Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

Design and Magnetic Field Measurement of the S-LSR Compact ElectronCooler
H. Fadil1, A. Noda, T. Shirai, ICR, Kyoto University, Kyoto, Japan
M. Grieser, MPI für Kernphysik, Heidelberg, Germany
N. Miyahara, K. Noda, H. Ogawa NIRS, Chiba, Japan.
T. Fujimoto, S. Shibuya, AEC Ltd. E. Syresin, JINR, Dubna, Russia

Abstract
A compact electron cooler has been designed andconstructed for the cooler ring S-LSR. A homogeneous
magnetic field in the cooler provides confinement for theelectron’s transport from the gun through the cooling
section to the collector. The field distribution wasinvestigated with 3-dimensional calculations and precise
field measurements were performed after construction of
the electro-magnets. The length of the good field regionof 0.43m is achieved. Adiabatic condition is satisfied forthe electron motion along solenoid axis. The magnetic
field distribution inside the collector is also investigatedand optimized in order to optimize primary and secondaryelectron capture.

1 INTRODUCTION
The S-LSR [1] electron cooler is shown in figure 1. It
consists of an electron gun that generates an electron
beam at the thermionic cathode and a transport system
consisting of solenoid and toroid guiding fields. The
electron gun, of Perveance 2.2µP delivers a maximum
current of 80mA at electron energy 1.1keV. After theinteraction of the electrons with the ion beam in thecooling section, the electron beam is recaptured at thecollector. The detailed design of the electron gun andmagnetic guiding system were presented previously [2-3].
The design value of the longitudinal field is 500G and themaximum field in the gun section is 1500G
corresponding to a maximum expansion factor of 3.

2 FIELD MEASUREMENTS
After the construction of the electron cooler magnets
was completed, measurements of all 3 components of themagnetic field were performed. We have utilized a highresolution Hall probe with precision better than 0.1G or
2.10-4 for a main field component of 500. The
measurement along the straight section was done with a3-axis stage controlled by a computer. The measurementof the fields inside the toroid, gun and collector was donewith a aluminium rail installed inside the electromagnets
prior to assembly. Figure 2 shows the measurement withthe stage. The three probes are installed on an aluminium
rod which is inserted inside the cooling section via theopening in the toroid. The probes are calibrated against
NMR data, and also perform automatic temperature
calibration.

Fig.1 Schematic view of the S-LSR cooler

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

Fig.2 Measurement of the magnetic field with the 3-axis stage. Thepicture shows the upstream toroid section and the steering magnet.

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Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

The adiabatic parameter is very small in the cooling
sectio0.0n.4

2.1 Gun and toroid Section

χ ad =||
B ∂sadiabatic paramterλ|| ∂B(1)eB
λ|| =,ωc =meωclongitudinal magnetic field Bs [G]

1250

1000

(2)

1500 GCATHODE

1000 G

500 G
350 G

250
-2000

-1600

-1200-800

-400

0.00
CoolingSection

ToroidSection

GunSection
CATHODE-1600-1200-800-4000longitudinal coordinated s [mm]

750

500

0.01

-0.02
-2000

The adiabatic condition is χad << 1. Figure 3 shows themeasured magnetic field from the gun section to thecooling section. The cathode is positioned at s=-1550mm
and the centre of the cooling solenoid corresponds to s=0.

1500

0.02

-0.01

where, λ|| is the spiral length of the cyclotron motion

2πv||

1500G
1000G
500G
350G

0.03

The electron gun of the S-LSR cooler will be mainly
utilized for the regime with expansion factor of 3. Thisregime corresponds to maximum magnetic field of 1500G
at the cathode surface. The measurement was performedfor maximum field of 1500G, 1000G, 500G and 350G.
The variation of the magnetic field along the beam axis ischaracterized by the adiabatic parameter χad defined as

0longitudinal coordinate s [mm]Fig.3 Distribution of the longitudinal magnetic field along thebeam axis of the S-LSR electron cooler for various expansions.

Using equations 1 and 2 we calculated the adiabatic
parameter along the electron beam axis form themeasured distributions. The result for electron energy
1.1keV is plotted in figure 4. We observe that theadiabatic condition is fulfilled for all field magnitudes
with a maximum adiabatic parameter bellow 0.04 for
1500G. Also it should be noted that the adiabaticcondition is also satisfied inside the toroid section. Thisshows that an optimized discrete coil topology canachieve good adiabatic conditions for electron motion.

