Linear and circular accelerators Ion Accelerator Physics and Technology Oliver Boine-Frankenheim, Gesellschaft für Schwerionenforschung (GSI), Darmstadt Tel. 06159 712408, O.Boine-Frankenheim@gsi.de o Overview: History and accelerator types (I) o Beam dynamics: Acceleration and synchrotron motion (I/II) o Beam dynamics: Bending, focusing and betatron motion (II) o Advanced : Beam intensity limits (III) o Advanced : Storage rings and beam cooling (III) o The GSI accelerator facility (IV) I: Friday II/III: Monday IV: Wednesday at GSI
Particle energies Energies in ev Expected mass of the Higgs boson > 100 GeV Zur Anzeige wird der QuickTime Dekompressor TIFF (Unkomprimiert) benötigt. W, Z exchange bosons of the weak force 82 bzw. 93 GeV =1 V eu=1.602 10-19 J=1 ev 1 kev= 10 3 ev 1 MeV= 10 6 ev 1 GeV= 10 9 ev 1 TeV= 10 12 ev Rest mass of the anti proton: E=mc 2 Excitation energies in nuclei Ionisation energies in heavy atoms Ionisation energy of the hydrogen atom 0.938 GeV MeV kev 13 ev
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The GSI accelerator facility Ion sources Unilac SIS18 ESR Wednesday! Tumor therapy
Plasma ion sources Where do the ions come from? Ions are produced in a ionized gas ( plasma ) In thermal equilibrium the Saha equation describes the amount of ionization in a gas n i n n 3 10 27 ( k B T) 3/2 n i Ionization energy: I j e I j k T B (j: charge state) Highly stripped ions require high plasma temperatures and good plasma confinement. High ion currents are achieved for lower charge states ions.
Plasma ion sources Example: Electron cyclotron ion source 70µA Pb 26+ hot plasma High current sources: e.g. > 10 ma U 4+
Particle acceleration Basic equations Equation of motion: 1. Electrostatic acceleration: Relativistic parameters: 1 γ = β = v 1 β 2 c 2. Radiofrequency (RF) acceleration: Change of particle energy: with
Electrostatic accelerators Cockcroft-Walton accelerators 1928 Cockcroft & Walton start designing a 800 kv generator encouraged by Rutherford 1932 Generator reaches 700 kv and C&W split lithium with 400 kv protons. Zur Anzeige wird der QuickTime Dekompressor TIFF (LZW) benötigt.
Electrostatic accelerators Modern Cockcroft-Walton at FNAL Fermi Lab Cockcroft-Walton (700 kv):
Electrostatic accelerators Van de Graff generator and Tandem accelerators 1931 Van de Graaff generator (basic design) Two-stage tandem accelerator Approx. 10 MV can be reached
Acceleration with time varying fields Wiederöe RF accelerator 1924 Ising proposed time-varying fields across drift tubes: resonant acceleration. 1928 Wideröe (in Aachen) demonstrates Ising s principle with a 1 MHz, 25 kv oscillator. Length of the drift tubes: l i = 1 2 v it RF Particle energy: (E s ) i = 1 2 mv 2 i (E s ) i +1 = (E s ) i + qv 0 sinφ s l i = T RF 2 2 m (E + iqv sinφ ) s 0 0 s ω RF = 2π T RF For 10 (100) MHz and 2 MeV protons we get a maximum drift tube length of 1 (0.1) m!
RF accelerators Simplified scheme E = qv 0 RF sin(2πf RF t) RF station(s) Circular accelerator Linear accelerator (Linac)
RF cavities Simple model of a resonant cavity Ansatz: E z, B θ Resulting E-field in r: Maxwell equation in cylindrical coordinates: Solution: 0-order Bessel function Boundary condition E(r=R)=0 : Eliminating B: Example: R=1 m f 100 MHz
RF accelerators and structures at GSI UNILAC linear accelerator Zur Anzeige wird der QuickTime Dekompressor TIFF (Unkomprimiert) benötigt. f HF =36 MHz ( IH ) f HF =108 MHz ( Alvarez )
Circular accelerators B y Homogenous B-field in y-direction: rf station : ω RF = hω 0 θ R &θ = ω 0 = v qb θ R = y γ m ( cyclotron frequency ) Rigidity : v θ p = qbr E = γ mc 2 pc Example: 1 TeV protons and B=2 T results in R=1.6 km (L=10 km) Superconducting magnets (> 6 T) result in higher energies for the same R.
Cyclotron Constant (magnetic) bending field increasing radius ω 0 = v θ R = qb y γ m = const. (Cyclotron frequency) Zur Anzeige wird der QuickTime Dekompressor TIFF (LZW) benötigt. ω 0 = ω HF = const. Lawrence and Livingston, Berkeley, 1932
Synchrotron Example: GSI synchrotron SIS Synchronous rf frequency: rf cavity ω HF = hω 0 = h qb y γ m Constant radius variable B Feld R = p qb = const. Ion: U 73+ E inj =11.4 MeV/u E max = 1 GeV/u BR=18 Tm (10 T/s) Cycle=1 Hz Bending magnets Focusing magnets Synchrotron principle: E.M. McMillan, Uni. of California, 1945 Storage ring! Circumference: 216 m rf cavity
Livingston Diagramm Challenge: highest particle energies
CERN Large Hadron Collider (LHC) (under construction) Protons anf heavy ions (Pb) Energy: > 1 TeV Protons in the ring: 3x10 14 Current: 0.5 A Total beam energy: 3 MJ Magnetic bending field: 8 T Circumference: 27 km!
Evolution of (proton) synchrotron intensity Challenge: higher beam power cycle rate in ()
US Spallation Neutron Source (SNS) (under construction) 'Hands on maintenance': beam loss < 1 W/m at 1 GeV 100 m Ion: Protons Energie: 1 GeV (0.88c) ppp: > 1E14 Taktrate: 60 Hz Beam power: 2 MW Extensive beam physics modeling and computer simulations for the accelerator design.
Electron cooling of high energy antiprotons at FNAL Challenge: higher beam quality Principle of e-cooling (G. I. Budker, Novosibirsk, 1966) electron collector electron gun high voltage platform magnetic field electron beam ion beam 4.3 MeV electrons from Pelleton 20 m long interaction section Lecture on Monday! Zur Anzeige wird der QuickTime Dekompressor TIFF (LZW) benötigt. Recycler/Main ring tunnel Demonstrated cooling of 8 GeV pbars in July 2005