98 NI minister KB UP . monitorowa ... . . 66 V her i ladica C. ORNL UNCLASSIFIED durante OR - -- ORNV-p-1786 Paper to be includeci in process ., Symosium on Protection Against Radiations in Space, Gatlinbure,. . October 12-ilt, 1964 CONF-780-7 THE VALIDITY OF THE STRAIGHTAJEAD APPROXIMATION IN SPACE VEHICIE SHIEIDING STUDIES* - R. G. Alsmiller, Jr., D. C. Irving. W. E. Kinney, and H. S. Moran Oak Ridge National Laboratory Oak Ridge, Tennessee MASTER COPY Many of the shielding studies for manned space vehicles have been carried out in what is usuall.y called the "straightahead approximation." This approximation greatly simplifies the computation but its use necessarily introduces inaccuracies. To test the validity of the approximation, cal- culations have been carried out and compared with results obtained with the angular distribution of the secondary particles properly taken into account. To define the approximation as it is used here, we note that, in general, . Fix = Fz; (E',E,'.ñ ) , (1) where Fyn = the number of particles of type i per unit energy range per unit solid angle possessing kinetic energy E and direction given by the unit vector ñ after a particle of type j with kinetic energy E and direction n' undergoes either an elastic or a nonelastic collision. In the straightahead approximation the quantity F;, is approximated by F: (E',E,ñ'. ) = f 1 (E',E) • *ijles 25 *Research sponsored by the National Aeronautics and Space Administration (NASA Order R-104) under Union Carbide Corporation's Contract with the V. S. Atomic Energy Commission. where att (11(E',E) = f f 7(',,ñ":ñ ) an . (3) 0 0 The delta function in Eq. (2) ensures that all emergent particles have the same direction as the incident particle, and Eq. (3) follows from inte- grating Eq. (2) over all solid ankies. It must be carefully notes that as defined here the straightahead approximatior. applies to both elastic and nonelastic collisions. Furthermore, all cmergent particles are assumed to go in the forward direction; i.e., no attempt is made to discriminate against those particles which are emitted in the backward quadrant. To ensure that any differences which exist between the approximate and the exact calculation are due to live approximation being considered and not to differences in nuclear data, the straightahead calculations presented here have been carried out using the NIC code with which the exact calculations were done. The only change made in the code was in the angular distribution of the scattered particles. In Fig. I the results of the approximate and exact calculations are com- pared for the case of a 400-MeV proton beam isotropically incident on a slab of aluminum followed by a 30-cm-thick sluh of tissue. The solid curves are the results of the exact calculations, while the plotted points are the results of the approximate calculations. The primary proton, secondary proton, and secondary neutron fluxi's incident on the tissue are defined to be those fluxes which would emerge from the aluminum if the tissue were absent. The dose as a function ofüepili in the tissue is broken into five contributions: 1. the primary proton ionization cose, 2. the dose from secondary particles produced by primary protons in the ů tissue, si the secondary proton dose, 4. the secondary neutron dose, 5. the backscattered. dose, i.e., ühe dose from all particles which are produced in the tissue and cross into the aluminum. Since the primary protons travel in a straight line (multiple Coulomb scattering was not included in the calculation), the exact and approximate calculations are the same for the primary proton ionization dose. The approxi- mate secondary proton dose and secondary neutron dose are slightly too large, particularly in the first few centimeters of tissue, while the approximate primary proton secondary dose is too small in the first few centimeters. There is, of course, no approximate backscattered dose. . The same calculations are compared again in Fig. 2, but this time the . dose is given in rems rather than rads. The rem calculation was carried out in the same manner as that described by W. Kinney and C. D. Zerby." The agreement between the exact and approximate calculations is roughly the same as in Fig. l. In Fig. 3 the results for 100-MeV protons isotropically incident on a 10-g/cm slab of aluminum followed by a 30-cm-thick slab of tissue are given. In this case the primary protons do not penetrate the shield and so we have exact doses only from secondary protons, secondary neutrons, and backscattered particles. In fact, the approxillitie Secondary proton dose is zero within the statistics; so only the secondesoy !.