INJECTION PAINTING, FOIL & TARGET DISTRIBUTION

1. SNS ASAC Review INJECTION PAINTING, FOIL& TARGET DISTRIBUTION Joanne Beebe-Wang BNL, Upton, NY 11973, USA September 13, 2000

2. Introduction • What is injection painting: • It is an injection with a controlled phase space offset between the centroid of injected beam and the closed orbit in the ring to achieve a different particle distribution from the injected beam. • Why injection painting for SNS: • to satisfy target requirements • to reduce beam losses due to space charge • to reduce foil hits (foil life-time, beam loss at foil) Joanne Beebe-Wang

3. y y foil foil x x Basic Painting Schemes Correlated painting Anti-correlated painting Joanne Beebe-Wang

4. px Foil P ax(t) bx(t) x(t) x Co cx(t) Q P1 Ci Analytical Expression It is a 4-D problem (x, x’, y, y’). But, if 1) distribution of injected beam can be expressed as n(x,x’,y,y’)=nx(x,x’) ny(y,y’) 2) the bump in (x, x’) phase space moves independently from (y, y’), it becomes a 2-D by 2-D problem. In normalized x, px phase space, if - changes slow compare to betatron oscillation, particles injected at P paint the same phase space as particles injected at P1. Maximum x is determined by the particles injected at Q. Joanne Beebe-Wang

5. Analytical Expression (continued) Particle distribution due to transverse phase space painting: for a single particle: If the distribution of injected beam is Gaussian with 0x and 0y where where I0(z) is the modified Bessel function of order zero, and center offset ( x0(t), x’0(t)) Joanne Beebe-Wang

6. Analytical Expression (continued) • From the analytical expression of particle distribution we can find out: • Very high local density at the center of the beam if x(t)=y(t)=0. So, one should not have zero offset in 4-D phase space any time. • Correlated painting will give a rectangular shaped beam distribution with high density along the diagonal line, and low density on the x- and y-axis. • If 0x <<  x(t) and 0y <<  y(t), anti-correlated painting with offsets  x(t) = A t1/2 ,  y(t) = B (tinj -t)1/2 will give a KV-like particle distribution at time tinj . Joanne Beebe-Wang

7. Basic Painting Schemes Correlated painting with/without space charge x=5.82 y=4.80 inj,x=4.93m inj,y=7.24m  inj,x=0.11 inj,y=0.07 inj. RMS,Nor=0.5mm-mr Final =120 mm-mr Joanne Beebe-Wang

8. Basic Painting Schemes Anti-correlated painting with/without space charge x=5.82 y=4.80 inj,x=4.93m inj,y=7.24m  inj,x=0.11 inj,y=0.07 inj. RMS,Nor=0.5mm-mr Final =120 mm-mr Joanne Beebe-Wang

9. Basic Painting Schemes painting scenarios correlated anti-correlated Beam shape without SC RectangularOval Beam emittance evolution Small to large~ constant Final emit. x+y(mm-mr) 120+120160 Foil-hit rate (11 linac dist.) 6.1  8.38.0  10.5 Max foil temp. (K) (11 linac dist.) 2113  2273 2248  2376 Horizontal aperture (H ) 1:11:1 Vertical aperture (V ) 1:11:1.5 Susceptible to coupling YesNo Capable for KV painting NoYes Paint over halo YesNo Horizontal halo/tail Normal Normal Vertical halo/tail NormalLarge Satisfy target requirements LikelyNot likely Bump function Square root;Square root; candidates exp(-t/0.3ms);exp(±t/0.6ms); for optimization CombinationSinusoidal Joanne Beebe-Wang

10. Work is in progress in developing injection bumps that optimize between the goals: Beam profile without SC Meeting target requirement Reducing loss at primary collimator Reducing space charge tune shift Reducing foil-hitting rate (depends on details) Beam profile without SC Example bump function: exp(-t/) with =0.3msec Example bump function: Sq-root 0.3 msec (time constant) 0.6 msec Injection Bump Optimization Joanne Beebe-Wang

11. Foil Heating & Foil Miss Injected Beam Distribution Foil Temperature [K] Joanne Beebe-Wang

12. Foil Heating & Foil Miss (continue) Injected Beam Distribution Foil Temperature [K] Joanne Beebe-Wang

13. End to End Simulation Foil Miss, Foil Hit & Foil Temperature Joanne Beebe-Wang

14. Foil Lifetime Tests on BNL linac • Same beam size, same energy deposition/pulse • Lifetime = 5-80hrs on BNL linac depending on foil thickness, fabrication and mounting methods • SNS repetition rate = 9 BNL linac repetition rate • Maximum 24 foils on the foil changing chain

15. Foil Heating & Scattering Joanne Beebe-Wang

16. Foil Hits & Beam Loss Beam loss as a consequence of foil traversal through the following mechanism: (1GeV proton, foil=300g/cm2, foil traversal rate=7hits/particle) • Nuclear Scattering estimated fractional loss=3x10-5 • Particle loss in gap due to energy straggling estimated fractional loss=3x10-6 • Transverse emittance growth due to multiple Scattering estimated =4x10-2mm-mr Joanne Beebe-Wang

17. Radiation due to Nuclear Scattering Particle Loss (Fraction) Radiation at Injection Area

18. Injection Beam Loss Beam loss caused by injection errors: • Major sources of beam loss that go to the injection dump: • Foil Inefficiency (FI) • Foil 400200g/cm2 • FI = 210% • Foil miss (FM) • (see figures) • Injection dump limit: • FM + FI  10% Transverse position Linac emittance error error c at injection=inj-0.5 mm-mr Joanne Beebe-Wang

19. Injection Errors caused by Injection Mismatch There could be three kinds injection errors caused by injection mismatch. They cause emittance growth in the circulating beam. Current design: UN=120mm-mr, inj,y=7.24m, inj,y=0.042, p/p=0.25% • Steering MismatchExpected x = 0.2 mm, x’ = 0.2 mradRMS,UN =0.9 mm-mr • Dispersion Mismatch Designed D = 7 cm, expected D’= 0.02 RMS,UN =0.004 mm-mr •  -function Mismatch Expected /M = /M = 0.025 RMS,UN =0.02 mm-mr The impact on circulating beam emittance growth is negligible. Joanne Beebe-Wang

20. Target Distribution Beam requirements at the target Joanne Beebe-Wang

21. Conclusions • Simulation shows that correlated painting has better chance to meet the target requirement and may minimize halo. Anti-correlated painting causes excessive halo at full intensity. • Halo/tail driven byspace charge and magnet errors can be reduced by splitting tunes. • Injection error increases foil-miss rate which causesincreased dump load and decreased beam power. Its impact on beam emittance growth is negligible. • Injection , -function mismatch can reduce foil heating. It can also be used to reduce the foil traversal rate for increased linac emittance. Joanne Beebe-Wang