High Intensity Accelerators

Transcription

1 High Intensity Accelerators

2 High Intensity Accelerators SNS, Oak Ridge, TN J-PARC, Tokai-mura, Japan Chinese SNS, Dongguan

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4 U.S. Spallation Neutron Source (SNS)

5 Beam Power The mean beam power is given by P = NeEf where N is the total number of particles E is the (mean) energy of the beam (ev) f is the repetition rate (Hz) Machine N( ) E (GeV) f (Hz) P (MW) SNS (ORNL) ISIS (RAL) ESS NF

6 Studies of High Intensity Accelerators TRIUMF Kaon Factory, Vancouver, Canada European Hadron Facility (EHF) ISIS, RAL, UK MW CONCERT, CEA, Saclay, 30 MW US Spallation Neutron Source, Oak Ridge, Tennessee 1.4 MW J-PARC, Tokai-mura, Japan 0.75 MW Chinese and Indian Spallation Neutron Source projects 0.2 MW Neutrino Factory Proton Drivers, 4 MW at 5, 8, 10, 15, 30 GeV Fermilab proton accelerator studies at 16 and 20 GeV

7 Requirements Very low levels of (uncontrolled) beam loss achieved by removing in advance, at special collectors, beam that is likely to be lost in undesirable places requires advanced collimation systems aim is 1 W/m High current ion source and linac (40-80 ma) Sophisticated beam accumulation systems. For proton machines, requires use of H beam with charge-exchange injection gaps chopped in linac bunch train achromatic arc to remove beam halo phase space painting techniques to create required transverse distribution and good longitudinal bunching factor to lower spacecharge clean extraction system Neutrino Factories also require short bunches, compressed to 1,ns rms

8 Charge exchange Bunch compression scheme injection system, with beam dumps for unstripped particles High current H - ion source Achromat for longitudinal and transverse halo removal Fast beam chopper

9 Limitations imposed by pulse length on target Design of a high intensity proton/ion driver is dictated by the pulse requirements at the target For example: A spallation neutron source requires a 0.6 µs proton pulse on target = a pulse of length 0.6 µs in the ring plus a gap of 200 ns for the extraction kicker rise time (plus 50 ns for safety) = ring revolution period is at least τ = = 850 ns If energy is 1.5 GeV, γ = /0.938 = 2.6, β = 1 1/γ 2 =0.923 = circumference is βcτ = 235 m = mean radius R = 235/2π = 37.5m

10 Fast Beam Chopper Create gaps in the linac beam so that bunches fit together in the ring, leaving gaps for eventual ring extraction. All particles fall in stable regions of longitudinal phase space, so minimising beam loss. E Linac frequency (say) 330 MHz = train of micro-bunches separated by 3 ns. Bunches can be diverted to dedicated beam dumps by electrostatic deflector, but rise time has to be < 2.5 ns for clean chopping

11 RAL 3.0 MeV Chopper, 324 MHz 4.6 m Chopper 1 (fast transition) Beam dump 1 Chopper 2 (slower transition) Beam dump 2 ʻCCLʼ type re-buncher cavities

12 Space-Charge Image Effects λ +λ λ +λ y 1 6h y 14h + y 12h y 1y Perfectly conducting collector plates parallel to beam pipe = infinite system of images +λ at ±4nh + y n =1, 2,... λ at ±2(2n 1)h y n =1, 2,... z λ +λ 1 (2h + y) 1 (4h y) Images produce an electrostatic field on the bunch given by λ 1 (6h + y) E i y = λy 2πɛ 0 n=0 1 (2n + 1) 2 h 2 y 2 = λ 8ɛ 0 h tan πy 2h.

