2. A complete simulation of cosmic rays access to a Space Station Davide Grandi INFN Milano, ITALY

3. Primary cosmic rays access Arrival directions  in,  in Particle rigidity (unchanged) R detector position  det,  det Unknown: Direction (magnetosphere)?  asym,  asym Position (magnetosphere)?  out,  out A transfer Function F( ,R)

4. AMS detector AMS 01 10 days mission 51.6° inclination orbit Primary cosmic rays Secondary cosmic rays (atmosphere) Geomagnetic effects Protons electrons and Helium AMS 02 3 years mission Superconductor magnet Nuclei separation (RICH & TRD) Antimatter spectra Cosmic ray spectra Secondary spectra

5. The Earth Magnetosphere Internal contribute Electric currents inside the Earth surface Well known model IGRF 2005 Updated every 5 years External contribute Solar wind (asymmetric shape) Birkeland regions Ring current Tail current No dipolar field !

6. Tsyganenko 96

7. Simulaton structure Earth grid (sphere) 3600 points uniformly distributed Arrival directions grid (emisphere) 1800 incoming angles Rigidity grid 31 rigidity bins (AMS) 2*10 8 protons Solar parameters IGRF parameters june1998 Altitude 400 km (AMS) Time limit 10 seconds Space limit same shooting surface

8. The Earth and the arrival directions

9. Data processing CPU power Alpha stations (DS10 & DS20) CONDOR distributed CPU (INFN) Linux Farm (1.2 GHz 256 MB Ram) Programming skills Fortran code Runge-Kutta 6 th order NASA subroutines Perl5 machines administration

10. Primary tracing Exclude particles below geomagnetic cutoff less than 70% of Stoermer formula calculation (dipolar) Up to the end of the magnetosphere Last point position Last point asymptotic direction

11. Solar effects 1998 AMS 01 solar data Modified magnetosphere Empirical formula (Sibeck 1991) Solar wind (de)compression Next mission solar activity? 2004-2005 parameters (AMS 02)

12. Error estimate Secondary cosmic rays exclusion 10 -2 Algorithm uncertainty 10 -4 Primary error Related to flux error (rigidity) Angular reconstruction +/-0.5°

13. AMS data renormalization Geomagnetic latitude separated Primary spectrum above cut-off ( law  (R)=R -   with  =2.79) Primary and secondary mixing around cutoff Secondary spectrum above cut-off (work in preparation)

14. Main goals Transfer Function Primary/Secondary cosmic rays in intermediate regions Secondary cosmic rays production in upper atmosphere Angular distribution of rigidity cutoff Interplanetary flux: assumed to be isotropic

15. Different approaches I. Magnetosphere forward tracing I. Efficiency:7.4 * 10 -4 (1.5 * 10 10 protons) II. Near Earth forward tracing I. Efficiency: 1.6-5.0*10 -1 (10 6 protons) III. Near Earth backward tracing I. Efficiency: 9.9*10 -1 II. Where? AMS orbit!

16. The simulation approach

17. First results: fluxes

19. First Results: angles

20. Work in progress Complete protons tracing Renormalization of data Forward tracing for secondary production study Transfer function mapping

21. Work to do New Tsyganenko 2001 subroutine Code speed optimization (C) Renormalization of data (AMS fluxes) Atmosphere model and interactions Solar phases study AMS –02 solar parameters from old ones Complete cosmic rays flux simulation for AMS-02 mission

22. Conclusions Secondary particles seem to be present above cutoff For  m < 0.2 and 0.2 <  m < 0.3 up to 20 GeV energy Primary particles below cutoff For slightly different rigidities huge difference in magnetosphere origin Need to be determined a Transfer Function