Introduction to Accelerator Physics

Transcription

1 Introduction to Accelerator Physics Part 1 Pedro Castro / Accelerator Physics Group (MPY) Introduction to Accelerator Physics DESY, 24th July 2017 DESY CERN Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 2 1

2 Applications of accelerators Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 3 Applications of Accelerators (1) Particle colliders for High Energy Physics (HEP) experiments Fixed target experiments Two s collider experiments Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 4 2

3 Applications of Accelerators (1) Particle colliders for High Energy Physics experiments Example: the Large Hadron Collider (LHC) at CERN Lake Geneva Mont Blanc Geneva built between 2001 and 2009 Higgs discovery: July km superconducting magnets (inside a cryostat) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 5 Worldwide > About 120 accelerators for research in nuclear and particle physics Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 6 3

4 Applications of Accelerators (2) Light sources for biology, physics, chemistry experiments Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 7 Applications of Accelerators (2) Light sources for biology, physics, chemistry experiments Electromagnet B structural analysis of crystalline materials X-ray crystallography (of proteins) X-ray microscopy X-ray absorption (or emission) spectroscopy Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 8 4

5 Example: Positron-Elektron-Tandem-Ring-Anlage (PETRA) positron-electron tandem ring accelerator at DESY built between 1976 and 1978 HEP experiments: gluon discovery: 1979 JADE CELLO, PLUTO 2.3 km long 0.5 GeV e-/e+ e+e- collisions at 2 x 19 GeV MARK J 7 GeV TASSO Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 9 Example: Positron-Elektron-Tandem-Ring-Anlage (PETRA) positron-electron tandem ring accelerator at DESY built between 1976 and 1978 HEP experiments: gluon discovery: GeV e-/e+ 40 GeV protons 2.3 km long 0.5 GeV e-/e+ protons 7 GeV pre-accelerator for HERA synchrotron radiation since 1987 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 10 HERA 5

6 Example: Positron-Elektron-Tandem-Ring-Anlage (PETRA) positron-electron tandem ring accelerator at DESY built between 1976 and 1978 HEP experiments: gluon discovery: 1979 Max von Laue hall 300 m 2.3 km long e-/e+ pre-accelerator for HERA synchrotron radiation since 1987 PETRA III since 2009 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 11 Max von Laue hall 14 lines 30 exp. stations e- e- photons Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page

7 Example: Positron-Elektron-Tandem-Ring-Anlage (PETRA) positron-electron tandem ring accelerator at DESY built between 1976 and 1978 HEP experiments: gluon discovery: 1979 hall nord 2.3 km long e-/e+ hall east pre-accelerator for HERA synchrotron radiation since 1987 PETRA III since 2009 PETRA III Extension from 2014 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 13 Worldwide > About 120 accelerators for research in nuclear and particle physics > About 70 electron storage rings and electron linear accelerators used as light sources (so-called synchrotron radiation sources ) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 14 7

8 Applications of Accelerators (3) Accelerators in medicine For radioisotope production proton + stable isotope transmutation radioactive isotope For radiotherapy and radiosurgery: x-rays and gamma-rays ions (from protons to atoms with atomic number up to 18, Argon) neutrons Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 15 Applications of Accelerators (3) Accelerators in medicine For radioisotope production For example: cyclotron 18 MeV proton accelerator Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 16 8

9 Applications of Accelerators (3) Accelerators in medicine For radioisotope production For example: target p 18 MeV proton accelerator Oxygen-18 (stable) (transmutation) Fluorine-18 (half-life time = 110 min.) 97% of decays Oxygen-18 + positron Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 17 Applications of Accelerators (3) Accelerators in medicine For radioisotope production For example: target p 18 MeV proton accelerator Oxygen-18 (transmutation) Fluorine-18 (half-life time = 110 min.) Fludeoxyglucose ( 18 F) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 18 9

10 Applications of Accelerators (3) detectors!! Positron Emission Tomography (PET) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 19 PET Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 20 10

