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Galactic cosmic ray transport methods and radiation quality issues
Nucl. Tracks Radial. Meas., Vol. 20. No. 1, pp. 65-72, 1992 hr.J.Radial. Appl. Instwn.,
0735-245x/92 S5.00 + .oO Pergamoo Rem pk
Part D
Printed in Great Britain
GALACTIC
COSMIC RAY TRANSPORT METHODS RADIATION QUALITY ISSUES
AND
L. W. TOWNSEND, J. W. wIlSON, F. A. ~ClNOTT.4 and J. L. SEWN Mail Stop 493, NASA Langley Research Center, Hampton, VA 23665-5225, U.S.A. (Received 4 M&I
1991)
Abstract-An overview of galactic cosmic ray @CR) interaction and transport methods, as implemented in the Langley Research Center GCR transport code, is presented. Representative results for solar
minimum, exo-magnetospheric GCR dose equivalents in water are presented on a component by component basis for various thicknesses of aluminum shielding. The impact of proposed changes to the currently used quality factors on exposure estimates and shielding requirements are quantified. Using the cellular track model of Katz, estimates of relative biological effectiveness (RBE) for the mixed GCR radiation fields are also made.
1. INTRODUCTION
estimate RBE (relative biological effectiveness) values for the mixed radiation fields will be described. Details of the GCR environment itself will not be described. They are discussed elsewhere in this issue (Benton er ul., 1992).
the Earth’s magnetosphere, the two main sources of radiation hazards to crews of manned space missions are energetic solar particle events (SPEs) and galactic cosmic rays (GCRs). For a SPE, the major concerns center upon acute effects resulting from very large radiation doses accruing in a short period of time (hours or days). Without adequate protective shielding, e.g. a storm shelter, crews could receive mission-threatening or life-threatening exposures (Townsend et al., 1991a, b). Details of methods used to describe SPE transport and interactions are given in a companion paper (Cucinotta er al., 1992). For GCR particles, the main source of concern is cumulative exposure to the HZE [high charge (Z), high energy (E)] component. These particles, classified as high-LET (linear energy transfer) radiations, deposit large quantities of energy per unit distance traveled in tissue and shield materials. Therefore, they may be much more damaging than conventional low-LET radiation such as X-rays or @Co gamma rays. In this paper, methods for accurately describing the interactions and transport of GCR particles through bulk materials, as implemented in the current version of the Langley Research Center (LaRC) GCR transport code, HZETRN, will be described. To illustrate the computer code capabilities, representative GCR dose equivalents in water will be presented on a component-by-component basis for several of the most prevalent ions in the incident GCR spectrum. An assessment of the impact on exposure estimates and possible GCR shielding requirements resulting from proposed changes to the radiation quality factors (ICRP, 1990) will be quantified. Finally, use of the cellular track model of Katz (Katz et al., 1971) to BEYOND
2. GALACTIC COSMIC RAY TRANSPORT THEORY As high energy galactic cosmic rays traverse bulk matter, such as a spacecraft, their radiation fields change composition through interactions with the materials in their paths. As a result of these interactions, the internal radiation environment within the spacecraft can differ appreciably from the incident external environment. These alterations in the incident radiation environment depend upon the thickness, geometry, and material composition of the target. They are described by transport models which relate the transmitted fluxes, as functions of spatial location, kinetic energy, and directions of particle motion, to the incident fluxes. The main interaction processes involved in the transport of these radiation fields through bulk matter are (1) ionization energy losses through collisions with atomic electrons; (2) nuclear elastic and inelastic collisions; and (3) nuclear break-up (fragmentation) and electromagnetic dissociation interactions. The latter are particularly important because fragmentations result in the production of reaction products which alter the elemental and isotopic composition of the transported radiation fields. The radioactive decay contributions of the transported fragments are ignored because their decay times are typically much longer than the time required for the radioactive fragment to exit the spacecraft or undergo a subsequent nuclear collision. 65