13 Equation of motion of bunch centre is d m 0 (γv) =e dt ( E ) γ 2 Ei, = d dt (γẏ) = e m 0 ( E ) γ 2 Ei y (1) γż = γ 0 β 0 c (2) where γ 0, β 0 are the values on entry to the chopper. ( ) = y e = m 0 γ 0 β0 2 E 0 1+β 2 1 c2 0 y β 2 0 y 2 Ei y γ 2 0, (y = dy dz ). In absence of images, solution is y = 1 µβ 0 (cosh(µz) 1) where µ = ee 0 m 0 γ 0 β 0 c 2

14 In absence of images, solution is y = 1 µβ 0 (cosh(µz) 1) where µ = ee 0 m 0 γ 0 β 0 c 2 With images, numerical integration. Effect of images is attract the beam, so that it hits the plates earlier allow reduced deflecting voltage For example, in ESS, the images cause the beam to hit the collector 67 mm sooner; alternatively, the deflecting voltage can be reduced from 846 V to 707 V (-16.4%) to hit the same spot

15 Linac Front-End High current ion source, µa, ɛ nrms 0.2π mm.mrad, good lifetime. RFQ to focus and bunch the beam. Fast beam chopper. Low-intermediate energy stages < 200 MeV SNS RFQ ISIS ion source EU HIPPI study RAL FETS

16 Beam Funnel The aim of a funnel is to double the linac current by doubling the frequency of the micro-bunches: Best done at low frequencies I linac = Nef linac. Very high space charge levels present problems Measures needed to avoid large emittance growth

17 ESS Reference Funnel 8 cell achromat under linear space charge; last two cells discarded (no bends). Each cell has 45 o transverse phase advance (~85 o without space charge) and 180 o longitudinally over 4 cells.

18 Funnel Dynamics High space charge, rms emittance concerns RMS emittance growth caused by non-linear space charge forces Non-linear effects can be minimised by uniform betatron oscillations β max and β min same in both horizontal and vertical planes. For 2D parabolic distribution with elliptical cross section and longitudinal line density λ, E x = 8λx [ ] 1 x2 (2a + b) a(a + b) 3a 2 (a + b) y2 b(a + b) With a b, effectively create a stationary distribution, with space-charge forces in equilibrium with the external focusing forces and minimum nonlinear field energy. Require zero dispersion at funnel outlet Expect microbunches at outlet to have essentially the same properties as input bunches (same bunch length, same energy spread)

19 Normal Conducting Linac SNS Linac World s first high-energy superconducting proton linac Design: 60 Hz rep.rate Design energy: 1 GeV Superconducting Linac

20 Achromat Halo on the linac beam will give injection losses that are difficult to localise Purpose of the achromat is to strip this halo (transversely and longitudinally) and prepare the beam for ring injection Achromat adjusts momentum spread and focuses the beam to the correct spot size on the injection foil

21 H - foil stripping: bends unwanted particles to beam dumps Linac focusing structure continued for smooth transition Debunching, energy ramping, horizontal, vertical and momentum collimation 4 cells, 90 o phase shift/cell Match parameters to required spot size for injection

22 Typical Achromat Lattice Functions Longitudinal halo removed through the use of a high normalised dispersion: p x = x β + D x p = ( ) ɛ D x p β +. β p D x β is the normalised dispersion

23 Accumulation of Particles in a Ring Object: to increase beam intensity. For spallation sources and neutrino factories need to inject ~10 14 protons per pulse Closed orbit bump magnets move circulating particles out to combine with incoming beam. Enhanced beam is then moved back onto the ring central orbit.

24 Normalised Phase Space x η = x β, η = β (x + αβ x ) x Ring phase at injection point γx 2 +2αxx + βx 2 ɛ becomes η 2 + η 2 ɛ η Injection turns rotate at constant radius η

25 Proton v. H - Injection Proton injection via magnetic or electrostatic septum. Liouville s theorem applies and severely restricts the number of turns (~20) H- injection via charge exchange: a stripping foil removes two electrons from incoming particles to produce a beam of H+. Non-Liouvillean system, allows more injection turns (several thousand). Heating and scattering in the foil are the main problems.

26 Proton injection using a septum magnet y Septum edge Ring aperture machine centre closed orbit Incoming beam x Normalised phase space

27 Circulating beam in ring Incoming linac beam y x Normalised phase space

28 y x Normalised phase space

29 y x Normalised phase space

30 y x Normalised phase space

31 Proton Transverse Injection: Septum y y Single plane injection x e.g. linac emittance 5 mm.mrad; ring emittance 50 mm.mrad. Number of turns for zero loss ~6 x x Two plane injection with tilted septum x e.g. linac emittance 4 mm.mrad; ring emittance 50 mm.mrad Number of turns for zero loss ~22

32 Multi-turn Injection Injection in zero dispersion region using a septum and programmed orbit bumps, could be several slow kickers For n-turn injection, final emittance in ring is ɛ >nɛ i, by Liouville s Theorem Optimal packing is achieved with mismatched injection α i β i = α β = x o x o, β ( i β ɛi ɛ ) 1 3. [suffix i refers to incoming beam, suffix o refers to closed orbit, no suffix on ring parameters.]

