accelerator physics and ion optics introduction

Transcription

1 accelerator physics and ion optics introduction Sytze Brandenburg sb/accphys2007_1/1

2 course literature book used as guideline for the course An introduction to particle accelerators Edmund Wilson Oxford University Press, 2001 ISBN selected topics from proceedings of CERN accelerator school 1992 General accelator physics course proceedings of CERN accelerator school 1994 Cyclotrons, linacs and their applications sb/accphys2007_1/2

3 additional literature alternative book for the course (in German) Physik der Teilchenbeschleuniger und Ionenoptik Frank Hinterberger Springer Verlag, 1997 ISBN links and references on search the web sb/accphys2007_1/3

4 material on CD-ROM proceedings CERN Accelerator School 1992 General accelerator physics course proceedings CERN Accelerator School 1994 Cyclotrons, linacs and their applications Principles of charged particle acceleration Stanley Humphries sb/accphys2007_1/4

5 prerequisite knowledge electricity and magnetism Maxwell equations: differential and integral form mechanics pendulum special relativity relation velocity vs. energy and momentum Lorentz transformation sb/accphys2007_1/5

6 course lay-out introduction accelerator applications accelerator types physics & technology development how to keep the particles on track single particle optics beam optics transverse & longitudinal matching beam to accelerator what makes life difficult imperfections and resonances special topics damping, cooling and synchrotron radiation cyclotrons injection and extraction.. sb/accphys2007_1/6

7 goals and objectives knowledge principles of acceleration and guiding function of ion optical elements (first and second order) behaviour of single particles vs. beam phase space; emittance conservation orbit stability in circular accelerators properties matched beam for an accelerator lattice effects of aberrations, imperfections; resonances ability calculate first order beam optics in a lattice design a beamline in first order sb/accphys2007_1/7

8 assessment home work assignments contribute up to 20 % of final grade written exam exam grade is lower limit for final grade sb/accphys2007_1/8

9 outline introduction accelerator applications physics & technology of accelerators historical development accelerator types DC-accelerators RF and pulse accelerators linear accelerators circular accelerators reading: Wilson; chapter 1 CERN accelerator school 1992 (CAS94-01); chapter 1 sb/accphys2007_1/9

10 accelerator applications medicine radioactive isotope production (diagnostics and therapy) X-ray diagnostics X-ray and electron therapy charged particle therapy industry welding X-ray diagnostics ion implantation (semi-conductors, surface hardening) material analysis (structure, composition) material modification; micro machining sb/accphys2007_1/10

11 accelerator applications science nuclear physics particle physics condensed matter physics material science biochemistry archeology sb/accphys2007_1/11

12 accelerator types isotope production cyclotron X-ray diagnostics, welding DC accelerator X-ray and electrontherapy linac ion implantation DC accelerator archeology DC accelerator material analysis DC accelerator, linac, cyclotron material modification DC accelerator, linac, cyclotron ion therapy cyclotron, synchrotron nuclear physics cyclotron, linac, synchrotron, storage ring particle physics synchrotron, storage ring, linac condensed matter physics material science biochemistry synchrotron, storage ring for synchrotron radiation sb/accphys2007_1/12

13 accelerator market in the EU particle physics 3 synchrotron radiation 10 nuclear physics 15 ion therapy 3 + several under construction X-ray and electron therapy ~3000 (NL: ~100) X-ray diagnostics > (NL: ~1600 in ziekenhuis + ~5500 bij tandartsen) sb/accphys2007_1/13

14 some accelerator types sb/accphys2007_1/14

15 physics of accelerators classical electrodynamics (Maxwell) guiding, focussing and acceleration space charge effects beam wall interaction beam beam interaction quantum electrodynamics synchrotron radiation (electrons) atomic physics beam vacuum interaction thermodynamics cooling sb/accphys2007_1/15

16 technology of accelerators developments superconductivity increase in energy (LHC) ultra high vacuum (<10-12 mbar = 3 x10 4 atoms/cm 3 ) storage rings computation detailed understanding: maximize intensity optimization mechanical and (electro-)magnetic design automated control and supervision material engineering high precision machining sb/accphys2007_1/16

