CCC-0107: ETRAN, Electron Transport and Gamma Transport with Secondary Radiation in Slab by Monte-Carlo

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CCC-0107 ETRAN. (Abstract last modified 06-MAY-1992)

ETRAN, Electron Transport and Gamma Transport with Secondary Radiation in Slab by Monte-Carlo

Abstract Table of Contents:

1. NAME OR DESIGNATION OF PROGRAM - ETRAN.

2. COMPUTER FOR WHICH PROGRAM IS DESIGNED AND OTHER MACHINE VERSION PACKAGES AVAILABLE -

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Explanation of the status codes.

Program-name Package-ID Status ETRAN-15 CCC-0107/01 Obsolete ETRAN-16B CCC-0107/02 Tested ETRAN CCC-0107/03 Obsolete ETRAN CCC-0107/04 Tested

Machines used: Package-ID Orig.Computer Test Computer CCC-0107/02 IBM 370 series IBM 370 series CCC-0107/04 IBM 360 series IBM 3084Q

3. NATURE OF PHYSICAL PROBLEM SOLVED - ETRAN computes the transport of electrons and photons through plane-parallel slab targets that have a finite thickness in one dimension and are unbound in the other two-dimensions. The incident radiation can consist of a beam of either electrons or photons with specified spectral and directional distribution. Options are available by which all orders of the electron-photon cascade can be included in the calculation. Thus electrons are allowed to give rise to secondary knock-on electrons, continuous bremsstrahlung and characteristic x-rays; and photons are allowed to produce photo-electrons, Compton electrons, and electron- positron pairs. Annihilation quanta, fluorescence radiation, and Auger electrons are also taken into account. If desired, the Monte- Carlo histories of all generations of secondary radiations are followed. The information produced by ETRAN includes the following items:
1) reflection and transmission of electrons or photons, differential in energy and direction;
2) the production of continuous bremsstrahlung and characteristic
   x-rays by electrons and the emergence of such radiations from
   the target (differential in photon energy and direction);
3) the spectrum of the amounts of energy left behind in a thick
   target by an incident electron beam;
4) the deposition of energy and charge by an electron beam as
   function of the depth in the target;
5) the flux of electrons, differential in energy, as function of the depth in the target.

4. METHOD OF SOLUTION - A programme called DATAPAC-4 takes data for a particular material from a library tape and further processes them. The function of DATAPAC-4 is to produce single-scattering and multiple-scattering data in the form of tabular arrays (again stored on magnetic tape) which facilitate the rapid sampling of electron and photon Monte Carlo histories in ETRAN.
The photon component of the electron-photon cascade is calculated by conventional random sampling that imitates the physical processes of compton scattering, photon electric absorption, and pair production. In the calculation of the electron component, no attempt is made to follow successive individual interactions with atoms and atomic electrons because these are too numerous. Instead, a Monte Carlo model is used in which attention is focused on the effect of groups of successive collisions.
The electron tracks to be sampled are divided into a large number of short segments, and the energy loss and angular deflection in each segment are sampled from pertinent theoretical multiple scattering distributions. At the end of each short step, the direction of motion of the electron is changed by a multiple scattering angular deflection that is sampled from the Goudsmit-Saunderson distribution. This distribution is assumed to be the same for all short steps lying within a given step. The energy loss in a step, resulting from the cumulative effect of many inelastic collisions, is sampled from a distribution that is a convolution of a Landau distribution with a Gaussian. An option is also provided for using the continuous-slowing-down approximation in which energy-loss fluctuations are disregarded and the energy loss by collisions is simply computed with the use of the stopping power formula.
The production of knock-on electrons is sampled in each short step with the use of a probability distribution derived from the Moller cross section for collisions between free electrons (binding effects are disregarded). Histories of these particles are then followed by procedures identical with those used for the primary electrons.
The production of continuous bremsstrahlung photons is sampled in each short step with the use of a probability distribution derived from the bremsstrahlung cross section (Bethe-Heitler theory with modifications taking into account the correct high-frequency limit, empirical corrections, etc.). The probability is usually quite small that more than one bremsstrahlung photon will be produced in a single short step. Allowance is made for such a contingency by sampling the frequency of bremsstrahlung production events from a Poisson distribution. The energy of the secondary bremsstrahlung photons is subtracted from the energy of the electrons producing them. Thus photon emission contributes to the energy-loss straggling of the electrons. The photons are started out at a random position in the short step in a direction relative to that of the primary electron specified by the sampled intrinsic bremsstrahlung emission angle. For problems in which the production of the thick-target bremsstrahlung is of prime interest, there is an option to increase the rate of occurrence of bremsstrahlung events artificially by a specified factor.
The production of secondary characteristic x-rays in each short step is sampled with the use of the k-ionization cross sections of Arthurs and Moiseiwitsch and Kolbenstvedt. The programme is arranged so as to treat simultaneously many slab targets with different thicknesses.
Boundary crossings (transmission and reflection) usually occur in the middle of a short step. The energy with which the electron crosses the border is determined by subtracting from the energy at the beginning of the step an energy loss sampled from the Landau- Blunck-Leisegang distribution for the fraction of the step taken to the boundary. The direction at the time of crossing is determinedby changing the direction of motion at the beginning of the short step involved, using a deflection sampled from an exponential approximation to the Goudsmit-Saunderson distribution for the fraction of the short step to the boundary.
The target is subdivided into many thin sublayers of equal thickness, and the energy deposited in each sublayer is recorded for each sampled track. The energy allowed to be deposited is that dissipated by electrons in inelastic collisions resulting in the production of slow secondary electrons with energies below the chosen cut-off-value. The energy given to fast secondary electrons with energies above the cut-off is not immediately scored, because the histories of these electrons are followed further so that the energy may eventually be deposited in a sublayer different from the one in which the electrons were produced. Bremsstrahlung losses are similarly not scored immediately. Photons are allowed first to penetrate further through the medium so that the energy of the electrons set in motion by them may eventually be deposited in a different sublayer.
The treatment of charge deposition is quite similar to that of energy deposition, involving the scoring of charge deposited in sublayers. A track is assumed to "end" when the residual range of the electron is so small compared to the size of the sublayers that escape to a different sublayer is no longer possible. When secondary electrons are produced, either as the result of a knock-on collision or as the result of Compton scattering or photon-electric absorption, a unit charge is withdrawn from the sublayer in which the electron is born. The charge is then allowed to be carried to a different sublayer. Electron-positron pairs are excluded from this scheme because on the average their production does not lead to a net transfer of charge.
The electron flux is computed in ETRAN as a quantity differential in energy but integrated over all directions. (*) A Monte Carlo estimate of the flux is obtained by dividing the target into many sublayers and scoring the tracklength of electrons with specified energies in each of the sublayers. The average tracklength per incident electron divided by the thickness of the sublayer provides an estimate of the average flux in the sublayer.
The flux calculation includes primary as well as secondary electrons with energies down to some cut-off value which is chosen so that the electron is effectively trapped in the sublayer in which it finds itself, because its residual range is smaller than the distance to the nearest sublayer boundaries.
(*) In the IBM 360/75 version, the flux differential in angle is also computed, and a distinction is made between the flux in the forward and backward directions.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM - No dimensional limitations are noted.

