A Monte Carlo computer program was developed for the computation of photocurrents and photoemission in gamma (X-ray)-irradiated materials. The program was used for computation of radiation-induced surface currents on space vehicles and the computation of radiation-induced space charge environments within space vehicles

Chadsey, W. L.

Ragona, C.

English

NASA Technical Reports Server

AMONTECARLOPHOTOCURRENT/PHOTOMISSIONCOMPUTERPROGRAM
W.L. Chadsey and C. Ragona
The Re-Entry and Environmental Systems Division
General Electric Company
Philadelphia 19101
Abstract
A Monte Carlo computer program (POEM) has been
developed for the computation of photocurrents and
photoemission in gamma (x-ray)-irradiated materials.
The program has been used for application to the com-
putation of radiation-induced surface currents on space
vehicles and the computation of radiation-induced space-
charge environments (IEMP) within space vehicles. The
program has been successfully correlated with published
expirmental data.
POEM is a composite analytical-Monte Carlo com-
puter program which calculates the photoemission from
a gamma (x-ray)-irradiated slab of material. The pro-
gram uses analytical routines to calculate photon flux
attenuation, energy deposition and electron production
within the slab, and uses a Monte Carlo routine to cal-
culate the electron transport through the slab and the
emission from the slab. The objective of using the
analytical photon transport routine is to avoid the com-
putation time-consuming complexity of a pure Monte
Carlo model. When using a Monte Carlo photon trans-
port routine, in order to produce a sufficient number of
Compton scattering and photoelectric interactions to
afford reasonable statistics for the initial energy-angle
distributions of the electrons requires a great number
of photon histories (typically several hundred thousand
histories). To reduce the computation time required,
an analytical routine has been incorporated in POEM to
compute photon transport.
The POEM program calculates the net photocurrent
within a material and the electron emission current
from a material including the energy flux, energy spec-
trum, and angular distribution for an arbitrary incident
photon spectrum. The emission can be calculated in
either the direction of the incident photon flux or the
reverse direction. In either case the program assumes
normal incidence of the photon flux on the emitting slab,
although with minor modification the program could
treat an arbitrary angle of incidence. It is assumed
that the time-dependence of the electron emission cur-
rent is the same as the time-dependence of the incident
photon flux, i.e. the model is quasistatic.
The emission calculation includes the Compton
electrons, photoelectrons (K and L), and Auger elec-
trons (L) resulting from the scattering and absorption
of the primary x-ray flux. The emission calculation,
at present, does not include second generation (knock-
on) electrons nor the electrons produced by the scat-
tering and absorption of fluorescent or bremsstrahlung
radiation. A study is planned to investigate techniques
for the inclusion of these effects, including a more rig-
orous treatment of the Compton scatter radiation.
I. Introduction
The description of the current density and energy-
angle distribution of gamma ray or x-ray induced
electron emission is required in the study of transient
radiation effects on electrical systems and in the de-
velopment of fast radiation detectors. A rigorous cal-
culation of the electron emission requires both a Monte
Carlo photon transport calculation of the electron
source distributed throughout the irradiat_-_ matter mud
a Monte Carlo electron transport calculation of the in-
tensity and energy-angle distribution of the multiple
scattered electron flux at the emission surface. Be-
cause of the low quantum efficiency for the production
of primary electrons (Compton, Auger, and photo-
electrons) by photons, it has been experienced that a
very large number of photon histories are required in
the Monte Carlo photon transport calculation to produce
a statistically acceptable description of the electron
source. Several hundred thousand photon histories
have been found necessary for a typical incident photon
environment, requiring on the order of 40 minutes
computation time (using the ONE-D (1) code on the GE
635 computer). The need exists for a less costly com-
putational tool. A purely analytical electron emission
model (2, 3), on the other hand, while providing an
inexpensive computation of the electron emission flux,
does not properly treat electron multiple scattering
and so does not provide a valid description of the
angular distribution of emission.
