cyclotron

Cyclotron for 70 MeV protons, built in 2008, University of Nantes (France)

Magnet of the first Belgian cyclotron (1947).

A cyclotron (from Greek κύκλος, kýklos , Latin cyclus "arc", "circle") is a particle accelerator , more precisely a circular accelerator . A magnetic field directs the ions to be accelerated into a spiral-like path , on which the acceleration path is traversed again and again; they are accelerated by an electric field .

In cyclotrons, ions are accelerated to energies of around 10 to 500  MeV . Cyclotrons are not very suitable for energies that are large compared to the rest energy of the particles. Therefore, they are not used for electrons . The world's largest cyclotron is located at the TRIUMF facility in Canada.

story

27-inch cyclotron of the Radiation Laboratory at Berkeley with M. Stanley Livingston (left) and Ernest O. Lawrence (photo from 1935)

Internal structure of the vacuum chamber of Lawrence's 27-inch cyclotron with the two duants. The two connections for the acceleration voltage can be seen on the right; the deflection electrode is at the lower edge of the lower duant, the target is still in the vacuum chamber to the left.

Several electrical engineers and physicists independently presented ideas for a cyclotron in the 1920s, for example by Dennis Gábor in Berlin in 1924, by Eugen Flegler in Aachen in 1926, by Max Steenbeck in Kiel in 1927 and by Leó Szilárd in Berlin in 1929, who had a patent registered for this. ^{However ,} all these considerations were not followed by any practical implementation. A cyclotron was first realized in 1930 in Berkeley by Ernest O. Lawrence and his doctoral student M. Stanley Livingston . Also in 1930, Jean Thibaud built a cyclotron in Paris, which, however, received little attention.

At the beginning of 1929, Lawrence came across a publication by Rolf Wideröe in which he described a linear accelerator with two acceleration stages and which prompted him to build a cyclotron. ^, But it was not until February 1930 that implementation began, initially for a short time by his assistant Edlefsen and from the summer by Livingston. In September Lawrence presented his project for the first time at a conference, and in December Livingston succeeded in accelerating hydrogen molecular ions to the energy of 6  keV with an acceleration voltage of only 300 V. This first cyclotron had the maximum orbit radius and was operated with magnetic flux densities of up to 0.55   T. With a magnet that was borrowed for a short time in January 1931, 1.27 T and thus an ion energy of 80 keV could be achieved. ${\displaystyle \mathrm {H} _{2}^{+}}$ ${\displaystyle R=4{,}5\,\mathrm {cm} }$ ${\displaystyle B}$

Immediately afterwards, work began on a second, larger cyclotron, the 10-inch cyclotron, with and , with which protons could also be accelerated in sufficient numbers. In January 1932, protons could be accelerated with this device after 150 orbits to an unprecedented 1.2 MeV; the beam current was about 1 nA. This proved the technical feasibility of this type of accelerator, which was called "magnetic resonance accelerator" in the early years. The term "cyclotron" comes from laboratory jargon and was only officially used from 1936. ^, ${\displaystyle R=11{,}5\,\mathrm {cm} }$ ${\displaystyle B_{\mathrm {max} }=1{,}4\,\mathrm {T} }$

A cyclotron with higher ion energy had to have a larger diameter. It was made possible because the Research Corporation bore the significantly increased costs and Lawrence was able to acquire a magnet from a discarded Federal Telegraph Company Poulsen transmitter . This cooperation led to the founding of the Radiation Laboratory as early as 1931 . As a result, three systems were built by 1939: the 27-inch cyclotron ( deuterons with up to 6 MeV), the 37-inch cyclotron (deuterons with up to 8 MeV) and the 60-inch cyclotron (deuterons with up to 20 MeV, helium nuclei with up to 40 MeV). The beam current has also been increased significantly, from 1 nA for the 10-inch cyclotron to 150 μA for the 37-inch cyclotron. ^, These newer cyclotrons also allowed productive nuclear physics research for the first time. In 1940/1941, for example, a group led by Seaborg synthesized plutonium for the first time by bombarding uranium with deuterons from the 37-inch and 60-inch cyclotron. Another application, even in the early years, was cancer treatment with neutrons. The 60-inch cyclotron was the prototype for several facilities outside of Berkeley. Also companies like General Electric , Philips and BBC now built cyclotrons. By 1945 there were already at least 15 plants in the US and 10 in the rest of the world.

