1. Simulation of 14C production rates for the troposphere and stratosphere in weak geomagnetic intensity at 26,000 yr BP
1 Graduate School of Science and Engineering,
Yamagata University
2 Departments of Physics, Yamagata University
TAIICHI SATO1, HIROHISA SAKURAI 2, YUI TAKAHASHI1
SAORI NAMAI1

2. Introduction
Motivation: In order to investigate periodic variations in 14C concentrations relating to an 11-yr solar cycle at 26,000 yr BP, we have been measuring the 14C concentrations of the single-yr tree rings using AMS.
Atmospheric Δ14C variation
in the duration of yr BP
Variation of the earth dipole moment
in the duration of yr BP
40% weaker
40% higher
The geomagnetic dipole moment is roughly in anti-phase to 14C concentrations.
In the vicinity of 26,000 yr BP, the geomagnetic dipole moment was approximately 40%
of the present days.
For the weak geomagnetic state of the earth, we show simulated results of the 14C production rates.

3. Process to 14C from cosmic rays
Solar modulation of cosmic rays
11-yr cyclic variation~28%
The geomagnetic intensity
at 26,000 yr BP was
40% Weaker
than at the present.
Geomagnetic field
14C
Atmosphere
14C
14CO2
Global carbon cycle
Variation of 14C concentrations
~ 3‰
14C concentrations
~ ?%
Data
What is the solar moderation of 14C concentration at weak geomagnetic fields?

4. The Measurements of the 14C concentrations in single-yr tree rings
KAMINOYAMA Tree Rings
Profile for 14C concentration of single-yr tree rings
at cal BP
approximately cal BP
(Calibration curve : IntCal09)
Preliminary data
Ring number: 100
Diameter: 30cm
Height: 30cm
Ring width:1.0mm
N38◦ 07’ E140◦ 17’
14C concentrations are measured by AMS facilities.

5. Simulation of 14C production rates
EXPACS
(Excel-based Program for calculation
of Atmospheric Cosmic-ray Spectrum)
(Sato T et. al., 2008)
Process of the simulation
Cosmic rays
Expacs calculates neutron spectra
for anywhere in the atmosphere
at the altitudes.
Solar moderation
(Solar moderation parameter : Φ)
Neutron spectrum F (E,h,λ)
EXPACS
Effect of geomagnetic field
(cutoff rigidity : RC)
Atmosphere (Altitude : h)
Neutron spectrum:
F(E,h,λ)[atoms/cm2/s/MeV]
P(h): 14C production rates
F(E,h,λ) : Neutron energy spectrum at
an altitude and an magnetic latitude
N(h): Number density of nitrogen atoms /cm3
s(E): 14N(n,p)14C Cross Section
Calculating 14C production rates

6. Geomagnetic cut-off rigidity
(N. Lifton, D.F. Smart and M.A. Shea,2008)
M*：Geomagnetic dipole moment ratio
M＊＝　M/M1950
（ yr BP : M*=0.4 ）
λ ：Dipolar geomagnetic latitude
(λ<|±60°|)
Geomagnetic latitude (λ)
Solar modulation parameter
(Ilya G, Usoskin et. al., 2011)
We applied for the simulation the solar modulation parameters from1987 to 2009.
11-yr solar modulation
The maximum is at 1991
The minimum is at 1997

7. Comparison between EXPACS and Geant 3
Geomagnetic dipole moment ratio M*=1
Solar modulation parameter Φ = 550
J. Masarik and J. Beer（1999）
Average at EXPACS : 2.19
Average at Geant 3 : 2.21
Geomagnetic latitude (λ)
The 14C production rate by EXPACS was comparable to that by Geant 3.

8. The altitude distributions of the 14C production rates
14C kg/yr/km
14C kg/yr/km
The peak altitude of the 14C production rates is approximately 12 km.
The maxima of the 14C production rates are near the tropopause.
(The tropopuse is approximately 13 km.)

9. The troposphere components of the production rate as a function of geomagnetic intensity
are gradually decreasing to the weak
M*.
The decreasing rate is approximately
2.5% at both the Solar maximum and
minimum of the 11-yr cycle.
The low energy component of primary
cosmic rays increases.
The production rate at the stratosphere
is relatively abundant compared with
at the troposphere.

10. If the variation at the present is 3‰
The variation of 14C production rates related to the 11-yr solar cycle as function of geomagnetic intensity
The S/SM*=1correspond to the M*
The M* in vicinity of 26,000 yr BP is
approximately 0.4.
S/SM*=1
In 26,000 yr BP, the variation of production rates is 1.6 times at the present.
It is estimated that the variation of 14C concentrations related to the 11-yr solar cycle in the vicinity of 26,000 yr BP is 4.8 ‰.
If the variation at the present is 3‰

11. Summary
We have measured 14C concentrations of the single-yr tree rings using AMS,
in order to investigate periodic variations of 14C concentrations relating to
an 11-yr solar cycle at 26,000 yr BP.
We have globally simulated the 14C production rates as functions of latitude,
longitude, and altitude using EXPACS to investigate the affection of weak geomagnetic
intensity to the 14C production.
Results of simulation
The peak altitude of the 14C production rates was approximately 12 km,
indicating the maxima at near the tropopause.
The decreasing rate of troposphere components is approximately 2.5% at both the
Solar maximum and minimum of the 11-yr cycle. It indices the low energy
component of primary cosmic rays increases at stratosphere relatively.
For the geomagnetic intensity in the vicinity of 26,000 yr BP,
the variations of 14C production rates increase to 1.6 times of the variations
of present.
It is estimated that the variation of 14C concentrations related
to the 11-yr solar cycle in the vicinity of 26,000 yr BP was 4.8 ‰
If the variation at the present was 3‰.

12. EXPACS was
developed for the estimation of the atmospheric cosmicray
spectrum based on the “PHITS (Particle and Heavy
Ion Transport code System) based Analytical Radiation
Model in the Atmosphere,” PARMA. It calculates neutron,
proton, He nucleus, muon, electron, positron and
photon spectra for anywhere in the atmosphere at the
altitudes, when we set geomagnetic cut-off rigidity
and solar modulation parameter.
RADIATION RESEARCH 166, 544–555 (2006), Sato Tatuhko, JAEA
RADIATION RESEARCH 170, 244–259 (2008)