order for the luminosity not to degrade too muchwithin a collision, the beta function for the proton beamat the IP is set approximately equal to the rms proton
bunch length. In this approximation, the Laslett tuneshift
can be written as∆ν L =

Np

rp

σ

4πγ

*2
p

3
p

C
2π

must be carried out in order to determine the optimum
value of the collision frequency.
For the case of unequal electron-proton bunch sizes, theluminosity is given by

L=

Ne N p fc
2π [σ e*2 + σ *2
p ]With Ne = 1.1x10 , Np = 1.0x10 , fc =150 MHz, σ e =25*
32µm and σ p = 60 µm, the luminosity is equal to 6.2x10-2-1
cm sec .
Point design 2 utilizes the extremely small emittancesthat are possible from a linac. It assumes that electron
cooling of the protons results in proton beam size at theIP equal to the electron beam size, 25 µm. The proton
11bunch population remains at 1x10 similar to LHC and
RHIC. The Laslett tuneshift is now equal to 0.024 and theelectron beam parameters remain the same as in design 1.
33This parameter set yields a luminosity of 2.1x10 . The
average current in the linac of 0.264 A and the average
current in the ring of 2.4 A. Table 1 summarizes theparameters for the two point designs.
10

11

*

Table 1: Parameter table for linac-ring scenarios
where C is the ring circumference and rp the classical18
radius of proton 1.534 x 10− m. Clearly this tuneshiftsets a limit on the ratio of N p / σ *2
p . Assuming a proton
beam rms normalized emittance of 2 µm (consistent with
LHC and RHIC specifications), the rms beam size for
protons at the IP is 60 µm, for a beta function of 10 cm.
Then the number of protons per bunch at the Laslett
11
tuneshift limit of 0.004 is equal to 1x10 . The ring
circumference is approximately 500m.
The number of electrons per bunch can either be limitedby the beam-beam tuneshift of the proton beam or by thesingle-bunch transverse Beam Breakup (BBU) in the
linac [9]. Beam-beam tuneshift of the protons below
0.004 sets the number of electrons per bunch equal to10
1.1x10 . A simple estimate for the emittance growth due
to single bunch BBU in the linac, for an rms bunch lengthof 1 mm and betatron wavelength in the linac of ~50 m,
suggests that the amplification parameter remains lessthan ~1 if the number of electrons per bunch does not
11
exceed 1.5x10 . Should this effect become a serious
limit, BNS damping can be used. Therefore, in this casethe limit on Ne is set by the beam-beam tuneshift, and notby the single-bunch BBU.
The bunch collision frequency should be maximized
subject to the constraints of parasitic collisions, user
requirements and possibly the electron cloud effect in the
proton ring. We have assumed a bunch separation of 6.66
nsec or 150 MHz repetition rate primarily driven by user
considerations as they are presently understood. Clearly adetailed design of the interaction region that satisfies bothuser requirements and accelerator physics considerations

Parameter

Units

Design 1

Design 2

Ee
Ep
Ne
Np
fc
*
σe
*
σp
εe
εp
*
βe
β *p
p
σz
σez
ξp
∆νL
De
Ie
Ip
L

GeV
GeV
ppb
ppb
MHz
µm
µm
nm
nm
cm
cm
cm
mm
−
−
−
A
A
cm2sec-1

550
101.1x101.0x1011
150
25
60
6
36
10
10
10
1
.004
.004
.78
.264
2.4
6.2x1032550
10
1.1x101.0x1011
150
25
25
6
6.25
10
10
10
1
.004
.024
4.6
.264
2.4
2.1 x 1033

3 ACCELERATOR PHYSICS ISSUES OF
THE PROTON RING
We examine transverse and longitudinal intrabeamscattering and collective effects. Estimates of theemittance growth of the electron beam due to a single
collision with the protons, although not a proton issue,

will also be given here, as it may impose a limit on the
proton bunch population.