In the Soviet Union, it was decided as early as 1932 at the suggestion of George Gamow and Lev Myssowski to build a cyclotron in Leningrad . It was finally completed in 1937 by Kurchatov and Igor Kurchatov . Apart from Thibaud's cyclotron, which did not get past the first step, it was the first European accelerator of this type. In Paris, Frédéric Joliot-Curie began building a cyclotron, but this was delayed by the Second World War. Only after the armistice between Germany and France could it be completed in 1942 with the collaboration of Walther Bothe and Wolfgang Gentner . In 1943 a cyclotron was set up in Heidelberg in Bothe's institute and put into operation; Gentner had received information and blueprints from Lawrence and his associates in Berkeley in 1938/39. This cyclotron was created in cooperation with Siemens. Independently of the Reich Post Ministry, Manfred von Ardenne built a cyclotron in Miersdorf near Berlin from 1941 , but due to various delays - the magnet was only delivered at the beginning of 1943 and a bomb attack in 1944 destroyed Ardenne's Lichterfelde laboratory - it was not used until the end of the war came. The total weight of the cyclotron was around 60 tons, the chamber diameter was 1 m.

The first particle accelerator built at CERN in 1950 was a cyclotron.

Classic cyclotron

Classic cyclotron

The classic Lawrence cyclotron consists of a large electromagnet with a homogeneous and time-constant field and a flat circular vacuum chamber between the poles. Inside the chamber are the duants , two hollow, semi-circular, open-sided metal electrodes (called Dees because of their D-shape ) and an ion source in the center . The duants are part of a high-frequency resonant circuit. In the gap between them, an alternating electric field forms at right angles to the magnetic field. This accelerates an ion "packet" alternately into one of the two duants.

There is no electric field inside the duants; Here, under the Lorentz force of the magnetic field, the ions describe circular arcs whose curvature always has the same direction (counterclockwise in the drawing on the right). With a suitably selected frequency of the AC voltage, according to the equation below, the ions reach the gap again after a full cycle of the AC voltage, so that they are further accelerated there. Due to the increase in speed in the acceleration gap, the radius of the next arc is slightly larger; this results in the spiral-like track as a whole.

At the outer edge of the chamber there is usually a deflection electrode, a so-called septum . Its field in relation to a ground electrode opposes the magnetic deflection and thus directs the particle beam to an external target, the target .

The radius of the circular arc that the ions pass through in the duants results from the centripetal force, here the Lorentz force, the speed of the particles and their mass to , where is the ion charge and the flux density of the magnetic field. So the radius increases in proportion to the speed. It follows that the time taken to traverse a duant is independent of . This means that the time between two polarity reversals of the acceleration voltage must always be the same, i.e. an AC voltage with a fixed frequency ${\displaystyle r}$ ${\displaystyle v}$ ${\displaystyle m}$ ${\displaystyle r=mv/(qB)}$ ${\displaystyle q}$ ${\displaystyle B}$ ${\displaystyle \pi r/v}$ ${\displaystyle v}$

${\displaystyle f={\frac {|q|}{2\pi \,m}}B}$,

the so-called “ cyclotron frequency ” to which Duanten must be applied. This greatly simplifies the technical implementation. After several orbits, the ions leave the cyclotron when , the distance of the septum from the center, becomes . You then have the speed . Your final energy is with that ${\displaystyle r=R}$ ${\displaystyle v_{\mathrm {max} }=(q/m)\cdot RB}$

${\displaystyle E={\frac {q^{2}}{2m}}(RB)^{2}}$.

Surprisingly, the size of the acceleration voltage plays no role in this consideration: it only determines the number of required revolutions and the residence time of the ions in the cyclotron.

The flux density of iron magnets is limited to about 1 to 2 Tesla due to the saturation of the iron . At = 1.0 T the cyclotron frequency is z. B. for protons 15 MHz, for deuterons and helium nuclei it is about half as large. In classical cyclotrons, final energies of around 10 MeV (protons), 20 MeV (deuterons) and 40 MeV (helium nuclei) were reached after around 50 revolutions. ${\displaystyle B}$

Higher particle velocities

The classic cyclotron only works at non -relativistic particle velocities; at higher speeds, the period of rotation of the ions no longer remains constant, but increases noticeably, i.e. they get “out of step” with respect to the constant acceleration frequency. This corresponds to the fact that the equation given above for the cyclotron frequency is only approximately valid. The exact equation, valid at all particle velocities, is obtained if the mass of the ions is replaced by ${\displaystyle v}$ ${\displaystyle m}$ ${\displaystyle \gamma m}$

${\displaystyle f={\frac {|q|}{2\pi \,\gamma m}}B}$.