The POEM (photoemission) computer program
was developed to provide a computational tool for the
calculation of photon radiation-induced electron emis-
sion which would be relatively inexpensive to use but
would include a proper treatment of electron multiple
scattering. POEM is a composite analytical-Monte
Carlo program, using analytical routines to calculate
photon flux attenuation and primary electron produc-
tion in the material and a Monte Carlo routine to
calculate the electron transport to the surface of the
material. Whereas a typical electron emission cal-
culation required 45 minutes computation time (on
the GE 635) with a pure Monte Carlo cede, the same
calculation requires only 3 minutes computation time
with POEM, without apparent, significant sacrifice in
accurancy.
POEM calculates the electron emission from a
gamma or x-ray irradiated slab of material. The pro-
gram assumes normal incidence of the x-ray flux on the
emitting slab, although with minor modification the pro-
gram could treat an arbitrary angle of incidence. The
emission current, energy spectrum, and angular dis-
tribution are calculated both in the direction of the in-
cident radiation and in the reverse direction& (Hence,
786
https://ntrs.nasa.gov/search.jsp?R=19720010057 2020-03-17T03:46:38+00:00Z
the program may be used to calculate the net primary
photocurrent across any plane within the irradiated ma-
terial.) It is assumed that the time-dependence of the
electron emission current is the same as the time-
dependence of the incident photon flux, i.e. the model is
quasistatic.
The emission calculation includes the Compton elec-
trons, photoelectrons (K and L), and Auger electrons (L)
resulting from the scattering and absorption of the pri-
mary x-ray flux and (in an approximate treatment) the
Compton scattered x-ray flux. The emission calculation,
at present, does not include second generation (knock-on)
electrons nor the electrons produced by the scattering
and absorption of fluorescent or bremsstrahlung radia-
tion. The electron transport calculation is strictly valid
only for electron energies greater than the K absorption
edge of the emitting material. The code seems to pro-
duce reasonable results, however, down to somewhat
lower energies.
POEM has been evaluated through the comparison of
computational results to published experimental data for
electron emission induced by Cul_ x-radiatlon and Co 60
gamma radiation,and through comparison to superflash
x-ray-induced electron emission data obtained by the
author. The comparisons to the published data are pre-
seated herein.
II. Program Description
II. 1 Photon Transport
The radiation intensity I (photons/cm 2) at the point
x of initiation of electron emission is calculated assam-
ing a simple exponential attenuation of the intensity,
I ix, E7) = Io (E7) e"q'tx (I)
where Io (ET,)is the incident intensity,x is the distance
from the irradiated surface, and_ is the totallinear at-
tenuation coefficient. The assumption of exponential
attenuation, of course, implies the complete absorption
of a photon in any interaction. This is strictlytrue only
of the photoelectric interaction. In a Compton scatter
interaction,the photon recedes from the point of col-
lisionwith reduced energy and altered direction. This
Compton scattered radiation is treated by an approxima-
tion: rather than reducing the photon fluxby decreasing
the energy of each Compton scattered photon while
holding the number of photons constant (which would
censlderably complicate the calculation),the number of
photons Is reduced in each Compton interaction holding
the photon energy constant. Mathematically this is done
by introducing a Compton attenuationcross-section Or'
which is the sum ofthe Compton absorption cross-
section #ct and a fraction f of the Compton scatter
cross-section crs,
_" = _a + f_s (2)
The total linear attenuation coefficient _ is then given by
p a S (3)
where 1.is the photoelectric cross-section and p is the
density. Values for the fudge factor f have been selected
by comparisons of exponential attenuation Calculations to
Monte Carlo calculations.
II. 2 Electron Production
The irradiated slab is divided into incremental slabs
of thicknesses A x such that _tAx << I, i.e. so that the
photon flux variationthrough the zone is calculated in
each zone for which there is a significantprobability of
escape, i.e. in each zone for which the maximum path
length of the electrons produced in the zone is larger
than the normal distance to the emitting surface.
(Remember thatthe maximum electron path length is
considerably greater than the extrapolated electron range
range because of multiple scattering.)