66
L. W. TOWNSEND
2.1. Heavy ion transport
Pi(E)=exp[-A,~Oe$$dE],
The overall propagation of these radiation fields is described by a Boltzmann equation, which can be derived from considerations of mass and energy conservation. Its solutions give values of particle fluxes and energies everywhere within and exiting the boundaries of the target medium. For GCR particles, the typically large ion kinetic energies allow one to neglect changes in particle direction because of collisions. This is called a straightahead approximation. The one-dimensional Boltzmann equation is then written (Wilson et al., 1984) g + aitE) [
GSitE)4itx, E) 1
In equation (I), 4, is the flux of type i ions at position x with motion along the x axis and energy E in units of A MeV, a,(E) is the corresponding macroscopic nuclear absorption cross-section in units of cm-‘, S,(E) is the change in E per unit distance (e.g. the stopping power per unit projectile mass), and a,(E) is the cross-section, in units of cm-‘, for producing ion i from a collision by ion j. Solution methods for equation (1) are usually optimized for the specific transport problem being investigated. For accelerator-beam studies, solutions can be obtained using analytic methods in a perturbation expansion (Wilson et al., 1984) 4,(x. E) = f b:“‘(x. E). n=cl
(2)
where n = 0 denotes the primary beam, n = 1 denotes secondaries produced by fragmenting of the primaries, n = 2 denotes tertiaries produced by fragmenting of the secondaries. etc. For the GCR transport problem, the incident GCR particles possess broad energy spectra; therefore, a different solution technique is required for computational efficiency (Wilson et al., 1987a). This is accomplished by using the first two terms of the perturbation expansion in an iterative procedure which effectively sums subsequent generations of reaction products to all orders. The result is
3,(x + h, E) =
z
$,(x. E ) $,(.~. 6).
(3)
where 3,(x. E) = %(-0$,(s,
E6= R;‘[;h
E).
+R,(E)]. + R,(E)].
(m = i,,j).
(4a) (4b)
(4d)
and v,, the range scale parameter relation is vi&(E) = v,R,(E),
(5)
with R,(E) the range of ion i with energy E, and A, is its mass number. The first term on the right-hand side of equation (3) represents attenuation of the incident primary ions. The second term on the righthand side represents production and attenuation of projectile ion secondaries. The distance h is usually chosen large enough to minimize the number of iteration steps while concomitantly minimizing the error resulting from neglect of tertiary production in h. Equation (3) can be used to propagate the solution a distance h beyond x. Taking the initial point on the boundary then allows propagation to any arbitrary depth within the interior. The computational algorithm represented by equation (3) has been verified to within 2% accuracy by comparison with an analytical benchmark (Wilson and Townsend, 1988).
2.2. Nucleon transport To characterize the radiation fields produced by primary and secondary nucleons (neutrons and protons) from incident galactic cosmic rays, a deterministic coupled neutron-proton transport code, BRYNTRN, has been developed (Wilson et al., 1989). Because of the high energies involved, the straightahead approximation is again introduced into the Boltzmann transport equation to yield
=xjx&,(E,
E’)4j(X, E’) dE’,
J
(6)
E
for protons. For neutrons, there is no stopping power contribution S(E) so that it becomes
=
1 I
1 E;.=R,-‘[h
er al.
I' j,CE, E’M,,x.
E’) dE’.
(7)
6
where the j, are differential cross-sections for elastic and non-elastic collision processes, and the remaining symbols are defined following equation (1). Solutions to equations (6) and (7), similar in form to equations (3) and (4), have been extensively described elsewhere (Wilson et al., 1989). These computational algorithms were verified to within 1% accuracy by direct comparison with an analytical benchmark solution for a continuous space proton input spectrum (Wilson et al., 1988a). A more detailed discussion of BRYNTRN can also be found in a companion paper (Cucinotta et al., 1992).
