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A STUDY ON MIRROR INFLECTOR AND BEAM CENTERING IN K-130
CYCLOTRON USING ECRIS
B.Shoor, P.S.Chakraborty, VECC, DAE,
1/AF, Bidhannagar, Kolkata
Abstract
In K-130 variable energy cyclotron, ion beams
produced in ECR ion source are injected vertically on the
mirror inflector located at the centre of the cyclotron and
comes out horizontally in the median plane of the
cyclotron for further acceleration by dee voltage.
We choose non-scaling mode of operation as dee
voltage is kept near its maximum and the beam orbits
trajectory do not have a constant pattern. For beam
centring the dee voltage should be approximately 5.5
times the injection voltage. Here we have considered the
injected beam as well as inflector parameters and tried to
find out at what condition the maximum transmission is
possible.
inflector). As in our cyclotron dee voltage limitation is 70
kV so it gives an idea at what maximum voltage we can
inject the ECR beam in mirror inflector:
V0 (maximum) = 12.5 kV (70/5.5 = 12.7)
MIRROR INFLECTOR
O.D=26 mm
I.D=23
mm
20 mm
Outer
Casing
Grid Mess
Slit
INTRODUCTION
To accelerate vertically injected beam from ECR ion
source in cyclotron two things are important:
 Suitable mirror inflector for proper transmission
 Initial centring of beam in the cyclotron
Figure 2: Schematic view of inflector
3
2
Dee Insert
1
0
-6
-4
-2
0
-1
2
4
6
Dummy Dee Insert
Inflector
-2
All Units in inches
Electrode
16 mm
-3
Figure 1: Schematic view of central region with initial
orbits
Fig.1 shows the central region of K-130 cyclotron with
dee and dummy dee inserts and inflector at the centre of
machine. Beam centring calculation had been done by
PINWHEEL Code [1] and different species of ion was
considered at different injection voltage V0. Proper
centring was obtained by changing the following
parameters:
1. Rotation of inflector on its axis
2. Gap between inserts
3. Starting phase (buncher phase)
4. Dee voltage
It is seen from the output of the PINWHEEL code that
dee voltage requirement for proper centring is around 5.5
times the injection voltage [2] irrespective of the species
(multiplying factor may differ in case of other type of
Now let us consider the mirror inflector as shown in
Fig.2. Here outer casing and grid mess is at ground
potential and electrode is at +ve high potential (about 10
kV). Inflector diameter is 26 mm as shown in Fig.2. After
the inflector is placed at the centre of cyclotron machine,
the gap between dee insert and inflector becomes 8 mm.
So if the inflector diameter is further increased, it will
initiate sparking between inflector and dee.
The electric field E applied between grid mess and
anode has components EZ and EY along Z-axis and Y-axis
X-axis along Dee
Z-axis
Y-Axis across Dee
Z
X
ION
R0
Ez
Z0
Ey
X0
Y0
Horizontal Plane
α
Y0
Y
Vertical Plane
Figure 3: Ion trajectory inside inflector
Y
respectively (Fig.3). EZ opposes the vertical motion and
EY accelerates the particle along Y-axis in magnetic field
free condition. For a centred uniform magnetic field B0,
an ECR beam injected with ions of charge q, rest mass m0
and momentum P0, the particle moves along Y-axis
(vertical plane, Fig.3) and also along X-axis due to the
magnetic field (Horizontal Plane, Fig.3), the radius of
curvature ρ is defined as [3]:
  P0 qB   2V0 B 
0

0
1
2

Z0 (as well as R0) increases with higher the injection
energy per nucleon and lower the operating frequency as
shown in Fig.4.
(1)
where ω is angular velocity.
It can be further simplified as
  69.66  Q A V0  / f MHz

