Lawrence’s
Cyclotron Accelerator and Its Developments
Gerry Resmi Liyana (1106009910)
Department of Physics Faculty of Mathematics and Natural Sciences
University of Indonesia
Dec 9, 2014
Outline
Introduction
Timeline of Inventions
Classical Cyclotron
Relativistic considerations
Development of cyclotron devices
Notable Examples
Conclusion
References
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Introduction
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Cathode ray tubes ~ late 1800s
Van de Graff ~ 1930
Cockroft and Walton ~ 1920
Earlier accelerators were electrostatic field based
Practical limitations using high voltage:
problem with corona, insulation and design
of vacuum tubes were difficult
Fig 1. Source: http://what-when-how.com
Fig 2. Source: http://cst.mos.org/sln/toe/history.html
Fig 3. Source: http://blazelabs.com/e-exp15.asp
Introduction (cont)
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“It is required a vacuum tube many meters long to accelerate
lighter projectiles (such as alpha particles). Therefore, bending
those particles into a circular path to send them through the
same electrode repeatedly was better.”
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Timeline of Inventions
Timeline of Inventions
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1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
1910: Rutherford
1925: linac
1931: cyclotron
1940: betatron
1947: electron synchrotron
& Synchro-Cyclotron
1930: electrostatic
1952: proton synchroton
1960: functional storage ring
2000: Strijckmans proposes
isochronous cyclotron
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The Classical Cyclotron Accelerator
The Experimental Method
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Connected to
high frequency
oscillator
Peak value
4000 V Electrodes
(Semi circular hollow plates)
B - field
Fig.5 The dees, driven by an RF oscillator, lie
between the poles of a magnet excited by direct current.
Fig.4 Diagram of experimental method for multiple acceleration of ions [Phys. Rev. 40, 19]
http://www.nobelprize.org/nobel_prizes/themes/physics/kullander/
Fields provide
focusing effect!
Experimental Arrangement
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Fig.6 Diagram of apparatus for the multiple acceleration of ions[Phys. Rev. 40, 19]
Fig.7 Tube for the multiple acceleration of light ions – with cover removed [Phys. Rev. 40, 19]
Principle of Operation
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Fig.8 How the cyclotron works. Source: http://www.americanradiohistory.com/Archive-Radio-Craft/1940s/Radio-Craft-1947-Jun.pdf
Governing Relation in Cyclotrons
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B into paper
A positive particle q sees a centripetal force at right angles to the direction of motion:
v
qF
Bvqrr
mv ˆ
2
The angular frequency of rotation
mqB /
Gyrofrequency
qB
m vr
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Relativistic Considerations
Relativistic Considerations
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The relativistic mass can be rewritten as
02
0
2
0
11
mm
c
v
mm
Lorentz factor
The angular frequency of rotation
2
0
1'
c
v
m
qB
m
qB
This modification has the following effect
on the gyrofrequency
For example:
86,0'155.1%50 c
v
14,0'1.7%99 c
v
Proton Energy % Frequency
decrease
10 MeV ~1%
250 MeV ~21%
1.0 GeV ~52%
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How to manage the relativistic change in mass?
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Development of cyclotron devices
Development of cyclotron devices
• There are at least 3 kinds of cyclotrons:
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CLASSICAL CYCLOTRON
SYNCHRO – CYCLOTRON
ISOCHRONOUS – CYCLOTRON
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Classical (Review)
• CLASSICAL: (original)
– Operate at fixed frequency (ω=qB/m) and ignore the mass increase
– Works to about 25 MeV for protons (ϒ=1.03)
– Uses slowly decreasing magnetic field ‘weak focusing’
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Synchro – Cyclotron
Synchro – Cyclotron
• SYNCHRO – CYCLOTRON: let the RF frequency ω decreases as
the energy increases
– ω = ω0/ ϒ to match the increase in mass (m= ϒ m0)
– Uses same decreasing field with radius as classical cyclotron
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ISOCHRONOUS-CYCLOTRON
Isochronous – Cyclotron
• ISOCHRONOUS: raise the magnetic field with radius such that the
relativistic mass increase is just cancelled
– Pick B = ϒ B0 {this also means tat B increases with radius}
– Then ω=qB/m = qB0/m0 is constant
– Field increases with radius – magnet structure must be different!
