Low-Voltage Electron-Beam Simulation Using the Integrated Tiger

Chapter 8

Downloaded by STANFORD UNIV GREEN LIBR on October 14, 2012 | http://pubs.acs.org Publication Date: May 5, 1996 | doi: 10.1021/bk-1996-0620.ch008

Low-Voltage Electron-Beam Simulation Using the Integrated Tiger Series Monte Carlo Code and Calibration Through Radiochromic Dosimetry 1

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Douglas E. Weiss , Harvey W. Kalweit , and Ronald P. Kensek 1

Corporate Research Process Technologies Laboratory, 3M Company, St. Paul, MN 55144-1000 Simulation Technology Research Division, Sandia National Laboratories, Albuquerque, NM 87185-1179

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ITS(the Integrated Tiger Series) is a powerful, but user-friendly, software package permitting state-of-the-art modeling of electron and/or photon radiation effects. The programs provide Monte Carlo solution of linear time-independent coupled electron/photon radiation transport problems. A simple multi-layer slab model of a low voltage curtain electron beam was constructed using the ITS/TIGER code and it consistently accounted for about 71% of the actual dose delivered across the voltage range of 100 300 kV. The differences in calculated values was principally due to the 3D hibachi structure which effectively blocks 22% of the beam and could not be accounted for in a ID slab geometry TIGER model. A 3D model was constructed using the ITS/ACCEPT Monte Carlo code to improve upon ID slab geometry simulations. Faithful reproduction of the essential geometric elements involved, especially the window support structure, accounted for 86-99% of the dose detected by routine dosimetry.

Since numerical experiments tend to be cheaper, faster and easier than physical ones, computer modeling of electron beams can be very advantageous provided that the software is sufficientiy easy to use, sufficiently flexible to model the important parts of the hardware, and sufficiently accurate for confidence in the results. Over the years, the U.S. national laboratories have developed powerful computer programs to solve problems involving the transport of electrons and photons. Examples of such codes which permit modeling of arbitrary geometries using the Monte Carlo technique are ETRAN(Electron TRANsport)(see Chapter 7 of Reference 7), ITS 3.0(the Integrated TIGER Series)(2), EGS4(Electron-Gamma Shower)(3) and MCNP(Monte Carlo N-Particle)(4). 0097-6156/96/0620-0110$12.00/0 © 1996 American Chemical Society In Irradiation of Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1996.


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ETRAN was originally developed at the National Institute of Standards and Technology(formerly the National Bureau of Standards) to solve electron problems with energies up to a few MeV, gradually being extended up to a GeV, but restricted to a few materials in simple geometries. ITS, developed at Sandia National Laboratories, is based on the same ETRAN physics package, but extends to any number of materials in arbitrary geometries with a much more practical user interface. EGS was developed at the Stanford Linear Accelerator Center originally for highenergy(many GeV) cascades down to electron energies of 1 MeV, gradually being extended down to 10 keV. MCNP was developed at Los Alamos National Laboratory originally to treat photons and neutrons, with the electron physics of an earlier version of ITS added more recently. Of course, different codes will have different strengths. To name only one of each: ETRAN and ITS-3.0 presentiy have the most sophisticated physics for low-energy electrons, EGS4 has an option for the most detailed treatment of boundary-crossing for electrons and MCNP has very powerful, built-in variance-reduction techniques for photon transport. However, selection of which code to chose is often more arbitrary: namely, whichever is perceived to be the most expedient for the user. Such was the case in our selection of ITS 3.0. ITS 3.0, EGS4 and MCNP each enjoy a world-wide user base. In particular, ITS has been employed, for example, in the assessment of personnel radiation hazards, the disposal and cleanup of radioactive waste, the pasteurization and disinfestation of foodstuffs, the radiation vulnerability of satellite systems, electron-beam joining, the sterilization of hospital waste, radiation treatment planning, and the safety of nuclear power reactors. A comprehensive survey of ITS experimental benchmarks and engineering applications can also be found in Chapter 11 of Reference 7. In this paper, we have employed the code for prediction of dose, depth/dose profiles and dose distributions in low voltage electron beams, now becoming more common place as a solvendess industrial process technology. There are many variables associated with electron beam processing, including all of the elements of process variability and gradient cure. Thin film radiochromic dosimeters are commonly used for dose measurement and calibration of electron beams, but often the results of dosimetry can not be correlated with the specific dose absorbed by thin coatings(2 microns) or dissimilar materials. A good coupled electron-photon transport simulation code can help address these types of problems. The specification of a cure gradient as a function of voltage, thickness, density and atomic number can be modeled. The effects of backscatter, air gaps and window thickness, and the effects of compositional variability on depth/dose penetration can also be screened. For the past three decades, Monte Carlo calculations of low-energy beam dose distributions in various absorbing media have shown agreement(see Chapters 8 and 11 of Reference 7 and included references). Comparisons for simpler geometries are more definitive due to the greater fidelity of the simulation and often greater precision in the measurement. In particular, it has been shown that for degraded electron beams having primary energies in the 200-400 keV region and incident in air perpendicular to simplegeometry absorbers, there is reasonable agreement(generally within 5%) between experimental data provided by radiochromic film dose mapping and Monte Carlo calculations of dose distribution(5).