6. TYPICAL RUNNING TIME - Estimated running time on the IBM 360/75 for the packaged sample problem: DATAPAC-4: 5 minutes; ETRAN-16B: 3 minutes.

CCC-0107/04:

NEA-DB executed the test cases on IBM 3084Q. The following CPU times were required:
DATAPAC-6: 6.04 seconds; ETRAN-16D: 13.20 sec; ETRAN18G: 14.76 sec; INCLUDE run to generate ETRAN-16D source program: 3.54 sec;
INCLUDE run to generate ETRAN-18G source program: 4.23 sec.

7. UNUSUAL FEATURES OF THE PROGRAM -

9. STATUS
CCC-0107/01: 04-NOV-1996 Obsolete
CCC-0107/02: 01-OCT-1972 Tested at NEADB
CCC-0107/03: 06-MAY-1992 Obsolete
CCC-0107/04: 06-MAY-1992 Tested at NEADB

10. REFERENCES  -
- G. Nurdin:
  "Calcul de l'energie deposee dans quelques detecteurs gamma a
  l'interieur d'un fantome"
  (October 1988).
CCC-0107/02:
- M.J. Berger and S.M. Seltzer:
  Electron and Photon Transport Programs - 1. Introduction and Notes
  on Program DATAPAC-4.  NBS 9836  (June 10, 1968)
- M.J. Berger and S.M. Seltzer:
  Electron and Photon Transport Programs - 2. Notes on Program
  ETRAN-15.  NBS 9837  (June 10, 1968)
- ETRAN - Monte Carlo Code System for Electron and Photon Transport
  Through Extended Media.  Supplement to CCC-107.
CCC-0107/04:
- M.J. Berger and S.M. Seltzer:
  Electron and Photon Transport Programs - 1. Introduction and Notes
  on Program DATAPAC-4.  NBS 9836  (June 10, 1968)
- M.J. Berger and S.M. Seltzer:
  Electron and Photon Transport Programs - 2. Notes on Program
  ETRAN-15.  NBS 9837  (June 10, 1968)
- ETRAN - Monte Carlo Code System for Electron and Photon Transport
  Through Extended Media.  Supplement to CCC-107

11. MACHINE REQUIREMENTS - The programme requires the use of a large computer. It is operable on the UNIVAC 1108 and the IBM 360/75, with standard I-O and two tape units or direct access devices.

CCC-0107/04:

Main storage requirements to execute the different modules of this package on IBM 3084Q are as follows:
DATAPAC-6: 280K bytes; ETRAN-16D: 388K bytes; ETRAN-18G: 708K bytes; INCLUDE runs: 216K bytes.

12. PROGRAMMING LANGUAGE(S) USED -
CCC-0107/02: FORTRAN-IV
CCC-0107/04: FORTRAN-IV

13. OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED -
CCC-107A/ETRAN 15 (UNIVAC-1108 version) as distributed by RSIC requires the availability of a FORTRAN V compiler.
CCC-107B,C/ETRAN 16 and 16B are operable on the IBM 360/75 operating system using OS/360 FORTRAN H compiler.

CCC-0107/04:

The test runs were performed on IBM 3084Q under MVS-SP.

14. ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS -

15. NAME AND ESTABLISHMENT OF AUTHOR -
      Center for Radiation Research
      National Bureau of Standards
      Washington, D.C.

17. CATEGORIES -

- J. Gamma Heating and Shield Design

Keywords: ELECTRON BEAMS, ELECTRONS, MONTE CARLO METHOD, SCATTERING, SLABS, TRANSPORT THEORY