Here is

${\displaystyle \gamma ={\frac {1}{\sqrt {1-\left({\frac {v}{c}}\right)^{2}}}}}$

the Lorentz factor and the speed of light. For becomes obvious and the simpler expression results again. ${\displaystyle c}$ ${\displaystyle v\ll c}$ ${\displaystyle \gamma \approx 1}$

There are two further developments of the classic cyclotron that allow higher particle velocities: the synchrocyclotron and the isochronous cyclotron. A further solution, also for extremely relativistic speeds, is the synchrotron .

synchrocyclotron

So that the cyclotron can be used for higher particle velocities, the high frequency can be modulated, i. H. during the acceleration process according to the gradually decreasing cyclotron frequency of the particles, for example by means of a rotating capacitor in the resonant circuit. Such synchrocyclotrons were built in the 1950s and reached up to 800 MeV with light ions. Their disadvantage is that only a narrow group of particle bunches can be accelerated at the same time. The next group can only "start" when its run is complete and the high frequency has returned to the initial value. The beam is therefore inevitably pulsed, with a low duty cycle of the order of 1%. This is usually disadvantageous for physical experiments, but irrelevant for some applications.

isochronous cyclotron

The synchrocyclotron has been technically superseded by the isochronous cyclotron . In this case, instead of modulating the high frequency, the rotation frequency is kept constant even for relativistic ions by using an inhomogeneous magnetic field, namely one that increases towards the outside. However, such a field has a defocusing effect on the beam, i.e. scattering. Isochronous cyclotrons could therefore only be built after Livingston and others had discovered strong focusing . For this purpose, the magnet is designed sector by sector in such a way that its field has alternating positive and negative gradients in the radial direction . This gives focus; it corresponds to the sequential arrangement of converging and dispersing lenses for light, with focusing as the net effect. If the magnet is accordingly divided into individual sector-shaped, i.e. pie-shaped individual magnets, each with its own winding, one speaks of a sector cyclotron . In the case of the compact cyclotron , on the other hand, the sectors are realized by the shape of the pole shoes on a common magnetic yoke.

Some newer isochronous cyclotrons have superconducting magnet windings to save energy . Also, not two, but three or more acceleration electrodes are often used; they too are called duants, or Dees in laboratory jargon, although they are not D-shaped.

The amperage of an isochronous cyclotron beam is typically between about 10 and 100 microamps.

H ⁻ cyclotron

Cyclotrons for protons, the most commonly used ions, work in some cases as an H ⁻ cyclotron . In them, negative hydrogen ions, so-called hydride ions (H ⁻ , “H minus”) are accelerated. After acceleration, these pass through a graphite foil ("stripper") placed in the gap, which "strips off" the two electrons. The ion is now a proton and, because of its reversed charge, is deflected to the other side, i.e. out of the cyclotron, in the cyclotron's magnetic field. Compared to the deflection plate method, this type of beam extraction allows for larger current intensities of the beam.

applications

Radiation therapy treatment room with neutrons produced by a cyclotron

Cyclotrons are used e.g. B. in physical research to trigger nuclear reactions . However, they are also used medically, for example for the production of radionuclides for diagnostic purposes such as positron emission tomography (PET) . Many of the radionuclides used in this way have very short half-lives , from minutes to a few hours; therefore they cannot be transported far and must be produced close to where they are used. A proton cyclotron with typically 15 to 30 MeV is suitable for this. In Germany there are about 25 cyclotron systems that produce these radionuclides.

Cyclotrons are also used for particle therapy. Protons are accelerated to up to 250 MeV and used either directly to irradiate the patient or to generate neutron radiation . There are six such systems in Germany (as of January 2017). If heavier ions, such as carbon ions, are to be used, a synchrotron must be used for sufficient penetration depths .