GCR TRANSPORT 3. INTERACTION
METHODS
PARAMETERS
AND RADIATION
For nucleon-nucleus collisions, equation replaced by (Wilson et al., 1988b)
3.1. Stopping power
c.&i,
In passing through a material, an ion loses a substantial fraction of its energy to electronic excitation of the material. For energies greater than a few MeV per nucleon, Betbe’s theory using the Born approximation is adequate provided appropriate corrections to Bragg’s rule, shell corrections, and effective charge are included (Wilson, 1983). Proton stopping powers are taken from the parametric expressions of Andersen and Ziegler (1976). A modification to their shell corrections, however, has been added to ensure a smooth transition to Betbe’s asymptotic formula. For alphas, the electronic stopping power is not derivable from proton stopping power at low energies because of the neglect of higher order Born terms. Instead, the parametric fits to experimental data, given by Ziegler (1977b) are used. Electronic stopping powers Sj for ions of charge greater than two are scaled to the proton stopping powers S, as s,=v,:$
E) -f
(10) is
(E)a,O’),
(11)
where uA(j) = 45Ap’(l - 0.018 sin @,),
(12)
and the angle eA is eA = 2.94 ln(A,) + 0.63 sin[3.92 ln(A,) - 2.329]- 0.176. The energy-dependent f(E)
(13)
amplitude is
= 1 - (0.3 e-O.u + 0.76 e-E/i34 x (0.4 + 0.9 e+‘30) sin 8r,
(14)
where 8 ,=1.44
(E<25MeV),
(15a)
and 8 r= 1.33 In(E) - 2.84
(otherwise).
(15b)
(8)
where vj = Zj /A,. At sufficiently low energies, the energy lost by the ion because of nuclear collisions becomes important. The nuclear stopping theory used herein is a modified form (Ziegler, 1977a) of the theory of Linbard et al. (1963). The total stopping power is obtained by summing electronic and nuclear components. 3.2. Nuclear absorption For nucleus-nucleus interactions, the macroscopic absorption cross-sections are obtained by using
where the pi are the elemental constituent-number densities for the target, and the u,~ are the microscopic nuclear absorption cross-sections for the nuclear collision pair. There are given by the energyindependent expression a,b,(i,j) = nri(Af’3 + A:” - 0.2 -A;’
61
QUALITY
- A,-‘)2, (10)
where r, = 1.26 fm and the Ak(k = i, j) are the atomic mass numbers for the colliding nuclei. Equation (10) accurately estimates these cross-sections at high energies but significantly underestimates them below 100 A MeV (Townsend and Wilson, 1986). Fully energy-dependent cross-sections, calculated by using fully energy-dependent, quantum-mechanical scattering models and validated by detailed comparisons with experimental data, have been published (Townsend and Wilson, 1985). These will be incorporated into the transport code in the future.
3.3. Nuclear fragmentation At present there is no suitably accurate theory for predicting nuclear fragmentation (break-up) crosssections for all collision pairs at all energies of interest. Detailed quantum-me&a&al formulations based upon optical potential considerations are being developed (Townsend et al., 1985). These methods are too complex to use in a transport calculation and poorly represent light ion production because of an incomplete understanding of the complete fragmentation process. As an alternative, a semiempirical abrasion-ablation model has been developed (Wilson et al., 1987b). Although independent of the incident ion’s kinetic energy, as suggested by recent studies (Townsend et al., 1986), the model conserves fragment mass and charge, is physically realistic, has only a single adjustable parameter, and agrees very well with available experimental data. In the Langley semiempirical model, tbe classical, geometric abrasion-ablation model of Bowman et al. (1973) is modified to include frictional-spectator interactions (FSI) through the use of higher order corrections to the abraded prefragment excitation energies. In this method, the nuclear fragmentation cross-sections are given by o,, (Z,, A,) = F, exp[ - R IZ, - SA, + TA$3n]a(AA),
(16)
where according to Rudstam (1966) R = 11.8 Aj”“s, S = 0.486, T = 3.8 x lo-‘, and F, is a normalizing factor such that
$%d% A,>= u(M),
(17)
L. W. TOWNSEND
68
which ensures charge and mass conservation. The Rudstam formula for a(AA) is not used because his AA dependence is too simple and breaks down for heavy targets. Instead, the cross-section for removal of AA nucleons is estimated using a(AA)
= nb; - nb:,
(18)
where b, is the impact parameter at which Asbr nucleons are abraded by the collision and Aabl nucleons are ablated, in the subsequent prefragment de-excitation, such that Aa,,
+ Aab,(b~) = AA -!,
(19)
and similarly for b, Aabr(b,)+Aa,,(b,)=AA
+!.
