Cosmic-Ray Antiproton Spatial Distributions Simulated in Magnetosphere

Michio FukiFaculty of Education, Kochi University

2-5-1, Akebono-cho, Kochi 780-8520, JAPAN

ECRS2004Aug.31-Sep.3

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) BESSBESS, CAPRICE, etc. AMS, HEAT, PAMERA…

Where and How much natural Where and How much natural anti-protonsanti-protons exist exist around the Earth ?around the Earth ?

Computer simulation estimates the spatial and energy distributions, to make clear the antiproton origin.

１） Energy Spectrum

Mode energy ～　 0.3 – 0.7 GeV Mode energy ～ 2.0 GeV

Fisk BESS

●Protons 　　　　　　　　　　　　　　　　　　　● Anti-protons（ < 1/10000 ）

２ )Radiation spatial distribution (Alt.400km)

●Proton & electron （ by Mir ）　　　　　　● Neutron （ RRMD ＠ STS ）

Where anti-protons ？

Abundant in SAA and both magnetic poles

Solar-min

Solar-max

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 atmospher

e ） 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 protonsThree injection models for protons

GCR

CRAP

CRAND

Anti-proton Energy Spectra from Monte Carlo Simulation

Multi-Chain-model for p-A collision, each 100,000 events

・ Accelerator data and simulation 　・ Simulation in lab. system

200

100

50

GeV

Eo=

20

10

5

GeV

2.3 Energy spectrum form Analytical form Monte Carlo form

Kinetic energy spectral function (Model-Ⅰ＆Ⅱ )

Em: mode energy, a, b: spectral power index 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)

(anti)neutron decay-time:τ= 900sec, 　 yield time ｔ = 0.2sec.

ab

ba

mEabCwhere

EECEF

/

, / )(

　，

１

22 1/1 /1

),()}/({ )(

mcwhere E

EFtEG，

τ

3. Computing method and parametersSolve 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

ModelⅠ

GCR

モデル -II

モデル -III

Input 100,000 protons

ModelⅡ

CRAP

ModelⅢ

CRAND

4. Results: Spatial distribution(1)

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-IIIInput 100,000 particles East tail

Antiprotons/Model-IIIInput 100,000 particles West tail

Looks gathering in SAA

Same color means same particle (orbits)

Spatial distribution(4)

Proton rich around 4000 km and antiprotons rich in 2000 km

Low altitude components → SAA

Altitude distribution cross section (Φ=-50deg(SAA) and 130deg(opposite side) )●Protons ●Antiprotons

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)

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

Radiation belts Decayed (anti)protons make Van-Allen radiation belts (CRAND; Cosmic ray Albedo neutron decay ： model )Ⅲ 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 More statistics ！ 100K partilcles→1M…..now,10K/1day(Pentium4,2.4GHz)

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 Theory ・ Simulation （ coming ） Experimental data

Other solar effects magnetic fields, of Sun, Planets