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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

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Page 1: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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

Page 2: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Outline

Introduction

Timeline of Inventions

Classical Cyclotron

Relativistic considerations

Development of cyclotron devices

Notable Examples

Conclusion

References

20/12/2014 Presented by Gerry Resmi Liyana 2

Page 3: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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

Page 4: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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

Page 6: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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

Page 7: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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The Classical Cyclotron Accelerator

Page 8: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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!

Page 9: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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]

Page 10: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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

Page 11: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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

Page 13: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Relativistic Considerations

Presented by Gerry Resmi Liyana 13

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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Page 14: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Presented by Gerry Resmi Liyana 14

How to manage the relativistic change in mass?

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Development of cyclotron devices

Page 16: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Development of cyclotron devices

• There are at least 3 kinds of cyclotrons:

Presented by Gerry Resmi Liyana 16

CLASSICAL CYCLOTRON

SYNCHRO – CYCLOTRON

ISOCHRONOUS – CYCLOTRON

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Page 17: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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’

Presented by Gerry Resmi Liyana 17 20/12/2014

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Synchro – Cyclotron

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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

Presented by Gerry Resmi Liyana 19 20/12/2014

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ISOCHRONOUS-CYCLOTRON

Page 21: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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!

Presented by Gerry Resmi Liyana 21 20/12/2014

Page 22: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Magnet Structure

Presented by Gerry Resmi Liyana 22

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

Page 23: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Orbit Stability

Presented by Gerry Resmi Liyana 23

Fig 10. Radial (a) and axial (b) oscillations about a circular equilibrium orbit (c).

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Page 24: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Orbit Stability (cont)

Presented by Gerry Resmi Liyana 24

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?

Page 25: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

The principle of Thomas focusing to solve the axial orbit instability

Presented by Gerry Resmi Liyana 25

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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Page 26: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

Positive and Negative ions

Presented by Gerry Resmi Liyana 26 20/12/2014

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

Page 27: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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Notable Examples

Page 29: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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

Presented by Gerry Resmi Liyana 29 20/12/2014

Page 30: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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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Page 31: Lawrence’s Cyclotron Accelerator - Gerry's Notes · 1931: cyclotron 1940: betatron 1947: electron synchrotron & Synchro-Cyclotron 1930: electrostatic 1952: proton synchroton 1960:

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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