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OPTICS OF AXIAL INJECTION LINE OF K-130
VARIABLE ENERGY CYCLOTRON
Santanu Paul#, P.S. Chakraborty, Atanu Dutta, Md. Z.A. Naser, B. Shoor,
M.K. Dey, A.Chakrabarti
Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata, India
Abstract
The K130 variable energy cyclotron at Kolkata is
presently accelerating alpha, proton and deuteron beams
using an internal PIG ion source. This cyclotron is
presently being used as primary source of beams (alpha
and proton) for rare ion beam facility and also for doing
nuclear physics experiments, radiochemistry and radiation
damage studies etc. It has been decided to re-commission
the axial injection system, so as to facilitate the users to
perform experiments utilizing heavy ion beams. This
paper is going to describe the beam optics calculation of
the axial injection beam line staring from ECR ion source
to the Inflector located in the centre of the cyclotron.
INTRODUCTION
There has been a demand of utilizing heavy ion beams
as projectiles for doing experiments for which a program
has been undertaken to accelerate high charge state heavy
ions in K130 cyclotron. The high charge state heavy ions
will be produced in an external electron cyclotron
resonance ion source (ECRIS) and then transported to the
centre of cyclotron through an axial injection beam
transport system. In the centre of the cyclotron an
inflector is located which will bend the beam by 90
degree to the horizontal plane for further acceleration.
The central region of the cyclotron will also be modified
for proper acceleration of the heavy ions.
Operating conditions
The operating conditions to accelerate heavy ion in
K130 variable energy cyclotron are as follows:
 The charge to mass ratio (q/m) of the heavy ions that
will be accelerated in K130 cyclotron has been
considered to be 0.25 taking into account the
maximum achievable average magnetic field and
lowest radio-frequency of the accelerating voltage.
 For proper beam centring, the accelerating dee
voltage requirement is around 5.0 times the injection
voltage. In K130 cyclotron, the maximum dee
voltage can be as high as 70 kV. So the maximum
injection voltage of ECRIS will be (70 kV/5) =14.0
kV. Hence for beam optics calculation injection
voltage of ECRIS has been considered to be 15.0 kV
with tolerances.
 The rigidity of the beam has been calculated to be
0.035195 Tesla-meter considering the above values
of q/m and injection voltage. Hence the momentum
is 0.01055 GeV/c.
 The emittance of the extracted beam of ECRIS is
considered to be 198 (6x33) π mm mrad in both the
transverse plane.
Axial injection system
The axial injection system has been categorically
divided into two sections.
 Horizontal beam transport system
 Vertical beam transport system
Horizontal section will describe the beam optics from
ECRIS to the point from where axial magnetic field of
cyclotrons also has to be taken into account for further
calculation. Vertical section starts at this point and
describes the beam optics up to centre of cyclotron where
inflector is located.
HORIZONTAL SECTION
The horizontal section of the axial injection system is
shown in Fig 1. The beam coming out from ECRIS is
circularly symmetric and the first magnetic element after
the ion source has been a solenoid magnet. The solenoid
focuses the extracted beam from ECRIS to the object
point of a 90 degree horizontal analyser. From this object
point to the image point located after the analysing
magnet, the optical condition chosen for beam
transmission has been point to point and unity
magnification to both the transverse plane. The analysing
magnet has pole face rotation in both entry and exit face
for focussing in both the transverse plane.
Fig. 1: Horizontal section
The object and image distances are same and turns out to
be 0.95 meter. From this image point which is the object
of the next beam transfer, the optical condition chosen has
been point to point and but magnification less than unity.
This is because of controlling the vertical extent, so as to
transmit the beam without any loss through the 90 degree
vertical bending magnet. This image point becomes the
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 The radius of curvature of 90 degree analysing
magnet and 90 degree bending magnet is 40 cm and
corresponding arc length is about 62.8 cm.
place along the injection path, physically due to the
rotation of ions around the z-axis. The consequent
increase in phase space area can be minimized by having
a small waist size at the median plane [2].
16
1600 Amp
14
12
Bz (kGauss)
object point for the next beam transfer. The image point,
located after the 90 degree bending magnet, is the
common point of the existing ECRIS beam line. The
optical condition for vertical transmission has been the
same as 90 degree horizontal analysing magnet. The 90
degree bending magnet has same specification like 90
degree analyser. From this point the axial magnetic field
contribution has to be taken into account for further beam
optics calculation up to inflector. The specifications of the
magnetic elements are follows:
1056 Amp
10
8
700 Amp
6
4
2
 The pole face rotation angle of the analysing and
bending magnet is 30.19 degree.
