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APR 27 1965
ORMA P-1133
l/VF-5 0
- 5/
A LOW ENERGY SEPARATED ORBIT CYCLOTRON*
WE. *
MASTER
E. D. Hudson, R. S. Lord, and R. E. Worsham
Oak Ridge National Laboratory
Oak Ridge, Tennessee
Summary
LEGAL NOTICE -
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occur only if the field gradients are within
certain limits. These required gradients vary
with ß and with the e/m of the accelerated :
particle in the usual fashion, as in AG synchro-
trons.
Acceleration in the SOC is achieved by rf
cavities placed at equal angular intervals about
a ring of alternating gradient guide field magnets
wrapped in a flat spiral. Coaxial cavities with
two accelerating gaps and having voltage uniform
with radius appear to be more economical than
tapered rectangular cavities, for machines up
to 100 MeV. Deuterons and alpha particles
can also be accelerated in a proton machine by
operating it on a harmonic nurnber differing by
a factor of two. About 5% adjustment in mag-
netic field is necessary to correct H when B
is twice Ba:
For the high energy stages of SOC (above
100 MeV) the tapered rectangular cavity appears
to be the most economical. For the region
below 100 MeV, however, the introduction of
the "coaxial" cavity results in reduced rf power
and cavity costs. Fig. 2 shows the general
outline of a 10 to 50 MeV SOC with coaxial
cavities. A single sector magnet and a coaxial
cavity are shown in Fig. 3.
The concepts of the separated orbit
cyclotron wer first proposed in 1962 by
F. M. Russell of Rutherford High Energy Labor-
atory, England, while spending a year at the
Oak Ridge National Laboratory.
Each sector magnet has a "triplet
alternating gradient element for each turn. A
typical stage usually has 15 to 30 turns and
consequently 15 to 30 pairs of elements driven
from a common yoke structure by a common
coil pair. This arrangement requires le 88
power than a design with individual coils for
each of the elements. The average field
between the pole tips is 7000 gauss, and the
gradient is about 3500 gauss per inch.
The separated orbit cycloiron (SOC), 3, 4
being considered at ORNL features a strong
focusing dc magnetic guide field wrapped into
a flat spiral, so that an ion beam passes through
discretu separated turns. The general appear-
ance of an SOC may be seen in Fig. I which
shows a model of a 350 to 800 MeV machine.
A "Cw" beam is accelerated by fixed-frequency
rf cavities placed in a ring alternately with
sector magnets.
Three requirements must be met for
operation of the machine. First, it must be
isochronous. The length of the orbii path for
each revolution must be such that the particle
"'flight time" remains constant from revolution
to revolution. Second, the operating frequency
of the rf cavities must be such that there is a
fixed integral number of rf periods during each
revolution. This is commonly referred to as
the harmonic number; it may be either even or
odd. Third, the phase of each cavity must be
adjusted so that the synchronous particle
crosses the gap at the phase stable angle, about
30° before the rf voltage reaches a maximum,
Each cavity has two accelerating gaps
separated by a distance BX/2 so that the phase
of the voltage is appropriate as the particles
cross the gaps. As contrasted with the
tapered rectangular cavity in which the voltage
varies approximately sinusoidally with radius,
the voltage in the coaxial cavity is uniform with
radius. The maximum voltage in either case
must be the same to achieve the same orbit
separation at maximum radius. The orbit
separation for the coaxial cavity, where the
gap voltage is constant with radius, is shown
in Fig. 4. At 10 MeV the separation between
orbits is 10 in. , decreasing to 5 in, at 50 MeV.
An energy gain of 40 MeV is obtained in 14
turns, or orbits, with coaxial type cavities
while 19 turns are required when tapered
rectangular cavities are used. The additional
power in the cavity resulting from the higher
voltage at the small radii is more than compen-
sated by the fact that nearly all of the coaxial
cavity is useful in accelerating the beam. A
large part of the rectangular cavity cannot be
used because the voltage is too low, but it must
be excited.
The average field strength in the guide
field magnets must be appropriate for the
momentum of the particles at every point in the
machine. Focusing, or stable motion, will
*Research sponsored by the U. S. Atomic
Energy Commission under contract with Union
Carbide Corporation.
A further advantage is that the number of
orbits is reduced in a machine having coaxial
cavities, since the energy gain per revolution
is larger at small radii. This results in a
lower cost magnet and a possible relaxation in
fabrication tolerances. The characteristics
