Transcript Document

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
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1. INTRODUCTION
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2. METHOD (Models)
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Equation of Motion
Magnetic Fields
Injection Conditions
3. RESULTS
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Where/How much Anti-protons
Formation of Radiation Belts
Spatial Distributions
4. CONCLUSIONS
1. INTRODUCTION
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1-1 Antiprotons and Magnetosphere
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Balloon experiments (Anti-protons and Protons)
SPACE STATIONS (protons, electrons)
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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
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2-2 Magnetic Fields (static)
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in case : Dipole Fields ….. Störmer theory
 Rotation
 Bounce
 Drift
(spiral)
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IGRF (International Geomagnetic Reference Fields)
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Spherical harmonic functions, 12th order
SAA region (low intensity) (South American Anomaly)
Inside Magnetosphere
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Additional outer-belt components (Beard-Mead) in Magnetopause
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2-3 Injection model
Initial conditions
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I） ｐ (free protons from out of magnetosphere)
Cosmic-ray proton
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II） ｐ ＋ Ａ → ｐ ＋ Ｘ (interaction with air)
20 km assumed , albedo proton
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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.
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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
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I） ｐ (free protons from out of magnetosphere)
Cosmic-rays
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II） ｐ ＋ Ａ → ｐ ＋ Ｘ (interaction with air)
20 km assumed , albedo proton
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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.
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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
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Kinetic Energy Spectrum （Model-I&II）
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F ( E ) １ / C  E  E ,
a
b
where C  b / a  Em
ba
Em: mode energy, a, b: spectrum power index
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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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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)
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3. RESULTS
Trapping Probability
 Three solutions
Escape …. Leave from
the magnetosphere
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Arrive …. Reach to the
Earth
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Trap …. Chaotic motion Escape
in magnetosphere
Arrive
(⇒ Van-Allen Radiation Belts)
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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)
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Poles Surface
distribution
@400km
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Proton Model-I
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100000 events
Anti-proton Model-I
Poles diffused
continued
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World Surface
distribution
ISS@400km
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Proton Model-III
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10000 particles
Anti-proton
Model-III
SAA gathering
Spatial Distribution (3)
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Height Distribution (Φ=-50,130deg)
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Protons
・Antiprotons
4. CONCLUSIONS
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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
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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.