17 particle physics around 1900 charged particles produced in gas discharges negative: cathode rays electrons (Thomson) positive: Kanalstrahlen; ~1700 x heavier than electrons elements atomic number Z mass, chemical properties emission spectra radioactivity α-, β- and γ-radiation: penetration in matter; charge; mass electromagnetic radiation (radiowaves, light) X-rays photo-electric effect (Nobelprize A. Einstein, 1921) atoms: no clear picture of structure heavy positively charged particle(s) electrons sb/accphys2007_1/17

18 particle physics around 1900 Rutherford et al. (1911): scattering α-particles from gold: comparison with Coulomb-scattering between point particles dσ Q1Q 2 2πsinϑ = dϑ 16πε0E ϑ kin,1 2 4 sin 2 conclusions Q 1, Q 2 = Z 1 e, Z 2 e; -e is electron charge mass and positive charge in a small nucleus deviations at small scattering angle screening by electrons size of atom (~0.1 nm) deviations at large scattering angle hard sphere collision size of nucleus (~10 fm) Rutherford s conjecture: nucleus = protons and electrons inconsistent with Heisenberg uncertainty relation for electrons sb/accphys2007_1/18

19 particle physics around 1900 Rutherford (1919): nuclear reaction 14 N(α, p) 17 O prediction of existence neutron idea: hard sphere collision needed for nuclear reaction size and charge of nucleus Coulomb barrier conclusion: energy of several MeV needed for protons and α-particles acceleration with DC voltage not feasible production of energetic particles for nuclear reactions: use Lorentz force F = q(e + v B) to accelerate charged particles sb/accphys2007_1/19

20 electrostatic accelerator: Cockroft-Walton 1928: tunneling hypothesis (Gamow) lower energy needed acceleration with DC feasible 1932: first nuclear reaction with accelerated protons 7 Li + p 2α 7 Li + p 7 Be + n E p = 400 kev discovery neutron Rutherford laboratory sb/accphys2007_1/20

21 electromagnetic force production of energetic particles for nuclear reactions: use Lorentz force F = q(e + v B) to accelerate charged particles magnetic force q(v B) perpendicular to velocity does not contribute to acceleration can be used for focussing and guiding B determines curvature of trajectory electric force qe component parallel to velocity: acceleration γmv q component perpendicular to velocity: focussing and guiding 2 γmv E determines curvature of trajectory E ρ = q B ρ = sb/accphys2007_1/21

22 acceleration techniques linear accelerators electrostatic radio-frequency (RF) electric field induction (pulsed EM field) particles focussed by accelerating field or separate magnetic and electric fields circular accelators RF electric field induction particles guided and focussed by magnetic fields sb/accphys2007_1/22

23 electrostatic accelerator: principle electrons emitted by hot filament cathode: negative high voltage (~10 kv) anode: grounded steering plates time base signal simplest example: oscilloscope sb/accphys2007_1/23

24 electrostatic accelerator: principle electrons emitted by hot filament cathode: negative high voltage (~10 kv) anode: grounded steering plates time base signal CRT of J.J. Thompson, 1897 sb/accphys2007_1/24

25 electrostatic accelerator: Cockroft-Walton Greinacher cascade voltage distributed over m any electrodes to control focussin g high current I = 100 m A V m ax 2 M V injector for high energy, high intensity accelerators load effects voltage drop n 3 I/ωC voltage ripple n 2 I/ωC large C; high U 0 and ω created 13/11/05 18:19 1/1 m odified 13/11/05 18:19 sb/accphys2007_1/25

26 electrostatic accelerators: focussing acceleration and focussing: static electric field V1 > V2: positive particles accelerated from 1 to 2 first half gap focussing, second half defocussing particle more time in first half net focussing effect de 0 dt = sb/accphys2007_1/26

27 electrostatic accelerator: van de Graaff insulating conveyor belt: transport charge to HV-dome motor power: V I + friction voltage divider column potential definition focussing sb/accphys2007_1/27

28 electrostatic accelerator: van de Graaff HMI van de Graaff sb/accphys2007_1/28

29 electrostatic accelerator: tandem van de Graaff accelerate negative ions to HV-dome (OK for many elements) pass ions through a foil or high pressure region to remove a number of electrons: positive ions in chargestate Q+ accelerate positive ions to ground E = (Q + 1) V sb/accphys2007_1/29

30 electrostatic accelerator: tandem van de Graaff Oak Ridge tandem sb/accphys2007_1/30