For ε0,n=60 µm, εn = 800 µm, Np has to be less than 1.5 x
1210 particles per bunch, well below our design
specification.

3.1 Intrabeam Scattering (IBS)
To calculate the diffusion rates we follow the treatmentof reference [10]. At 50 GeV for the parameters of point
design 1, the diffusion time of both transverse andlongitudinal IBS is approximately 20 minutes, which
implies that electron cooling with cooling rate of similar
magnitude is required. While technically challenging,such cooling appears feasible. For point design 2 the rate
for transverse IBS is ~16 secs and for longitudinal IBS is~1.5 minutes. The required increase of damping
decrements could possibly be achieved not only by anincrease of the electron beam current but also by better
shaping of the beam.

3.2 Collective Instabilities
The longitudinal mode coupling or microwave instability,
for Ζ P / n ~0.25 Ω consistent with LHC [11] and theTevatron [12], limits the number of protons per bunch to12
to ~6x10 . The transverse mode coupling instability,
12
limits the proton bunch population to ~1.8 x 10 , for4
Z ⊥ ~ 5 x 10 Ω (scaled from LHC). In conclusion, bothtypes of instabilities occur at proton bunch populations
above the design parameters we chose.

3.3 Electron Beam Emittance Growth due to aSingle Collision
A single collision disrupts the electron beam and causes
emittance growth. In an energy recovering linac, theelectron beam with degraded phase space has to berecirculated for energy recovery. Deceleration in the linac
cavities can result in scraping and beam loss due toadiabatic antidamping. Therefore, the amount of tolerable
beam loss at the linac exit (where the beam size islargest) imposes a limit on the tolerable emittance growth
due to a single collision. This, in turn, imposes a limit on
the number of protons per bunch.
Let us assume that the maximum tolerable beam loss is 4
6x10− which corresponds to 1 µA out of 250 mA, basedon Jefferson Lab experience. Assuming a gaussian
distribution of the electrons, aperture size of 7 cm and an
average beta function in the linac of ~50 m, the maximum
rms normalized emittance, consistent with this amount ofbeam loss is calculated to be 800 µm. In the small
disruption limit, the emittance growth of the electron
beam due to a single collision with the proton beam ofintensity Np is given by [13]:ε n2 = ε 0,2 n + (0.194 re N p ) 2

4 ACCELERATOR PHYSICS ISSUES OF
THE ENERGY RECOVERY LINAC
We will examine accelerator transport issues, Higher
Order Mode (HOM) power dissipation and BBU
phenomena. We will briefly discuss the beam-beam kinkinstability and present a stability condition in the linear
approximation.

4.1 Accelerator Transport
Energy Recovery Linacs (ERLs) must have the ability toconfine two beams of different energies in the same
focusing structure. Lack of this ability may impose aconstraint on the ratio of injected to final beam energies.
A linac optics design has been devised for injectionenergy of 10 MeV and final energy of 5 GeV [14,15], in asingle pass linac, using TESLA cavities operating at a
gradient of 20 MV/m. Focusing is provided by triplets
placed between cryomodules and the beta functions inboth planes do not exceed ~60 m. This linac design is
optimised for high multipass BBU threshold, as we will
see later.
Understanding the origin of and being able to control
beam loss are crucial in an ERL with the parameters
outlined above. In the JLab IRFEL several indicatorsplace an upper limit on the amount of beam loss in therecirculator to 2 µA out of 5 mA. This amount of loss,
although extremely small may be unacceptable for the
ERL design discussed here, as it can potentially give riseto hundreds of kW of uncontrolled, lost beam power.
More work is required to understand both the origin of theloss and possible cures.

