Design of Electron Ion Collider – eRHIC1

Deajn Trbojevica, Stephen Brooksa, Ilan Ben-Zvia, Vadim Ptitsyna, Thomas Rosera, Vladimir Litvinenkoa,b, Francois Meot, Nicholaus Tsoupas, Wuzheng Meng, Joseph Tuozzollo, Yue Hao, Peter Thieberger, Chuyu Liu, Michiko

Minty, George Mahler, Elke C. Aschenauer, Oleg Tchoubar, David Gassner, and Wang Gang

a Brookhaven National Laboratory, Bldg. 911B, Upton NY-11973-5000, USA

b Stony Brook University, Department of Physics and Astronomy, Stony Brook NY 11794-3800, USA

Abstract

We present a design of polarized electron - proton/He3 and ion collider eRHIC in the present tunnel of the existing Relativistic Heavy Ion Collider (RHIC). Polarized electrons are accelerated up to the maximum energy of 21 GeV with a 1.334 GeV Energy Recovery Linac - ERL using two Non-Scaling Fixed Field Alternating Gradient (NS-FFAG) arcs. 70% polarized protons have an energy range 25-250 GeV, while the light ions (d, Si, Cu) and heavy ions (Au, U) have an energy range 10- 100 GeV/u, while the polarized He-3 ions 17-167 GeV/u. The ions (protons, He3, ions) will be with a reduced emittance obtained by coherent electron cooling. Electron and ion beams collide with an angle of ~10 mrad, with a beta-squeeze of *=5 cm, luminosities above 1034 can be reached by using the crab cavities.

Keywords: Electron Ion Collider, FFAG-Fixed Field Alternating Gradient, ERL- Energy Recovery Linac

1. Introduction

A possible future Electron Ion Collider (EIC) at Brookhaven National Laboratory will be placed in the existing tunnel of the superconducting Relativistic Heavy Ion Collider (RHICeRHIC). This is a design for the additional electron accelerator to provide polarized electrons with an energy range between 5-21 GeV. Electrons will collide with existing polarized protons or He3, or with other heavy ions from deuterons to Uranium.

The existing RHIC – the QCD facility, has been producing fascinating results with an extraordinary performance above any expectations. RHIC represents a complicated complex of many accelerators starting with the polarized proton source (development of the polarized He3 has already started) with a linacs or Electron Ion Beam Source (EBIS) with Radio Frequency Quadrupole (RFQ) and linacs, able to produce multiply stripped heavy ions from deuterium to uranium. The polarized protons/He3 or heavy ions

continue after the linacs their path towards RHIC by getting injected into the booster accelerator and then to the Alternating Gradient Synchrotron (AGS), after which they are injected into two superconducting rings in opposite direction. So far there were collisions of fully stripped gold ions at energies 3.8, 4.6, 5.8, 10, 14, 32, 65 and 100 GeV/u, U-U at 96.4 GeV/u, Cu-Cu at 11, 31, and 100 GeV/u, polarized protons p-p at 11, 31,100, 205, 250, 255 GeV, d-Au at 100 GeV/u and initial 3He-Au. RHIC is the only collider in the world with ability to collide unequal species and polarized protons. Achieved peak luminosities in collisions of the fully stripped gold ions Au-Au at 100 GeV/u are 195∙1039 cm-2s-1, and for polarized protons p-p with 245∙1030 cm-2s-1. A comparison between the three colliders: the Tevatron at Fermilab 110∙1030 cm-2s-1 and the LHC at CERN 493∙1030 cm-2s-1 (scaled to 255 GeV). The QCD facility RHIC studies the formation of the quark-gluon plasma a state of the matter at sufficiently high energies. RHIC has showed a

formation of the “perfect liquid” formed during quark gluon plasma formation. This system of accelerators and one of the two superconducting rings in RHIC will be reused in the future EIC while electron will arrive from a new accelerator.

Electron acceleration comes from a single superconducting linac achieving energy of 1.34 GeV, as presented in the upper right corner in Fig. 1. The lattice design for producing electrons with energies up to 21.2 GeV is based on multiple passes through the linac with energy recovery (ERL). After polarized electrons are accelerated to the 15.8 or 21.2 GeV and collided with the polarized protons or ions, their energy is taken away in the same linac. They have the same number of passes through the linac as electrons during acceleration, but at the negative sine voltage so their energy is recovered. They reach the initial injection energy during the last pass. The “blue” hadron ring is shown schematically above the two electron beam lines (upper left corner in Fig. 1.) Orbit offsets in the NS-FFAG rings are shown in the middle on the left side in Fig. 1. The hadron Interaction Region (IR) magnets are shown at the bottom in Fig.1 with electrons and ions passing with 10 mrad angle.