(20)
et al.
absorbed per gram of target material) is computed from a D,(x, >E) = A, S,(E’)C#Q(X, E’) dE’. (24) 5E For risk assessment, the dose equivalent is obtained from H,(x, >E) = Ai
m QF, (E’)Si(E’M,(xt I
(21) where F is the fraction of the volume in the geometric overlap region between the colliding nuclei, and C, and C, are the maximum chord lengths of the intersecting surfaces in the projectile (p) and target (t). Expressions for F, given elsewhere (Wilson et al., 1987b), differ depending upon the relative sizes of the colliding nuclei and the nature of the collision (central vs peripheral). The number of ablated nucleons, Aa,,,, is computed from (22)
which assumes that a nucleon is ablated (evaporated) for every 10 MeV of excitation energy. In equation (22), E, represents excitation energy associated with the surface energy contribution from abrasion, and resulting from E Fs, represents the contributions frictional-spectator interactions. The only arbitrarily adjusted parameter in this model is a second order correction to the expression for the surface energy term. Because the dissociation of projectile and target nuclei by their interacting Coulomb fields may be important for some heavier nuclei at high energies,
alrae = anuc +a,,. Methods (Norbury however,
gem, crosscross-
(23)
CT,, have been developed and for use with this fragmentation model
for estimating
parameterized
ef al.. 1988). They are not currently m the GCR transport code.
4. DOSIMETRIC
E;u,(E’)&,(x,
E’) dE’,
(26)
and
Aabr=FAp[l -0.5exp(-C,il)-0.5exp(-C,/E.)]
the electromagnetic dissociation contributions, must be added to the nuclear fragmentation section, u,,,. to yield the total fragmentation section
(25)
where QF denotes the quality factor which relates absorbed dose to risk. These are LET-dependent quantities obtained from ICRP-26 (1977). For target fragments and nuclear recoils produced by protons, the absorbed dose and dose equivalent are given by
The number of abraded nucleons is estimated from the geometric overlap volume and the mean free path in nuclear matter, i. as
Aab,= (E, + EFsr): 10 MeV,
E’) dE’
E
used,
QUANTITIES
After the particle fluxes for each species (proton or HZE) have been determined, the dose (energy
H,+(x, >E)
E;’Q4 (E’)~jp(E’Mp,(E’)dE’ (27)
=q I
E
where Ei is the average recoil energy of the jth fragment. For propagating neutrons, all of the dose and dose-equivalent results from target nuclear recoils and fragments are computed using equations identical in form to (26) and (27).
5. DOSE-EQUIVALENT
RESULTS
Utilizing the space radiation transport methods described in the previous sections, estimates of dose equivalent in water behind 0 gcrn-* and 10 gcrn-* thickness of aluminum shielding are displayed in Table 1. The input GCR spectra, for the solar minimum period, were obtained from the model promulgated by Adams (1987). No geomagnetic cutoffs are assumed, implying that these estimates are relevant for regions outside the Earth’s magnetosphere. The table includes separate entries for the seven most significant ion contributors to the total GCR dose equivalent. Note that particles heavier than helium (alphas), and their associated reaction products (secondaries and target fragments), account for approximately two-thirds of the total dose equivalent behind 10 g cm-* of aluminum shielding. Target fragments alone, however, account for only 4% of the total dose equivalent-about half the amount contributed by secondaries from heavy ion break-up processes. Contributions from mesons, antiparticles, and gamma rays are not yet incorporated into the transport code but are expected to be less than the target fragment contributions. As previously discussed in the section describing dosimetric quantities, the radiation risk (dose equivalent) is related to the absorbed energy (dose) by a
GCR
TRANSPORT
METHODS
AND RADIATION
69
QUALITY
Table 1. JXsc quivalent in water by GCR component* Incident
Primary ion dose
ion spccics
equivalent (cW
D
9.7
0
Mg Si Fe Rest
11.1 8.0 9.6 30.9 31.9
Total
119.2
E
Target Secondary ion dose quiialcnt (cW
fragment dose equivalent (cW
0 g cm- * Aluminum shield 0
Total dose eollivalent 9.7 7.0 4.9 11.1 8.0 9.6 30.9 37.9 119.2
0
4.9 7.0
P :
4.0 2.1 2.8
0 Mt? Si Fe Rest Total
4.8 3.2 3.7 8.7 11.9 41.2
IOg cmW2Aluminum shield 9.1 1.4 0.8
14.5 4.3 2.2
co.1
:,: 410 10.0 13.2 56.7
*Entries rounded to nearest 0.1 cSv.
