Injection, extraction and transfer

Transcription

1 Injection, etraction and transfer An accelerator has limited dnamic range. hain of stages needed to reach high energ Periodic re-filling of storage rings, like LH Eternal eperiments, like NG &(5&RPOH[ Transfer lines transport the beam between accelerators, and onto targets, dumps, instruments etc. LH: P: AD: IOLDE: PB: P: LINA: LEIR: NG: Large Hadron ollider uper Proton nchrotron Antiproton Decelerator Isotope eparator Online Device Proton nchrotron Booster Proton nchrotron LINear Accelerator Low Energ Ring ERN Neutrino to Gran asso

2 Beam Transfer lines Distinctions between transfer lines and circular machines Linking circular machines Trajector correction Emittance and mismatch measurement Deliver precision and errors Blow-up from betatron mismatch Thin screens: blow-up and charge stripping

3 Normalised phase space Real phase space γ Normalised phase space ; ma γ γ ; ma Ÿ Area H ; Area H ma ; ma γ ; ;

4 Distinction between Transfer Lines and ircular Machines s s n i n Moving from s to s through n elements

5 ircular Machine Twiss parameterisation ( cos µ sin µ ) sin µ [( ) ( ) ] ( ) cos µ sin µ cos µ sin µ ircumference L One turn L cos πq sin πq sin πq ( ) sin πq cos πq sin πq Periodicit condition for one turn (closed ring) imposes, This condition uniquel determines (s), (s) and µ(s) around the whole ring

6 ircular Machine Map the coordinates of a particle on each turn. Periodicit of the structure leads to regular motion Generate ellipse in phase space, defined b one set of and values Matched Ellipse a γ ma a γ Area a ma a

7 ircular Machine A beam injected with emittance, characterised b a different ellipse ( *, * ) generates (via filamentation) a large ellipse with the original,, but larger, ο,, After filamentation 3 4 > ο,, Matched ellipse determines beam shape

8 Transfer line ( ) ( ) ( ) [ ] ( ) µ µ µ µ µ µ µ sin cos sin cos sin sin cos No periodic condition eists Twiss parameters are propagated from beginning to the end of the line At an point in the line, (s) (s) are functions of One pass

9 Transfer line Map single particle coordinates at entrance and eit. Infinite number of possible starting ellipses transported to infinite number of final ellipses,, L, Transfer Line Entr Eit,

10 Transfer Line Initial, are defined for a transfer line b the beam shape at the entrance,, Gaussian beam Non-Gaussian beam (e.g. slow etracted) Propagation of this beam ellipse depends on the line Line optics is different for different input beams.

11 Linking ircular Machines γ γ Etraction Transfer Injection,,, (s), (s), (s), (s) s The Twiss parameters can be propagated when the transfer matri M is known,,,

12 Linking ircular Machines onstraints include Matching the trajectories Minimum bend radius Magnet aperture ost Geolog P to LH transfer line TI 8 Etraction Injection

13 Linking ircular Machines Matching the optics is a non-trivial process Parameters at start of line have to be propagated to matched parameters at the end of the line Need in theor to match 8 variables ( D D and D D ) Maimum and D values are imposed b magnet apertures Other constraints can eist (e.g. phase conditions for collimators, insertions for special equipment, like foils) Long transfer lines ideall designed in 3 separate sections Regular central FODO section F and D quads at regular spacing, ( bending dipoles) Initial and final matching sections independentl powered quadrupoles, with sometimes irregular spacing.

14 Linking ircular Machines Eample P to LH transfer line TI 8 (7m long) P LH Regular FODO lattice Initial matching section Final matching section

15 Linking ircular Machines P LH Regular FODO lattice Initial matching section Final matching section

16 Aperture Available aperture for the beam depends on optics (, D), trajector O, mechanical and alignment tolerance M, magnet aperture A, beam energ spread pp and emittance. Use general epression to evaluate number of beam available (k factor to allow for optical errors, tpicall.) M n k A O M ( D p p) A O

17 Aperture Aperture can be evaluated with optics and phsical line description ritical areas can be fitted with etra instruments or correctors Vertical beta function (m) and aperture (sigma) P to LH transfer line TI8 nv E

18 Trajector correction Trajector correction (steering) relativel straightforward. Use steering dipole magnets (correctors) to displace beam. Measure the response using a monitor (pick-up) downstream (π, 3π, ). eparate horizontal and vertical elements. H-correctors and pick-ups located at F-quadrupoles (large ). V-correctors and pick-ups located at D-quadrupoles (large ). In long lines, not all quadrupoles are equipped

19 Trajector correction teering in matching sections, etraction and injection region requires more care Often ver limited in aperture Injection oscillations important for performance Global correction can be used which attempts to minimise the RM offsets at the BPMs, using all or some of the available corrector magnets. Eample P to LH transfer line TI 8 correction Random alignment and field errors simulated; trajector measured with all or some of available BPMs orrection made with dedicated corrector dipole magnets

20 Uncorrected trajector, with growing as a result of random errors in the line. The RM at the BPMs is 3.4 mm, and ma is.mm Trajector correction orrected trajector. The RM at the BPMs is.3mm and ma is mm

21 Uncorrected trajector, with growing as a result of random errors in the line. Trajector correction orrection with some monitors disabled If the BPM phase sampling is poor, the correction algorithm can make the trajector ver bad, while all the monitor readings being ~zero. in this case 85mm ma! Note vertical scale!