The number of Compten electrons produced (per
cm 2) in a zone, location xi, by photons of energy ET is
CTAx
N I (i e P
c (ET' xi) = (E , xi) - )
where _ = q_ + {rs is the total Compton mass attenuation
coefficient and the photon intensity I (E , x.) is given byt
equation (1). The initial energy-angle _robability dis-
tributlons of the Compton electrons are given by Klein-
Niehina. (4)
The number of photoelectrons produced in the zone
x by photons of energy ETis
_--TAx
Np(ET, xi) = I(E_, xi) (1-e P
where 1" is the photoelectric mass attenuation coefficient.
It is assumed that for all photon energies greater than
the K edge the ratio of L to K photoelectrons produced is
equal to the ratio at just above the K edge, l.e.
n.__L = 1"(E K - ¢)
nK 1"(EK+ _) - 1"(EK- ¢) (6)
where EK is the K edge and ¢is an infinitesimalenergy
increment. The angular distributionof the photoelec-
trons is given by Fischer and Sauter (4),theformer for
low energy photelectrons (_ < < 1), the latterfor high
energy electrons (fie 1).
The number of Auger electrons (L only)produced in
the zone xi by photons of energy ET is
N A (E), Xi) = (1-fK) NK
, P (E , xi) (7)
787
where _ is the number of K photoelectronsproduced
and fK is the K fluorescence yield given by.(5)
4
Z
4
z + 304 (8)
where Z is the atomic number. The angular distribution
of the Auger electrons is assumed isotropic.
The total electron initial energy-angle probability
distribution for each zone of the emitter is calculated by
summing for each photon energy the Compton, photo-
electric and Auger distributions and then integrating
over the photon energy spectrum.
II. 3 Electron Transport
The transport of the electrons to the emitting sur-
face is calculated using the POET (6) Monte Carlo elec-
tron transport program which has been incorporated into
POEM. POET is a condensed history Monte Carlo pro-
gram. In the condensed history Monte Carlo method,
the results of multiple scattering theory are combined
with Monte Carlo techniques to form a consistent ap-
proach to electron transport calculations in the media of
finite dimensions. Since the large majority of electron-
atom interactions involve small angel deflections and
small energy loss, the condensed history random walk
approach is applicable to electron transport ( it is not
applicable to photon transport due to the large scattering
angles involved in the majority of collisions). Rather
than calculate the trajectories of the electrons as they
undergo each coulomb interaction, a random walk com-
putation is performed in such a way that each step takes
into account the combined effect of many collisions. The
electron history is divided into logarithmically-spaced
energy intervals. For each step of the random walk the
path length increment traveled by the electron, corres-
ponding to the energy loss increment, is computed using
the Bethe-Moller stopping power. (7-9) By random
sampling from the angular distributions calculated using
the Goudsmitt-Saunderson theory (10) of multiple scatter,
the direction of travel of the electron after each random
walk step is obtained.
For each electron history the random walk com-
putation is initiated by random selection of an initial
location within the electron production zone (from a
uniform distribution within the zone) and a random se-
lection of the initial electron energy and velocity direc-
tion (from the computed energy-angle probability dis-
tribution for the zone). The random walk computation is
continued until either the electron escapes from the
emitting surface or until the residual path length of the
electron is smaller than the normal distance to the dis-
tance to the emitting surface (so that in this continuous
slowing down approximation the electron has zero pro-
bability of escape).
III. Comparison of Computational Results
With Experiment Data
III. 1 Energy Spectrum
E. P. Denisov, et. al (11) of Leningrad State Uni-
versity published in 1963 the results of an expirment in
which the structures of the x-ray photoemission energy
spectra from aluminum, titanium, chromium, and iron
photocathodes were measured. The photocathedes con-
sisted of a thin layer of the test material (thicker than
the maximum exit depth of the electrons) sputtered on a
planar glass substratum at the center of an evacuated,
spherical collector. The energy structure of the photo-
emission was determined by measuring the collected
current as a function of the bias potential between the
photocathode and the collector. The photocathodes were
irradiated by CuK_ x-rays (8 kev). The experimental
results for the four photocathedes are compared to the
POEM calculations of the energy structure shown in
Figure 1. The experimental and calculational results are
compared by adjusting the arbitrary normalizations such
that the primary maxima are equal. (No attempt was
made to compare the gross emission currents since
these data were not published by Denisov, et. al.). The
agreement of the structures of the calculated and the
experimental spectra is good except for the low energy
spike in the experimental spectrum, which Denisov, et. al.