0
0
 Half aperture of the analysing and bending magnet is
40 cm. Desired field is about 900 Gauss.
50
100
150
200
Z (mm)
250
300
 Effective length of the solenoids is 36 cm. Desired
field is about 2.0 kilo Gauss.
Fig. 3: Magnetic field along the axial injection hole for
three different field levels.
Two transverse plane of the beam on the inflector
becomes strongly coupled due to axial magnetic field of
cyclotron. This results in high divergence of beam and
beam loss in the central region. Such high divergence
cannot be made zero but can be minimised. For this a
provision has been in the horizontal section for a
telescopic rotator. The beam envelop of horizontal section
is shown in Fig. 2. Beam line optics calculation has been
done by Graphic version of Transport code [1].
That some optical element is needed along the injection
path just to confine the beam can be readily seen from
Fig. 4, where the envelope of a beam for a waist size of
2mm at the median plane is traced backward with axial
field corresponding to 1056A excitation (B0 = 10.938
kGauss). Calculations shows that for achieving
satisfactory beam confinement, two solenoids of effective
lengths 210 and 250 mm located at 400 and 1800 mm
respectively from the median plane are sufficient (fig 4).
Axial + Solenoids
Axial Field Only
35
30
25
20
15
10
5
0
180
R (mm)
135
Fig. 2: Beam envelop of horizontal section.
90
45
0
0
500
1000
Z (mm)
1500
2000
VERTICAL SECTION
The magnetic field along the axial hole of the cyclotron
magnet was calculated using the TOSCA code for various
current excitations. The field, as shown in Fig. 3. is
characterized by a sharp gradient at the beginning of the
yoke and then it decreases gradually along the axis. The
axial field near the entry to yoke hole (z ~ 1.45 m) is
found to be less than 0.02% of the central field even at
maximum excitation. It is assumed that no axial field
exists beyond z = 2m from the median plane, although
field values of the order of 40 to 60 gauss are anticipated.
Coupling between the two transverse planes will take
Fig. 4: Radial envelope for ions traced backward from a
1mm half-width at median plane.
Inflection into the median plane
Initially it is planned to use an electrostatic mirror for
beam inflection into the median plane. A further increase
of emittance at the inflector exit is produced by the mirror
due to the intrinsic coupling introduced for the two
transverse subspaces, as shown in Fig. 5, where an
upright beam (1mm200mrad) at mirror entry in shown at
mirror exit. The increase of emittance produced by the
axial field and inflector can be minimized, not cancelled,
by selection of a proper rotation angle of the coordinate
system of the injected uncoupled beam and the inflector.
The formalism developed by Bellomo et. al [2] has
been followed to study the effect of the mirror on phase
space for mirror tilt angle 47.5o and bending radius 12
mm and also the effect of beam rotation on the emittance
growth. The total angle of rotation needed for optimal
matching, is party contributed by the larmor rotation
provided by the existing cyclotron axial field plus the
solenoids as needed for beam confinement purposes and
partly the angle between the coordinates system of the
vertical injection line and the mirror. The rest of the
rotation, if required, can be provided by a rotator system
accommodated in the horizontal section of beam line.
Calculations show that rotation in the range  30o will be
sufficient to keep the emittance growth to within 25%
limit.
X' mrad
400
200
X mm
0.4
0.2
0.2
0.4
200
400
Z' mrad
40
20
Z mm
7.5
5
2.5
2.5
5
7.5
20
40
Fig. 5: Phase space plots at mirror exit. x = z = 218 mmmrad.
CONCLUSION
The study of the axial injection system for the K130
variable energy cyclotron, as reported in this paper,
addresses the issue of beam confinement in the axial hole
and the emittance growth during inflection into median
plane. Mirror inflectors also introduces a transversallongitudinal coupling which was not accounted for in
calculations and also requires detailed investigations.
Nonetheless, the control of the beam size at the inflector
entrance and the rotation angle is quite important for the
control of the overall emittance increase. The control of
the rotation angle within the useful range can be obtained
with the telescopic rotator without changing the telescopic
condition.
REFERENCES
[1] PSI Graphic Transport Framework by U.Rohrer based on a
CERN-SLAC-FERMILAB version by K.L.Brown et.al.
[2] G. Bellomo et al., Nucl. Instr. And Meth 206 (1983) 19.