31 electrostatic accelerator: tandem van de Graaff installed at Center for Isotopereseach (CIO) for 14 C dating: count the number of 14 C-atoms relative to 12 C age of material sb/accphys2007_1/31

32 electrostatic accelerator: limitations corona discharge is also used to stabilize voltage surface currents on insulators of acceleration column discharge in insulation gas discharge on surfaces (surface roughness) air insulation : 2 MV high pressure N 2 and SF 6 : up to 25 MV sb/accphys2007_1/32

33 RF linear accelerator RF electric field parallel to velocity particles in phase with RF field (polarity): bunched beam λrf length bunches l b β 2 spacing bunches db = nλrf sb/accphys2007_1/33

34 Widerö linear accelerator (1928) acceleration in gaps E = qv sin ϕ shielding by drift tubes during polarity reversal (1/2 T RF ) βiλrf λrf iqv sin ϕ length of drift tube li = = (v <<c) 2 c 2m phase (axial) focussing by proper choice of ϕ additional transverse focussing needed (in drifttubes) sb/accphys2007_1/34

35 Widerö linear accelerator (1928) acceleration in gaps E = qv sin ϕ shielding by drift tubes during polarity reversal (1/2 T RF ) βλ λ iqv sin ϕ length of drift tube li = i RF = RF (v <<c) 2 c 2m phase (axial) focussing by proper choice of ϕ additional transverse focussing needed (in drifttubes) sb/accphys2007_1/35

36 RF linear accelerator: further developments development of accelerating cavities based on waveguide principle higher energygain, higher frequency superconducting cavities also used in large synchrotrons mainly injectors for synchrotrons largest linac: 3 km electron LINAC Stanford (USA) sb/accphys2007_1/36

37 induction linear accelerator current pulse in winding around ferromagnetic core B d E = Eidl = Bids t dt C S pulses in phase with beam beam pulses typical t = 50 ns I = 2 ka sb/accphys2007_1/37

38 circular accelerators betatron cyclotron synchro-cyclotron isochronous cyclotron synchrotron storage ring sb/accphys2007_1/38

39 betatron (1923) Widerö design ray transformer beam secondary winding of transformer beam guided in circular orbit with separate magnet B d E = Eidl = Bids t dt stable orbit C d B B guide 1 d = dt 2 dt πr S acc 2 da sb/accphys2007_1/39

40 betatron (1941) Kerst : working prototype breakthrough: orbit stabilisation with non-homogeneous field only used for electrons sb/accphys2007_1/40

41 orbit stabilisation F = qv B F z = q(v r B θ -v θ B r ) homogeneous field: B r = B θ = 0 F z = 0 v z 0 spiral motion around z-axis, no stability azimuthally symmetric field: B θ = 0 B z decreases with radius B r towards center F z towards midplane particle oscillates around midplane vertical stability, weak focussing sb/accphys2007_1/41

42 betatron Kerst with first and largest betatron sb/accphys2007_1/42

43 cyclotron (1931) Lawrence and Livingston inspired by Widerö linac: wound-up linac sb/accphys2007_1/43

44 cyclotron vacuum chamber first cyclotron 10 cm sb/accphys2007_1/44

45 cyclotron homogenous magnetic field isochronous (non-relativistic) mv 2 qvb R mv Bq orb = = ν = R Bq 2 π m accelerate with RF electric field with ν RF = ν orb theory: homogeneous field no vertical orbit stability large beamlosses pratice: due to fringefield effects B z decreases with radius marginal vertical orbit stability gradual loss of synchronism: energy limit sb/accphys2007_1/45

46 cyclotron relativistic effects γ 2 mv γmv Bq orb = qvb R = ν = = f(r) R Bq 2πγm rapid loss of synchronism: energy limit ~ 20 MeV protons only useful for ions (m p /m e = 1836) two solutions vary ν RF periodically: pulsed acceleration, synchro-cyclotron requires phase focussing (McMillan, Veksler; 1945) restore isochronism B z (r) = γ(r) B z (0): isochronous cyclotron B z increases with radius no vertical stabililty introduce sectors in magnetic field (Thomas; 1938): strong focussing sb/accphys2007_1/46

47 cyclotron modern isochronous cyclotron at KVI superconducting coils high field, compact machine 200 MeV protons sb/accphys2007_1/47

