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1

INTERNATIONAL STANDARD

ISO TS 15391
VERSION 2004 October

Technical Specification



_____________________________________________________ Space Environment (Natural and Artifical) Probabilistic model for fluences and peak fluxes of solar energetic particles Part I Protons

Technical Specification

_____________________________________________________________


2

ISO TS 15391 VERSION 2004 OCTOBER

FOREWORD

The International Organization for Standardization (ISO) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing international standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. Draft international standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an international standard requires approval by least 75 percent of the member bodies casting a vote. International Standard ISO WD 15391 was prepared by Technical Committee ISO/TC 20, Aircraft and Space Vehicles; Sub-Committee SC 14, Space Systems and Operations, Working Group WG4, Space Environment (Natural and Artificial).


3

ISO TS 15391 VERSION 2004 OCTOBER

CONTENTS

Page

1. Applicability scope 2. Definitions, meanings, abbreviations 3. Principles of the model 4. Calculation techniques 5. Prompt calculation technique Tables

4 5 6 8 11 13


4 ISO TS 15391 Space environment (natural and artificial) Probabilistic model for SEP fluences and peak fluxes Part I: Protons

1. APPLICABILITY SCOPE

The present Specification is intended for calculating the probability for SEP event protons to have an impact on hardware and on biological and other objects when in the space. The Specification establishes a probabilistic model for the 4 Â 104 MeV SEP event proton fluences and peak fluxes in the near-Earth space beyond the Earth magnetosphere under varying solar activity.


5 ISO TS 15391 2. DEFINITIONS, NOTATION, AND ABBREVIATIONS Term Solar energetic particles or Solar cosmic rays Solar energetic particle event Wolf ( = sunspot) number Notation Abbreviation SEP, or SCR SEP event W Definition High-energy (4 MeV) charged particle of solar origin. Appearance of the high-energy charged particle flux caused by the solar chromosphere flare and (or) the solar coronal ejection (CME). W=k(10g+f), where g is sunspot group number; f is the total sunspot number on the visible solar disc. k is the coefficient adjusting various

observation conditions.
Solar activity level 13-month smoothed month sunspot number or predicted by NOAA month sunspot number: INTERNET http://www.sec.noaa.gov/Data/ Calendar time period for that the SEP peak flux or fluence is model calculated. The accidental number of the SEP events during the some observation or space mission duration. The mean number of SEP events observed or predicted for large number observation periods or mission duration. Proton energy ­ [MeV]. Proton rigidity ­ [MV] The total (time-integrated) number of protons in a given SEP event (or in a set of SEP events) that traverse a unit area from all directions from solid angle 4 [proton/cm2]. Differential proton fluence energy (E) distribution in a single SEP event (or in a set of SEP events) [proton/(cm2·MeV)]. Integral proton fluence energy (E) distribution (at E above a given level) in a given SEP event (or in a set of SEP events) [proton/cm2]. The 30 MeV proton fluence of SEP event 2 [prot/cm ]. The time-maximum number of the protons in a single SEP event that traverse a unit area normally to a given observation direction in unit time through unit solid angle 2 [proton/(cm ·sr·s)].The fluxes of protons with different energy reach maximum values at different times. Differential proton peak flux energy (E) distribution in a given SEP event (or in a set of SEP events) [proton/(cm2srsMeV)]. Integral proton peak flux energy (E) distribution in a given SEP event (or in a set of SEP events) [proton/(cm2srs)]. Probability for a given fluence of SEP with energy E to be exceeded. Probability for a given peak flux SEP with energy E to be exceeded.

