Particle Accelerators. The Electrostatic Accelerators

Transcription

1 Particle Accelerators The Electrostatic Accelerators

2 References K. Wille The Physics of Particle Accelerator, Oxford University press pag 1-29 H. Wiedeman Particle accelerator physics volume 1, chapter 3 Just for your knowledge: A. Sessler, E. Wilson, ENGINES OF DISCOVERY, World Scientific

3 Principle of operation

4 Current in electrostatic accelerators

5 Paschen s law When the pressure increases, the collision probability increases, but the path between two collisions decreases, so also the energy transferred to an electron is decreased. When the pressure us very low, the path between two collision is quite large, but the probability of a collision is relatively smaller.

6 Cockroft Walton Cockroft and Walton were able to accelerate protons to hundreds of kev. In 1932 they bombarded Lithium with 700 kev protons and transmuted it into Helium and other elements. This was the first time that a particle accelerator had been use to trigger a nuclear reaction. Cockroft and Walton were awarded the Nobel prize in 1951.

7 Van der Graf In a Van de Graaff generator charges are mechanically carried by a conveyor belt from a low potential source to a high potential collector. Van de Graaff generator can reach several MV and are still used in DC accelerators ~2MV in air Up to 20+ MV in SF6!

8 Using Van der Graf

9 Pigeon droppings Under normal operation, because the electrodes were very smooth and almost perfect spheres, Van de Graf generators did not normally spark. However, the installation at Round Hill (MIT) was in an open-air hanger, frequented by pigeons, and here we see the effect of pigeon droppings.

10 Public science in the 30s

11 Tandem Reverse ion charge state in middle of Van de Graaff allows over twice the energy gain The stripper is usually a gas Source is at ground

12 Example Br ion in a Tandem with Vo = 20 MV. Br ( A = 79 ) charge Z = -1. The beam is accelerated to 20 MeV From the stripper, Ar (density l 1μg/cm 2 ), the beam comes out with a spectrum of charge with a maximum around Z+ 7, and it arrives to Z+ 10. Filtering the Z+= 10 ions, these are again accelerated to the energy E= (1 + Z ) qvo = 220 MeV ( 220/79 = 2.8 MeV/nucleon = 2.8 MeV/A).

13 Atomic Mass Spectroscopy Resolve 1 atom of 14 C over of other Carbon atoms!

14 Dating old documents AMS was used to date ashes found in Newfoundland in a Europeantype settlement. These ashes were dated back to the XIth century. A Viking map featuring Newfoundland was shown to be older than Columbus trip to America. AMS has contributed to establish that North America was visited by Vikings well before other European nations

15 Limits of electrostatics accelerators The maximum achievable voltage is limited by discharge A further disadvantage of accelerating particles with high voltages is that either the source of the particles or the measuring instruments (or even both) have to be at high voltage, which makes any operation rather awkward and even dangerous.

16 Advantages of Electrostatic Machines Voltage may be very precisely controlled allows a detailed study of nuclear reactions and in particular narrow resonances in energy Another interesting application is in the extensive study of the reactions that take place in stars, rather low energy by nuclear physics standards, and therefore requiring exacting work. In 1983 a Nobel Prize was awarded to William Fowler, of Caltech, for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe Experimental work that was all carried out on electrostatic machines.

17 Particle Accelerators The Electrodynamics Accelerators

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19 The Wideroe accelerator R. Wideroe proposed an accelerator by using an alternating voltage across many alternating gaps. His professor refused any further work because it was sure to fail. Wideroe still published his idea in Archiv fur Electrotechnic

20 Wideroe accelerator Original drawing from the Wideroe thesis Source: The Infancy of Particle Accelerators Life and Work of Rolf Wideröe

21 Wideroe accelerator The field is shielded inside the tubes The charge experiences a field only between the gap During the drift in the tube the field change polarity in the following gap The charge experience always an accelerating field The largest voltage is U max

22 Length of the tubes The length increases as the square root of the energy Higher RF frequency decreases the tube length, but Which is the best phase for 0?

23 Alvarez type accelerator

24 Phase stability If the phase is below 90 degrees a particle that gain more that the reference energy travels fasters and in the following gap will experience a smaller value of the accelerating field.

25 Phase stability implies transverse instability

26 Circular accelerator The main costs of an accelerator are the infrastructures and the power sources In a linear accelerator the particles pass through any accelerating structure only once It is convenient to build a circular machine where the particle go through the same accelerating structures many times In such a machine a magnetic field is used to confine or to bend the trajectory of the particles The main disadvantage is the emission of Synchrotron radiation Circular machine are well suited for massive particles, while they are not convenient for electron with energy higher than hundreds of GeV

27 Hadron versus lepton collider hadron collider at the frontier of physics huge QCD background not all nucleon energy available in collision lepton collider for precision physics well defined CM energy polarization possible after LHC lepton collider energy determined by discoveries consensus E cm 0.5 TeV p e+ e- p

28 Circular versus Linear Collider accelerating cavities N N S S many magnets, few cavities need strong field for smaller ring high energy high synchrotron radiation losses (E 4 /R) high bunch repetition rate high luminosity source main linac few magnets, many cavities need efficient RF power production higher gradient shorter linac single pass need small cross-section for high luminosity: (exceptional beam quality, alignment and stabilization)

29 Cost of Circular & Linear Accelerators cost Circular Collider Linear Collider Circular Collider ΔE turn ~ (q 2 E 4 /m 4 R) cost ~ ar + b ΔE optimization: R~E 2 cost ~ ce 2 LEP200: ΔE ~ 3%; ~200 GeV e - energy Linear Collider E ~ L cost ~ al

30 Polar coordinate system

31 The Betatron dp dr db db e B r er ee dt dt dt dt E ds 2 RE d dt E ds mv r 2 evb 0 p mv erb d B dt 2 2 R db( R) dt

32 Wideroe ½ condition ( ) 2 RBR d dt 2 2 R db( R) dt d dt 2 R db( R) dt 1 B( R) B( R) 2 The particles are injected close to the zero of the magnetic field=maximum of electric field. These particles are extracted close to the maximum of the magnetic field=zero of electric field

33 Injection and extraction

34 Electrons vs protons The betatron is used mainly for electrons p qrb R max max Using R=1.23 m and B=8.1kG p max 300 MeV/c It is a good result compared to the electron rest mass (0.511 MeV) but not in comparison with proton rest mass ( MeV)

35 Weak focusing I y x F x mv r 2 evb y Only on the reference orbit is zero r R x R(1 x/ R) B y R By x By B0y x B0y 1 x B0 y x R