1. Stripping foil studies for Project-X A.I. Drozhdin May 29, 2012 Outline 1. H - handling in the beam line: a) foil stripping b) stripping due to Blackbody radiation c) stripping due to residual gas d) magnetic field stripping 2. Foil stripping injection simulation a) stripping efficiency b) excited states hydrogen H o atoms

2. The Project-X E kin =8 GeV beam line consists of 6 sections: a)matching section between Linac and FODO lattice, b)amplitude collimation (3 cells without bending magnets), c)momentum collimation and jitter correction section (6 cells with dipoles), d)straight section is included for proper positioning of the Linac and beam line at the Fermilab site (6 cells), e)second part of momentum collimation (6 cells) and f)matching section between FODO lattice and Recycler Ring. The location of stripping foils and beam dumps are shown by a vertical bars directed down in in the bottom figure. Nov.15, 2004 A.Drozhdin H - handling in the beam line May 29, 2012 A.Drozhdin Momentum collimation Amplitude collimation

3. An amplitude and momentum collimation is done by stripping of H - ions at the foil located upstream of the focusing quadrupole and then intercepting of H o atoms and protons (H + ) by the beam dump located in 5 m downstream of the focusing quadrupole. Dump 8 Dump 2 May 29, 2012 A.Drozhdin H - foil-stripping for beam collimation Without collimationWith collimation Particles passed through the foil (H +)

4. H - stripping due to Blackbody radiation The Doppler Effect (top figure) shifts lab frame infrared photons (green curve) to energies (blue and magenta) in excess of the range where the cross section of photodetachment (red) is large. The stripping rate is increased by 3 order of magnitude with H - ions energy rise from 0.8 to 8 GeV (middle). The beam pipe temperature (bottom) lowered to liquid nitrogen temperature (77 K) permits to decrease the photodetachment rate by 3 order of magnitude. Ref. H.C.Bryant and G.H.Herling, Journal of Modern Optics, 53, 45 (2006). May 29, 2012 A.Drozhdin Photodetachment cross section Blackbody Radiation spectrum Blackbody at 300 K is 1/L=5.7e-07 1/m for E kin =8 GeV

5. H - stripping due to residual gas The total electron loss cross section can be expressed as: The total electron loss cross section for H, He, N, O and Ar from the measurements and scaled to 8 GeV are presented in theTable The loss rate due to collision with i-th species of the residual gas is andhere The measured residual gas pressure in the FNAL A150 beam line, and calculated loss rates are shown in Table Fef. G.H.Gillespie, Phys. Rev. A 15, 563 and A 16, 943 (1977), G.H.Gillespie, Nucl. Intr. & Meth. B 2, 231 (1984) and B 10/11, 23 (1985) May 29, 2012 A.Drozhdin p strip =

6. Magnetic field stripping When an H - ion with momentum P moves in magnetic field B, it experi- ences an electric field E that is the Lorentz-transform of the magnetic field in the lab system: The stripping of H - ions by the magnetic field (Lorentz stripping) was calculated using (M.A.Furman) equation for ion's lifetime in its own rest frame system. In a range of E=1.87-7.02 MV/cm A=3.073e-14 s-MV/cm C=44.14 MV/cm. The mean decay length in the lab system is The stripping probability was calculated as Ref. G.M.Stinson et al., Nucl. Instr. & Meth. 74, 333 (1969) The rates of stripping in the Pc=8.8889 GeV beam line elements Blackbody at 300 K: 5.7e-07 1/m Residual gas at P=1e-08 torr: 1.8e-08 1/m Magnetic field at 500 Gauss: 6.4e-10 1/m A sum of stripping probabilities at each element of beam line for every particle of the beam was calculated using STRUCT. May 29, 2012 A.Drozhdin Pc=8.8889 GeV Pc=2.7844GeV Pc=0.954263 GeV

7. Painting injection scheme: K1-K4 – painting kicker-magnets HBC1-HBC4 – bump magnets for circulating beam displacement at the foil to the injection trajectory Foil – for H - stripping to H + H o Dump – for unstripped beam absorbing May 29, 2012 A.Drozhdin Foil stripping injection The HBC2 magnet should have low magnetic field (~500Gauss) to eliminate H - stripping by magnetic field.

