The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

OPTIMIZATION OF COMPACT ELECTRON COOLER FOR THE S-LSR
RINGH. Fadil1, A. Noda, T. Shirai, ICR, Kyoto University, Kyoto, Japan
M. Grieser, MPI für Kernphysik, Heidelberg, Germany
K. Noda, NIRS, Chiba, Japan
E. Syresin, JINR, Dubna, Russia
Abstract
The electron cooling technique in the S-LSR will be
used to cool and store 12C6+ ions with total energy
2MeV/u produced in a laser induced source. The S-LSR
has a total circumference of 22.56m and a straightsection length of 1.86m. A compact electron cooler withcooling solenoid length of 0.8m and toroid radius of
0.25m was designed and will be installed in the S-LSR.
The electron gun with Perveance of 2.2µP achieves amaximum current of 80mA necessary for efficient carbon
beam cooling. The gun geometry is optimized bynumerical simulations in order to reduce the transverse
electron beam temperature.

1 INTRODUCTION
The S-LSR project initiated by ICR of Kyoto
University and NIRS, consists of a 12C6+ carbon ionsinjector system utilizing a laser induced ion source, and acompact cooler ring equipped with both an electron
cooling and laser cooling devices [1-2]. The cooling ofcarbon ions in the S-LSR has the peculiarity that theinjected beam has a large momentum spread (∆P/P=1%).
Feasibility studies for effective cooling of carbon ion
beam with large momentum spread had been carried out
at the TSR with positive results [3-4]. Numericalsimulations of cooling times with BETACOOL [5] codefor 12C6+ with energy 2MeV/u, momentum spread of 1%
and emittances of 50/10π.mm.mrad, have shown that acooling time of 200ms in all degrees of freedom ispossible with electron current of 50mA, electron beam
radius of 2cm and an adiabatic expansion factor of 2 at
S-LSR [6]. In this work we present the computer
simulations carried out in order to optimize the electron
cooler for the specifications of the S-LSR project.

2 SPECIFICATIONS
The compact cooler ring S-LSR has a total
circumference of 22.56m and a maximum magnetic
rigidity of 1Tm. The ring super-periodicity is 6, which
limits the length of the straight section to about 1.86m.
The ring will store and cool 7MeV protons from theexisting proton linac at ICR and 2MeV/u carbon ions

1e-mail address: fadil@kyticr.kuicr.kyoto-u.ac.jp

Fig.1 Schematic view of the S-LSR cooler

from the laser ion source. The electron cooling device isdesigned and optimized for operation in two energy
modes corresponding to carbon and proton cooling. For
2MeV/u carbon ions, the electron beam energy is 1.1keV,
which limits the available beam current. The main
parameters of the cooling device are shown in table 1.
Numerical simulations of the cooling time [6] showedthat the magnetic expansion factor Bgun / Bcool of 2 or 3 issufficient to efficiently cool the longitudinally hot carbon
ion beam. The magnetic field of 1.5kG in the gun section
and of 0.5kG in the cooling section is utilized for thecurrent design.

Table 1 Parameters of the S-LSR electron cooler
Cooler solenoid length, m
0.8
Bending toroid radius, m0.25
Magnetic field (gun/cooling), kG
1.5/0.5
Maximum adiabatic expansion factor
3Field uniformity in cooling solenoid
5x10-4
Electron energy, keV
1-5Cathode radius, mm15Electron beam current, A0.05 - 0.4
Gun Perveance, µP
2.2
β-function at cooling section, m
1.7/2.4

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

3 HARDWARE DESIGN
The schematic layout of the S-LSR electron cooler isshown in figure 1. The limited space in the straightsection of the ring puts stringent restrictions on thelength of the cooling section and the radius of theequilibrium electron orbit inside the toroidal section. In
the current design the length of the cooling solenoid is0.8m and the toroidal bending radius is 0.25m.

3.1 Electron Gun
An electron gun is proposed for the S-LSR with threeelectrodes: a flat cathode of diameter 30mm, a Pierce
electrode and an anode, which achieves a high enough
Perveance of 2.2µP. For carbon beam cooling themaximum current is 80mA and for proton beam coolingthe current is more than 400mA. The diameter of anodeaperture is 60mm and the distance between the cathodesurface and the anode is 5mm. Figure 2 shows thesimulated electron trajectories during the adiabatic

Fig.3 Effect of the adiabatic expansion on the transverse
temperature of the electron beam.

