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 2. METHOD (Models) 3. RESULTS 4. CONCLUSIONS
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 , 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)

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

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
1 GeV (energy dependent)
Model I II
III
Escape
99 %
18 %
81 %
Arrive
<1 %
82 %
Trap
1.5%

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

15. continued
Protons ～ 0.1 GeV, 1000 trials

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

17. Anti-proton Model-III
continued
World Surface distribution
Proton Model-III
10000 particles
Anti-proton Model-III
SAA gathering

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

19. 4. CONCLUSIONS These are qualitative discussions
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.