interpret to be the secondary electron contribution to the
emission spectrum. The three peaks in the energy
spectrum due to the K photoelectron, L photoelectron,
and Auger electron contributions to the spectrum can be
seen in both the calculated and measured spectra.
III. 2 Emission Current, Angular Distribution
Ebert and Lauzon (3) of the Lawerence Radiation
Laboratory published in 1965 the results of an experiment
in which they measured the quantum efficiency (electrons
emitted per incident photon) and the angular distribution
of the gamma-ray induced electron emission from car-
bon, aluminum, copper, cadmium, and lead targets.
Two sets of target thicknesses were used: one set of
targets with thickness equal to the range of a 1.25 Mev
photoelectron, and another set with thickness of one-
tenth the range. The targets were irradiated b_ a col-
limated beam of 1.25 MeV gammas from a Co 6v source.
The emission current was measured by a Faraday cup;
the (cumulative) angular distribution was measured by
varying the solid angle subtended by the Faraday cup.
The Ebert and Lauzon results are compared to the
POEM calculations for the quantum efficiency in Table
1 and for the (differential) angular distribution shown in
Figure 2. The agreement in both quantum efficiency and
angular distribution is excellent. The agreement in
quantum efficiency is net remarkable; Ebert and Lauzon
had comparable success using an analytical model to
calculate quantum efficiency. What is significant is the
788
SOURCE601"25Mev_]_ 1_'_e-_Co_
I_ I_l FARADAY
TARGET CUP
TEST CONFIGURATION
QUANTUMEFFICIENCY (ELECTRON/PHOTON)
(1)
(2)
TARGET THICKNESS(CM) POEM_ EXPERIMENT
CARBON 2.03 X I0-I 9.68 X 10-3 9. 14 X 10-3
2.26X I0-2 2.57X I0 -3 2.46 X I0 -5 (3)
ALUMINUM 2.27 X I0-I 7.96 X I0 -3 7.97 X I0 -3
1.27X 10-2. 1.80 XIO -3 1.99 XIO -3
COPPER 5.24X 10-2 6.10 XIO -3 6.13 X 10-3
5.12 X I0-3 2.09 X I0 -3 2.04 X 10-3 (4)
TABLE 1. COMPARISON OF POEM RESULTS WITH
EXPERIMENTAL DATA OF EBERT AND LAUZON (3)
agreement in the angular distribution. Ebert and Lauzon
found that calculations of the angular distribution made
using an analytical model, which assumed rectilinear
electron transport, were in complete disagreement with
the experimental data. Here, then, is the key advantage
of the Monte Carlo calculation: analytical models which
cannot properly treat electron multiple scattering, but
rather assume rectilinear transport, provide no valid
information as to the angular distribution of photoemis-
sion.
C onclusions
Comparisons of computational results with experi-
mental data have shown the POEM cede to be quite
adequate for the calculation of photon radiation-induced
electron emission, at least in the limited ranges of
photon energies for which test data were available for
comparison. More test data, especially in the x-ray
energy range, 1 keV to 1 MeV, are required for ad-
ditional code verification. One shortcoming of the POEM
cede is its neglect of the secondary (knock-on) electrons.
A study is planned of computational techniques for the
inclusion of the secondary electrons in the emission
calculation.
(5)
(6)
(7)
(s)
(9)
(10)
(11)
References
E.T. Kennedy, "One-D: A Monte Carlo Gamma
Transport Computer Program," General Electric
Company, RESD, PIR-8121-111, (Sep 1966).
N. Kusnezov, "Photon-lnduced Charge Emission"
Lockheed, B-70-69-6 (Aug. 1969).
