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

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Calculation of Cosmic-Ray Proton and Anti-proton
Spatial Distribution in Magnetosphere
ICRC2003
OG.1.5.2

• Michio Fuki,
• Ayako Kuwahara, Nozomi, Sawada
• Faculty of Education, Kochi University
• JAPAN

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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

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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

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2. METHOD (Model)

• 2-1 Equation of Motion

Lorentz Force V velocity,m mass , c light
velocity, BMagnetic Field (static),qelectric
charge, E 0No Electric Field
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• 2-2 Magnetic Fields (static)
• in case Dipole Fields .. Störmer theory
• Rotation (spiral)
• Bounce
• Drift

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• 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

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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- ? (decay from albedo neutron)
• t 900 sec, decayed proton
• Anti-protons are similar, but they are created.
• III) p A ? p n n- X (pair-creation)
• n- ? p- e ? (decay from anti-neutron)

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three models
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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- ? (decay from albedo neutron)
• t 900 sec, decayed proton
• Anti-protons are similar, but they are created.
• III) p A ? p n n- X (pair-creation)
• n- ? p- e ? (decay from anti-neutron)

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2.4 Energy Spectra
Fisk
BESS
Mode energy 0.3 0.7 GeV
Mode energy 2.0 GeV
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continue

• Kinetic Energy Spectrum (Model-III)
• 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)

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Calculation

• 3-dimentional equations solved by time
• Runge-Kutta-Gill method
• Ranged from RE(6,350km) to 10RE
• 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)

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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 _at_ 1 GeV (energy dependent)
Model I Model II Model III
Escape 99 18 81
Arrive lt1 82 18
Trap 0 0 1.5
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Spatial Distribution (1)
Model-II
Model-I
Model-III
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continued
Protons 0.1 GeV, 1000 trials
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Spatial Distribution (2)

• Poles Surface distribution
• _at_400km
• Proton Model-I
• 100000 events
• Anti-proton Model-I
• Poles diffused

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continued

• World Surface distribution
• ISS_at_400km
• Proton Model-III
• 10000 particles
• Anti-proton Model-III
• SAA gathering

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Spatial Distribution (3)

• Height Distribution (F-50,130deg)
• Protons Antiprotons

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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

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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.