Fig.4 Variation of the adiabatic parameter along the beam axis
from the gun section to the centre of the cooling solenoid.

2.2 Cooling section
The length of the cooling section of the S-LSR cooler
is 0.8m. The cooling time measured in the laboratory
frame depends on the ring averaged cooling force and is
proportional to the effective length of the cooling section.
The electron beam motion is constrained by the field linesof the guiding magnetic field. The transverse fieldcomponents in the cooling section cause a transverse
relative velocity component between ions and electrons
which affects the efficiency of the cooling. Moreover,due to this transverse motion there is a detuning of thelongitudinal velocity matching between electrons andions, which reduces further the cooling force. Theeffective length of the cooling section is therefore limitedby the transverse field of the toroid magnets, which in thecase of this device is rather large, about 70G in maximum,
due to the small radius of the equilibrium orbit of thetoroid (250 mm). Two additional Helmholtz coils oflength 100mm, radius 150mm and 8 turns each, areplaced at both ends (s=±325 mm) of the cooling section
outside the main solenoid in order to compensate thetransverse magnetic field. The measured transverse fieldB⊥ is shown in figure 5. When the Helmholtz correction
coils are not excited the effective length of the cooling
section Leff is 240mm, where the good field region isdefined as | B⊥ | ≤ 0.25G or | B⊥ / B|| | ≤ 5.10-4 for B|| =500G. Leff is increased to 430mm or about 2% thecircumference of the ring when the dipole coils are
excited with a current of 10A. Therefore we havesucceeded to recover more than 50% of the cooling
section (800 mm) for effective cooling by this correction
scheme. However, in order to improve further the field469

Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)
quality to better than 5.10-4 additional correction coils areneeded.

field. We have found that a slightly negative longitudinal
field of -1.5G (produced by mirror field coil in thecollector) on the bottom of the collector cup is effectivein trapping secondary electrons leaving the surface.
However as can be seen in figure 7, a too strong negative
field of -45G will cause the primary electron beingreflected before reaching the cup surface. Thereforeconfiguration (b) with a reverse field of -1.5G is utilized
in the S-LSR cooler which is effective in trapping bothprimary and secondary electrons.
(a)

2.0

transverse magnetic field Bt [G]1.5

Without correction
With correction

1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0

-200

-100

0

100200longitudinal coordinate

Fig.5 Transverse magnetic field distribution in the cooling section(-250≤ s ≤250) for cases with and without dipole correction; Leff
increased from 240mm to 430mm, or 2% the total circumference(b)

In the cooler design, there are excess Ampere-turns at
the transitions between the solenoids and the toroids, due
to the discrete coil topology in the toroids. The
longitudinal field shows a bump at these transitions as
can be seen in figure 6. Additional longitudinal fieldcorrection coils were placed at the transition locations inorder to reduce the field bumps are shown in figure 6(case with correction).

(c)Longitudinal magnetic field Bs [G]600

Fig.7 Trajectories of the primary electron beam fordifferent field magnitudes; (a) 57G, (b) -1.5G, (c) -45G
500

3 CONCLUSION
400

without correctionwith correction

300-1500-1000-50005001000

Longitudinal coordinate s [mm]Fig.6 Reduction of longitudinal field bumps with correction coils.

2.3 Collector section

The S-LSR compact electron cooling device has been
constructed. The measurement of all 3 components of themagnetic field has been performed and the device
parameters optimized in order to achieve high field
quality (adiabatic condition). The effective length of thecooling section is 430mm or 2% of the ring
circumference and the adiabatic parameter along thebeam axis is kept bellow 0.04. An image field coil is usedin the collector in order to create a slightly negative field
which is optimized for both primary and secondary
electron capture.

After leaving the cooling section the electrons reach thecollector, which should collect the electrons with highefficiency. One relevant factor which influences thedesign of the collector is the distribution of the magnetic470

Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

REFERENCES[1] A. Noda et al., EPAC 2002, Paris (2002), p. 224.
[2] H. Fadil et al., Proc. of COOL03, to be published inNIMA.
[3] H. Fadil et al. Proc of SAST2003, Tsukuba(2003) p.
140.

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