Accelerators. W. Udo Schröder, 2004

Transcription

1 1 Accelerators

2 Overview Electrostatic Accelerators Cascade Van de Graaff V.d.G. Tandem generator Accelerator 2-3 stages steady (DC) beam, high quality focusing, energy, currents; but low energies Accelerators 2 Electrodynamic Accelerators Cyclotrons Synchrotons Linacs conventional, Wideröe, Alvarez sector-focusing pulsed (AC) beam, high energies but lower quality focusing, energy definition, lower currents Advanced Technology Accelerators New principles: Collective acceleration, wake-field acceleration conceptual stage

3 Voltage multiplier (Greinacher, 1921; Cockcroft-Walton, Cockcroft-Walton (Cascade) Generator Rectifier B 1 2U 0 U 0 U B1 A 1 Accelerators 3 U=Q/C () - () A 0 U 0 sinωt Rectifier B 0 2U 0 U 0 U A1 Transformer Ground U A0

4 Ion Source Cockroft-Walton Pre- Accelerator Voltage doubling for each stage. Typical range order ~ n 100 kv ~ 10 MV Accelerators 4 CW used here to charge an enclosed metal terminal containing the ion source. Provides pre-acceleration of ions produced in the source allows magnetic analysis CW Generator

5 Accelerators 5 Conducting Sphere Acceleration Tube insulating - Ground Plate Van de Graaff Electrostatic Accelerators Ion Source q HV Terminal Charging Belt/ Pelletron Corona Points 20kV Charger 10-4 C/m 2 Van de Graaff, 1929 Operating limitations: 2 MV terminal voltage in air, MV in pressure tank with insulating gas (SF 6 or gas mixture N 2, CO 2 ) - R R R R R R R Acceleration tube has equipotential plates connected by resistor chain (R), ramping field down. Typical for a CN: 7-8 MV terminal voltage

6 Accelerators 6 Early Van de Graaf Accelerators

7 Tandem Van de Graaffs Built in the late 1950s, 2 stage and 3-stage (Brookhaven), to increase beam energy Accelerator structure enclosed in pressurized tank (SF 6 ) Corona rings to homogenize electric field. Accelerators 7 Ground q Corona Rings HV Terminal U Foil Stripper q q - Corona Rings Ground Negative- Ion Source Belt q -

8 HV Terminal Accelerators 8 The Yale MP Tandem Corona Rings Intershield Tank

9 Munich University MP Tandem MP Tandem 9 Ion Source Accelerators Vacuum Beam Line 90o Deflection Magnet

10 gas channel Stripping Probability for Heavy Ions solid C Foil Charge distribution 1 f( q) = exp 2 2πσ Average q, ( q q) 2 2σ 2 variance σ 2 Accelerators 10 O 2 U, 10MeV U, 15MeV q Z 12 avz for q Z 0.3 a= 0.16( He), 0.18( N2, Ar) 0.4 = σ = ( ) Z nvmz ( α) / nnz ( β ) for 0.3 < q Z 0.9 v = 1.38 E A MeV velocity Tabulation: Chaki&Elmore UR-NSRL-240, 1980

11 Accelerators 11 q Wideröe 1928, Alvarez RF Power T λ L= v = β β = 2 2 After gap n : = 2( qu ) m 0 vn n velocity Linear Accelerators v c Linear trajectory, no deflection magnet, no radiative losses Hollow drift tubes, E-field-free interior, contain magn. focusing elements. Accelerating gap between 2 drift tubes on different el. potential U(t) = U 0.sin (ωt) 10MHz-3GHz on all gaps alternating E field switch polarity while particle is hidden.

12 Acceleration with Linac Alternating directions of the gap fields, change while particle is hidden inside drift tube. Accelerators 12 Flash Player Movie Q: Phase conditions change during acceleration, particle speed. Is continuous operation possible, without loss of particles?

13 U, E Voltage U(t)~U 0 sin(ωt) at the gaps t s =φ s /ω Phase Stability Voltage encountered at gaps: t=φ/ω t ideally synchronous particle Accelerators 13 Phase angle of particle: φ = φ s ω (t-t s ), force F=qU 0 /(gap length L) d dt 2 d dt ϖ F cosφ φ φ φ φs = 0 ( ) s ( ) 2 s ps : = φ 2 φ ϖφ φ = differential equation Stability analysis for Stable oscillations about synchr. phase for cosφ s >0, φ s < 90 0 inject during first quarter cycle! φ 0

14 CERN Proton Linac Accelerators 14

15 Cyclotrons Charged particles in electromagnetic fields, E, B Accelerators 15 q B r B: Magnetic guiding field v Lorentz Force = ( F q E v B) E = 0: F = p = q v B p = q r B orbit radius r, r B 0 0 ( ) p= q r B, equilibrium orbit at r = p= mv v = ϖ r ϖ p qb q = B ParticleCyclotron Frequency m

16 Accelerators 16 ω field - Cyclotron Max. Energy E Cyclotron Frequency q ϖ 0 = B same for all v m Acceleration, if ω field = ω 0 Equilibrium orbit r: p = qbr maximum p max = qbr Maximum Energy ( ) 2 ε = qbr max 2m = K q A Relativistic effects: m W = ε m o c 2 shape B field to compensate. Defocusing corrected with sectors and fringe field. 2

17 new Cyclotron Resonance Condition f=1, matched Accelerators 17 Accelerating rf voltage has to be switched with frequency of gap crossings: qb ϖrf = ϖ0, particle = m ϖ rf f = = 1! ϖ 0, particle f=1.1, mismatched

18 Relativistic Correction Particle Cyclotron Frequency Accelerators 18 r B r ϖ 0 = q B for small velocities v m Relativistically W = = ε 2 2 : mc mc 0 kin 2 qc ϖ0 ϖ( W ) = B for relat. velocities v W d ϖ ( W) ϖ ( W ) = decreases with incr. ε kin dw W W W = ϖ ϖ Example: projectile m 0 c 2 =A 938 MeV, energy change ε kin = 20 AMeV ω/ω = - W/W = 20 MeV/938 MeV = 0.02 ü φ = per turn out of phase within 12 turns! Correction: increase B(r) radially. Undesirable consequence: defocusing of beam in inhomogeneous B!

19 Accelerators 19 r B B z (r)=b z (r 0 )[r/r 0 ] -n 0<n<1 field index Focusing in Inhomogeneous Fields r orbit z m ζ nϖ0 ( qb0 ) ζ = 0 ζ = z/ r0 ϖr = 1 nϖ0 m ρ mϖ [1 n] ρ = 0 ρ = r/ r ϖ = n ϖ ϖ = v/ r z 0 0 B z θ r B r B r Fringe Field B z F z F z ( ) Fringe field restoring forces drive particle to median plane ( F ) z = p z = q v B = qvbr z F = p mr θ = q v B = qvb 2 r r z r Particle prescribes Betatron Oscillations Does not correct for relativistic increase in m! 0

20 Accelerators 20 r The Sector-Focused Cyclotron How to make B both radially concave (to correct for relativistic m) and convex (to have the desired fringe field bulge)? Valley B Peak r Peak orbit Adjust directions of B r and B θ by shaping the pole faces: spiral arms In transition regions between magnetic peaks and valleys, v r 0. Particle drifts radially B r Peak B θ Peak Exit: Above median plane z > 0: F z =-qv r B θ <0 focus below plane, z < 0 F z =-qv r B θ > 0 focus Entrance: defocus Peak

21 From Ion Source to Cyclotron Accelerators 21 Movie from: NSCL/MSU

22 The End Accelerators 22