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Calculation of Cosmic-Ray Proton and Anti-proton Spatial Distribution in Magnetosphere

ICRC2003. OG.1.5.2. 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 Where/How much Anti-protons 2. METHOD (Models)

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Calculation of Cosmic-Ray Proton and Anti-proton Spatial Distribution in Magnetosphere

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  1. ICRC2003 OG.1.5.2 Calculation of Cosmic-Ray Proton and Anti-proton Spatial Distribution in Magnetosphere Michio Fuki, Ayako Kuwahara, Nozomi, Sawada Faculty of Education, Kochi University JAPAN

  2. Index • 1. INTRODUCTION • Where/How much Anti-protons • 2. METHOD (Models) • Equation of Motion • Magnetic Fields • Injection Conditions • 3. RESULTS • Formation of Radiation Belts • Spatial Distributions • 4. CONCLUSIONS

  3. 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

  4. 2. METHOD (Model) 2-1 Equation of Motion Lorentz Force； V ：velocity，ｍ： mass ， ｃ ： light velocity， B：Magnetic Field (static)，ｑ：electric charge， E = 0；No Electric Field

  5. 2-2 Magnetic Fields (static) • in case : Dipole Fields ….. Störmer theory • Rotation (spiral) • Bounce • Drift

  6. 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

  7. 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 , albedoproton • III）ｐ ＋ Ａ →　ｎ ＋ Ｘ ｎ → ｐ ＋ e－ ＋ ν (decay from albedoneutron) τ ＝ 900 sec, decayedproton 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)

  8. three models

  9. 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)

  10. 2.4 Energy Spectra Fisk BESS Mode energy ～0.3 – 0.7 GeV Mode energy ～ 2.0 GeV

  11. continue • Kinetic Energy Spectrum （Model-I&II） 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)

  12. 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)

  13. 3. RESULTS Trapping Probability • Three solutions • Escape …. Leave from the magnetosphere • Arrive …. Reach to the Earth • Trap …. Chaotic motion in magnetosphere (⇒ Van-Allen Radiation Belts) • Probabilities of three solutions from 3 models Typical @ 1 GeV (energy dependent)

  14. Spatial Distribution (1) Model-II Model-I Model-III

  15. continued Protons ～ 0.1 GeV, 1000 trials

  16. Poles Surface distribution @400km ProtonModel-I 100000 events Anti-proton Model-I Poles diffused Spatial Distribution (2)

  17. World Surface distribution ISS@400km ProtonModel-III 10000 particles Anti-proton Model-III SAA gathering continued

  18. Height Distribution (Φ=-50,130deg) Protons・Antiprotons Spatial Distribution (3)

  19. 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

  20. 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.

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