multiplicative, LET-dependent quality factor Q. Current values, as specified by the International Commission on Radiological Protection (ICRP, 1977) are displayed in Fig. 1 as a function of LET. Recently, revised values of Q have been proposed (ICRP, 1990) based upon advances in risk assessment methods. These new Q values are also displayed in Fig. 1. To investigate the potential impact of the revised Q values on galactic cosmic ray risk assessments, we have used the HZETRN computer code to calculate annual dose equivalent in water as a function of absorber thickness (up to 30cm) for the solar minimum GCR spectrum beyond the Earth’s magnetosphere. The results are presented in Fig. 2. For water thicknesses up to lOcm, the dose-equivalent predictions using ICRP-60 quality factors are nearly 15% larger than those obtained with the ICRP-26 Q values. At 30 cm water thickness, this difference is reduced to 6%. At the spacecraft shield design level, this potential increase in Q (and therefore dose
equivalent) could double the required shield thickness (Townsend et al., 1990). 6. CELLULAR
TRACK MODEL
The Katz cellular track model has been described elsewhere (Katz et al., 1971; Katz, 1986). Here, for completeness, we will include a brief outline of its basic concepts and its extension to the mixed radiation fields of the GCR environment. Extensive details and applications can be found elsewhere (Cucinotta et al., 1991). Proceeding with the present discussion, the biological damage from propagating ions is caused by secondary electron (delta ray) production. Cell damage is separated into two types: a grain-count regime where random inactivations occur along the ion track, and a track-width regime where many inactivations occur and are said to be distributed like a “hairy rope”. Cellular response is described by four parameters: (1) m, the number of
40 r ----ICRP-60 -
RESULTS
----
ICRP-60
-
ICRP-26
ICRP-26
i
I
Ol
I
IO
loo
I loot
LET(keV/micron) FIQ.
1. Quality factor as a function of LET according to ICRP-26 and ICRP-60.
Watrr
thicknear
(cm)
FIG. 2. Annual dose equivalent vs water-absorber tbickners for galactic cosmic rays at solar minimum. Results are displayed for ICRP-26 and ICRP-60 quality factors.
IO
L. W. TOWNSEND
targets per cell; (2) D,, the characteristic X-ray dose; (3) eo, the cross-sectional area of the cell nucleus within which the damage sites are located; and (4) K, a measure of the size of the damage site. The transition between the grain-count and track-width regimes takes place at Z*2/~f12 on the order of 4, where Z* is the effective charge number and fl is the velocity. The grain-count regime is at the lower values of Z*2/~f12 and the track-width regime is at the higher values. To account for the ability of cells to accumulate sublethal damage, two modes of inactivation are identified. For cells damaged by single ion traversals, the ion-kill (intratrack) mode occurs. The fraction of cells damaged in this mode is P = a/a,,, where a is the single-particle-inactivation cross-section. Cells not damaged in the ion-kill mode can be sublethally damaged by the delta rays from the passing ion and then inactivated in the gamma-kill mode by cumulative addition of sublethal damage due to delta rays from other passing ions. The surviving fraction of a cellular population N,, after irradiation by a fluence of particles F, is written as N - = II, x xi ) NCI where the ion-kill survivability
is
IT,= emaF, and the gamma-kill
survivability
where DX=-D,ht[l-(l-$--l,
is the X-ray dose at which this level is obtained. Equations (28x36) describe the cellular track model for monoenergetic particles. Katz (1986) has previously considered this model for mixed radiation fields. In order to apply this model to the mixed radiation fields seen in space, a replacement of the cross-section and particle fluence number (aF) with the GCR fluxes (r#~~(x, E)) and their corresponding crosssections is required. The ion-kill term, which will now contain a projectile source term (including projectile fragments) and a target fragment term, is written as aF = 1
dE,4j(xv
/ +
/
s
aF = c I (30)
(31)
a = a,[1 - exp( -Z*2/K/?2)]m.
