Download New Improved Operational Model for Cosmic Ray Effects in Space

International Conference on Physics in Memoriam
Acad. Prof. Matey Mateev
Peter Velinov, Simeon Asenovski, Lachezar Mateev
Institute for Space and Solar-Terrestrial Research, BAS
Alexander Mishev
Institute for Nuclear Research and Nuclear Energy, BAS
Sodankyla Geophysical Observatory (Oulu unit)
The influences of galactic and solar cosmic rays (CR) in the middle
atmosphere and lower ionosphere are mainly related to ionization and
excitation. In this way, CR modify the electric conductivity in the middle
atmosphere and the electric processes in it. One fundamental problem in the
understanding of interaction between CR and the neutral components in the
atmosphere is precisely determination of the electron production rate profiles.
The effects of galactic and solar cosmic rays in the middle atmosphere can
be computed with our model CRIMA. We take into account the CR modulation by
solar wind and the anomalous CR component also. A new analytical approach for
CR ionization by protons and nuclei with charge Z in the lower ionosphere and
the middle atmosphere is developed. For this purpose, the ionization losses
(dE/dh) for the energetic charged particles according to the Bohr-Bethe-Bloch
formula are approximated in different energy intervals (two ionization losses
intervals, one charge Z decrease interval and intermediate coupling intervals).
Electron production rate profiles q(h) are determined by the numerical
evaluation of a 3D integral with account of cut-off rigidities. For calculations are
used computer algebra systems Wolfram Mathematica 7 and Maple 14, and
Pascal procedures.
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


An introduction in Cosmic Ray Ionization Model for the
Atmosphere (CRIMA)
Reviews of the main results and computer simulations
made by CRIMA
Some results by CORSIKA simulations in middle and lower
atmosphere
Future development and conclusions





CR are main ionization agent in middle atmosphere and lower
ionosphere
The influence of CR penetration in the Earth’s atmosphere is
important for understanding of the solar-terrestrial relationships and
space weather
The presented model is developed on the base of Bohr-Bethe-Bloch
theory for ionization losses due to charged particles penetration
through substance
This new generalized model contributes to the better accuracy of the
problem solution towards the experimental data
An intermediate transition region between neighbouring energy
intervals is introduced and the charge decrease interval is taken into
account
104 m-2 s-1 ~ 109 eV
10-2 km-2 yr-1 ~1021 eV
“knee”
“ankle”
Energy intervals approximation in six steps of the ionization losses
function according to Bohr-Bethe-Bloch theory and with account of
experimental data :
2.57  103 E 0.5

0.23
1540 E
2
 0.77
1 dE 
231 Z E


 dh 68  Z 2 E 0.53
1.91 Z 2

2
0.123

0.66  Z E
if kT  E  0.15 MeV/n
, interval 1
if 0.15  E  Ea  0.15Z 2 MeV/n , interval 2
if Ea  E  200 MeV/n
, interval 3
if 200  E  850 MeV/n
, interval 4
if 850  E  5  103 MeV/n
, interval 5
if 5  103  E  5  10 6 MeV/n
, interval 6
E – kinetic energy of particles
kT – thermal energy
Interval 2 – charge decrease interval
Z – charge of the penetrating particle
(1)


The energy cut-offs (atmospheric and geomagnetic) determined the
starting point of CR differential spectrum at the top of the atmosphere
The atmospheric cut-offs are derived for those values of the traveling
substance path, which correspond to the actual energy interval of the
ionization losses function
~
h
E

Emin
where:
h
dE
   (h)dh    h  H (h)
1  dE  h

 1
  dh 
~ - traveling substance path
h
ρ(h) - neutral density in the atmosphere at altitude h
H(h) – scale height
( 2)


Interval 1
1285 ~
0.5 
E A1 h   
h  kT  
 A

2
(3)
Interval 2 (charge decrease interval)


1185.8 ~ 

0.5
E A2 h   0.150.77  0.9228 0.150.5  kT  
h
A



1 / 0.77
(4)
Interval 3


EA3 h  Ea1.77  0.3182  Z 2 0.150.5  kT 

 0.345  Z E
2
0.77
a
 0.15
0.77

0.5



~ 1/1.77
 408.87 Z / A h
2
(5)

Interval 4





Z2 ~
0.5
1.53
E A4 h   200  104.04
h  0.081 Z 2 0.150.5  kT  
A



 0.088  Z 2 Ea0.77  0.150.77  0.254  2001.77  Ea1.77

1/ 1.53
(6)
Interval 5


1.91 Z 2 ~
0.5
E A5 h  
h  850  1.49 103  Z 2 0.150.5  kT  
A




 1.6 10 3  Z 2 Ea0.77  0.150.77  4.67 10 3 2001.77  Ea1.77  0.018  8501.53  2001.53 

(7)
Interval 6



Z2 ~
0.877
E A6 h   5000
 0.579
h  4.5 104 Z 2  0.150.5  kT 0.5  4.88 104  Z 2 E 0.77  0.150.77 
a
A