48 particle physics around 1935 atomic model complete: nucleus consists of protons and neutrons electrons bound in Coulomb-field nucleus sb/accphys2007_1/48

49 particle physics around 1935 atomic model complete: nucleus consists of protons and neutrons electrons bound in Coulomb-field nucleus basic theory for α-, β- and γ-emission by nuclei strong nucleon - nucleon interaction established quantum physics: interaction via particle exchange EM-interaction: infinite range massless photons strong interaction: short range massive particle Heisenberg uncertainty principle: mc MeV high energy accelerator needed for production sb/accphys2007_1/49

50 synchrotron (1950) higher energy: larger radius 200 MeV proton Bρ = 2.2 Tm 1000 MeV proton Bρ = 5.7 Tm for synchro-cyclotron-like accelerators huge magnets alternative approach acceleration in several stages constant radius orbit magnetic field and ν RF vary during acceleration; pulsed operation (cf. synchro-cyclotron) sb/accphys2007_1/50

51 synchrotron requires phase focussing transverse focussing weak focussing: dipole magnets with radially decreasing B z needs large magnet gaps strong focussing combined function dipole magnets with alternating strong radial fieldgradient no possibility for fine-tuning separated function homogeneous dipole magnets for bending quadrupole magnets for focussing sb/accphys2007_1/51

52 storage / collider ring development Standard Model: zoo of particles up to Higgs very heavy, exotic particles (e.g. mass W ±, Z 0 ~ GeV) ( ) beam fixed target: energy available for reaction Ecm = 2 E mc +m c investment explodes colliding beams E cm = 2 (E beam + mc 2 ) low density compared to fixed target low event rate sb/accphys2007_1/52

53 collider ring two beams in opposite direction electrons + positrons (LEP) protons + protons (LHC, under construction at CERN) experiment performed in ring interaction zones with very small beamsize colliding protons with E kin = 100 GeV: E cm = 200 GeV fixed target E cm = 200 GeV: E kin = GeV sb/accphys2007_1/53

54 storage ring / collider ring sb/accphys2007_1/54

55 LHC: largest storage/collider ring circumference 27 km proton energy 7000 GeV sb/accphys2007_1/55

56 Livingston chart: equivalent energy vs. time sb/accphys2007_1/56

57 presentations and excercises presentations and excercises available in PDF-format on sb/accphys2007_1/57

58 next lecture reading Wilson: chapter 2 Transverse motion CERN Accelerator School 1992, CERN report chapter 2 Basic course on accelerator optics sb/accphys2007_1/58

59 Greinacher cascade combination of two circuits is a voltage doubler + rectifier stacking n circuits leads voltage multiplication with factor n sb/accphys2007_1/59

60 pulse generator capacitors charged in parallel triggering spark gaps: all capacitors in series U out = n U in state of the art performance n = 100 U out = 6 MV I out = 500 ka pulse duration 40 ns sb/accphys2007_1/60

61 orbit stability (Widerö 1928, Steenbeck 1935, Kerst 1941) field in vicinity of reference orbit at radius R 2 γmv restoring force Fr ( r) = qvby ( r) r x orbit deviation x : r R x R = + = 1+ R Taylor expansion in first order 1 1 x = 1 r R R By ( R) R By ( R) x By ( r) = By ( R) + x = By ( R) 1+ x By ( R) x R By ( r) By ( R) 1 n x = + R 2 γmv x x Fr ( r) = 1 qvby ( R) 1 n R R R sb/accphys2007_1/61

62 orbit stability 2 γmv y R 2 2 γmv x d x Fr ( x ) = ( 1 n) = γm 2 R R dt particle oscillates around reference orbit with ω x = ω0 1 n for n > 1 particle orbit becomes unstable (imaginary ω x ) at reference orbit F r (R) = 0 : = evb ( R ) nomenclature oscillation around reference orbit: betatron oscillations Q x, ν x = ωx ω orb : betatron frequency, number of betatron period per turn sb/accphys2007_1/62

63 orbit stability for vertical stability similar reasoning Fy ( z) = qvb x B x B B = 0 = y y x 2 y v y in first order B x ( y ) = nb y ( R ) Fy ( y ) = γmn R R R particle oscillates around reference orbit with ω y = ω0 n for n< 0 particle orbit becomes unstable (imaginary ω y ) simultaneous radial and axial stability 0 < n < 1: weak focussing sb/accphys2007_1/63