2. A microscope for gluons

An EIC will be used to study the “spin puzzle” determine quark and gluon contributions to the proton spin, what is the spatial distribution of quarks and gluons in nuclei – a “microscope for gluons”. During collision of electrons with heavy ions quantitative probe of the universality of strong fields in AA, pA and eA will be studied. This is going to be an ultimate QCD laboratory. The eRHIC will be able to collide 50 mA 80% polarized electrons with 15.9 GeV energy or electrons with an energy range between 6-21.2 GeV with reduced electron current of 20 mA due to a synchrotron radiation (limit set to be less than 10 MW for the whole eRHIC). Electrons will be able to collide with 70% polarized protons in an energy range 25-250 (275*) GeV, with light ions (d, Si, Cu) Heavy ions (Au, U) or polarized 3He with energies 17-167 (184*) GeV. [A removal of existing separation dipoles DX, as they are not necessary anymore – only one ring will be used, might make higher energies possible*.

2.1. eRHIC parameters

The new EIC collider eRHIC should achieve very large luminosities of the order of 1034 due to expected small emittance of both electron and proton/ion beams. A new coherent electron cooling is proposed and will be tested very soon in the existing RHIC collider. An angle of 10 mrad will be used between electron and polarized protons/ions to allow clean passage of electrons through the detectors without synchrotron radiation to the detector. This will be possible by using the crab cavities preserving the luminosity achieved in collisions without an angle. Due to a small emittance ta very strong focusing of the beam at the interaction point can be applied with the *= 5 cm. The angle of 10 mrad between electrons and protons/ions will be possible using very special magnets for protons/ions close to the interaction point with no-magnetic field regions for electrons to be able to pass without their path affected.

Fig. 1: Layout of eRHIC: Existing “Blue” superconducting ring, two electron NS-FFAG beam (left-up) lines (with beam orbits on left), linac, Polarized electron Gatling gun, Combiners and Separators (up-middle), Detector Schematic (middle) at 6 o’clock, and the Superconducting Linac (up-right).

There is an intensive R&D on a “Gatling Gun” with 24 GaAs cathodes with beams merged longitudinally, as polarized electron guns today can not produce required high intensity beam of 50 mA. Most of the eRHIC parameters are presented in Table 1. The last three rows in Table 1 show luminosities for the base line design with full acceptance detector but with the 15% reduced hadron beam intensity presently achieved, allowing operation with the present RHIC vacuum chamber and without space charge

compensation. The improved RHIC superconducting ring with removal of the not-necessary separation dipoles as only one of the rings is used. This allows higher energy operation and higher luminosity. The ultimate BNL eRHIC performance is obtained after the beam pipe in the superconducting ring is being covered with a vacuum chamber coating to reduce the heating and beam-wall impedance. A full 360 bunch spacing will be available– raising the total number of bunches and improving the detectors’ rate of acceptance.

Table 1: BNL eRHIC beam parameters and luminosities

e p 3He2+ 197Au79+

Energy (GeV) 15.9 250 167 100CM energy (GeV) 122.5 81.7 63.2Bunch freq. (MHz) 9.4 9.4 9.4 9.4Bunch Int. (nucl.), 1011 0.33 0.3 0.6 0.6Bunch charge (nC) 5.3 4.8 6.4 3.9Beam current, mA 50 42 55 33Hadron rms N (m) 0.27 0.20 0.20

Electron rms N (m) 31.6 34.7 57.9* (cm) (both planes) 5 5 5 5Hadron beam-beam 0.015 0.014 0.008Electr. Beam disruption 2.8 5.2 1.9Space charge par. 0.006 0.016 0.016rms bunch length, cm 0.4 5 5 5Polarization, % 80 70 70 nonePeak L, 1033 cm-2s-1

1.5 2.8 1.7Improve L, 1034 cm-2s-1

1.5 2.8 1.7Ultimate L, 1035 cm-2s-1 1.5 2.8 1.7

2.2. Introduction to NS-FFAG

Significant simplification and cost reduction in the electron acceleration is possible by using the non-scaling Fixed Field Alternating Gradient (NS-FFAG) transfer lines.

Fig. 2: Scaling FFAG with orbits parallel to each other.

The two NS-FFAG beam lines placed in the existing RHIC tunnel, allow multiple passes though the linac without additional beam lines. This reduces the linac size but enhances the load on the superconducting cavities. The NS-FFAG advantage is a large energy range with the fixed field linear magnets. A first NS-FFAG proof of principle Electron Model for Multiple Applications (EMMA) was built in Daresbury Laboratory in England [4].

Fig3: Non-Scaling FFAG, defocusing magnet is in the middle, aperture size is smaller, and orbits are not parallel.