for the 10-50 MeV SOC are tabulated in Table I.
When the rf gap. i8.eguard to BX/4 the particles
PUSTENT CLEARANCE OBTAINED. READE TV P^14 the particles
ALIS IS APPROVED. PROCEDURES
BLE W THE RGDEJVING SECTAN.
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References
1.
receive 90% of the energy they would have
received if the rf gap had been very small. The
synchronous particles cross the cavity gap
where the voltage is 86.6% of maximum, or
30°, before the voltage peaks. These factors
reduce the voltage gain per gap crossing to
78% of the peak voltage.
F. M. Russell, Nucl. Inst. and Meth. 23,
229-230 (1963).
R. S. Lord and E. D. Hudson, "Magnet
for 800-MeV Separated Orbit Cyclotron,"
to be published in the proceedings of this
conference.
N. F. Ziegler, "Accelerating Ciavities for
an 800-MeV SOC," to be published in the
proceedings of this conference.
SOC machines with an injection energy of
50 kV have been considered. Although such
a machine can be built, present studies indicate
that it has a very small, if not negligible,
acceptance mainly because the large voltage
gain per gap crossing produces radial oscilla-
tions larger than the beam pipe aperture. The
oscillations are caused by the particles having
an incorrect energy. Since particles can be
accelerated when the voltage is from - 30° to
+60° from the phase stable angle of -30°, the
percent energy spread in the beam will be
fairly large in the low energy stages when the
rf voltage is large. For this reason it appears
that an injection energy near 10 MeV may be
more suitable for the low energy SOC.
R. E. Worsham, "The Beam Dynamics
of the SOC," to be published in the
proceedings of this conference.
Figure Captions
Fig. 1-Model of 350-800 MeV SOC showing
magnet sectors alternating with accel-
eraiing cavitics. The beam is injected
and extracted through 90° magnets.
The SOC described above was designed
for the acceleration of protons. A brief study
has shown that it is also possible to accelerate
deuterons and alpha particles in the same
machine. Since the magnetic rigidity (the ratio
of momentum to charge) of a deuteron or alpha
particle is approximately equal to that of a
proton traveling at exactly twice the velocity,
Fig. 2-Schematic of 10-50 MeV SOC with coaxial
cavities. The beam is injected by
having a higher field in the first pair of
poles and extracted by reducing the
length of the last pair.
Fig. 3-Model of a single sector of the 10-50
MeV SOC. Only the beam tubes and
the cavities are under vacuum.
Fig. 4- Orbit separation and energy vs radius
for a cavity design having constant
voltage with radius, but with tapered
gap and hence tapered electric field.
type if the harmonic numbers differ by a factor
of two. Magnet trimming coils would be
required to correct for the slight difference in
rigidity (caused by the non-integral mass ratios).
The inagnetic field correction would be only a
few hundred gauss out of 7000, about 5%, see
Fig. 5. The lower accelerating potential
required for deuterons could probably be
achieved simply by exciting the cavities with
less rf power. It is also possible to vary the
energy of the output end of the accelerator in
steps by using different harmonic numbers.
Some such possibilities are tabulated in Table II;
the required field corrections are small, as
shown in Fig. 6.
Fig.5_ Magnetic field vs radius for accelerating
protons, deuterons, and alphas in the
same machine,
Fig. 6-Magnetic field correction required in
each pole as a function of radius to
operate a ninth harmonic SOC on
higher harmonics at reduced input and
output energies. The values of B
required are given in Table II.
In general, the use of alternating gradient
magnetic focusing introduces no special problems
because a generous amount of space is available
for the magnets and their coils. The SOC
principle allows the use of low frequency
(i. e,, 50 Mc/ 8); this results in large transit
time factors with wide cavity gaps, and permits
very high voltage using only existing rf tech-
nology.
Table I. Design Characteristics of a 10-50 MeV SOC.
Sectors
16
Orbits
14
.
Beam radius
Min
Max
Magnetic field
Gradient
Magnet copper
Magnet steel
Magnet power
84 in.
180 in.
7000 gauss
3500 G/in.
14 tons
327 tons
1 39 kW
Harrnonic number
Frequency
Wavelength (a)
Cavity voltage
RF gap
Min
Max
Phase stable angle
Cavity power
50 MC/ 8
236, 2 in.
260 kV peak
BA 74
8. 5 in.
18. 5 in.
-30°
525 kW
Table L. Operating Values for a 7-Sector, Multi-Particle SOC.
Injection
Energy
(MeV)
Bo
Final
Energy
(MeV)
Harmonic
Number
Particle
(KG)
10.00
4.94
9.81
8. 08
60.31
27. 75
55, 14
47. 36
7.000
6.939
6.893
6.287
6.66
5.59
4.75
38.63
32. 14
27.17
23. 29
5, 706
5.225
4.818
4.471
3. 56
3.13
2.77
2. 47
20.19
17.68
15. 61
13,88
4. 171
3. 908
3. 677
3, 471