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Magnet Structure
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Orbit stability is related to the magnetic induction as a function of the radius:
nrrB
1)(
Fig.9 field index n determines magnet structure
Field index n!
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This is used for Isochronous
Orbit Stability
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Fig 10. Radial (a) and axial (b) oscillations about a circular equilibrium orbit (c).
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Orbit Stability (cont)
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Fig 11. Radial forces for a zero field index; also valid in the mid-plane of for any field index
Fig 12. Axially focuussing forces Fz for a positive field index
Fig 13. Axially defocusing forces Fz for a negative field index
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An alpha particle, which has a positive electric charge, experiences Lorentz forces
How to prevent an axial orbit instability for n<0?
The principle of Thomas focusing to solve the axial orbit instability
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Fig 13. Magnet pole of an isochronous cyclotron, i.e. A sector focussed or AVF (azimuthally varying field) cyclotron plane (reproduced with permission of Jhon Wiley & Sons. Ltd from Strijckmans K. Charged particle accelerators. In;
Z.B. Afassi, editor. Chemical analysis by nuclear methods. Chichester (UK), 1994)
Fig 14. Thomas force acts always towards the median plane. The dot means that the particle has a velocity component from the paper and the cross that the particle has a velocity component towards the paper. (Heikkinen, Pauli, 1994)
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Positive and Negative ions
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Actually, the cyclotron can be used to accelerate not only the positive but also negative ions
For the positive ions For the negative ions
Axial orbit instability for n < 0 with the positive ions Axial orbit stability for n < 0 with the negative ions
Fig 15. Whether the “magnetic structure for n < 0” causes the axial ion orbit instability or not, it depends on the charge on the ion (positive or negative). “The magnetic structure for n < 0” doesn’t cause the axial orbit instability for the negative ions.
(a) (b)
Fz
Fz Fz
Br
Br Fz
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Notable Examples
Notable Examples
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Fig 15. SRC Cyclotron at RIKEN laboratory in Japan.
Source: http://www.nishina.riken.jp/facility/RRC_e.html Fig 16. One of the TRIUMF’s Cyclotrons.
Source: http://www.triumf.ca/headlines/current-events/new-milestone-for-tc-99m-production
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CONCLUSION
• E. O. Lawrence invented cyclotron which operate at fixed frequency (ω=qB/m)
and ignore the relativistic change in mass
• The relativistic change in mass was solved by:
Bohm and Foldy
o By raising the magnetic field with radius such that the relativistic mass increase is just cancelled
Strijckmans
o By decreasing RF frequency ω as the energy increases
• Initiated a big science, a new way of doing science
– Tevatron, LHC, etc
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References
• Lawrence, E. O., Livingston, M. S. Production of high speed light ions witout the use of
high voltages. Physical Review 40, 19- 35, Apr. 1, 1932.
• D. Bohm, L. Foldy. Theory of the synchro – cyclotron. Physical Review 72, 649, 1947.
• Strijckmans K. The isochronous cyclotron: principles and recent developments.
Comput Med Imaging Graph 2001; 25: 69 – 78.
• Heikkinen, Pauli. CYCLOTRONS. University of Jyvàskylâ, Accelerator Laboratory,
Jyvàskylâ, Finland (1994)
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References (cont)
• Pictures:
– http://what-when-how.com
– http://cst.mos.org/sln/toe/history.html
– http://blazelabs.com/e-exp15.asp
– http://www.nobelprize.org/nobel_prizes/themes/physics/kullander/
– http://www.americanradiohistory.com/Archive-Radio-Craft/1940s/Radio-Craft-1947-Jun.pdf
– http://www.nishina.riken.jp/facility/RRC_e.html
– http://www.triumf.ca/headlines/current-events/new-milestone-for-tc-99m-production
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