33 Optimal Conditions for Injection For an upright ellipse x2 A 2 + y2 B 2 = 1 curvature at end of x-axis is A B 2. y B A x Ring phase space: γx 2 +2αxx + βx 2 = ɛ η 2 + η 2 = ɛ κ = A/B 2 = curvature κ = 1 ɛ Injected turn phase space: γ i x 2 +2α i xx + β i x 2 = ɛ ( η 2 βγ i + α 2 β ) ( i β 2αα i +2ηη αi β i α ) β i β + β i β η 2 = ɛ i Make α i = α β i β (upright), then get β η 2 + β i β i β η 2 = ɛ i = curvature κ i = ( βi β ) ɛi Want κ i > κ or β ( i β ɛi ɛ ) 1 3

34 Charge Exchange Injection (H - ) y H - is converted to H o, then H + through removal of two electrons with a stripping foil x H + can be overlaid on H - in phase space x H + H - x (non-liouvillean) Any number of turns can be injected Recirculating protons can pass through foil Flexibility: allows phase space painting for improved beam distribution and reduced space charge effects

35 Charge Exchange Injection Charge exchange injection foil or laser stripping Foil issues: Foil material and stripping efficiencies Multiple Coulomb scattering; large angle and nuclear scattering Heating; stress and buckling Lifetime Radiation Stripped electrons Emittance growth Painting: Transverse and longitudinal coupling options for transverse painting options for longitudinal painting Unstripped (H ) or partially stripped (H 0 ) beam

36 Correlated painting Both horizontal and vertical orbit bumps produce oscillations progressing from small to large amplitude (or large to small) x y injection starts foil x x y injection ends

37 Anti-correlated painting Oscillations vary from small to large amplitude in one plane, large to small in the other. x injection ends y x foil y x injection starts

38 Space charge & halo formation Disadvantage of not painting over the halo

39 SNS injection Uses horizontal and vertical orbit bumps to paint the beam Independent H, V, L control Circular & square profile both attainable Energy corrector & spreader in HEBT Tolerable to momentum errors Small residual Δβ/β & dispersion

40 Vertical steering/horizontal painting Steering in one direction, painting in the other y injection ends y y foil x injection starts

41 Fermilab Proton Driver Injection Scheme Horizontal closed orbit bumps; vertical variation of beam angle

42 Painting using dispersion Uses programmed orbit bumps magnets for vertical painting Injects in region of non-zero dispersion Varies energy of beam in injection line to create horizontal painting If beam has momentum range p0 ± δp, ramp to p0!+ p ± δp." Then p δp particles oscillate about a centre in the range Dx ± p p p δp δp e.g. might ramp = 3 p p p Time msec Number of injected turns

43 ESS Injection Dipole Inject in a low field dipole (must avoid pre-stripping) B-Field chosen for optimal handling of H 0 excited states Simple magnet layout Easy handling of unstripped and partially stripped beam and stripped electrons

44 ESS Momentum Ramping and Vertical Orbit Bump Beam momentum spread is ramped [0,1] to [3,4] 10-3 during injection Orbit bumps chosen to minimise foil hits by re-circulating protons

45 Charge-Exchange Injection Considerations Circulating protons can pass through stripping foil. Need to minimise the foil traversals. SNS averages about 6 hits per proton over 1000 injection turns; ESS was optimised to < 1. Foil hits lead to heating and high temperatures, shortening foil life. Need quick disconnect system, easy replacement: SNS multi-foil chain Careful control of closed orbits and painting Ring lattice tunes Q x, Q y can be critical Space charge tune depression and tune spread can result in fourth order space charge resonances and destroy the beam Laser stripping schemes interesting but require very high laser power and efficiency