4.2 HOM Power Dissipation
Power in HOMs, primarily longitudinal, depends on the
product of bunch charge and average current and could
present a serious enough constraint that engineering
choices are imposed for improved cryogenic efficiency.
The power dissipated by the beam in HOMs is given by

Pdiss = 2kPQ I
where the factor of 2 accounts for the two beams in the
linac (accelerating and decelerating). For TESLA
cavities, the calculated loss factor is equal to 8.5 V/pC for
1mm rms bunch length, therefore the power dissipated by
the beam for average current of 0.264 A is approximately
8 kW per cavity. It is important to address the question ofwhere these losses go. An analytic model [16] suggests
that, for the parameters quoted here, a small fraction of
the total power, of the order of a few Watts, is expectedto be deposited on the cavity walls. Engineering studies
on HOM cooled absorbers between cavities orcryomodules are needed. Furthermore, the longitudinal
wakefields affect the energy of the particles along thebunch, inducing a correlated energy spread. The induced4
rms energy spread at 5 GeV is approximately 5.7x10−
for the loss factor of the TESLA cavities.

4.3 Beam Breakup
BBU refers to a variety of collective phenomena that canlimit the performance of srf energy recovering linacs.
These coherent effects include single-bunch, single-pass
phenomena which limit the charge per bunch, and multibunch phenomena which limit the average current. Single
bunch effects include energy spread induced bylongitudinal wakefields, and emittance growth induced bytransverse wakefields across the bunch. Both effects werediscussed earlier.
Multipass, multi-bunch BBU occurs when a recirculating
beam through a linac cavity leads to a transverse
instability. Transverse beam displacement on successive
recirculations can excite HOMs that further deflect theinitial beam. The recirculated beam and cavities form a
feedback loop, which, for beam current greater than thethreshold current of the instability, can be driven
unstable. The effect is worse in srf cavities because of thehigher Q’s of the HOMs. The threshold current depends
on various cavity and lattice parameters, including theQ’s, frequencies and R/Q’s of the HOMs, the beamenergy, the beta functions and phase advance in bothplanes and the recirculation path length.
A two-dimensional simulation code, TDBBU [17] hasbeen developed for the calculation of the thresholdcurrent in an actual machine configuration. TDBBU
simulations for the 5 GeV ERL linac with the optics
developed by Bazarov and discussed earlier and HOM
data from the 9-cell TESLA cavities [18], resulted in a
threshold current of about 205 mA [14,15]. This
threshold, although remarkably high, is still below theaverage current of our parameter sets. However the
typical growth rate of the instability just above thresholdis in the msec range, allowing for the possibility of using
feedback for the control of the instability.

places an upper limit on the product of the electron beam
disruption parameter De and the beam-beam tuneshift ofthe protons ξp :Deξ p ≤ 4ν s

where νs is the synchrotron tune of the proton beam.
According to this stability condition, design 1 is a factorof 7 below the threshold and design 2 is a factor of 1.3-3
below the threshold for νs equal to 6x10 .
Recently a simulation study was performed for the caseof bunches of equal bunch length and a linear beam-beamforce and chromaticity was found to increase the stability
threshold [20]. This instability has been observed innumerical simulations during the beam-beam studies of alinac-ring B-Factory at Jefferson Lab [21]. The code ispresently being used to simulate the more realistic case of
unequal bunches and a nonlinear beam-beam force.

5 FUNDAMENTAL LIMITATIONS
5.1 Luminosity at the Laslett and Beam-BeamTuneshifts Limit
The Laslett and beam-beam tuneshifts impose fundamental
limitations on the proton and electron bunch intensities.
The luminosity of an electron linac-on-proton ring collider
can be expressed in terms of the Laslett and beam-beamtuneshifts as follows:
γ 4 *2 4π 2π pσ
L=f ξ p ∆ν L C
2
β* c rp 

Figure 2 is a plot of luminosity vs. proton beam energy for*a beta function at the IP β =10 cm, an rms beam size at*
the IP σ = 40 µm and collision frequency fc = 150 MHz.
The ring circumference C has been minimized subject tothe engineering constraint of maximum magnetic field (inthis case B=4 Tesla). The red curve corresponds to ∆νL =0.004, which is a generally accepted value for the Laslett
tuneshift without cooling. The green curve corresponds to∆νL=0.04, achievable by cooling and consistent with thevalue assumed in the ring-ring scenario [2].

