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ELENA studies: Scattering Analysis

ELENA studies: Scattering Analysis . Tatiana Rijoff ( Technische Universität Darmstadt, CERN) Christian Carli (CERN). Thanks to. G. Iadarola , S. Gilardoni. Aim of the study:. Understand if the rest gas could be a problem for the circulating beam. What we studied:.

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ELENA studies: Scattering Analysis

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  1. ELENA studies:Scattering Analysis Tatiana Rijoff (TechnischeUniversitätDarmstadt, CERN) Christian Carli (CERN) Thanks to G. Iadarola , S. Gilardoni

  2. Aim of the study: Understand if the rest gas could be a problem for the circulating beam What we studied: • Beam losses for interaction with nuclei (same behavior for neutral and ionized gas) • Beam blow up for interaction with nuclei (same behavior for neutral and ionized gas) • Beam blow up for interaction with ions charge • Ionization of the rest gas caused by the beam Additional studies should be added to complete the job .. Courtesy of C. Carli

  3. ELENA cycle In some of the study steps it is necessary to know the beam energy (velocity) at a given time From ELENA report My derivation used in the following

  4. Rough representation of interaction r_int No interaction No interaction Ion Neutral Atom Blow up BU r_i loss loss r_a b_loss BU b_loss

  5. The impact parameter bloss The impact parameter loss is the maximum distance at which the incident particle is lost b_loss particle are lost when where θloss is the loss scattering angle Consider an incident particle with charge Z1e, with velocity ‘at infinity’ v0 and mass m which interacts with the electric field generated by a particle with charge Z2e the relation between the scattering angle and the impact parameter is and

  6. Loss interaction • Working hypothesis: • same acceptances AT in both transverse direction • an average TwissbetafunctionbT Impact parameter: z = atomic number of antiprotons = - 1 m = antiproton mass = 938 MeV/c2 v = antiproton velocity = βrelc c = speed of light = 2.998 108 βrel= antiproton relativistic beta = [0.015, 0.106] βT = Twiss beta function AT = Acceptance Gas Atom = N2 Z = atomic number for rest gas atom n = rest gas atoms density = 9.6 1010 part/m3 Loss cross section: Loss time: For diatomic molecules like N2, the model of ‘single ball’ must be modified. In a naive and pessimistic point of view we double the cross section (‘two balls)

  7. loss rate as function of the energy loss rate as function of the time

  8. τloss < beam lifetime (20 sec) Loss are not an issue

  9. Blow Up interaction Blow up coefficient for one type of scattering βc = velocity n = particles density ε = emittance βT = average beta twiss θ= scattering angle

  10. Blow Up interaction Neutral atom: Ion: Q = ion charge assumed ra = ri • Ions considered for N2: • N2+ • N+ (same as N22+) • N2+ For diatomic molecules, the Z2 must be multiplied by a factor 2

  11. t [s] βT = 3 m AT = 75 μm

  12. ELENA sigma comparison σbuin gives the biggest contribution

  13. To obtain the blow up time caused by the ions we need to know the ions density, to know the ions density we need the ionization cross section.

  14. Important: At LOW ENERGY we can not take the ionization cross section obtained for protons • Ionization cross section • at ELENA energy several effects differentiate the behavior of protons and antiprotons. • For example • the time of interaction is long enough so that • proton can attract the electron in atom before the ionization • antiproton can repel the electron in atom before the ionization • at very low energy for proton the effect of charge exchange must be taken into account. • …

  15. Where it was possible ionization cross section is obtained from experimental data: In the range [0.1,1] MeV data obtained from “Current status of antiproton impact ionization of atoms and molecules: theoretical and experimental perspectives “ Kirchner and Knudsen • Ionization cross section Otherwise ionization cross section is obtained from empirical formula: In the range [1. , 5.3] MeV data obtained applying the formula in “Non-dissociative and dissociative ionization of N2, CO, C02, and CH4 by impact of 50-6000 keV protons and antiprotons” Knudsen, Mikkelsen, Paludan, Kirsebom, Moller, Uggerhoj, Slevin, Charlton and Morenzoni

  16. Ion density

  17. Blow Up Interaction

  18. Blow Up Interaction

  19. Blow Up Interaction • Additionale effects caused by ions is negligible compared to the effect in the blow up for neutral rest gas • the value obtained is too small respect to others effects like the Intra beam scattering to be an issue

  20. Ions frequency • Considered a coasting beam • Modules from pyECLOUD by G. Iadarola with some customizations • Only electric field considered (low ions velocity -> magnetic field negligible) • for a better understanding of the phenomenon several size of the beam were tested • The statistic is obtained considering 1500 ions but I noticed values converge quickly to the final results (300 ions are enough) • Videos are made with number of ions ‘proportional’ to the one in the machine (N2+ > N22+ = N+ > N2+ )

  21. Electric field generated by beams of different size pyECLOUD by G. Iadarola

  22. Electric potential generated by beams of different size pyECLOUD by G. Iadarola

  23. Ions motion in the beam potential beam σ = 1mm beam σ = 3mm ions without initial velocity (no thermal motion) pyECLOUD by G. Iadarola

  24. Thank you for your attention

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