 1.4110 3 2001.77  Ea1.77  5.56 10 3 8501.53  2001.53  1257,45]1/ 0,877

(8)

The boundary crossing defines the energy transfer over the interval limits

Boundary crossing between intervals 1 and 2


1285 ~ 

E21 h   0.150.5  1.08 Ek0.77  0.150.77 
h
A 


2
(9)
Boundary crossing between intervals 2 and 3


2.9
1185.8 ~ 

E32 h    Ea0.77  2 Ek1.77  Ea1.77 
h
Z
A


1 / 0.77
(10)

Boundary crossing between intervals 3 and 4

408.87  Z 2
1.77
1.53
1.53
E43 h   200  3.93 Ek  200

A




~
h

1 / 1.77
(11)
Boundary crossing between intervals 4 and 5


 
~ 1 / 1.53
E54 h  8501.53  54.47Ek  850  104.04 Z 2 / A h

Boundary crossing between intervals 5 and 6



~
E65 h  5000 1.91 Z 2 / A h  3.3 Ek0.877  50000.877

(13)
(12)


They define the starting energy values of the interval limits before
entering of charged particles in the atmosphere
Initial energy of boundary between intervals 1 and 2
1185.8 ~ 

E0.15; 2 h   0.150.77 
h
A



1 / 0.77
(14)
Initial energy of boundary between intervals 2 and 3


 
~ 1 / 1.77
EEa ,3 h   Ea1.77  408.87 Z 2 / A  h
(15)

Initial energy of boundary between intervals 3 and 4

 

~ 1 / 1.53
E200, 4 h   2001.53  104.04  Z 2 / A  h

Initial energy of boundary between intervals 4 and 5


~
E850,5 h   850  1.91 Z 2 / A h

(16)
(17)
Initial energy of boundary between intervals 5 and 6


 
~ 1/ 0.877
E5000,6 h  50000.877  0.579  Z 2 / A  h
(18)


They define the energy decrease in the energy intervals without
boundary crossings
Energy decrease law in interval 1
1285 ~ 

E1 h    Ek0.5 
h
A



2
(19)
Energy decrease law in interval 2
1185.8 ~ 

E2 h    Ek0.77 
h
A


1 / 0.77
(20)

Energy decrease law in interval 3

 

~ 1 / 1.77
E3 h  Ek1.77  408.87 Z 2 / A  h

Energy decrease law in interval 4
~
E4 h  Ek1.53  104.04  Z 2 / A h 
1 / 1.53

(22)
Energy decrease law in interval 5


~
E5 h  Ek 1.91 Z 2 / A  h

(21)
(23)
Energy decrease law in interval 6


 
~ 1 / 0.877
E6 h  Ek0.877  0.579  Z 2 / A  h
(24)


The improved CR ionization model includes the electron production rate
terms in 6 energy intervals of the ionization losses function and 5
intermediate transition region terms between the basic intervals
Lower boundary of integration Emin. The following case of lower integration
boundary is assumed:
kT  EA1(h)  Emin  0.15 < Ea MeV/n



(25)
The lower bound of integration Emin is chosen as the maximum of the
atmospheric cut-off and the geomagnetic cut-off rigidity
The case of vertical penetration of cosmic rays is considered
This model can be extended to the 3-dimensional case in the Earth
environment with introduction of the Chapman function
E0.15; 2  h 
 0.15

0.5
0.5
qh  
2570  DE E1 h  dE   DE E21 h  dE  
Q 
 Emin

0.15

 h  
EEa , 3  h 
 Ea

0.23
0.23
1540  DE E2 h  dE   DE E32 h  dE  
 E0.15; 2 h 

Ea
E200, 4  h 
 200

0.77
0.77
231 Z   DE E3 h  dE   DE E43 h  dE  
 EEa , 3 h 

200
2
E850, 5  h 
 850


0
.
53
0.53
68  Z 2   DE E4 h  dE   DE E54 h  dE  
 E200, 4 h 

850
5000
E5000, 6  h 
dE


E5 h dE 
D
E

dh
E8 5 0, 5  h 

5000
dE
DE  E65 h dE  0.66  Z 2
dh
E

 D E E h
5000, 6
0.123
6
h


dE 


• The electron production rate values are proportional to the square of the charge (Z2),
flux intensity in the different energies and the neutral density in middle atmosphere
• Above 90 km ACR ionization dominates over GCR ionization
• The geomagnetic cut offs reflect the
influence of the geomagnetic field on
the CR penetration in the middle
atmosphere of the Earth.
• For the higher Rc are obtained the
profiles with smaller values.