 
(2)
= 69.66 * Sqrt [injection energy / nucleon]/ fMHz
where ρ in mm, V0 in kV, fMHz in MHz is the particle
accelerating frequency inside cyclotron and Q/A is the
charge-mass ratio.
By solving the equation of motion [3], it can be shown
that the ray enters perpendicularly and exits horizontally
at a particular value of E given as:
E  2V0 (  D cos  )
(3)
where α is mirror angle and D is transit time in the
inflector, which can be obtained [3] by solving the
following equation:
1 2
 D  tan 2 1  cos D 
2
Figure 4
A simple two dimensional inflector model is done in
RELAX3D Code [4] and equipotential lines are shown in
Fig.5. Between grid mess and electrode, uniform electric
field is in a limited region of 13 mm. The PINWHEEL
Code solution suggests that initial beam direction should
be towards dummy dee as shown in Fig.1. So the slit of
the inflector should be towards dummy dee. Fig.5 shows
the uniform field region is up to 4 mm to the left of
central line (ray 3 to ray 1 is 4 mm).
(4)
Vertical distance Z0 and radial distance R0 traversed in
this condition (Fig.3) can be obtained from the following
relation:
Z0 
1
 D
2
R0  Z 0
(5)
(6)
LIMITATIONS OF OUR INFLECTOR
Solving Eq. (4), for our inflector, we get D = 1.05.
Combining Eq. (2) with Eq. (5), we find:
QV
Z 0  36.57  0  / f MHz
A

(7)
Figure 5
To utilize the full uniform field space, beam on the
inflector should be off from the central line. Here if we
consider a beam of width 4 mm and if the beam is
projected 2 mm away from the central line i.e. along ray
2, we find vertical ray 1,2,3 comes to the horizontal ray
1,2,3. From Fig.5 vertical distance Z0 traversed by rays is
9.2 mm and passes through without any loss. So the
placement of inflector should not be on the centre of
machine but 2 mm off towards the dummy dee. One
additional advantage of this placement is inflector and dee
insert gap increases helping stability of dee voltage.
Once inflector is placed off-centered, maximum Z0 is
9.2 mm, which corresponds to beam having ρ=18 mm
[from eq. (5)]. So, ECR beam having ρ more than 18 mm
will start getting lost as it reflects in Fig.5.
From eq (2):
ρ = 69.66 * Sqrt [injection energy / nucleon]/ fMHz
For limiting value of ρ (18 mm) we find a relation
between injection energy per nucleon and corresponding
minimum operating frequency as shown in Fig.6.
applied was 15 kV (it was seen in our earlier ECR beam
run), i.e. maximum value of E was 30 kV/cm. So at this
limiting value of E a relation between charge-mass ratio
(Q/A) and corresponding maximum fMHz for different
values of V0 can be obtained, which is shown in Fig.7.
So, for Q/A = 0.25 and injection voltage = 12 kV,
particle frequency should be within 11 MHz. If particle
frequency is more, E should be more than 30 kV/cm.
Anyway if injection voltage = 8 kV, frequency limit is
13.5 MHz for same Q/A = 0.25. So injection voltage
should be such that E remains in the limiting value.
Figure 7
CONCLUSION
Figure 6
From Fig.6 minimum operating frequency of alpha beam
with injection voltage 8 kV (energy per nucleon 4keV) is
7.74 MHz; similarly minimum operating frequency of
Oxygen 4+ beam at injection voltage 8 kV is 5.47 MHz.
Eq.(3) can be further simplified for our inflector as
E  0.3935 f MHz


 V0


 Q 

 A 

(8)
Keeping the gap between grid and electrode of our
inflector as 5 mm, maximum voltage that could be
 ECR injection voltage limit is 12.5 kV.
 Inflector axis should be 2 mm off from machine
centre towards dummy dee
 Vertical distance Z0 changes with ECR beam and
operating particle frequency. So the inflector height
has to be adjusted accordingly.
 Only first harmonic beam is considered.
REFERENCES
[1] PINWHEEL Code, (MSU,USA)
[2] David J. Clark, 10th National Conference on Particle
Accelerators, Dubna, U.S.S.R., October 21-23, 1986
[3] G. Bellomo, D. Johnson, F. Marti and F.G. Resmini
Nuclear Instruments and Methods 206 (1983) 19-46
[4] Kost C J & Jones F W, RELAX3D Code, (TRIUMF,
Canada)