8. Injected and circulating beam locations at the foil during painting. The transverse dimentions of the foil are 14 X 18 mm. May 29, 2012 A.Drozhdin Injected beam at the foil Circulating beam at the central orbit Circulating beam after painting The removal from the foil may be reduced from 37 mm to 15 mm for these beam parameters if space in the accelerator is not restricted

9. Injection magnet parameters. May 29, 2012 A.Drozhdin

10. Typical parameters effecting the painting injection efficiency: Painting injection scenarios studied for accumulation of 1.47e+14 protons per pulse (ppp) in the Recycler Ring. May 29, 2012 A.Drozhdin

11. Lifetime of Stark States Hydrogen Atom in Magnetic Field Calculation and Estimation of Losses at Stripping Injection W. Chou, A.Drozhdin, Oct. 2004 The energy level of the hydrogen atom n is split in the uniform electric field into n(n+1)/2 sublevels [1]. Each sublevel can be characterized by a set of parabolic quantum numbers n 1, n 2, m such that the principal quantum number n = n 1 + n 2 + m + 1. The value of Г is inversely proportional to the lifetime of the atomic state. An Asymptotic formulae for Г is obtained by R.Damburg and V.Kolosov, see ref. at the next page: (8) where Expanding R in power series of F, we obtain (9), F - electric field strength, E o - energy level.

12. May 29, 2012 A.Drozhdin (11) References: Rydberg states of atoms and molecules, Editors: R.F.Stebbings and F.B.Dunning, Department of Space Physics and Astronomy Rice University, Cambridge University Press 1983, pp.31-71. R.J.Damburg and V.V.Kolosov, ''Theoretical studies of hydrogen Rydberg atoms in electric fields''. Semiempirical formula for Г: (10)

13. May 29, 2012 A.Drozhdin Lifetime T=1/Г of Stark states hydrogen atoms in magnetic field corresponding to electric field for hydrogen atoms of Pc=8.8889 GeV was calculated using equation 11. Lifetime is in a laboratory frame. An example for magnetic field of 0.15 T: The life time of H o atoms with n=3 is T=2e-09 sec. An average path length for this particle will be S=3e+08m/s*2e-09s>0.6m. These particles may survive or will be stripped to protons along the magnet, and may produce losses in the accelerator. Particles with n>3 will be stripped to protons very shortly at the entrance of this magnet and they will not increase the emittance of the circulating beam. Pc=8.8889 GeV

14. May 29, 2012 A.Drozhdin Carbon foil stripping efficiency estimation: H - ions energy Foil thickness H o remain after foil (MeV) (μg/cm 2 ) (%) 200 100 10.0% measurement 200 150 1.0% measurement 200 200 0.4% measurement 800 90 40.0% measurement 800 150 20.0% measurement 800 200 11.2% measurement 800 300 2.0% measurement 8000 200 23.0% cross section energy scaling 8000 300 9.5% cross section energy scaling 8000 400 4.0% cross section energy scaling 8000 500 1.5% cross section energy scaling 8000 600 0.5% cross section energy scaling References: - A.H.Mohagheghi et al., Phys. Rev. A 43, 1345 (1991). - N.S.Gulley et al., Phys. Rev. A 53, 3201 (1996). - R.C.Webber and C.Hojvat, IEEE Trans. NS 26, 4012 (1979). - B.Gervais et al., Phys. Rev. A 53, 3189 (1996). - P.Kurpick et al., Phys. Rev. A 58, 2183 (1998). - P.B.Keating et al., Phys. Rev. A 58, 4526 (1998).

15. May 29, 2012 A.Drozhdin Experimental data on H o yields produced by foil stripping of 800-MeV H - at 200 μg/cm 2 (1μm) graphite foil [2]. n=1, 2 93.3% n=3 3.6% n=4 1.5% n=5 0.7% n=6 0.3% n>6 0.6% total 100% Assuming that distribution of yields of different states n almost does not depend on the foil thickness, one may predict the behavior of different excited states atoms in the magnetic fields of injection system elements. References: Measurement of H(-), H(o), and H(+) yields produced by foil stripping of 800-MeV H(-) ions, M.S.Gulley, P.B.Keating, H.C.Bryant, E.P.MacKerrow, W.A.Miller, D.C.Rislove, S.Cohen, J.B.Donahue, D.H.Fitzgerald, S.C.Frankle, D.J.Funk, R.L.Hutson, R.J.Macek, M.A.Plum, N.G.Stanciu, O.B.van Dyck, C.A.Wilkinson, C.W.Planner, Physical Review A, Volume 53, Number 5, May 1996.

16. May 29, 2012 A.Drozhdin A stripping probability of Pc=8.88889 GeV H o Stark states hydrogen atoms in the B=1.2T bump-magnet HBC3: Atoms with n>1 pass less than 3mm, they will be stripped very shortly and will go to the circulating beam without emittance increase. The life time of H o atoms with n=1 is >100m. These atoms are survive and will go to the beam dump. If the stripping efficiency is 99% (at foil thicknes of 500μg/cm 2 ), the power load to the dump is 0.9% of injected beam power. B=0.055T B=1.2T

17. May 29, 2012 A.Drozhdin An example of Pc= 2.784437 GeV beam stripping: Lifetime of H - ions in a magnetic field (top). Calculated lifetime of excited states hydrogen H o atoms in magnetic field (middle and bottom).