46 SNS Foil device

47 Foil Heating Peak temperature strong function of linac beam size Minimum temp reached only 1 cycle even for 10 Hz (297 K) 9 Secondary Hit (270 turn) Project X intensity 3 x lower Peak temp ~ 1000 K Minimum equilibrium temp at 5 Hz < 600 K σ=1 mm Black, 1.5 mm, 2 mm (HINS, 270 turn) Temp due to linac beam only, included secondary hit Temp vs beam size

48 Problem - how to paint different distributions Consider the beam density distribution in normalised η-η phase space during multiturn injection. Define ρ 2 = η 2 + η 2 and let λ(ρ)ρ dρ be the number of particles populated within the phase-space annulus of radius ρ and thickness dρ. What is the closed orbit as a function of time needed to realise a uniform distribution in phase-space inside radius R during a total injection time of t max. Prove that the closed orbit function to create a Gaussian distribution λ(ρ) = N ( ) σ 2 exp ρ2 2σ 2 is approximately x o = 2σ ln ( 1 t t max ) where the injection is performed during a time 0 < t < t max

49 Solution Suppose particles are injected at a steady rate N/t max. Then λ(ρ)ρ dρ dt = N t max. (i) for a uniform distribution, λ = 2N, this integrates to R2 x 0 = R 1 t t max (ii) for λ =(N/σ 2 ) exp( ρ 2 /2σ 2 ), we obtain ρ dρ N exp ( ρ2 2σ 2 ) x o 0 = N t t max giving x 0 = σ 2 ln ( 1 t t max ).

50 Painting scheme comparison

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53 Longitudinal painting Momentum painting sharpen the painting pen by reducing momentum spread before injection (e.g. correcting energy jitter) Paint the momentum space by modulating the injecting beam energy RF steering Modulate RF voltages Use dual harmonic/barrier buckets

54 RF Voltage modulation controls bucket height Aim for good bunching factor to reduce transverse space charge effects Δp/p φ Momentum ramping in the injection line varies position of injected turn in the bucket f f = β β f = hω 2π = hβc 2πR R R = RF steering moves central axis of bucket up and down with respect to nominal ring energy ( 1 γ 2 1 γ 2 t ) p p Gymnastics in Longitudinal Phase Space

55 Injection into longitudinal phase space for Neutrino Factory booster synchrotron: 0.2 ms, ~150 turns, 180 MeV

56 Radio-activation High radio-activation at injection, extraction, collimation AGS (BNL): up to 10 msv/hour in localised areas High Beam loss Fermilab booster (30-40%): ramp tracking, debunching, recapture, transition, aperture. AGS Booster (20-30%): injection capture, initial energy ramp Los Alamos PSR (0.3% full energy accumulation): injection loss Injection, initial ramping, transition, instability 1-2 msv/hour average activation (30 cm, 4 hr cooling time) 1-2 W/m average beam power loss: 10 4 loss levels

57 Sources of Uncontrolled Beam Loss Linac structure and lattice change: mismatch Space-charge resonances: envelope oscillations, halo formation, non-equipartitioning, tune shift and tune spread. Physical aperture and momentum aperture limitations: dispersion, injection line, extraction channel, chicane perturbation Ring injection loss: premature H and H 0 stripping, foil hits Ring magnet errors: dipole-quadrupole tracking, eddy currents and saturation, fringe fields Instabilities: envelope, head-tail, microwave, coupled bunch, electron cloud Accidental loss: ion source and linac malfunction, extraction kicker failure

58 Low-loss Design Philosophy Localise beam loss to shielded areas 2-stage collimation, 3-stage beam- gap chopping/cleaning Low-loss design Design lattice with adequate aperture and acceptance A/ɛ > 2 Injection painting; injection and space-charge optimisation Q <0.2 Resonance minimisation; magnet field compensation and correction Impedance and instability control Flexibility Adjustable energy, tunes; flexible injection; adjustable collimation Foil and spares interchange Engineering reliability; heat and radiation resistant Accident prevention; immune to front end, linac and kicker faults

