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OG.1.5.2 ICRC2003 Calculation of Cosmic-Ray Proton and Anti-proton Spatial Distribution in Magnetosphere Michio Fuki, Ayako Kuwahara, Nozomi, Sawada Faculty of Education, Kochi University JAPAN Index 1. INTRODUCTION 2. METHOD (Models) Equation of Motion Magnetic Fields Injection Conditions 3. RESULTS Where/How much Anti-protons Formation of Radiation Belts Spatial Distributions 4. CONCLUSIONS 1. INTRODUCTION 1-1 Antiprotons and Magnetosphere Balloon experiments (Anti-protons and Protons) SPACE STATIONS (protons, electrons) BESS, CAPRICE, etc. AMS, HEAT, PAMERA… Where/How much are Anti-protons around the Earth ? Computer Simulation Study 2. METHOD (Model) 2-1 Equation of Motion d q mV V B F dt c Lorentz Force; V : velocity,m: mass , c : light velocity, B:Magnetic Field (static),q:electric charge, E = 0;No Electric Field 2-2 Magnetic Fields (static) in case : Dipole Fields ….. Störmer theory Rotation Bounce Drift (spiral) IGRF (International Geomagnetic Reference Fields) Spherical harmonic functions, 12th order SAA region (low intensity) (South American Anomaly) Inside Magnetosphere Additional outer-belt components (Beard-Mead) in Magnetopause 2-3 Injection model Initial conditions I) p (free protons from out of magnetosphere) Cosmic-ray proton II) p + A → p + X (interaction with air) 20 km assumed , albedo proton III)p + A → n + X n → p + e- + ν (decay from albedo neutron) τ = 900 sec, decayed proton Anti-protons are similar, but they are created. III) p + A → p + n + n- + X (pair-creation) n- → p- + e+ + ν (decay from anti-neutron) three models 2-3 Injection model Initial conditions I) p (free protons from out of magnetosphere) Cosmic-rays II) p + A → p + X (interaction with air) 20 km assumed , albedo proton III)p + A → n + X n → p + e- + ν (decay from albedo neutron) τ = 900 sec, decayed proton Anti-protons are similar, but they are created. III) p + A → p + n + n- + X (pair-creation) n- → p- + e+ + ν (decay from anti-neutron) 2.4 Energy Spectra Fisk Mode energy ~ 0.3 – 0.7 GeV BESS Mode energy ~ 2.0 GeV continue Kinetic Energy Spectrum (Model-I&II) F ( E ) 1 / C E E , a b where C b / a Em ba Em: mode energy, a, b: spectrum power index Em = 0.3 GeV for proton (solar quiet), Em = 2.0 GeV for anti-proton. Index a = -1, b = 1.5. For Model-III (decayed protons/anti-protons) G( E ) 1 / C E E / mc E a b 2 Calculation 3-dimentional equations solved by time Runge-Kutta-Gill method Ranged from RE(=6,350km) to 10・RE Time step sliced from 10 μsec to 10 msec One particle traced maximum 10 minutes Random Energy from 10 MeV to 10 GeV Random starting points and directions Random neutron decay by 900 sec (M-III) 3. RESULTS Trapping Probability Three solutions Escape …. Leave from the magnetosphere Arrive …. Reach to the Earth Trap …. Chaotic motion Escape in magnetosphere Arrive (⇒ Van-Allen Radiation Belts) Probabilities of three solutions from 3 models Trap Typical @ 1 GeV (energy dependent) Model I Model II Model III 99 % 18 % 81 % <1 % 82 % 18 % 0 0 1.5% Spatial Distribution (1) Model-I Model-II Model-III continued Protons ~ 0.1 GeV, 1000 trials Spatial Distribution (2) Poles Surface distribution @400km Proton Model-I 100000 events Anti-proton Model-I Poles diffused continued World Surface distribution ISS@400km Proton Model-III 10000 particles Anti-proton Model-III SAA gathering Spatial Distribution (3) Height Distribution (Φ=-50,130deg) Protons ・Antiprotons 4. CONCLUSIONS Cosmic-ray (anti-)protons apt to arrive in polar regions Decayed protons trapped to form Van-Allen radiation belts (CRAND; cosmic-ray albedo neutron decay) Lower energy protons well trapped due to life time Higher energy Anti-protons may remain in radiation belts Protons and anti-protons are gathered in SAA Proton tails are east and anti-protons are west Anti-protons center in altitude 2000km lower than protons These are qualitative discussions Closing More statistics is necessary for quantitative discussions for absolute flux, p-/p ratio, energy spectra and direction distribution. To compare with other theoretical results, simulation programs or coming experimental data.