22 Deliver precision Precise deliver of the beam is important. To avoid injection oscillations and emittance growth in rings For stabilit on secondar particle production targets Epress injection error in a (X X ) (γ ) a (ae) [(γ )] a Transfer line septum ; ; bumpers Kicker

23 Deliver precision tatic effects (e.g. from errors in alignment, field, calibration, ) are dealt with b trajector correction (steering). Also dnamic effects which var with each injection. Power suppl ripples Random effects like temperature variation stematic effects like kicker waveforms These dnamic effect produce a variable injection offset which can var from batch to batch, or even within a batch.

24 Deliver precision The errors in a line superimpose For uncorrelated errors the effects can be added quadraticall For correlated errors the effects must be added linearl The tpical pattern of errors can be generated with a Monte-arlo simulation Worst-case errors in families of magnets can be calculated analticall b introducing field errors into the Accelerator design code and calculating the resulting a

25 Deliver precision Eample power suppl ripples in P to LH line TI 8. Famil element rms a a,,pd[ mm mrad mm mrad Quadrupole MQF 5.E Quadrupole MQD 5.E Bumper MPLH.8E eptum ME.3E Dipole BH 5.E Dipole BH 5.E Dipole BH3 5.E Dipole BH4 5.E Dipole MBI.5E Dipole BV 5.E Dipole BV 5.E eptum BH5A 5.E eptum BH5B 5.E Kicker MKE.5E Kicker MKI.5E rms..95 linear sum.594.6

26 Blow-up from betatron mismatch Optical errors occur in transfer line and ring, such that the beam can be injected with a mismatch. Filamentation will produce an emittance increase. In normalised phase space, consider the matched beam as a circle, and the mismatched beam as an ellipse. Mismatched beam Matched beam

27 Blow-up from betatron mismatch [ ] ) sin( ) cos( ) sin( o o o φ φ φ φ φ φ A General betatron motion appling the normalising transformation for the matched beam an ellipse is obtained in normalised phase space γ new new new characterised b γ new, new and new, where

28 Blow-up from betatron mismatch λ λ o o b a R Mismatched beam Matched Beam D E ( ) ( ) H H A b H H A a ( ) γ new new H generall From the general ellipse properties* where and thus ( ) ( ) H H H H λ λ

29 Blow-up from betatron mismatch ) cos( ) sin( o o φ φ λ φ φ λ ) ( cos ) ( sin o φ o φ λ φ φ λ λ λ H new ince We can evaluate the square of the distance of a particle from the origin as The new emittance is the average over all phases ubstituting back for λ gives ) ( cos ) ( sin λ λ φ φ λ φ φ λ o o new where subscript refers to the matched ellipse, refers to the mismatched ellipse.

30 Blow-up from betatron mismatch A numerical eample. onsider b 3a for the mismatched ellipse Mismatched beam λ b a 3 D E D new.67 ( λ λ ) R Matched Beam

31 Emittance and mismatch measurement Beam screen provides densit profile of the beam Use emittance definition: Profile fit gives.

32 Emittance and mismatch measurement In a ring, is known so can be calculated from a single screen In a line, need measurements at 3 screens, plus the two transfer matrices M and M 3 measurement locations allows determination of, and s s s 3 V V V

33 Emittance and mismatch measurement γ γ ( ) ( ) : We have so that using we find ( ) ( ) ( ) ( ) ( ) ( ) : where

34 Emittance and mismatch measurement ( ) ( ) with and and ome algebra with the three above equations gives ( ) ( ) ( ) ( ) ( ) ( ) : ( ) ( ) ( ) 4 : : And finall we can evaluate omparing measured D o, E with epected values gives mismatch

35 Blow-up from thin scatterer Thin metal windows used to separate poor vacuum of transfer lines from good vacuum in circular machines. Thin beam screens (Al O 3,Ti) used to generate profiles. Emittance of the beam increases when it passes through, due to multiple oulomb scattering. θ s rms angle increase: θ s mrad 4. L [ ] Z inc. log c p[ MeV c] Lrad L L rad c vc, p momentum, Z inc particle charge e, L target length, L rad radiation length

36 Blow-up from thin scatterer particle with initial coordinates, θ s Ellipse after scattering rms distribution over whole beam becomes θs θs θ s and θ s are uncorrelated, so θs θs therefore θs Matched ellipse

37 s θ After filamentation the average divergence is Using Ellipse after filamentation Matched ellipse Gives For a thin scatterer ( ) s s s θ θ θ Also o s s θ θ and uncorrolated Blow-up from thin scatterer

38 harge stripping For LH heav ions, Pb 53 is stripped to Pb 8 at 4.5GeVu using a.8mm thick Al foil, in the P to P line minimised with low- insertion in the TTTT transfer line Emittance increase epected is about 8%

39 ummar Transfer lines present interesting challenges and differences from circular machines No periodic condition mean optics is defined b initial beam ellipse and transfer line lattice Matching at the etremes is non-trivial pecial measurement techniques needed Performance criteria include aperture and emittance blow-up