In Irradiation of Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1996.


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IRRADIATION OF POLYMERS

We have found the TIGER code of the Monte Carlo Integrated Tiger Series very useful for web product geometries because of the unlimited number of layers that can be modeled and the ability to independendy subzone each layer(2). Since the web structure is large compared to dimensions in the beam direction, the one-dimensional nature of TIGER is not a factor limiting accuracy and the assumption of infinite boundaries is a reasonable one. Setup is simplified and run times shortened compared to more comprehensive(and complicated) multidimensional codes. Complex 3-dimensional geometries comprised of widely different materials can be handled using the features of the ITS/ACCEPT code, in which combinations of fundamental geometric shapes are described using Boolean Logic; different materials parameters can be assigned to any geometric zone. Using ACCEPT, a full scale model of an Energy Sciences, Inc (ESI) ••Electrocurtain" electron beam system was constructed that includes reproduction of all major geometric features of the web chamber including metal plates, aluminum window clamp,titaniumwindow, copper block with 'hibachi' support structure, nitrogen gap, lead sideplates and steel backplate. The hibachi structure required the greatest amount of coding and contains 112ribbedslots which hold the titanium window against high vacuum. The electron source was modeled as a 2.54 cm by 40.64 cm rectangle to simulate the rectangular screen grid of the same dimensions at the cathode terminal of our electron beam. The source is assumed to be a planar wave based on the assumption that space-charge effects are not significant at the flux densities studied and that the thermal energies of the electrons as they reach the terminal grid are a small fraction of the accelerating potential. A multi-layered web target within the nitrogen inerted chamber was modeled to simulate a sandwich of materials consisting of a nylon FWT-60 dosimeter on top of a thick layer of paper moving on a biaxially oriented polyethyleneteraphthalate (PET) carrier web. Overview of the Monte Carlo Method. The Monte Carlo method is based on statistical averaging of individual trials to estimate the desired numerical answer. Each trial is the history of the events during the passage of a single electron through the defined geometries, and the final result is the average of the passage of many electrons. Specific events which make up such histories are constructed by using random numbers to sample probability distribution functions to determine the type of interaction occurring and the interaction parameters. Such parameters may describe the motion of an electron moving in a given material at a specified energy, the generation of secondary particles, and the motion of these particles and any further cascade. The energy deposited in the interaction volume is then calculated and summed with the results of interactions of other electrons in that same volume to arrive at the total energy distribution for the mathematical "experiment." Clearly, the greater the number of electron histories, the lower the statistical uncertainty(and the longer the runningtime)of a calculation. Due to the statistical nature of the results, any quantity of interest calculated by the code must have attached to it another quantity which represents the estimated statistical accuracy, typically expressed in terms of a standard deviation. In ITS, the total number of histories(source particles to be simulated) are divided up into an equal number of batches. In the present calculations, we typically ran 10 batches. The estimated mean value is simply the average of the mean values from each batch. The estimate of the standard deviation is the calculated deviation of this average value from each of the batch mean values. It is important to keep the code's estimate of the standard deviation a small fraction