Time period for that the calculations by Specification are possible Solar energetic particle events number Mean solar energetic particle events number Proton energy Proton rigidity Proton fluence

T n E R F

Differential proton fluence energy spectrum Integral proton fluence energy spectrum SEP event size Proton peak flux

dF/dE F(E) F(30) f

F(E) F F

E

30

Differential proton peak flux energy spectrum Integral proton peak flux energy spectrum Fluence probability function Peak flux probability function

df/dE f(E)

f(E) f

E

( FE
( f
E

)

)


6 ISO TS 15391 3. PRINCIPLES OF THE MODEL 3.1. The model establishes the sizes of the SEP event proton fluences and peak fluxes, which are expected, with probability , to get exceeded at a given solar activity level within a time interval T. 3.2. The solar activity level is described by smoothed mean month sunspot (Wolf) numbers . 3.3. Angular distribution of SEP fluxes in the Earth orbit beyond the Earth's magnetosphere is taken to be isotropic.

3.4. The SEP event size is taken to equal E 30 MeV fluence - F30 (proton/cm2),
or peak flux f30 (proton/(cm2ssr)). 5 3.5. The Wolf number dependence of the mean accepted F30 10 proton/cm2 or f30 0.12 proton/(cm2ssr) SEP events number is determined to be equal as:

=1.35·10-2


i

m

< Wi >

(1)

were m is the number of months with solar activity each during time interval T. 3.5.1 The differential distribution function of the F30 10 5 proton/cm2 SEP event number is taken to be the power-law with the exponential cutoff:

dN dF30

dN = Const dF30

- F301.32 , F30 exp 9 9 10

(2a)

3.5.2 The differential distribution function of the f

30

0.1 2 (proton/(cm2ssr) SEP event number

dN is taken to be the power-law with the exponential cutoff: df 30

dN = Const df 30

f

-1.32 30

f 30 exp 3 8.7 10

,

(2b)

Since the differential distribution functions are used in the Specification solely to simulate the sizes of random SEP events (the Monte-Carlo method), the value of Const is not needed in the calculations and, therefore, is not defined in the Specification.


7 ISO TS 15391 3.6. The differential energy spectra of the proton fluences (F) and peak fluxes (f) (referred to henceforth as energy spectra of ­ mean both ­ F and f) are power-law functions of proton rigidity R:

dR R dE = C (E )dE = (R ) dE 239
where

-

dR dE ; dE

(3)

R = E E + 2M o c

(

2

)

dR and = dE

R 2 + M oc R

(

22

)

=

1



,

E is the proton kinetic energy in MeV; Moc2 = 939 MeV is the proton rest energy; = v/c is relative particle velocity. The value of R= 239 MV corresponds to energy E = 30 MeV. At E30 the spectral index = o . At E<30 MeV, the SEP event proton energy spectra exhibit a droop. The differential proton energy spectra are described again by formula (3) with spectral index, which value is changing with energy:

E = o , 30
where is the droop index. Therefore, the following 3 parameters are used to describe the differential proton energy spectrum in range 4 E 104 MeV. spectral coefficient spectral index , - o,



(4)

(spectral) droop index - . 3.7. Calculation of the parameters of the differential proton energy spectra 3.7.1. Sets of the differential energy spectra parameters and and their random values. The set of parameters

y

(i )

( = oi ) ,

{

(i )

}
(
x- < x > 2
2 x

(5)

(y denotes any of the parameters , ) are described in terms of log normal distributions: .

(x ) =

1



x

2

exp-

)

2

,

(6)

where: x = log y (i ) ; = is the mean logarithm of the parameter o or ; x is the standard deviation of the log distribution.

()


8 ISO TS 15391 3.7.2. The mean spectral index o of proton fluence or peak flux spectrum, independent of SEP event size, is =5.9 =0.77 and the standard deviation of the log distribution is (6a)



lg

o

= 0.15

(6b)

if F30<1.0·109 for fluences or f30<1.2·103 for peak fluxes and



lg

o

= 0.075

(6c)

F301.0·109 for fluences or f301.2·103 for peak fluxes. 3.7.3. The mean spectral droop index of proton fluence or peak flux depends on event size F30 or f30 and spectral index o . The parameters of the lognormal functions for determining random values of are in fact determined for the value of A= +1 (to avoid zero and negative values):

< log A >= log(1.16

0.059

o 5.84

0.143

) and



logA=0.0777

(7)

were in case of proton fluence =F30/106 and for peak flux =f30/1.2. After that the lognormal distribution for A value determination is used and the random value is

determined as:

=10 A-1
If the Monte-Carlo generated spectral droop index is:

(8a)

<(0.4

o

0.4

-1)

(8b)

this random value of is neglected and a new random value is generated. 3.7.4. The spectral coefficient of the differential SEP event proton fluence or peak flux spectrum (Eq.3) for a given event size
30

(F30 or f30) is determined as: (9)

C =

30 ( o - 1) 239

4. CALCULATION TECHNIQUES The procedure to calculate the SEP event proton fluence sizes or peak fluxes, which are expected with a given probability to get exceeded at a given solar activity level within a time interval T, is as follows: 4.1. Calculation of the mean number of SEP events of fluence F30 105 protons/cm2 or peak flux f30 0.12 protons/(cm2· s·sr) size over time interval T - according Eq.1


9 ISO TS 15391 4.2 Calculation of N mission versions - n "random" SEP events being calculated for each of the versions. The cumulative fluences F(E) of every version are the sum of fluences each from n events, the peak flux of version f(E) is maximum peak flux from all n events. 4.2.1. The "random" number of SEP events for each mission version is calculated from the mean . If is small ( < 8), use is made of the Poisson distribution, which implies that the probability for n SEP events to be observed with the mean value is:

p( n, n ) =

exp( - n ) n n!

n

(10)

i.e., Kn = N·p(n,) versions are calculated at the number n of the SEP events with Kn 1. If 8, the Monte-Carlo method may be used to calculate the random SEP event number, with the values n taken according to the normal (Gaussian) distribution for each of the next mission versions.

p (n, < n > ) =
where =

[< n > - n] 2 , exp - 2 2 2 1

(11)

.
(i) 30

4.2.2. The SEP event fluence size F

within the F30 10 5 proton/cm2 fluence range or peak flux size

f

(i ) 30

within the f

30

2 0.1 2 proton/(cm · s·sr) range are Monte-Carlo simulated for each of the SEP

event "i" (1 i n) according to the distribution functions ­ (Eq.s. 2a or 2b). 4.2.3 The differential proton fluence F
(i )

(E )

or peak flux f

(i )

(E )

energy spectrum in each random

( SEP event i is determined using the parameters C ( i ) , oi ) , (i )

The calculation procedure is the following sequence of operations: · the Monte-Carlo method is used to find a random value of the differential proton energy spectrum
( index oi ) from lognormal distribution with parameters Eqs. 6a,b,c;

·

the Monte-Carlo method is used o find a random value of the differential proton energy spectrum droop index
(i )

by lognormal distribution with parameters Eq. 7-8a,b.

·

Eq. 9 is used to calculate the differential proton fluence or peak flux energy spectrum coefficient

C (i ) ;


10 ISO TS 15391 4.2.4 The integral proton energy spectra for proton fluences or peak fluxes for each SEP event are calculated on base of known spectral parameters of differential spectra:


F ( i ) ( E ) = F
E

(i )

(E )dE

f

(i )

( E ) =


E

f

(i )

(E )dE

(12)

4.2.5 The integral proton fluence energy spectrum is found for each mission version "m" by summing up the fluences F
(i )

( E ) of all n events:
n i

Fm ( E ) =



F

(i )

( E )

(13)

The integral proton peak flux energy spectrum is determined for each mission version "m" by selecting the highest flux for each of the energies E among the peak fluxes in n events:

f m ( E ) Max f

( ( E ))
(i )

(14)

4.2.7. Knowledge of the energy spectra of fluences and peak fluxes for a random space mission permits in the course of calculations to determine the fluence or peak flux probability functions ( selected energies Ek from 4 to 104 MeV. In order to do this: 4.2.7.1 The selected energy scale Ek according to users request is chosen. The recommend step may be, for example: Ek= 3.981 10
l -1 L

E

)

for

where L=5 or 10, or 20 or ...is the scale factor and l=1,2.3.....

