Transcript Document
Aug.31-Sep.3
ECRS2004
Cosmic-Ray Antiproton Spatial Distributions
Simulated in Magnetosphere
Michio Fuki
Faculty of Education, Kochi University
2-5-1, Akebono-cho, Kochi 780-8520, JAPAN
Abstract :
The recent balloon experiments as well as satellites and space-station
experiments have been demonstrated the flux and the energy spectrum of antiprotons
which naturally exist around the earth. Specially they are observed on the top of
atmosphere in the polar region and believed to be secondarily produced from the high
energy cosmic-ray interactions with interstellar matter. They have the characteristic
energy around 2 GeV and are influenced with the Earth's magnetic fields. I computed the
motion of antiprotons in the Magnetosphere region with some initial conditions and plotted
the spatial distributions of them. The antiprotons in the polar region are looked like
coming from the outer region. Meanwhile, the antiprotons in the space-station region are
trapped in the radiation belts. The source of the former may be the produced particles
from the collisions of Cosmic-rays on the Sun surface or in the extra-solar region. The
latter is explained by the model that antiprotons are originated in decay particles from the
antineutrons produced with the cosmic ray interactions in atmosphere. They gather in the
radiation belts as well as protons and electrons. The plots show that in the space-station
altitudes they are rich in the SAA region. In order to distinguish between antiprotons and
protons effectively, the differences of arrival directions of them are important.
1. Motivation
1-1 Experiments of anti-proton observation
Balloon experiments ⇒ antiprotons & protons
Satellites/Space-station ⇒ protons, nuclei，
electrons)
BESS, CAPRICE, etc.
AMS, HEAT, PAMERA…
Where and How much natural anti-protons exist
around the Earth ?
Computer simulation estimates the spatial and energy
distributions, to make clear the antiproton origin.
１） Energy Spectrum
●Protons
●Anti-protons（< 1/10000）
Fisk
Mode energy ～ 0.3 – 0.7 GeV
BESS
Mode energy ～ 2.0 GeV
２)Radiation spatial distribution (Alt.400km)
Where anti-protons？
●Proton & electron（by Mir）
●Neutron（RRMD＠STS）
Solarmin
Solarmax
Abundant in SAA and both magnetic poles
2. Computation model
2-1 Equation of Motion
Lorentz force F；
ｍ： mass ， ｃ ：light velocity，ｑ：charge，
V ： velocity，
B：magnetic field (static)，
⇒Magnetosphere（IGRF)
E = 0；⇒ no electric field
2-2 Injection models
(Initial conditions)
Protons
I） protons (free injection out of magnetosphere)
galactic (or solar) cosmic ray primary protons ：GCR
II） ｐ ＋ Ａ → ｐ ＋ Ｘ (nuclear collision with atmosphere)
creation＠20 km, Albedo protons ：CRAP
III）ｐ ＋ Ａ → ｎ ＋ Ｘ (nuclear collision with atmosphere）
ｎ → ｐ ＋ e－ ＋ ν (decay from albedo neutron)
τ ＝ 900sec, creation＜１０・RE， decayed protons ：CRAND
Antiprotons, （collision origin；pair creation）
I) galactic cosmic ray antiprotons (similar to protons)
II) ｐ ＋ Ａ → ｐ ＋ ｐ ＋ ｐ－ ＋ Ｘ (pair-creation)
III）ｐ ＋ Ａ → ｐ ＋ ｎ ＋ ｎ－ ＋ Ｘ (pair-creation)
ｎ－ → ｐ－ ＋ e＋ ＋ ν (decay from anti-neutrons)
Three injection models for protons
GCR
CRAP
CRAND
Anti-proton Energy Spectra
from Monte Carlo Simulation
・Accelerator data and simulation
・Simulation in lab. system
200
100
50
GeV
Eo=
20
10
5
GeV
Multi-Chain-model for p-A collision, each 100,000 events
2.3 Energy spectrum form
Analytical form
Monte Carlo form
Kinetic energy spectral function (Model-Ⅰ＆Ⅱ)
F ( E ) １ / C E a E b ,
where， C b / a Em
Em: mode energy, a, b: spectral power index
ba
set a = -1, b = 2.0.