11 Applications of Accelerators (3) detectors!! Positron Emission Tomography (PET) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 21 Worldwide > About 120 accelerators for research in nuclear and particle physics > About 70 electron storage rings and electron linear accelerators used as light sources (so-called synchrotron radiation sources ) > More than 7,000 accelerators for medicine radiotherapy (>7,500), radioisotope production (200) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 22 11

12 Applications of Accelerators (4) For industrial applications: Application Ion implantation ~ 9500 Electron cutting and welding ~ 4500 Electron and x-ray irradiators ~ 2000 Ion analysis (including AMS) ~ 200 Radioisotope production (including PET) ~ 900 Nondestructive testing (including security) ~ 650 Neutron generators (including sealed tubes) ~ 1000 with energies up to 15 MeV approx. numbers from 2007 (worldwide) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 23 Applications of Accelerators (4) For industrial applications: an example: electron welding acceleration up to kev electron magnets as focusing lenses as well as deflectors up to 15 cm deep welding effect Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 24 12

13 Worldwide > About 120 accelerators for research in nuclear and particle physics > About 70 electron storage rings and electron linear accelerators used as light sources (so-called synchrotron radiation sources ) > More than 7,000 accelerators for medicine radiotherapy (>7,500), radioisotope production (200) > More than 18,000 industrial accelerators ion implantation (>9,000), electron cutting and welding (>4,000) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 25 Worldwide > About 120 accelerators for research in nuclear and particle physics > About 70 electron storage rings and electron linear accelerators used as light sources (so-called synchrotron radiation sources ) > More than 7,000 accelerators for medicine radiotherapy (>7,500), radioisotope production (200) < 1% > More than 18,000 industrial accelerators ion implantation (>9,000), electron cutting and welding (>4,000) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 26 13

14 Worldwide > About 120 accelerators for research in nuclear and particle physics > About 70 electron storage rings and electron linear accelerators used as light sources (so-called synchrotron radiation sources ) > More than 7,000 accelerators for medicine radiotherapy (>7,500), radioisotope production (200) > More than 18,000 industrial accelerators ion implantation (>9,000), electron cutting and welding (>4,000) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 27 Applications of Accelerators (5) Many millions of television sets, oscilloscopes using CRTs (Cathode Ray Tube) TV oscilloscope Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 28 14

15 Applications of Accelerators (5) Many millions of television sets, oscilloscopes using CRTs (Cathode Ray Tube) acceleration 25 frames / s magnets as focusing lenses as well as deflectors 625 lines Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 29 Applications of Accelerators (6) X-ray tubes DC high voltage ( kv) VACUUM braking radiation or bremsstrahlung Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 30 15

16 Working with accelerators in the control room requires: -a lot of (accelerator) physics knowledge -a lot of (accelerator) engineering knowledge -some Sherlock Holmes skills Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 31 The case begins Accelerator Control Room Hamburg, DESY Sat. 12 th June o clock a.m. PETRA runs with a current of 75 ma 02:24 a.m.: lost Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 32 16

17 Circular accelerators: the synchrotron accelerating device bending magnet vacuum chamber injector straight sections Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 33 Dipole magnet! dipole magnets: tomorrow Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 34 17

18 Circular accelerators: the synchrotron accelerating device! radiofrequency acceleration: tomorrow bending magnet vacuum chamber injector straight sections Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 35 Circular accelerators: the synchrotron Low Energy Antiproton Ring (LEAR) at CERN (built in 1982) vacuum chamber bending magnet accelerating device Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 36 18

19 Circular accelerators: the synchrotron. B (perpendicular) R "# $ %&# %' momentum charge of the particle $()# *+ velocity magnetic field +,)# " $ ()+ "#,)# " $ / )0 1 (circular motion) (+ $ /) 1 1 $ /) (+ Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 37 Circular accelerators: the synchrotron injector accelerating device 1 straight sections magnet vacuum chamber +,)# " $ ()+ "#,)# " $ / )0 1 (circular motion) (+ $ /) 1 1 $ /) (+ $ 2345'64'! increase B synchronously with &$/) of particle Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 38 19

20 DESY (Deutsches Elektronen Synchrotron) DESY: German electron synchrotron Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 39 DESY (Deutsches Elektronen Synchrotron) DESY: German electron synchrotron, 1964, 7.4 GeV Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 40 20