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of the calculated quantity of interest. When this estimated fraction becomes large(>10%), the estimated traction itself is unreliable and may be larger than what is indicated. Another important aspect of electron/photon Monte Carlo is that the transport of photons is both faster and more accurate than that of electrons. The photons have a relatively large mean free path which means they typically pass through the material geometry of interest with few interactions(scattering events). The simulation can follow the photons from interaction site to interaction site accurately and efficientiy. The electrons, however, are constantiy interacting, changing direction and losing energy. It is completely impractical to follow the electrons from interaction point to interaction point. Therefore, the electrons are pushed a predetermined distance. The simulation then tries to account for the cumulative effect of all the multiple interactions which took place over this "step" length. This is termed the "condensed history" method. Overview of the ITS Package. There are four essential elements of the ITS system; (1) XDATA, the atomic data file, (2) XGEN, the program file for generating cross sections, (3) ITS, the Monte Carlo program fde and (4) UPEML, the update processor utility. The atomic data file,(l), contains the data for generating cross sections for arbitrary homogeneous mixtures or compounds of the first 100 elements. The two program files,(2) and (3), contain multiple machine versions of the multiple codes integrated in such a way as to take advantage of common coding. Their corresponding binary program libraries are input to the update processor,(4), which selects a particular code for a particular machine and makes any modifications requested by the user(referred to as an 'update' or a •correction run). The output of the processor in this case is FORTRAN code that is ready for compilation. Table I shows the eight member codes of the ITS Monte Carlo program file. From left to right, the codes grouped by column will be referred to as the standard codes, the P codes and the M codes, respectively. All member codes allow transport over the range of 1.0 GeV to 1.0 keV. All calculations in this work made use of the standard codes. These calculations take into account the primary electrons and all secondary radiations, including knock-on electrons from electron-impact ionization events, bremsstrahlung, Compton electrons, photoelectrons, and K-shell characteristic x-rays and Auger electrons resulting from electron and photon ionization events. 1

P Codes. Fluorescence and Auger processes in the standard codes are only allowed for the K shell of the highest atomic element in a given material. For some appUcations, for example, the calculation of energy spectra of low-energy escaping particles, it is desirable to have a more detailed model of the low-energy transport. In the P codes, a more elaborate ionization/relaxation model from the SANDYL(6) code was added to the standard codes. M Codes. In the M codes, the collisional transport of the standard codes is combined with the transport in macroscopic electric and magnetic fields of arbitrary spatial depen dence. This could be used for example, to model a magnetic field applied in an experiment to turn back electrons which would otherwise have escaped or in simulating a magnetic spectrometer.



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To run the programs in the ITS package, the flow of input and output must be understood. Apart from the atomic data fde, which is read by the cross-section generator, and the cross-section output fde produced by the generator which is read by the Monte Carlo, there are two other types of input required for running either the cross-section generator code or the Monte Carlo code. First, there is the set of instructions to the processor that tells it how to produce a compile-ready FORTRAN codefromeither of the program libraries. Simple syntax allows the user the option to modify the source code via deletions, insertions and replacements of FORTRAN code. The second type of input is that required by the resulting executable code. For example, the problem materials and energy range must be specified for the cross-section generator code, and the problem geometry and the source distribution must be defined for the Monte Carlo code. Operational Strategies. Real experiments are performed in the three dimensional world, but new users are urged to consider how the actual geometry may be simplified for modeling purposes. The input required to describe the TIGER geometry is quite straight forward: simply specify the material, number of subzones and layer thickness in centime ters. The input needed to describe arbitrary three-dimensional geometries requires some care and practice on the user's part. The ACCEPT code of ITS uses "combinatorial geometry"(see section 17.3 of Reference 1 for its three-dimensional input). In combinatorial geometry, geometrical regions are described as various logical combinations of a set of primitive body types(such as spheres, boxes, arbitrary polyhedra, ellipsoids, rectangular right cylinders, and truncated right cones). Logical combinations mean intersections(by an implied "AND"), unions(by an explicit "OR"), and negations. The escape zone is a region which completely surrounds the simulated universe that exists. When a particle enters the escape zone, the code considers it has escaped and will no longer continue to track it. The ability to visualize the specified geometry is essential for verifying the setup of three-dimensional simulations. Appendix I in the ITS User Manual(2) describes how a user may interface the called FORTRAN subroutines within ITS with their local plotting package. Other users have employed a geometry-modeling code system such as SABRINA(7) to view their constructed geometry, others have written a translator^) between AUTOCAD and ACCEPT for creating and/or displaying the specified geometry. Low Voltage Electron Beam Simulation. Our interest in this simulation was to determine how well dosimetry calculations using a Monte Carlo code correlated with actual dosimetry datafroman electron beam machine in use at 3M Company. A good correlation would lead to a calibrated model which could be used to simulate experiments quickly and in great detail with respect to energy deposition. Such a model could be used as a diagnostic tool and could extend the range of experimentation outside of the range of equipment capability. A central issue addressed here is the effective beam stopping power of the hibachi support structure. This structure can not be included in a one dimensional ITS/TIGER model but a full ITS/ACCEPT model was constructed so that the results between the two codes could be compared.


