1. Interactions with Rest Gas – Typical Case Interactions with Rest Gas – ELENA Quantitative analysis for ELENA Evaluations at 100 keV Ejection Energy Evaluations at 5.3 MeV Injection Energy Conclusions Effect of the residual Gas on the circulating Antiproton Beam 5 th April 2012, ELENA Beam Physics and Performance Committee C. Carli

2. Interactions with Rest Gas – Typical Case Different processes (see for AD N. Madsen, S.Maury and D. Möhl, NIM A 441, p 54-59):  Nuclear interactions (red): very rare  Large angle scattering outside acceptance (orange): close encounter with nucleus leading to slow losses  Multiple small angle scattering (blue): many small deflections add up an increase emittance Rms angles estimated integrating over all impact parameters taking (few) p-bars undergoing large angle scattering angles into account as well  No interactions for p-bars passing outside atoms interactions (black) (Charge state changing processes for ions) 5th April 2012, ELENA BPPC Residual Gas Effects C.Carli Nucleus Electrons Trajectories out side atom => no deflection Vacuum chamber

3. Interactions with Rest Gas - ELENA Very low pressure and velocity at 100 keV  Most p-bars do not interact with rest gas molecules (black): in average ~40 s between interactions!  Nuclear interactions (red): very rare  Large angle scattering outside acceptance (orange): large cross section due to low energy (losses slow due to low pressure and velocity)  Small angle scattering (blue): several deflections of one p-bar at 100 keV very unlikely Rms angles (and blow-up) strongly overestimated if p-bars undergoing large angle scattering angles are taken into account 5th April 2012, ELENA BPPC Residual Gas Effects C.Carli Nucleus Electrons Trajectories out side atom => no deflection

4. Quantitative analysis for ELENA Model adapted from analogous AD study  Separation of different cases for the impact parameter Incoming particle with mass m, charge Ze and initial velocity v i =  c Interacting with residual gas molecule with mass M = A*amu and charge Ze, with A atomic mass number, amu the atomic mass unit and Z the atomic number  Radius of atom roughly r a = 5 10 -11 Z 1/3 m Deflection of beam particle depends on impact parameter b b > r a : no deflection (total cross section for interaction  sc =  r a 2 ) For deflection  not too large, i.e. b not too small (otherwise projectile lost anyhow) Electrons neglected for scattering (standard procedure for that kind of problem) 5th April 2012, ELENA BPPC Residual Gas Effects C.Carli M, Ze m, ze, v i rara b > r a no deflection Impact parameter b

5. Quantitative analysis for ELENA Probably a pessimistic model  In reality, atomic radius not well defined and projectiles penetrating only outer part of residual gas atom will see a smaller field  Projectile exposed to field inside atom only Projectile loss if outside ring acceptance  Assume same acceptances A T in both transverse planes and an average Twiss betafunction  T  Loss for  T (  x’ 2 +  y’ 2 ) =  T  2 > A T  Loss for impact parameter below  Loss cross section: (for different acceptances in transverse planes: ) Relevant for rms emittance blow-up (neglecting large angles leading to loss): b loss < b < r a  Standard expression for adding angular spread with given (note a factor ½ for sharing deflection between two phases and another factor ½ for the general blow-up expression 5th April 2012, ELENA BPPC Residual Gas Effects C.Carli

6. Evaluations at 100 keV Ejection Energy Assume N 2 with pressure 3 10 -12 Torr at room temperature  Moderately pessimistic composition (large H 2 component gives longer life-time and less blow-up)  Residual gas density n = 9.6 10 10 m -3  Z = 7, A = 14  Atom radius r a = 0.96 10 -10 m, total cross section  sc =  r a 2 = 2.9 10 -20 m 2 At ejection (0.1 MeV) energy  Relativistic  and velocity:  e = 0.015 and v i =  e c  Total interaction rate: 2  sc n  e c = 0.024 s = 1/41 s … most p-bars are not scattered at all!! (factor 2 for 2 atoms per N 2 molecule)  Impact parameter for loss and loss cross section For  T = 3 m and A T = 50  m: b loss =2.5 10 -11 m,  loss = 1.9 10 -21 m 2, 2 n  loss  e c = 1/622 s For  T = 2 m and A T = 70  m: b loss =1.7 10 -11 m,  loss =.91 10 -21 m 2, 2 n  loss  e c = 1/1306 s  Blow-up (of transverse rms emittances) rates for the two cases above: For  T = 3 m and A T = 50  m:  bu = 9.6 10 -20 m 2 (  m/s), 2 n  bu  e c = 0.081  m/s For  T = 2 m and A T = 70  m:  bu = 7.6 10 -20 m 2 (  m/s), 2 n  bu  e c = 0.064  m/s (Taking p-bars scattered out of the acceptance (thus lost) into account would give much larger blow-up) 5th April 2012, ELENA BPPC Residual Gas Effects C.Carli

7. Evaluations at 5.3 MeV Injection Energy At injection (5.3 MeV) energy  Relativistic  and velocity:  i = 0.106 and v i =  i c = 0.317 10 8 m/s  Total interaction rate: 2  sc n  i c = 0.175 s = 1/5.7 s … still few interactions!! (factor 2 for 2 atoms per N 2 molecule)  Impact parameter for loss and loss cross section For  T = 3 m and A T = 50  m: b loss =4.7 10 -13 m,  loss = 6.9 10 -25 m 2, 2 n  loss  i c = 1/66 h For  T = 2 m and A T = 70  m: b loss =3.2 10 -13 m,  loss = 3.3 10 -25 m 2, 2 n  loss  i c = 1/138 h  Blow-up (of transverse rms emittances) rates for the two cases above: For  T = 3 m and A T = 50  m:  bu = 10.3 10 -23 m 2 (  m/s), 2 n  bu  i c = 0.0006  m/s For  T = 2 m and A T = 70  m:  bu = 7.3 10 -23 m 2 (  m/s), 2 n  bu  i c = 0.0004  m/s (Again taking p-bars scattered out of the acceptance (thus lost) into account would give –not that much- larger blow-up) 5th April 2012, ELENA BPPC Residual Gas Effects C.Carli

8. Conclusions … some surprising observations  Many p-bars do not interact all at 100 keV during expected plateau duration  Large single scattering events dominate (even at injection), NO multiple small angle scattering  Blow-up overestimated with standard formulas (taking lost p-bars for blow- up into account) At a first glance (independent verification would be good!)  Situation looks fine even at 100 keV.. some acceptable losses  Single large angle scattering events lead to tails?  Other effects (IBS..) likely to dominate blow-up Systematic investigations (similar to AD study) and verifications to be done  Take ramps into account (average over different energies)  Details of the lattice  … 5th April 2012, ELENA BPPC Residual Gas Effects C.Carli