21 02:24 a.m.: lost The Main Accelerator Control Room Hamburg, DESY Sat. 12 th June :24 a.m.: lost current [ma] time Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 41 PETRA runs with around the clock [ma] building 25f, HASYLAB 17 th July :45 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 42 21

22 PETRA runs with around the clock 24 hours [ma] 17 th July :45 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 43 An example of PETRA running with top-up modus on/off current [ma] lifetime 7~1.3 hours <$< = >?! top-up modus 21 st July :35-11:15 time Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 44 22

23 Beam lifetime The lifetime of an electron is mainly limited by two effects: rest gas scattering scattering with the Coulomb field of a gas atom the electron is deflected and lost in the surrounding vacuum chamber - bremsstrahlung γ large energy loss that leads to particle loss Coulomb scattering between two electrons from the same bunch E < 6 GeV bunch E > 6 GeV - electrons can gain or loose energy called Touchek effect depends on the density of the electron bunch Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 45 An example of PETRA running with top-up modus on/off current [ma] lifetime 7~1.3 hours top-up modus 21 st July :35-11:15 time Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 46 23

24 top-up modus electrons injected in PETRA current [ma] ~0.9 ma = 1% time Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 47 top-up modus What are the advantages of running in top-up modus? stable intensity conditions for measurements constant heat load on optical components (mirrors, filters, crystals ) " stable photon angle and position ( pointing stability ) " stable wavelength constant heat load on accelerator vacuum chamber increased stability of all systems diagnostics: small dynamic range Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 48 24

25 02:24 a.m.: lost The Main Accelerator Control Room Hamburg, DESY Sat. 12 th June :24 a.m.: lost current [ma] time Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 49 One example of PETRA run over 7 days Run number 4: 60 Bunches; 23 rd 30 th March, 2011 top-up timing problems vertical blow up power off in crate at DORIS RF problems and longitudinal instabilities RF?? RF?? magnet power supply RF?? loss without dump RF circulator water cooling RF circulator water cooling Source: K. Balewski (MAC report 2011) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 50 25

26 Beam lost at 02:24 a.m. The link to the electronic logbook: What to do? Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 51 The first suspect released: MPS is not guilty The Machine Protection System status from 12 th June 2010 at 02:26 vacuum system ok magnet system ok radio-frequency ok water cooling ok all systems up and running 12 th June :26 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 52 26

27 Electrons can be injected but cannot be stored! 500 µs 65 turns current injection problem or aperture problem? time current after a few turns current at injection Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 53 Next suspect: injection vacuum chamber stored reference trajectory Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 54 27

28 Next suspect: injection bending magnet stored injected Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 55 Next suspect: injection dipole dipole dipole stored free field region homogeneus field septum Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 56 28

29 Next suspect: injection + accumulation dipole dipole dipole stored injected septum Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 57 Next suspect: injection + accumulation dipole dipole dipole stored injected septum PETRA septum Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 58 29

30 Next suspect: injection + accumulation septum at the Proton Synchrotron Booster (PSB) at CERN (1) (2) stored injected (3) free field region homogeneus field Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 59 Next suspect: injection + accumulation kicker (very fast dipole) kicker (very fast dipole) kicker (very fast dipole) stored injected septum kicker field ~20 µs time Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 60 30

31 Electrons can be injected but cannot be stored! 500 µs 65 turns current injection problem or aperture problem? time current after a few turns current at injection Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 61 Next suspect: an aperture problem Hamburg, DESY Sat. 12 th June :24 a.m.: lost 07:00 a.m.: visual inspection in accelerator Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 62 31

32 Next suspect: the new octant in Max von Laue hall e- Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 63 Next suspect: the new octant in Max von Laue hall e m Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 64 32

33 Next suspect: the new octant in Max von Laue hall Undulator PU 10 Hamburg, DESY Sat. 12 th June :24 a.m.: lost 07:00 a.m.: visual inspection in new octant permanent magnets undulator field lines S N S N + Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 65 Next suspect: the new octant in Max von Laue hall Undulator PU 10 Hamburg, DESY Sat. 12 th June :24 a.m.: lost 07:00 a.m.: visual inspection in new octant undulator field lines electrons undulator S N S N + photons Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 66 33