3.2 Optimum angle of the Pierce electrodeThe Pierce electrode is an important part of theelectron gun. For a space-charge dominated electron gun,the shaped electrodes serve to establish correct potential
variation along the beam boundary. The analytic
derivation of Pierce [8] gives θP=67.5° for the angle ofthe electrode. This result holds when the following
condition is satisfied
2ra << dFig.2 Simulation of electron beam trajectories during
adiabatic expansion for Bgun=1.5kG, Bcool=0.5kG andEe=3.8keV (plot scales are not equal).
expansion of factor 3. The adiabatic expansion of theelectron beam due to the variation of the axial magnetic
field reduces the transverse temparature. This effect wassimulated by tracking the electron beam using theEGUN[7] code, and calculating the transverse
temperature T⊥ using the equation
kbT⊥ = 12 me (11¦ (vt − vt ) 2 + N ¦ (vr − vr )2 )N

(1)where kb is Boltzmann’s constant, me is the electronmass and vr and vt are the radial and azimuthal electron
velocities respectively. Figure 3 shows the simulationresults for cases with expansion factors 1 and 3, electronenergy of 3.8keV and electron current of 300mA. The
cathode is positioned at the longitudinal coordinate
Z=0mm and the cathode temperature is 1400K. For thecase without expansion, the calculated electron beam
temperature is about 120meVwhich is equal to thecathode temperature. However, with the adiabatically
expanded electron beam we reach a transverse
temperature of 40meV, which is consistent with theexpansion factor of 3.

(2)

where, ra is the radius of the anode aperture and d iscathode-anode gap. For the current design of the S-LSR
cooler gun we have ra=30mm and d=5mm in order toachieve high enough Perveance. This design does notsatisfy equation 2, therefore we have performed
numerical simulations in order to optimise the angle of
the Pierce electrode. The EGUN simulation wasperformed with electron energy Ee=3.8keV, electron
current Ie=300mA and magnetic field in gun section of
500G. The electron beam radius is 15mm. The results infigure 4 show the dependence of the radial electron
velocity at the exit of the gun section (Z=750mm) for
different radial positions inside the beam, on the angle of
the Pierce electrode. We see that the optimum angle
which minimizes the radial velocity for all electrons ofdifferent radial positions is located around 62°. The
standard angle of 67.5° is clearly not the optimum forthis specific design of the S-LSR gun. Similar result wasobtained for the azimuthal velocities. It should be notedthat this optimum angle depends on the shape of theanode as well as on the gap between the cathode edge
and the Pierce electrode. Similar calculations for electronenergies of 1.1keV and 7.5keV gave similar results with
an optimum angle around 62°. The dependence of thetransverse temperature defined by equation 1 on thePierce electrode angle was also calculated at the exit of
the gun section for electron energies of 1.1keV and7.5keV. The result is shown in figure 5. We see that theThe 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

Fig. 6 Electron beam trajectories inside the collector.

Fig. 4 Dependence of the radial electron velocity on theangle of the Pierce electrode (Ee=3.8keV, Bgun=500G,Ie=300A)
transverse temperature is minimized when the angle ofthe Pierce electrode is about 62°. The minimum
temperature of 120meV is consistent with the cathodetemperature of 1400K.

4 CONCLUSION
A compact electron cooling device has been designed
for the S-LSR project which will cool 2MeV/u carbon
ions and 7MeV protons. Numerical simulations havebeen carried out in order to optimise the design for thesetwo cooling modes. The Perveance of the gun is 2.2µP
and the optimum angle of the Pierce electrode is 62°. The
expansion scheme with expansion factor of 3 achieves atransverse temperature of 40meV. The electron collector
has been designed with an image field coil which
achieved good distribution of the electron beam on theinside walls of the cup. The collector will be optimised inorder to reduce the number of reflected electrons.

ACKNOWLEDMENTS

Fig. 5. Dependence of the transverse temperature on
the angle of the Pierce electrode.

3.3 Electron collector
The electrons exiting the cooling section, are guided bya second toroid coil towards the collector section. The SLSR electron collector is a water-cooled oxide-freecopper cup of diameter 120mm and length of 150mm.
The main solenoid in the collector section creates amagnetic field of 500G equal to the filed in the cooling
section. A short solenoid at the end of the collector
section creates a reverse image field which bends themagnetic field lines inside the cup as seen in figure 5.
This achieves a good distribution of the electrons hitting
the walls of the cup. The cup geometry and the reverse
image coil will be further optimized for secondary
electron emission [8] in order to minimize the loss
current and improve the vacuum conditions.

We are grateful to Dr. I. Watanabe, Mr. T. Nagafuchi
and Mr. E. Ono for their invaluable efforts. This work
was performed with the collaboration of NIRS and ICR
with the financial support of Advanced Compact
Accelerator Research Project from the Ministry ofEducation, Culture, Sports, Science and Technology.

REFERENCES[1] A. Noda et al., SAST2001, Osaka (2001), p. 125-127[2] A. Noda et al., EPAC 2002, Paris (2002), p. 224.
[3] H. Fadil et al., EPAC2002, Paris (2002), p. 1341.
[4] H. Fadil et al., “Electron Cooling of Longitudinally
Hot Ion Beams”, Accepted for publication in NIMA.
[5] I. Meshkov et al., Proc. of Beam Cooling and Related
Topics, Bad Honeff, Germany (2001)[6] E. Syresin et al., HIMAC internal report, NIRS
(2002).
[7] B. Herrmansfeld, SLAC 226, NC. 28.
[8] J. R. Pierce, “Theory and Design of Electron Beams”,
Van Nostrand, Princeton, NJ 1949.
[9] E. Syresin, NIMA 391 (1997), p.114-116