A combination of the NS-FFAG with the ERL has not been used before. The FFAG is not a new concept it had already been developed in 50’s independently by three different groups [1,3]. The concept is being revived lately especially in Japan, mostly due to today’s technological ability to build accurately required difficult magnetic field radial dependence. The magnetic field dependence on the radial axis follows the momentum dependence p=po(r/ro)k+1 as Br=Bo(r/ro)k. There are many advantageous properties of the “scaling” FFAG’s like: very large energy range with large momentum acceptance, zero chromaticity,

fixed radial and vertical tunes, orbits are separated and parallel for different energies, and etc. There are few disadvantages of the scaling FFAG’s like ~30% required opposite bending (this enhances the overall size and in the case of electrons produces larger synchrotron radiation loss) and a large aperture size. The NS-FFAG is a new concept developed during the Muon Collider Collaboration. The NS-FFAG arrived as one of possible solutions for fast acceleration of short lifetime muons. Author [5] has arrived independently to the NS-FFAG realizing a simple connection between the aperture and momentum range of the accelerator x=Dx∙p/p. The smaller the dispersion function, the smaller is the aperture for the required momentum range p/p. The synchrotron light source lattice requires the smallest dispersion function or dispersion invariant H function to obtain the smallest beam emittance. Author obtained the NS-FFAG with an energy range of three or momentum range of p/p=50% with apertures in centimetres, as the dispersion function was couple of centimetres. In addition the radial magnetic field dependence is a linear function: B = Bo + G∙x, allowing a very large dynamical aperture as there are no non-linear elements. Advantages of the NS-FFAG are: large energy range ~4 times of the initial energy, small physical aperture- small magnets size – small orbit offsets, linear magnetic filed dependence (large dynamical aperture) in radial direction, smaller size of opposite bending, extreme focusing – very small beam amplitude functions, and a small dispersion function. Disadvantages of the NS-FFAG are tune variation with energy, as well as the chromaticity, the time of flight is a parabolic function with a minimum around the central reference energy, a relatively limited energy range 4 to maximum 5 times.

2.3. eRHIC NS-FFAG ERL Lattice Design

The superconducting linac accelerates electrons to 1.322 GeV. The linac is connected to the two NS-FFAG beam lines with the spreaders (side after acceleration – as presented in upper right corner in Fig. 1), or combiners at the opposite side of the linac, connecting the NS-FFAG’s with the linac entrance. Each chicane line in the spreaders and combiners has to match the linac betatron and zero dispersion functions to the NS-FFAG functions. There are two NS-FFAG arc beam lines: one accepting electron beams with energies from 1.334 to 6.622 GeV, and the

second one for energies between 7.944 to 15.876 [or 21.164] GeV. The 12 MeV injector provides polarized electrons for the 1.322 GeV superconducting linac. Orbits in both NS-FFAG’s are shown in Fig. 4.

Fig.4: Orbits (Magnified x1000) in arcs: in the lower energy 1.334-6.622 GeV (left), and in the high-energy 7.944-15.786 [21.2] GeV beam lines.

The tunes’ variation per energy for the two RHIC NS-FFAG beam lines are shown in Fig. 5, while the time of flight for the two NS-FFAG beam lines is shown in Fig. 6. In the design procedure of the NS-FFAG beam lines the major concern was optimization on synchrotron radiation loss. The lattices were modified until the lowest possible radiation was achieved. A synchrotron radiation limit of 10 MW was set for the whole radiation loss in the eRHIC arcs.

Fig. 5: Tunes variation with energy in the two eRHIC NS-FFAG beam lines.

Fig. 6: Time of flight dependence of the two eRHIC NS-FFAG beam lines.

Fig.7 Synchrotron radiation loss for the two cases of acceleration: up to 15.9 GeV with 50 A beam, and to 21.2 GeV with 28.8 mA beam.

The synchrotron radiation from the two NS-FFAG beam lines is presented in Fig. 7.

The two cases: one of accelerating electrons to the energy of 15.9 GeV with a current of 50 mA is shown in dark blue colour, while the other where electrons are accelerated to 21.2 GeV is shown with the green colour. The two NS-FFAG beam lines, placed in the existing RHIC tunnel, follow the superconducting hadron beam line. The RHIC tunnel has six ~200 meters long straight sections the lines have to match.

Fig. 8: Straight section design of the eRHIC NS-FFAG beam lines.

The straight section design provided a basis of the by-pass design of the NS-FFAG beam lines around detectors as only the highest energy is taken away to collide with hadrons as shown in Fig. 9.

Fig. 9: By pass design around detectors in eRHIC with NS-FFAG.