«tron doses can actually be com- pared. The approximate secondary licitron dose is somewhat too large in this case, as it was in Fig. 1. Figures 4 and 5 give results ::.. iw additional cases: 100-MeV protons incident isotropically on 10 g/cm","arion followed by tissue, and 400-MeV protons incident isotropically on Cem of copper followed by tissue. Those results are not appreciably diffel:.:, i'r those obtained in the previous cases. In the cases presented here it $1.4.ightahead approximation appears to be quite good. The approximat:r: 110 ly overestimates the dose and appears to have approximately the kime validity for elements between carbon and copper. One must, however, avoid drawing very general conclusions on the basis of so few computations. It ist, be rememhered that the low-energy JL region ( < 100 MeV) is still to be treailů and may be important when one considers typical flare spectra. In the results just discussed the dise in tissue was calculated directly. An alternate procedure iö tie .lculate the straightahead approxi- mation current at the shield tissue interface and apply current-to-dose con- version factors to this current. Evcane of the approximation one has no information about the angular distribuitor of particles at the interface, but one may carry through the computaiion assuming either isotropic or normal incidence since conversion factor: ior these cases are available.“ The results of this procedure are shown in Table 1 for the case of a 400- Mev proton beam isotropically incident on a 30-g/cm² slab of tissue followed by a 30-cm-thick slab of tissue. Table 1. Doses Calculated for 400-MeV Protons Isotropically Inciaci vil ü 30g/cm--Thick Slab of Aluminur. Fw.is vied by Tissue Dose Calculated Wiin Normal With Isotropic Incuence Incidence Conversion Conversion racinir Factor Actual Dose Average Dose (rads) Primary protons 0.300x10°! Secondary protons 0.444x10-8 Secondary neutrons 0.164x10-8 Total 0.361x10-7 0.22x107 0.08 4x10-8 0.190x10-8 0.313x10-7 0.327x10-7 0.518x10-8 0.264x10-8 0.405x10-7 Average Dose (rems) Primary protons 0.452x10-? Secondary protons 0.614x10-8 Secondary neutrons 0.793x10-0 Total 0.592x10-7 0.337x10-7 0.033x10-8 0.6x10-8 0.1177x10-7 0.446x10-7 0.689x10-8 0.124x10-7 0.640x10-7 5-C1-Dept:1 Dose (rads) Primary protons 0.338x10-? 0.217x10-7 Secondary protons 0.745x10-0 0.641x10-8 Secondary neutrons 0.201x10-8 0.222x10-8 Total 0.433x10-7 0.303x10-7 0.412x10-7 0.905x10-8 0.346x10-8 0.537x10-7 Primary protons 0.517x10-/ Secondary protons 0.104x10-7 Secondary neutrons 0.109x1007 Total 0.730x10-7 5-cm-Deptin Dose (rems) 0.518x10-7 0.835x10-8 0.121x10-7 0.523x10-7 0.561x10-7 0.118x10-7 0.167x10-7 0.846x10-7 oso The first column in the tal.ie ives the doses obtained by exact calcula- tion, while columns 2 and 3 give t:1* ip roximate doses obtained by applying the conversion factors. The isotropic conversion gives an overestimate of both the 5-cm-depth dose and the avriredil dose. The normal conversi on under- estimates the primary proton and thic cose but overestimates the secondary proton and secondary neutron dose. In considering these results it must be remembered that since the calculations were carried out using Monte Carlo methods there are statistical erro):'issociated with each of the numbers in the table. Roughly speaking, a standard deviation of about 10% is to be associated with each entry. Results are given in Table 2 for 100-MeV protons isotropically incident on 10 g/cm of aluminum followed iny tissue. In this case essentially the only contribution comes from secondary neutrons, and both the normal and isotropic conversion overestimates this contribution. References 1. For an extensive list of references see: S. P. Shen, Astronaut. Acta 9, 28 (1963). ?. W. E. Kinney, The Nucleon Transport Code, NTC, ORNL-3610 (1964). 3. The exact calculations are reported elsewhere in these proceedings. See the paper "the Secondary-Particle Contribution to the Dose from Mono- energetic Proton Beams and the validity of Current-to-Dose Conversion Factors," by D. C. Irving et al. See the paper "Calculated Tisslie Current-to-Dose Conversion Factors for 4. Nucleons of Energy Below 400 niev," by W. E. Kinney and C. D. Zerby in these proceedings. 7- Table 2. Doses Calculated for 100-MeV Protons Isotropically Incident on a 10-g/cm2-Thick Slab of Aluminum Followed by Tissue Dose Calculated With Normal With Isotropic Incidence Incidence Conversion Conversion Factor Factor Actual Dose Average Dose (rads) Primary protons o Secondary protons 0.193xloedd Secondary neutrons 0.977x10-10 Total 0.996x10-10 0.169x10-9 0.163x10-9 0.195x10-9 0.195x10-9 Average Dose (rems) Primary protons 0 Secondary protons 0.238x10-11 Secondary neutrons 0.735x10-9 . 