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FEET
Fig. 1. Mudel of 350-800 MeV SOC: showing illugnet sectors alternating
with accelerating cavities. The beam is injected and extracted
through 90° magnels.
ORNL-OWO 65-1977

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R-15 11
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10 MOV
-
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-.
.-13.2 Mev,

46.8 M&V
50 MOV
CAVITY
"MAGNET
Fig. 2. Schematic on 10-50 MCV SOC with coaxial cavities. The boam
is injected by having a higher field in the first pair of polos and
extracted by reducing the length of thu last puir.

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10 15 20 25
INCHES

10
11 1.1. i Finn
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2
Fig. 3. Modol of a single sector of tho 10-50 MOV SOC.
tubos and the cavitlos are undur vacuum.
Only the beam
II
A
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.
ORNL-OWG 65-1975

L
CRBIT SEPARATION (in.)
ENERGY (MeV)
75
100
125 150
RADIUS (in.)
175
200
Fiy. 1. Orbit separation and hergy is facing for a cavily design having
constant voltage with radies, but with hispered gap and lience
tapered clectric fuld.
ORNL-DWG 65-639A

PROTONS
DEUTERONS
ALPHAS
B (kilogauss)
50
60
70
80 90
RADIUS (in.)
100
110
Fig. 5. Magnetic field vs radius for accelerating protons, deuterony,
and alphas in the maino niachine,
ORNL-DWG 65-640

'HARMONIC No. 15
HARMONIC NUMBERS 16 TO
18 SIMILAR TO 15
Br-Bo (gouss)
50
60
70
80
90
RADIUS (inches)
100
110
Fig. 6. Magnetic field correction required in each pole as a function of
radius to operate a ninth harmonic SOC on higher harmonics at
reduced input and output energies. The values of B. required are
given in Table II.
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DATE FILMED
6/ 21 /65







**
*
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--LEGAL NOTICE -

This report was prepared as an account of Government sponsored work. Neither the United
States, nor the Commigeion, nor y person acting on behalf of the Commission:
da. Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completeness, or usefulness of the information contained in this report, or that the use
of any information, apparatus, method, or process disclosed in this report may not infringe
privately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the
use of any information, apparatus, method, or process disclosed in this report.
As used in the above, "person acting on behalf of the Commission" includes any em-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such employee or contractor of the Commission, or employee of such contractor prepares,
disseminates, or provides access to, any information pursuant to his employment or contract
with the Commission, or his employment with such contractor.
END



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