34 Next suspect: the new octant in Max von Laue hall Undulator PU 10 Hamburg, DESY Sat. 12 th June :24 a.m.: lost 07:00 a.m.: visual inspection in new octant undulator field lines very flat undulator vacuum chambers 9mm 7 mm S N S N + Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 67 Next suspect: the new octant in Max von Laue hall a couple of months earlier vacuum chamber Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 68 34

35 citation from the logbook: What we have tried so far: time of entries citation from the logbook: Visual inspection of new octant: no findings Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 69 Next suspect: an aperture problem Hamburg, DESY Sat. 12 th June :24 a.m.: lost 07:00 a.m.: visual inspection in new octant 11:52 a.m.: start aperture scan Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 70 35

36 Need of focusing p r we need to focus the! / bunch injector accelerating device straight sections magnet vacuum chamber Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 71 Quadrupole magnets quadrupole magnet: B Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 72 36

37 Quadrupole magnets y quadrupole magnet: four iron pole shoes of hyperbolic contour B R hyperbola x µ 0I g = 2 R B x B y = g y = g x ( quadrupole gradient ) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 73 Quadrupole magnets y B " # " # x B y = g x F x = g x "# $ ()# * + (Lorentz force) Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 74 37

38 Classical mechanics: harmonic oscillator restoring force: "$$%& Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 75 Quadrupole magnets y B x = g y F y = g y defocusing B " ' " ' x B y = g x F x = g x focusing! Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 76 38

39 In light optics light rays ( : system focal length (: focal length defocusing lens 1 ( $ $ % ( * (, ( * (, if ( * $$(, $( focusing lens (light optics) 1 ( $ % ( 0.0 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 77 Quadrupole magnets QD + QF = net focusing effect: charged particle center of quadrupoles defocusing quadrupole (rotated 90 ) focusing quadrupole Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 78 39

40 Quadrupole magnets vertical defocusing horizontal focusing vertical focusing horizontal defocusing I N S B I B I S N rotated 90 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 79 I I = -I Quadrupole magnets QD + QF = net focusing effect: x-plane: defocusing quadrupole focusing quadrupole y-plane: focusing quadrupole defocusing quadrupole Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 80 40

41 Quadrupole magnets QD + QF = net focusing effect: x-plane: defocusing quadrupole focusing quadrupole QF QD QF QD QF QD QF QD QF QD focusing defocusing quadrupole quadrupole Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 81 Circular accelerator PETRA cell focusing quadrupole dipole magnet defocusing quadrupole dipole magnet focusing quadrupole Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 82 41

42 Circular accelerator cell corrector dipole focusing quadrupole dipole magnet corrector dipole defocusing quadrupole dipole magnet corrector dipole focusing quadrupole Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 83 Next suspect: an aperture problem Hamburg, DESY Sat. 12 th June :24 a.m.: lost 07:00 a.m.: visual inspection in new octant 11:52 a.m.: start aperture scan corrector dipole 184 hor. corrector dipoles 194 ver. corrector dipoles QF QD QF QD QF QD QF QD QF QD focusing defocusing quadrupole quadrupole Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 84 42

43 First useful hint: aperture problem Beam position monitor Hamburg, DESY Sat. 12 th June :24 a.m.: lost 07:00 a.m.: visual inspection in new octant 11:52 a.m.: start aperture scan 13:20 a.m.: stored 244 position monitors Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 85 First useful hint: aperture problem NW N NE Hamburg, DESY Sat. 12 th June 2010 W SW S SE E 02:24 a.m.: lost 07:00 a.m.: visual inspection in new octant 11:52 a.m.: start aperture scan 13:20 a.m.: stored 244 monitors W N E S horizontal pos. [mm] 2.3 km vertical pos. [mm] Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 86 43