S. Brooks came out with a solution for the NS-FFAG straight sections reducing adiabatically the bending angles of the combined functions magnets.

Fig. 10: Electron beam trajectories for the higher energy range NS-FFAG in the whole RHIC tunnel (without by-passes) magnified x1000.

As the combined function magnets in NS-FFAG eRHIC are made by misplaced focusing/defocusing

quadrupoles as the radius of curvature is very large ~280 m the reduction of the bending angles is reduction of the quadrupole offsets. The straight sections of the two-eRHIC NS-FFAG beam lines are presented in Fig. 8.The whole NS-FFAG simulation of the electron trajectories magnified in transverse direction for thousand times, at different energies is shown in Fig. 10.

Table 2: Synchrotron power from both NS-FFAG beam lines

El. current (mA) Energy (GeV) Sync. Power (MW)50 1.334-6.622 0.2650 1.334-10.5 3.250 1.334-15.8 10.228 1.334-21.2 9.8

Table 3: Beam and cell parameters of the NS-FFAG beam lines.

Parameter Low-Energy FFAG

High-Energy FFAG

Energy range 1.334–6.622 GeV 7.944–21.164 GeV

Energy ratio 4.96× 2.66×

Passes in linac 5 11

TOF range 54.7ppm (12cm) 22.4ppm (5cm)

Drift space 28.8cm 28.8cm

Tune range 0.036–0.424 0.035–0.369

Orbit (mm) 31.3 @rmax=23.6 12.6@ rmax=9.1

Max |B| 0.227 T 0.451 T

Gradients 9.986 T/m 49.515 T/m

The summary of the synchrotron radiation from both NS-FFAG beam lines is shown in Table 2, the summary of all parameters for the two NS-FFAG beam lines in eRHIC is shown in Table 3, while the cell magnet properties are shown in Table 4.

3. eRHIC beam bunch pattern

The length of the electron circumference defines the eRHIC bunch pattern. One RF bucket is a shift between two bunches, while at the top energy pass is a ½ bucket. A gap of 900 ns is created to eliminate ion accumulation. This gap is going to be used for the beam position of individual passes by introduction of the two bunches in the gap, one accelerating and the other one decelerating. Every 16 revolutions period one bunch is injected in the gap. This is presented in Fig. 11.

Fig. 11: eRHIC bunch pattern with the ion clearing gap and two bunches for the beam position measurements of individual passes.

Table 4: Basic properties of the two NS-FFAG cell magnets and lengths.

Element L (m) G (mrad) G (T/m) x (mm)Drifts 0.2876 0

BD-Low 0.9081 3.0576 9.986 -6.947QF-Low 1.0986 3.6990 -9.006 6.947BD-Hi 0.9081 3.0576 49.515 -3.901QF-Hi 1.0986 3.6990 -49.515 3.901

3.1. NS-FFAG superimposed on RHIC Tunnel

The NS-FFAG beam lines are placed in the present RHIC tunnel with two superconducting rings as shown in Fig. 12. The circumference of the high-energy beam line has to be very close to the existing hadron ring circumference to allow synchronization for collisions between electron and ion bunches. The electron beam is extracted from the high-energy NS-FFAG beam line by use of the horizontal correction magnets – a method developed by V. Litvinenko. A large orbit offset at the place of the magnetic septum is obtained only for a single energy while beams with other energies are not affected. Many other subjects of operation are studied: orbit correction for all energy beams with correction magnets placed inside of the misplaced quadrupoles, beam position detection, time of flight adjustment for each energy, M56 correction, commissioning procedure, etc. but this is not part of this report.

Fig. 12: NS-FFAG layout in the RHIC tunnel.

4. Summary

A concept of NS-FFAG has been very successfully applied for the first time together with the ERL in the design of the new EIC at eRHIC. Few important simplifications and the cost reductions are possible due to large energy acceptance of NS-FFAG beam lines.

Acknowledgments

Acknowledgments go to the whole rest of the team to their contributions to the project.

References

[1] T. Ohkawa, University of Tokyo, Tokyo, Japan, FFAG structure suggested earlier at a Symposium on Nuclear Physics of the Physical Society of Japan in 1953 (private communication).

[2] A. Kolomensky et al., Zh. Eksp. Teor. Fiz. 33, 298 (1957). [3] K. R. Symon, Phys. Rev. 100, 1247 (1955). [4] S. Machida et. All. In Nature Physics 8, 243-247 (2012).[5] D. Trbojevic, E. D. Courant, A.A. Garen, presented at the High

Energy Muon Colliders worskhop in Montauk HEMC-1999, published by AIP, Woodburry, New York, USA(2000), Editor King, Bruce J. ISBN 10: 156396953X ISBN 13: 9781563969539