4.4 Beam-Beam Kink Instability
The beam-beam force due to the relative offset between
the head of the proton bunch and the electron beam will
deflect the electrons. The deflected electrons will theninteract with the tail of the proton bunch through thebeam-beam kick. The electron beam acts similar to atransverse impedance for the proton bunch and can drive
the protons unstable. In the linear approximation anddisregarding the evolution of the wake within the proton
bunch, a stability criterion has been derived [19] which

Figure 2. Luminosity vs. proton beam energy at the Laslett
and beam-beam tuneshift limits, for two values of theLaslett tuneshift: 0.004 and 0.04. In both cases the beambeam tuneshift is 0.004.
In both cases ξ p =0.004. The horizontal line corresponds to
33

-2

-1

luminosity equal to 1.0x10 cm sec . Note that33
luminosity at the 10 level is not attainable with proton
beam energies up to 50 GeV as long as the tuneshifts
remain below 0.004. Furthermore, if the Laslett tuneshift
can be raised to values that exceed 0.004, then luminosity
33
at the 10 level is possible only for proton beam energies
above ~25 GeV.

5.2 Luminosity
Instability Limit

at

the

Beam-Beam

Kink

The beam-beam kink instability is an additional effect,
which could potentially impose a limit on the luminosityof linac-ring colliders. In the absence of more accurate
results at the present time, we will use the analytic
criterion presented above to re-write the luminosity at thestability limit of the beam-beam kink instability as:

 4 
L=
γ γ ν σ ′*2 fc
 rerp  e p s
The purple curve of Figure 2 is a curve of luminosity vs.
proton beam energy for 5 GeV electrons as given by theabove equation. The synchrotron tune has been set equal3
to 1x10− , the rms angular divergence of the beam at theIP, σ ′ = σ / β = 40 µm/10cm= 0.4 mrad and thecollision frequency fc =150 MHz. This curve, although
pessimistic, given that it has been derived based on acrude approximation, it nevertheless demonstrates thepotentially detrimental effect this instability could haveon reaching the desired luminosity and therefore the needfor a thorough investigation of the instability.
***

6 R&D TOPICS AND CONCLUSIONSPreliminary results of a feasibility study of an energy
recovering electron linac on a proton ring collider are33
presented. Luminosities at the 10 level appear attainable
and the linac-on-ring scenario presents a significant
advantage with respect to spin manipulations, energy
variability and synchrotron radiation power loading of thedetectors. No showstoppers have been found but anumber of important issues have been identified thatwould require focused R&D before such a facility isdesigned and built. These topics include: a) High current
polarized electron source [22,23]; b) High current (~100mA) demonstration of energy recovery, which includes
understanding and controlling beam loss, benchmarking
TDBBU and possibly developing feedback for themultibunch BBU instability, and understanding of HOM
power dissipation issues; c) Electron cooling and its
ramifications on Laslett and beam-beam tuneshifts and d)

Theoretical and, if possible, experimental investigation of
the beam-beam kink instability and feedback. Recently,
recirculating, energy-recovering linacs have attracted
much attention and are being considered for a number ofapplications, such as drivers for synchrotron radiation
sources [24], and high average power FELs. A number ofthe listed R&D topics, especially those related to theenergy recovery of high average currents, are being
pursued by these communities, so it is safe to assume that
progress will be rapid in these directions.

ACKNOWLEDGMENTS
We are grateful to Dr. Ilan Ben-Zvi (BNL), andProfessors Cameron (Indiana University) and Milner(MIT) for bringing this problem to our attention. This
work was supported by the US DoE contract No. DEAC05-84ER40150.

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