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Dosimetry Calibration and the "K" Curve. Calibration of the machine output to the measured dose is accomplished by way of the *K' value or machine constant which adjusts the machine output to the dose observed. The machine constant(K) is also known as the cure yield and appears in the 'KIDS equation, as it is commonly remembered, and shown in equation 1.(9) The K value changes as a function of voltage, especially below 175 kV. This is because the K value includes the effective stopping power of the window foil, air gap and other factors such as the window clamp support structure or "hibachi" and overspray. The shape of the K curve is mostiy determined by the window foil and air gap since this has the most direct attenuating effect on the electrons and this effect is strongly influenced by voltage. Downloaded by STANFORD UNIV GREEN LIBR on October 14, 2012 | http://pubs.acs.org Publication Date: May 5, 1996 | doi: 10.1021/bk-1996-0620.ch008

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TIGER Calculated Dose. Since the TIGER model output is the average energy deposited per electron in a specified material layer, the dose delivered by an electron beam can be directiy calculated without knowing "K". This is because the dose is directly related to the energy deposited per electron in a given layer times the current(number of electrons) divided by the area of the target material. There may still be a correction factor, k', to include, for example, 3-D effects that TIGER cannot model. The calculation is derived in the following manner: Dose calculation for continuous operation of an electron beam: (i) where: K=machine constant, I = current extractedfromfilament in mA, S = web speed in ft/min, A = area/sec = filament lengthfcm] x web speed [cm/sec], E = energy deposited per source electron(per cm ) per gram = Mev -cm /g-electron, k = correction factor The 100 Mrad conversion factor is derivedfromthe following relationship: 2

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1 MeV-cm /g-electron = 100 Mrad-cm /mA-sec The model k' value corrects the dose output calculated by the TIGER model to the dose experimentally observed for a specific machine and represents the lumping of the miscella neous factors that are not a part of this model, such as the •hibachi' structure. The average value of k' in the case modeled here was 0.71 and is mostiy derived from the 22% blockage of the beam by the hibachi structure. Hence, there are other apparent losses in this particular piece of equipment as well, possibly a result of other 3D structures such as the aluminum window clamp that surrounds the window area. Accept Calculated Dose. In ACCEPT, the dose is directly related to the energy deposited in a specific zone per electron times the current (number of electrons per unit time) divided by the total grams of the target material. The dose calculation for continuous operation of an electron beam is given by equation 2. Dose = K * 1 =100Mrad xT E Ix B * L 1 [d*T*W*L] S

(2)

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TABLE I. Monte Carlo Member Codes of ITS


GEOMETRY 1-D 2-D/3-D 3-D

-40 -201

ENHANCED PHYSICS TIGERP CYLTRANP ACCEPTP

STANDARD CODES TIGER CYLTRAN ACCEPT

-30 1

-20 1

-10 1

0 1

10 1

20 1

MACROSCOPIC FIELDS CYLTRANM ACCEPTM

30 1

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Source

Hibachi Aluminum Clamp Web

Steel Backplate

"PROjr Figure 1: 3-D End View Plot of ACCEPT Electron Beam Model. (Reproduced with permission from reference 17. Copyright 1994 RadTech International North America.)