Em = 0.3 GeV for protons (solar minimum era),
Em = 2.0 GeV for antiprotons.
Decayed proton/antiproton spectra (Model-Ⅲ)
G( E ) {t /(τ )}F ( E ),
where， 1 E / mc2 1/ 1 2
(anti)neutron decay-time:τ= 900sec, yield time ｔ = 0.2sec.
3. Computing method and parameters
Solve 3D equation of motion（1） numerically by time
Adamus-Bashforth-Moulton 6th method used
(better than Runge-Kutta-Gill 4th method)
Range： RE(=6,350km)+20km ～ 10・RE（in magnetosphere）
Time step： variable，10 μsec（<1000km） ～ 10 msec（outer）
Time limit： trace up to max.600sec(10 min.)
Magnetosphre fields: static, IGRF (inner region)
+ Mead (outer region)
Use Monte Carlo simulation for initial conditions
Energy range： 10 MeV ～ 10 GeV random
Sample from Energy spectrum
Starting position and direction： random（uniform, isotropic）
（Anti）neutron decay：random（τ＝900 sec），＜ 10・RE
4. Results:
Spatial distribution(1)
ModelⅡ
CRAP
モデル-II
ModelⅠ
GCR
ModelⅢ
CRAND
モデル-III
Input 100,000 protons
Spatial distribution (2)
・） Surface distribution in
Polar region @400km
Protons/Model-I
input 100,000 particles
Aurora zone
Antiprotons/Model-I
input 100,000 particles
Wide spread
Spatial distribution (3)
・） World surface
distribution on ISS
@400km
Protons/Model-III
Input 100,000 particles
East tail
Antiprotons/Model-III
Input 100,000 particles
West tail
Looks gathering in SAA
Same color means same particle (orbits)
Spatial distribution(4)
Altitude distribution
cross section (Φ=-50deg(SAA) and 130deg(opposite side) )
●Protons
●Antiprotons
Proton rich around 4000 km and antiprotons rich in 2000 km
Low altitude components → SAA
Differences of arrival directions between
protons and anti-protons
ISS@400km
● Protons
Input 100,000 particles
from above: north east
from below: south east
● Antiprotons
Input 100,000 particles
from above: south west
from below: north west
4. Conclusions
Polar region (High latitude)
Radiation belts
Cosmic-ray (anti)protons arrive to both polar regions
（by modelⅠ）・・・・due to Rigidity Cut-off
Antiprotons is more spread than protons in polar regions
Decayed (anti)protons make Van-Allen radiation belts
(CRAND; Cosmic ray Albedo neutron decay：modelⅢ)
Low energy（<0.1GeV）decayed protons are trapped widely
High energy（～1GeV）antiprotons are trapped in inner zone
Antiprotons are gathered in low altitudes (～2000km)
at ISS altitudes
Protons and antiprotons are same gathered in SAA region
Arrival directions are opposite for protons (north east)
and antiprotons (south west)
Tails of protons are east, tails of antiprotons are west
（These are qualitative）
5. Discussions and future subjects
Spatial distribution of protons and antiprotons are
simulated qualitatively
Needs quantitative discussion by unified model：
Flux, p－/p-ratio, （nuclei, isotope, anti-helium?）
Energy spectrum, Direction distribution.
Production rate，Trapping time，Leakage rate．
Time fluctuation （short,long）.
Solar activity, Modulations etc.
Needs comparison with other results
More statistics！
100K partilcles→1M…..now,10K/1day(Pentium4,2.4GHz)
Theory・Simulation
（coming）Experimental data
Other solar effects
magnetic fields, of Sun, Planets