4.2.7.2. A scale of the argument sc j is chosen ­ fluences or peak fluxes with a step not larger than

10

0.01 j

where j=1,2.3.....The initial value of the argument for fluences must be 105, for peak fluxes 0.12. For each space mission version the integral proton fluences F(Ek) or peak fluxes f(Ek) are

4.2.7.3.

calculated according to (Eq.s 13 and 14) for selected energies Ek. 4.2.7.4. The probability functions are calculated for selected energies Ek. The value of 1/N is added to the probability function value

(

k, j

)

for all argument values if

k, j

sc j .

As a result by the end of the calculation of all N space mission versions, the fluence or peak flux probability functions are also ready to be used.


11 ISO TS 15391 4.2.8. The fluence or peak flux probability functions ( FE sizes or the proton fluences FE or peak fluxes f
E

)

or ( f

E

)

are used to calculate the

for energies above E at a given value. In other
E

words, the fluences and peak fluxes which exceed FE and f

will be observed with the probability of .

4.2.9. Applied problems can readily be solved using the energy spectra for given and values, rather than the families of the integral probabilities ( FE

)

or ( f

E

)

. For this purpose, the sizes of

fluences FE or peak fluxes fE must be calculated according to the family of curves (4.2.4) for a set of energies at a given probability ( ( FE ) = const or ( f
E

)

= const).

4.2.10. The integral spectra FE and fE calculated for given probability, can be used to find the parameters of the differential spectra F(E) or f(E) in the form of Eq.3-4, which describe the integral energy spectra F or fE, (after integration). 5. PROMPT CALCULATION TECHNIQUE 5.1. The present Specification includes information on the results of calculating the SEP event proton fluences and peak fluxes for the most frequently used integral probability sequence (= 0.9, 0.842, 0.5, 0.158, 0.1, and 0.01) and for the sequence of the expected mean SEP event numbers n =1, 2, 4, 8, 16, 32, 64, 128, and 256. The information is presented to be the parameters of the differential energy spectrum, whose form is similar to the differential energy spectra of single SEP events (see Eq.s (3)-(4) above). The Specification tabulates the parameters
E

C

,< n >

,

o ,< n >

, and

,< n >

for the above sequences of the and values. The prompt particle fluence and peak flux calculations involve: 5.1.1.Calculation of the mean number by Eq. 1. In all cases the number of mission versus N was taken equal to 4105. 5.1.2 Calculation of three parameters C parameters from
,< n >

,

o ,< n >

, and

,< n >

using the tabulated spectral

Tables 1-3 for proton fluences and Tables 4-6 for proton peak fluxes for probabilities =0.9, 0.842, 0.5, 0.184, 0.1, 0.01 are done.


12 ISO TS 15391

If the resultant data on the mean expected SEP event number and on the prescribed probability fail to coincide with the tabulated and values, then three parameters must be found by interpolating the tabulated data; 5.1.3 After that, the resultant values of the three parameters are substituted in Eq.s. (3) and (4) to
calculate the differential proton energy spectra. 5.1.4. In case the integral proton energy spectra are to be calculated, they must be energy-integrated.


13 ISO TS 15391

Table 1 (corrected, October, 12, 2004) Spectral coefficients of the SEP proton fluences differential energetic spectrum C (cm MeV ) 1 2 4 8 16 32 64 128 256 1.92E+04 1.37E+05 9.42E+05 5.05E+06 2.15E+07 7.50E+07 2.06E+08 0.9 4.53E+03 3.46E+04 2.37E+05 1.48E+06 7.25E+06 2.85E+07 9.04E+07 2.35E+08 0.842 0.5 8.43E+03 5.76E+04 3.66E+05 1.99E+06 8.56E+06 2.90E+07 7.51E+07 1.71E+08 3.68E+08 0.158 2.99E+05 1.60+06 6.50E+06 2.04E+07 4.66E+07 9.20E+08 1.72E+08 3.16E+08 5.65E+08 0.1 9.62E+05 4.21E+06 1.48E+07 3.43E+07 6.78E+07 1.21E+08 2.10E+08 3.60E+08 6.25E+08 0.010 3.77E+07 6.57E+07 1.04E+08 1.49E+08 2.09E+08 2.88E+08 4.09E+08 5.87E+08 8.83E+08
-2 -1
,< n >

