Evaluation of the flux Evaluation of the flux of CR nuclei inside of CR nuclei inside the magnetospherethe magnetosphereP. Bobik, G. Boella, M.J. Boschini, M. Gervasi, P. Bobik, G. Boella, M.J. Boschini, M. Gervasi,

D. GrandiD. Grandi, K. Kudela, S. Pensotti, P.G. Rancoita, K. Kudela, S. Pensotti, P.G. Rancoita

Outline● Abundances at 1 AU● Observation data: AMS-01 & HEAO-C3● Dependence on Z/A● TF● AMS-01 He data reproduced using the TF● Spectra of p, He, C and Fe at AMS-01 orbit● Abundances at AMS-01 orbit● Conclusions

The Cosmic abundance Among the Galactic Cosmic Rays (GCR) protons

are largely the most abundant, but also the amount of Helium nuclei and electrons is relevant. In addition the presence of heavier nucleons, like Carbon, Nitrogen, Oxygen and Iron, is not negligible, in particular taking into account the amount of energy they can deposit.

The knowledge of the isotopic abundances can affect, for instance, the calculations regarding the radiation damage and dose at LEO’s.

The Cosmic abundanceEnergy spectrum of protons, Helium, Carbon, and Iron at 1 AU.

The Data setWe have get data of protons and Helium from the AMS-01 detector in the energy range 0.2-200 GeV (0.074-113 GeV/n), and heavier ions (from Z=4 to Z=28) from the HEAO-3-C2 in the energy range 0.6-35 GeV/n. Data have been collected almost in comparable periods of solar activity (similar sunspot number and comparable modulation potential), HEAO: 1980, AMS-01: 1998. Experimental conditions are also comparable: altitude and inclination of the orbit, angular acceptance of the detectors.

The effect of MagnetosphereThe Earth magnetic

field provides a shield against the penetration of CR down to the Earth surface. The result is a rigidity cut-off below which CR can not penetrate

The value of the rigidity cut-off is position dependent. We have considered the AMS geomagnetic regions (M).

Transmission FunctionWe have computed trajectories related to 3600 locations uniformly distributed over a complete sphere surrounding the Earth at an altitude of 400 km.

Trajectories are back-traced using the IGRF 2000-2005 as internal field model and the Tsyganenko T96 external field model.

We have used a magnetopause following the Sibeck equations and have introduced an empirical magnetosphere upper boundary at 25 Re in the night-side region.

The lower boundary is a sphere containing the 99% of the atmosphere, placed at 40 km of altitude.

Transmission FunctionWe have then computed the Transmission Function, the probability for a CR to penetrate inside a region M: a particle with a rigidity lower than the rigidity cut-off can not enter the magnetosphere. This threshold value is decreasing going towards the magnetic poles.

Flux inside the magnetosphere

The cut-off for the same geomagnetic region occurs at the same value of rigidity, but at different values of kinetic energy: inside the magnetosphere the rigidity represents the natural parameter describing CR spectra.

Looking at the TF, or at the flux spectrum, in terms of kinetic energy instead of rigidity we can see a shift in nuclei respect to protons, because the ratio:

o Z/A 1/2 for nuclei

o Z/A 1 for H (protons)

Transmission Function

Comparison with data

Flux of primary He CR inside the magnetosphere

Calculations are compared with AMS-01 data

Flux inside the magnetosphere

Flux_primaries = TF * Flux_cosmic

protons (red), He (green), C (blue), and Fe (cyan) geomagnetic regions: M1 and M7

Relative abundances Cosmic Abundances

The ratio has been computed using the integral flux above 0.8 GeV/nucleon.

He/p = 6.66 x 10-2 C/p = 1.88 x10-3 Fe/p = 1.78 x 10-4

The Cosmic abundanceEnergy spectrum of protons, Helium, Carbon, and Iron at 1 AU.

Relative abundances Inside the Magnetosphere

The ratio has been computed using the total flux integrated in each magnetic region.

Geomagnetic region

He/p C/p Fe/p

M1 1.6 10-1 5.6 10-3 6.5 10-4

M2 1.6 10-1 5.4 10-3 6.6 10-4

M3 1.5 10-1 5.4 10-3 6.6 10-4

M4 1.5 10-1 5.1 10-3 6.0 10-4

M5 1.6 10-1 5.1 10-3 6.3 10-4

M6 1.5 10-1 4.8 10-3 5.4 10-4

M7 1.4 10-1 4.1 10-3 4.3 10-4

Flux inside the magnetosphere

Flux_primaries = TF * Flux_cosmic

protons (red), He (green), C (blue), and Fe (cyan) geomagnetic regions: M1 and M7

Relative abundances Enhancement factors

Enhancement_factor (M) = Ratio (M) / Ratio_cosmic

Geomagnetic region He/p C/p Fe/p

M1 2.4 3.0 3.7

M2 2.4 2.9 3.7

M3 2.3 2.9 3.7

M4 2.3 2.7 3.4

M5 2.4 2.7 3.5

M6 2.3 2.6 3.0

M7 2.1 2.2 2.4

Conclusions: Results Inside the magnetosphere the rigidity selection of the CRs is responsible for the isotopic abundances.

The rigidity cut-off for ions occurs at lower kinetic energy respect to protons.

At AMS-01 orbit the ions/protons flux ratio is larger than the cosmic flux ratio by a factor ~ 2-3 up to the magnetic region 7.

This result is depending on the mass number and on the geomagnetic region considered.

The TF approach can allow one to calculate the isotopic abundances at any orbit once the isotopic flux in known at 1AU.