See also

• cyclotron resonance

literature

• Frank Hinterberger: Physics of particle accelerators and ion optics . 2nd Edition. Springer, Berlin 2008, ISBN 978-3-540-75281-3 ( limited preview in Google book search).
• Klaus Wille: Physics of particle accelerators and synchrotron radiation sources . 2nd Edition. Teubner, Stuttgart 1996, ISBN 3-519-13087-4 .

web links

Commons : Cyclotrons  - Collection of images, videos and audio files

• Images and information on the Bonn Isochron Cyclotron
• Simulation of a cyclotron

Remarks

1. ↑ ^{a b c} Dimensions as for the "10 - inch " cyclotron relate to the diameter of the pole shoes.
2. ↑ The ion energy depends on and on. however, could hardly be increased. For one thing, that would have required the development of entirely new magnets; on the other hand, it would also have grown, which was also not feasible at the time. This second limitation was also the reason why the newer cyclotrons of the 1930s did not accelerate protons but deuterons or helium nuclei. ${\displaystyle R}$ ${\displaystyle B}$ ${\displaystyle B}$ ${\displaystyle B}$ ${\displaystyle f}$

itemizations

1. ^ K. Sonnabend, Physics Journal Volume 17 (2018) Issue 12 Page 10
2. ↑ John J Livingood: Radioactivity by Bombardment . In: Electronics . tape 8 , no. 11 , November 1935, p. 6–9 ( online [PDF; accessed 2 April 2016]).
3. ↑ ^{a b c d e f g h i j} JL Heilbron, Robert W. Seidel: Lawrence and His Laboratory. A History of the Lawrence Berkeley Laboratory . volume I. University of California Press, Berkeley 1989, ISBN 0-520-06426-7 ( online [accessed 26 March 2016]).
4. ↑ Pedro Waloschek (ed.): The infancy of particle accelerators: Life and work of Rolf Wideröe (=  DESY report 94-039 ). 1994, p.  41 , doi : 10.1007/978-3-663-05244-9 ( limited preview in Google Book Search – Autobiography of Wideröe; also Vieweg, 1994, ISBN 978-3-663-05246-3 ).
5. ↑ Vince Telegdi : Szilard as Inventor . In: Physics Today . October 2000, p.  25-28 .
6. ↑ Rolf Wideröe: On a new principle for producing high voltages . In: Archives of Electrical Engineering . tape 21 , No. 4 , 1928, p. 387-406 , doi : 10.1007/BF01656341 .
7. ↑ Michael Hiltzik: Big Science: Ernest Lawrence and the Invention that Launched the Military-Industrial Complex . Simon & Schuster, 2015, ISBN 978-1-4516-7603-7 , part 1, chap. 3.
8. ↑ Ernest O. Lawrence, NE Edlefsen: On the production of high speed protons . In: Science . tape 72 , no. 1867 , October 10, 1930, p. 376-377 , doi : 10.1126/science.72.1867.372 .
9. ↑ Milton Stanley Livingston: The Production of high velocity hydrogen ions without the use of high voltages . PhD thesis. University of California, Berkeley 1931, p. 9, 19 ( online [PDF; accessed 26 March 2016]).
10. ↑ Ernest O Lawrence, M Stanley Livingston: The production of high speed light ions without the use of high voltages . In: Physical Review . tape 40 , 1932, p. 19-37 , doi : 10.1103/PhysRev.40.19 .
11. ↑ ^{a b c d e} M. Stanley Livingston: Early history of particle accelerators . In: Advances in Electronics and Electron Physics . tape 50 , 1980, p. 1–88 , doi : 10.1016/S0065-2539(08)61061-6 ( limited preview on Google Book Search).
12. ↑ Glenn T. Seaborg: The plutonium story (=  LBL report 13492 ). September 1981 ( online [accessed 29 March 2016] OSTI identifier 5808140).
13. ↑ Chronology of the VG Kchlopin Radium Institute. (No longer available online.) Archived from the original on April 4, 2014 ; retrieved April 4, 2014 .  
14. ↑ D. Hoffmann, U. Schmidt-Rohr (ed.): Wolfgang Gentner: Festschrift for the 100th birthday . Springer 2007, ISBN 3-540-33699-0 , pages 17, 19, 22
15. ↑ Thomas Stange, Institute X. The beginnings of nuclear and high-energy physics in the GDR, Vieweg/Teubner 2001, p. 21 ff.
16. ↑ ^{a b c} Frank Hinterberger: Physics of particle accelerators and ion optics . 2nd Edition. Springer, Berlin 2008, ISBN 978-3-540-75281-3 ( limited preview in Google book search).
17. ↑ Seattle Cancer Care Alliance neutron therapy. Retrieved 29 March 2016 ("Behind the scenes" section).  
18. ↑ Johannes Ammer: Chemistry under time pressure . In: Süddeutsche Zeitung . No. 138 , 17 June 2011, p. 18 ( online [PDF; accessed 29 March 2016]).
19. ↑ Proton irradiation with a cyclotron at the RPTC. Retrieved March 29, 2016 .  
20. ↑ Particle therapy facilities in operation. Retrieved January 17, 2017 .