CORSIKA (COsmic Ray SImulations for KAscade) is a
program for detailed simulation of extensive air
showers initiated by high energy cosmic ray particles
Hadronic interactions at lower energies are described
either by the GHEISHA interaction routines, by a link
to FLUKA
Version CORSIKA 6.970 from July 19, 2010 (D. Heck et
al.)
1 1
Y ( x, E )  E ( x, E ) 

x Eion
Ion rate

q(h, m )   D( E , m )Y (h, E )   (h)dE
E0
Total ionization
EM ionization
Muon ionization
Hadron ionization
1 GeV Protons
5
10
Total Ionization
EM ionization
Muon ionization
Hadron ionization
10 GeV Protons
6
10
4
10
5
Y [sr cm g ]
3
2 -1
2 -1
Y [sr cm g ]
10
10
2
10
4
10
3
1
10
10
0
10
2
10
0
200
400
600
0
800
200
-2
600
800
1000
1200
-2
Atmospheric Depth [g cm ]
100 GeV Protons
400
Atmospheric Depth [g cm ]
Total ionization
EM ionization
Muon ionization
Hadron ionization
1 TeV Protons
Total ionization
EM ionization
Muon ionization
Hadron ionization
7
10
6
2 -1
Y [sr cm g ]
2 -1
Y [sr cm g ]
10
5
10
6
10
5
10
4
10
4
10
0
0
200
400
600
800
-2
Atmospheric Depth [g cm ]
1000
200
400
600
800
-2
Atmospheric Depth [g cm ]
1000
Y ~ spectrum
Total ionization
EM ionization
Muon ionization
Hadron ionization
1.5 GeV Protons
5 GeV protons steep spectrum
70 deg inclined
Total ionization
EM ionization
Muon ionization
Hadron ionization
6
10
5
2 -1
Y [sr cm g ]
2 -1
Y [sr cm g ]
10
4
10
5
10
4
10
3
10
2
3
10
10
0
200
400
600
800
1000
-2
Atmospheric Depth [g cm ]
0
200
400
600
800
1000
-2
Atmospheric Depth [g.cm ]
Total ionization
EM ionization
Muon ionization
Hadron ionization
spectrum of 9 GeV protons
70 degrees inclined
6
70 degrees inclined
6
10
2 -1
Y [sr cm g ]
2 -1
Y [sr cm g ]
10
Total ionization
EM ionization
Muon ionization
Hadron ionization
spectrum of 15 GeV protons
5
10
5
10
4
10
4
10
3
10
0
3
10
200
400
600
800
-2
0
200
400
600
800
-2
Atmospheric Depth [g.cm ]
1000
1200
Atmospheric Depth [g.cm ]
1000
qsolar minimum
qsolar maximum
100
90
Experimental
data
80
-3
q [ion pairs s cm ]
70
-1
60
50
40
30
20
10
0
0
200
400
600
800-2
Atmospheric Depth [g cm ]
1000
1200
Fluka
15 GeV protons steep spectrum
70 deg inclined
Total ionization
EM ionization
Muon ionization
Hadron ionization
Gheisha
Total ionization
EM ionization
Muon ionization
Hadron ionization
2 -1
Yield function Y [Ion pairs sr cm g ]
6
10
5
10
4
10
3
10
2
10
0
200
400
600
800
-2
Atmospheric Depth [g cm ]
1000
summer profile
winter profile
US standard
Protons 1 GeV
2 -1
Yield function Y [sr cm g ]
5
1,2x10
4
8,0x10
4
4,0x10
0
200
-2
Atmospheric Depth [g cm ]
summer profile
winter profile
US standard
1 TeV protons
7
2 -1
Yield function Y [sr cm g ]
4,0x10
7
2,0x10
0,0
200
400
600
-2
Atmospheric Depth [g cm ]
Rate
Rate
Rate
Rate
100000
Depth [ m, a.s.l.]
10000
1000
100
0,01
0,1
1
10
100
-1
-3
Q [ion pairs s cm ]
1000
10000
h
08 00
h
23 00
h
08 00
h
23 00
40
40
60
60
N
N
N
N
h
Rate 08 00 60N
h
Rate 23 00 60N
h
Rate 08 00 80N
h
Rate 23 00 80N
100000
Depth [ m, a.s.l.]
10000
1000
100
-1
10
0
10
1
10
2
10
3
10
-1
4
10
-3
Q [ion pairs s cm ]
5
10
6
10
Solar Influence on Climate
The general aim is to investigate the effects of solar variability
on the climate of the lower and middle atmosphere. Variations in
the solar spectral irradiance, as well as solar energetic particles
and galactic cosmic rays may impacts on the thermodynamic,
chemical, and microphysical structure of the atmosphere.
Space Weather
"Space Weather" is a term related the science and applications
arising from short-term variations of the Sun, propagation of
energetic particles and electromagnetic emissions through
interplanetary space, and effects on technology and humans orbiting
in geospace and on the Earth's surface. It includes rapid phenomena
such as solar flares and coronal mass egections, effects of shock
waves at the magnetosphere, global magnetic storms
Future plans
Improvement of CRIMA
Operational CRIMA model for computer simulations and visualization
Determination of basic parameters in heliophysics and space physics
Application of CRIMA model
Ionization rate
Atmospheric chemistry
Comparison with
experimental data