59 Neutrino Factory

60 Neutrino Factory Drivers 5 GeV 50 Hz 4 MW 15 GeV 25 Hz 4 MW 30 GeV 8.33 Hz 8 GeV 50 Hz 4 MW

61 Proton Driver for a Neutrino Factory High intensity ~10 14 protons Achieved with phase space painting in RCS booster 50 Hz rep rate Booster circumference 400 m Bunch area (h=3) 1.1 ev.sec ns bunch compression Achieved with FFAG accelerator MV per turn for 3.3 ns rms, improved by higher harmonic component to 1.9 ns FFAG circumference ~800 m Delayed extraction of bunches to meet requirements of muon accelerators and decay rings May be easier with FFAG than synchrotrons

62 Techniques for Generating Short Bunches High RF voltage High RF frequency Bunch rotation in phase space Use of unstable fixed point Use of transition energy (incl. FMC lattices, isochronous rings etc) (Review by M. Brennan, Workshop on Instabilities, BNL, June 1999)

63 Bunch Compression ~1-2 ns rms ( ω0 ) 1 2 ( 2πβ 2 E η ) 1 4 Bunch length φ L = A 1 2 πβ 2 E hev cosφ s High RF Voltage Bunch shortens as RF voltage increases during adiabatic compression, but only as fourth root of V. Required voltage rapidly becomes very large. High RF frequency Leads naturally to shorter bunches but with small longitudinal emittance and high charge per unit phase space area. Experience of high intensity machines suggests an empirical limit of 1-2 x /ev.s for machines which pass through transition. However, no theoretical basis exists.

64 Bunch Rotation Slow adiabatic decrease of RF voltage to reduce momentum spread without emittance increase. Rapid increase of RF voltage so that the mis-matched bunch rotates in ¼ synchrotron period into upright configuration. Factors of 2-4 in compression, but emittance growth unless bunch is used immediately. Susceptible to instabilities (e.g. microwave) and beam loading. High frequency instabilities increase ε L and limit compression. Large transverse space charge tune spread, orbit distortions and path-length variations. Volts reduced adiabatically from 300kV to 25 kv, then increased rapidly to 500 kv. Bunch compression factor = 2.2

65 Bunch Compression using Unstable Fixed Point Bunch length: ±12.5 ns (5.6 ns rms) Momentum spread: ±5.0 x 10-3 Longitudinal emittance: ε L ~ 0.7 ev.s Number of particles per bunch: 2.5 x Switch phase of RF voltage to unstable fixed point to stretch bunch. Then switch RF phase back to stable fixed point so that bunch rotates to upright position with minimum length. Compression factor may be distorted by non-linear voltage regions.

66 Unstable Fixed Point + Separate Compressor Ring Stretch bunch at unstable fixed point (γ<γt, volts on) Transfer to separate compressor ring with γ>γt for phase space rotation. No volts needed. Non-linearity problems exist but are reduced.

67 Flexible Momentum Compaction Lattice Lattice gymnastics involving frequency slip parameter η=1/γ t2-1/γ 2. Set η=0 and impose RF voltage to create large Δp/p without change in bunch length. Switch η back on and bunch will rotate to short length. Experiment at Brookhaven AGS with transition jumping quadrupoles achieved 2.5 ns for 5 x protons (factor ~3 in compression) η=0: Δp/p increase without bunch lengthening η<0, phase space rotation to upright (compressed) position

68 Compression using transition Work with γ close to, and just above, γ t. Space charge assists compression. High RF voltage (1.5 MeV at h=8) based on ϕ s =180 o Simulation gives the required 1 ns bunches but sensitive to space charge depression of γ t.

69 Bunch Compression in the RAL 5 GeV Synchrotron Driver During final 500 revs of accelerating cycle, an additional h=24 voltage system swings in, rising to a peak of 500 MV Final bunch length =1ns rms, ε L =1.0 ev.s, Δp/p=1.6%. Space charge depresses γ t which may be a problem for machines working near transition. Longitudinal space charge can be reduced using an inductive impedance Z // /n (~5Ω, say). Acceleration to 5 GeV and final compression (γ t =6.5, γ = 6.33 at top energy, η= ) Voltages chosen to avoid instabilities (microwave: V sc < 0.4 V applied ). As bunch length decreases, Δp/p increases and higher order momentum effects need to be taken into account. Lattice resistant to space charge effects