Table 2 (corrected, October, 12, 2004)

Spectral indexes of the SEP proton fluences differential energetic spectrum



o , ,< n >

1 2 4 8 16 32 64 128 256

0.9 5.92 5.45 5.31 5.21 5.14 5.12 5.05

0.842 8.01 5.68 5.40 5.27 5.19 5.13 5.09 5.04

0.5 6.24 5.47 5.31 5.23 5.15 5.09 5.04 4.99 4.97

0.158 5.29 5.22 5.14 5.11 5.02 4.97 4.93 4.88 4.85

0.1 5.29 5.16 5.12 5.02 4.92 4.92 4.87 4.81 4.80

0.010 4.98 4.92 4.86 4.76 4.68 4.61 4.59 4.57 4.61


14 ISO TS 15391

Table 3 (corrected, October, 12, 2004) Droop indexes of the SEP proton fluences differential energetic spectrum

,< n >

1 2 4 8 16 32 64 128 256

0.9 0.11 0.03 0.05 0.08 0.12 0.16 0.17

0.842 0.73 0.06 0.03 0.06 0.10 0.13 0.16 0.17

0.5 0.18 0.03 0.04 0.08 0.13 0.16 0.18 0.18 0.18

0.158 0.04 0.10 0.14 0.20 0.21 0.20 0.20 0.18 0.17

0.1 0.08 0.14 0.20 0.21 0.22 0.20 0.19 0.17 0.16

0.010 0.22 0.22 0.21 0.18 0.15 0.12 0.10 0.07 0.06

Table 4

Spectral coefficients of the SEP proton peak fluxes differential energetic spectrum C ,< n > (cm-2sr-1s-1MeV-1) /P 1 2 4 8 16 32 64 128 256 1.40E-02 0.146 0.495 2.35 8.33 23.0 45.9 0.9 5.02E-03 2.49E-02 0.150 0.83 3.60 12.2 28.1 54.7 0.842 0.5 8.91E-03 5.24E-02 0.311 1.58 5.97 18.1 36.5 61.3 96.1 0.158 0.316 1.61 6.13 18.7 36.1 61.7 92.8 134 181 0.1 1.03 4.23 13.9 30.9 53.6 82.4 122 160 216 0.010 36.1 64.5 95.7 137 179 226 274 320 314


15 ISO TS 15391

Table 5 Spectral indexes of the SEP proton peak fluxes differential energetic spectrum 1 2 4 8 16 32 64 128 256 5.81 5.39 5.27 5.19 5.08 5.06 5.12 0.9 8.11 5.56 5.32 5.23 5.16 5.08 5.00 5.13 0.84 0.5 6.21 5.42 5.29 5.20 5.10 5.05 4.97 4.88 5.11 0.158 5.29 5.21 5.11 5.07 4.94 4.87 4.78 4.71 5.07 0.1 5.26 5.14 5.08 4.99 4.89 4.80 4.73 4.62 5.03
o ,< n >

0.010 4.89 4.84 4.78 4.70 4.57 4.49 4.44 4.35 4.71

Table 6 Droop indexes of the SEP proton peak fluxes differential energetic spectrum 1 2 4 8 16 32 64 128 256 0.9 0.08 0.02 0.06 0.12 0.15 0.22 0.28 0.842 0.81 0.03 0.03 0.07 0.13 0.18 0.21 0.30 0.5 0.17 0.01 0.04 0.10 0.14 0.21 0.21 0.19 0.27 0.158 0.04 0.11 0.15 0.21 0.20 0.20 0.18 0.15 0.24 0.1 0.09 0.14 0.19 0.22 0.20 0.18 0.16 0.12 0.21
,< n >

0.010 0.18 0.19 0.17 0.15 0.11 0.08 0.00 -0.03 -0.02