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where: K = machine constant, I = current extractedfromfilament in mA, S = web speed in fVmin or cm/sec, E = energy deposited per source electron in modeled dosimeter = MeV/electron, d = density of dosimeter composition in g/cm , T = thickness of modeled dosimeter(cm), W = width of modeled dosimeter(cm), L = length of modeled dosimeter(cm) The ACCEPT calculation differsfromthe TIGER calculation in several ways. Because the source is described in full detail in the input file, the filament length is already factored into the ACCEPT energy output and is therefore not included in equation 2 for area calculation; web speed alone is sufficient. ACCEPT does not calculate dose in MeVcm /g-electron as does TIGER. Standard output is in MeV of energy deposited in a given subzone per source electron. Therefore, the energy(MeV) needs to be divided by the total grams in the modeled dosimeter zone to get dose per source electron. The total grams is the product of the density times the volume. Since we are converting the calculated dose, we need to use the volume of the dosimeter used in the model which is length(L) times width(W) times thickness(T). By dividing by the total grams(density times volume), we have converted E into units of MeV/g-electron. Now we need to multiply by the number of electrons hitting the actual dosimeter chip when it has moved the length of our dosimeter used in the model. This is just the current I times an effective "time" which is the ratio of the model length L divided by the web speed S. Since L appears in both the numerator and the denominator, the calculation will be independent of the size of L(provided it is long enough to prevent energyfromleaking out the ends). 3


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Geometry Verification. Plots of the geometric construction are outputted by ACCEPT when the key word PLOT is used in the input fde, followed by specification of scale and angles of perspective. These output files were plotted using GNUPLOT(70) and are shown in Figures 1 and 2. Figure 1 shows an "end view" cross-section of the electron beam. In this side view, the source appears as a line suspended in the vacuum above the window clamp/nitrogen-inerted chamber construction with the web suspended in the chamber. Note the individual rib slots that support thetitaniumwindow against the vacuum. Figure 2 shows a top view of the chamber construction; the ribbed hibachi structure is the most prominent feature. Within it is a rectangle which represents the grid source of electrons. The center strip in the web(vertical) direction represents a dosimeter that is 28 cm long x 10cm wide. The dosimeters are actually only one cm square but a 10 cm width was used for calculation purposes to provide better statistics with fewer histories. This is possible because the model cross-web distribution is uniform. However, this was not true experimentally. The electron beam source non-uniformity was not accounted for in this Monte Carlo simulation model. Experimental Routine transfer dosimetry was performed using Far West Technologies FWT-60 nylon Radiachromic dosimeters(77). These dosimeters, like some others, are sensitive to humidity and temperature during exposure to radiation(/2-/4). They are also sensitive to light in general(75). Therefore, certain precautions were followed. The


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"PROJ2"

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-10

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Figure 2: 3-D Top View Plot of ACCEPT Electron Beam Model. The array of vertical lines in the center of the figure is the hibachi structure that supports the window foil. The rectangular outline centered within this array describes the location of the grid source of electrons. The vertical column traversing the center of the figure is a dosimeter strip, the wider vertical outline is the web. Other rectangular shapes describe the window support structure and clamp. (Reproduced with permission from reference 17. Copyright 1994 RadTech International North America.)


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dosimeters were kept in a chamber to maintain 52% relative humidity(R.H.) during storage. During handling and exposure, the ambient conditions were 50% R.H. with an air temperature of about 24° C. A total of 36 dosimeters were mounted by an edge onto a double thickness of index cards taped together to cover the full width of the web(30 cm). The dosimeters were spaced 2.5 cm apart and 3 deep across the 30 cm web width. The cards of dosimeters were passed through an ESI "Electrocurtain" model CB300 electron beam on a carrier web. The dosimeters were left uncovered during their passage through the electron beam at a web speed of 50 +/- 0.5 fpm with a current of 10 mA. The current was incremented an additional 0.1 to 0.8 mA as the voltage was increased from 100 to 300 kV to compensate for a certain amount of known current leakage in the system. The voltage was increased at increments of 25 kV from a voltage setting of 100 kV up to 300 kV. The momentary temperature increases during the irradiation do not affect the dosimetry readings at the dose rates studied(7

Low-Voltage Electron-Beam Simulation Using the Integrated Tiger

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