P.J. Ebert and A.F. Lauzon, "Measurement of
Gamma Ray Induced Secondary Electron Current
from Various Elements," IEEE Tran. Nuc. Sci.
(Feb. 1966), pp. 735-741.
C.M. Davisson, R. D. Evans, "Gamma-Ray
Absorption Coefficients," Rev. Mod. Phy. 24, No.
2 (Apr. 1952).
U.E. Condon and H. Odishaw, Handbook of Physics,
McGraw-Hill, New York, (1958), pp. 7-125.
E.T. Kennedy, "POET: A Monte Carlo Electron
Transport Program (Vol. I), GE TIS No. 67SD253,
(April 1967).
H. Bethe, Handbuch der Physik 24, (1933) p. 491
C. Moiler, Ann Physik 14 (1932), p. 531
F. Rhorlich and B. Carlson, Phys. Rev. 93,
(1954), p. 38
M. Berger, in Methods in Computational Physics,
ed. by B. Alder, Academic Press, New York,
(1963), pp. 207-213.
E.P. Denisov, V.N. Schemelev, A.N. Mezhevich,
and M.A. Rumsh, "Analysis of the Energy Structure
of X-Ray Photoemission From a Massive Cathode,
"Soviet Physics. Solid State 6.. (1965) p. 1047.
789
RELATIVE
AMPLITUDE
20'
15
I0
5
0
0
I
SECONDARY
ELECTRONS
__L-AUGER ELECTROh
PEAK__
Ezr---
I
CuK_ _/.
Xe__. _ EMITTER-
TEST CONFIGURATION-
I
K-PHOTOELECTRON
4 6 8
ENERGY (Key)
RELATIVE
AMPLITUDE
20
15
IO
5
0
O
SECONDARY
4
AUGER
ENERGY (Kev)
Figure la. Electron Emission Energy Spectrum -
Aluminum --- Comparison of Calculations with
Experimental Data (CuK _ x-Radiation
Incident on Target)
Figure lc. Electron Emission Energy
Spectrum - Chromium
RELATIVE
AMPLITUDE
25
20
;5
IO
5
0
0
SECONDARY
/[-
I
I I
MONTE CARLO (POEM)
-- EXPERIMENT (DENISO_
et. al., REET)
AUGER
4 6 8
ENERGY (Key)
RELATIVE
AMPLITUDE
3O
25
SECONDARY
I
20 [ I
/ '15. I
0 2
AUGER
\
4
ENERGY (Kev)
6
Figure lb. Electron Emission Energy
Spectrum - Titanium
Figure ld. Electron Emission Energy
Spectrum - Iron
790
EMISSION EFFICIENCY
PER UN IT SOLID ANGLE
(8) x Io 3
ELECTRONS
PHOTON - S R
10
8
7
6 ---
5
4
3
MONTE-CARLO
_ EXPERIMENT (EBE RT
-- 8 LAUZON, REF :3)--
TARGET
2 _CONFIGURATION --
I
"" "t==,=,
0 "=='_ _
0 I0 20 30 40 50 60 70 80 90
8 - (DEGREES)
PHOTON-SR
I6
° I
, --_ _.TE CARL°--
_L_ --EBERT_ LAUZO.
3 "1=
2
_==._0
0 I0 20 30 40 50 60 70 80 90
8(DEGREES)
Figure 2a. Electron Emission Angular Distribution -
Carbon Target (Electrons Per Unit Solid Angle
Per Incident Photon) (1.25 Mev Co 60 Gamma
Radiation on Target)
Figure 2e. Electron Emission Angular
Distribution - Cooper Target
7
5
E(8)X I0 3 4
ELECTRONS
3
PHOTON-SR
\ ---I___ MONTE-CARLO--EBERT t_ LAUZON
0 I0 20 30 40 50 SO 70 80 90
-(DEGREES)
Figure 2b. Electron Emission Angular
Distribution - Carbon Target
791


A Monte Carlo photocurrent/photoemission computer program

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server