0.103x10-8 Total 0.738x10-9 0.103x10-8 0.117x10-8 0.117x10-8 5-cm-Depth Dose (rads) Primary protons 0 Secondary protons 0 Secondary neutrons 0.178x10-9 Total 0.178x10-9 0.235x1009 0.235x10-9 0.309x10-9 0.309x10-9 5-cm-Depth Dose (rems) Primary protons 0 Secondary protons 0 Secondary neutrons 0.129x10-0 Total 0.129x10-8 0.139x10-8 0.139x10-8 0.173x10-8 0.173x10-8 . List 01 Figures 18. No. Dwg. No. 64-9309 Comparison of Straight lead use Results with Exact Results (in rads ) for the Case of 400- MeV Protons Isotropical.ly Incident on a 30-6/cma- thick slab of Aluminura '6110ved by Tissue. Comparison of Straighi: read bse Results with 64-9311 Exact Results (in re, por the Case of 400- MeV Protons Isotropicoily Incident on a 30-g/cm- thick slab of Aluminu. Pollo:red by Mssue. Comparison of Straight head Pose Results with 64-9315 Exact Results for the case 2: 100-MeV Protons Isotropically Inciden: -92 :0-g/cm-thick 64-9313 Slab of Aluminum Followed by Tissue. Comparison of Straighur head Dose Results for the Case of 100-MeV Protos Isotopically Incident on a 10-g/cm²-thick slab of Carbon Followed by Tissue. 64-9308 Comparison of Straighuhead inse Results for the Case of 400-MeV Protons Isotropically Incident on a 10-g/cm -thick slab of Copper Followed by Tissue. ...... ..... -.. UNCLASSIFIED OKNL DWG. 64-9309 400 MEV PROTONS INCIDENT ON 30 GM./SQ. CM. OF AL+TISSUE. oooooooooooooooooou o cooroud over 100000000 tattetit tim 2 ܣܩܣܤܦܣ ܦܤܤܣܣܦܣܬ ܟܦܢܚܬ A .ܓ܂ ttttttttt ttttttttt. X X X X X X xxx XXX X X X X X Lihtott XXX. X X DOSE. RAD/SEC./UNIT ISOTROPIC FLUX 1. PRIMARY PROTON IONIZATION DOSE 2. PRIMARY PROTONS, OTHER DOSE 3. SECONDARY PROTON DOSE 4. SECONDARY NEUTRON DOSE 5. BACKSCATTERED DOSE O PRIMARY PROTON IONIZATION DOSE A PRIMARY PROTONS, OTHER DOSE + SECONDARY PROTON DOSE X SECONDARY NEUTRON DOSE 10:10 STRAIGHTAHEAD APPROXIMATION 104 Boot 5.0 15 20 30 35 DEPTH IN TISSUE. CM. UNCLASSIFIED ORNL DWG, 64-9311 400 MEV PROTONS INCIDENT ON 30 GM./SQ. Ci1. OF AL + TISSUE. 970 0 Do 2ext 4 X XE +*] 2 X + + XU ſ ++1 DOSE, REM/SEC./UNIT ISOTROPIC FLUX 1. PRIMARY PROTON IONIZATION DOSE 2. PRIMARY PROTONS, OTHER DOSE 3. SECONDARY PROTON DOSE 4. SECONDARY NEUTRON DOSE 5. BACKSCATTERED DOSE O PRIMARY PROTON IONIZATION DOSE A PRIMARY PROTONS, OTHER DOSE + SECONDARY PROTON DOSE X SECONDARY NEUTRON DOSE STRAIGHTAHEAD APPROXIMATION 15 25 30 35 DEPTH IN TISSUE. CM. ... .. . to... ........ . .. . . ...... ..... ........... ..... - . . . UNCLASSIFIED ORNL DWG. 64-9315 100 MEV PROTONS INCIDENT ON 10 GM./SQ. CM. OF AL+TISSUE. 10 25 у ХХ х 1. xxxx 1x x x | NX DOSE, FAD/SEC./UNIT ISOTROPIC FLUX 1. SECONDARY PROTON DOSE 2. SECONDARY NEUTRON DOSE 3. BACKSCATTERED DOSE SECONDARY NEUTRON DOSE, STRAIGHTAHEAD APPROXIMATION 5.0 35 25 15 20 DEPTH IN TISSUE. CM, UNCLASSIFIED ORIAL DWG. 64-9313 100 MEV PROTONS INC TOENT ON 10 GM./SQ. CM. OF C+TISSUE. 10 * + படப்படப் * 24 - *** XXX + * 4/ 1. SECONDARY NEUTRON DOSE 2. BACKSCATTERED DOSE X SECONDARY NEUTRON DOSE, STRAIGHTAHEAD APPROXIMATION DOSE . RAD/SEC. /UNIT ISOTROPIC FLUX 5.0 DEPTH IN TISSUE. CM. vürvücgroooooooooooooooooooooooo att AAAAAAAAAAAAA AZ Anazarda *** ttttttttttttttttnera lo xx xx xx xx xx xx xa “х , хүxxx * * text #x DOSE, FIND/SEC./UNIT ISOTROPIC FLUX 1. PRIMARY PROTON IONIZATION DOSE 2. PRIMARY PROTONS, OTHER DO SE 3. SECONDARY PROTON DOSE 4. SECONDARY NEUTRON DOSE 5. BACKSCATTERED DOSE 0 PRIMARY PROTON IONIZATION DOSE A PRIMARY PROTONS, OTHER DOSE + SECONDARY PROTON DOSE X SECONDARY NEUTRON DOSE STRAIGHTAHEAL APPROXIMATION 1045o Hot S DEPTH IN TISSUE. CM. . - - - - - - - --- DATE FILMED 4 / 7 765 Strumica e tyre te i propone - LEGAL NOTICE This report was prepared as an account of Government sponsored work. Neither the United Sta.es, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, exprossed or implied, with respect to the accu- racy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method. or process disclosed in this report may not Infringe privately owned rights; or B. Assumes any liabilities with respoct to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission” includes any em- ployee or contractor of the Commission, or employee of such contractor, to the extent that such employee or contractor of tho Commission, or employee of such contractor preparcs, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor. . - t . ... 1 --- END . .