44 First useful hint: horizontal aperture problem NW N NE Hamburg, DESY Sat. 12 th June 2010 W 244 monitors SW S SE E radiofrequency systems 02:24 a.m.: lost 07:00 a.m.: visual inspection in new octant 11:52 a.m.: start aperture scan 13:20 a.m.: stored W N E S horizontal pos. [mm] vertical pos. [mm] Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 87 First useful hint: horizontal aperture problem NW N NE Hamburg, DESY Sat. 12 th June 2010 W SW S SE E 02:24 a.m.: lost 07:00 a.m.: visual inspection in new octant 11:52 a.m.: start aperture scan 13:20 a.m.: stored corrector dipole QF QD QF QD QF QD QF QD QF QD focusing defocusing quadrupole quadrupole Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 88 44

45 First useful hint: horizontal aperture problem NW N NE new octant Hamburg, DESY Sat. 12 th June 2010 W SW S SE E 02:24 a.m.: lost 07:00 a.m.: visual inspection in new octant 11:52 a.m.: start aperture scan 13:20 a.m.: stored 244 monitors W N E S horizontal pos. [mm] after flattening the orbit Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 89 horizontal aperture problem in the new octant citation from the logbook: the problem is at the end of the new octant current [ma] second hint: vacuum pressure raise in the new octant lost 02:24 a.m. aperture scan + trajectory corrections vacuum pressure [mb] vacuum pressure vacuum pressure current Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 90 45

46 horizontal aperture problem in the new octant PU13 PU14 60 m second hint: vacuum pressure raise in the new octant current [ma] 02:24 a.m. vacuum pressure [mb] vacuum pressure vacuum pressure current Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 91 visual inspection inside the vacuum chamber PU13 PU14 endoscope Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 92 46

47 visual inspection inside the vacuum chamber PU13 PU14 vacuum bellows endoscope Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 93 visual inspection inside the vacuum chamber an example of vaccum bellows vacuum bellows RF fingers Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 94 47

48 the problem was found: RF fingers Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 95 electric field of a relativistic particle )$0 0$0 )$ e e Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 96 48

49 electric field of a relativistic particle )$0 0$0 )$02 1 e 1? e z ; cylindrical coordinates 1 $ ( 61 $ ># 445 = 1$0 0 sin 0 ; </0 > 0 >!$ 1 1$0 0 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 97 electric field of a relativistic particle )$0 0$0 )$02 1 e 1? e z ; cylindrical coordinates 1 $ ( 1 ># 445 = > 0 >!$1 0$0 1 $ ( 61 $ ># 445 = 1$0 0 sin 0 ; </0 > 0 >!$ 1 1$0 0 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 98 49

50 electric field of a relativistic particle )$0 0$0 )$02 1 e 1? e z ; cylindrical coordinates!$1 0$0 1 $ ( 61 $ ># 445 = 1$0 0 sin 0 ; </0 > 0 >!$ 1 1$0 0 1 $ ( 1 ># 445 = > 0 > ;$0 $ ( 445 = 1! 0 > 0 ># > 1 A ;$ 4 2 $ ( 445 =! > 0 ># > Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 99 electric field of a relativistic particle )$0 0$0 )$ e e z!$1 0$0 1 $ ( 61 $ ># 445 = 1$0 0 sin 0 ; </0 > 0 >!$ 1 1$0 0 1 $ ( 1 ># 445 = > 0 >! ;$0 $ ( 445 = 1! 0 > 0 ># > 1 A ;$ 4 2 $ ( 445 =! > 0 ># >!! 0 Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page

51 RF fingers and wakefields vacuum chamber wall mirror currents Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 101 RF fingers and wakefields vacuum chamber wall RF fingers mirror currents RF fingers Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page

52 RF fingers and wakefields Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 103 RF fingers: improvements done old RF fingers were tilted outwards by 2 degrees new RF fingers have stronger tilt, more tension new design with RF fingers outside Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page

53 Summing-up of this part Circular accelerators: the synchrotron basic components dipole, quadrupole, undulator magnets, corrector dipoles injection system (kickers and septum) position monitors vacuum pumps, vacuum pressure monitors vacuum chambers, bellows rest gas scattering (limiting lifetime) accelerator physics Touchek effect (limiting lifetime) wakefields, RF shielding (RF fingers) collective effects basic concepts in operation top-up modus aperture scans trajectory (orbit) corrections Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page 105 Thank you for your attention Pedro Castro Introduction to Accelerator Physics 24 th July 2017 Page