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Optimization of Injection Painting Techniques for Particle Distribution in SNS

This review explores the concept of injection painting in particle accelerators, focusing on its application within the Spallation Neutron Source (SNS) at BNL. By adjusting the phase space of the injected beam, different particle distributions can be achieved, which enhances target fulfillment, reduces beam losses, and extends foil lifespan. The study outlines basic painting schemes, such as correlated and anti-correlated painting, and presents analytical expressions regarding particle distribution. The importance of optimizing bump functions for minimizing foil heating and maximizing beam efficiency is emphasized.

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Optimization of Injection Painting Techniques for Particle Distribution in SNS

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  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

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