(32)
where the effective charge number is _e-‘?58zq,
(33)
regime, where P > 0.98, we take
P = 1.
For cell transformation, the fraction formed cells per surviving cell is
of trans-
where N’/NA is the fraction of non-transformed cells, and a set of cellular response parameters for transformations m ‘, Dh , a;l , and K ’ are used. The RBE at a given survival level is given by
dE,$j(x, Ej)a*(Ej).
s
C dE,#j(x, Ej) [l - Pj(E,)Isj(E,) dEjdEa4m(x,Ea:Ej)
x 11- PmWI&(&).
(39)
Equations (37) and (39) are used in equations (29) and (30), respectively. The summations over all particle types in equations (37) and (39) represent the addition of probabilities from all ions in the radiation field that contribute to the end point under study. Estimates of biological damage to cell cultures from the GCR environment are detailed elsewhere (Cucinotta et al., 1991). In this work, we present estimates of RBE vs space-mission duration for C3HlOT1/2 cell cultures exposed to the GCR environment at solar minimum. In conventional dosimetry, the quality factor is defined to be independent of fluence. In the Katz model, however, the risk is fluence-dependent. From equations (35), (36), and (29), we see that the RBE values display a simple scaling with exposure time (mission duration). Here we find for N
(35) u
(38)
The gamma-kill dose fraction becomes
Dy=
where D is the absorbed dose. The single-particleinactivation cross-section is given by
RBE=%,
(37)
where the second term is the contribution of nuclear fragments produced locally in the biological medium. This may be written in terms of an effective-action cross-section a* for the passing ion, whose track is dressed by the local target fragments (nuclear stars), as
I
Di. = (1 - P)D
In the track-width
Ej)a,(E,)
C 1 dEmdEj4m(xvE, : Ejb,(E,), 0
is
dose fraction is
Z+=Z(l
(36)
(29)
xI = 1 - (1 - e-Ds/DO)m, The gamma-kill
et al.
-_1
NO
1,
w
GCR TRANSPORT
METHODS
AND RADIATION
QUALITY
71
lasting more than 2 yr, the current Qs are probably slightly conservative. Comparisons of Q vs RBE, as a function of shield thickness, are made in Table 6 of Cucinotta et cl. (1991). There it is noted that Q decreases much more rapidly than RBE as shield thicknesses are increased. Further radiobiological studies are clearly in order. sions
with
aF41,
(41)
Do ,__~l/m~-1+‘L”N*
(42)
that RBE
Then. scalinn the RBE as a function of duration in deep space ti the 1 yr value for a duration period of I (with F = nr) gives RBE(r) = (r/r,)l-’
+(“m)‘RBE(r,).
(43)
As a result, a one-hit (m 3: 1) system RBE becomes fluenceindependent as expressed by RBE(r) = RBE(r,);
(44)
a two-hit (m = 2) system is expressed by
and a three-hit (m = 3) system is expressed by
w Results of this scaling approximation, for cell death (loss of reproduction capability) and neoplastic transformation for C3HlOT1/2 cells in deep space behind 10 g cm-’ of aluminum shielding, are shown in Fig. 3 as a function of mission duration. Clearly, the usual assumption that the risk coefficients (Q or RBE) are fluence-independent may not be valid. For shorter duration missions (less than 1 yr), the risk of mammalian cells inside a spacecraft from GCR particles may be significantly larger than the risk estimated with current quality factors (ICRF’, 1977). For mis-
C3H10Tl/2
g .z c f
loo
Cells
---Cell tronsformotion ---Cell killing ICRP-26
REMARKS
A brief description of the Langley Research Center galactic cosmic ray transport code (HZETRN) has been presented. Included in the discussion were descriptions of the input physical interaction parameters (transport coefficients) as presently modeled. Methods used to convert the transported fluxes/fluences into absorbed doses and dose equivalents were also presented. To illustrate the capabilities of the computer code as a research and design tool, estimates of GCR dose equivalent in water behind and 10 g cms2 aluminum shielding were ogcm-’ presented on an input spectrum component-bycomponent basis. Dose-equivalent estimates using current (ICRP-26) and proposed (ICRP-60) quality factors were presented as a function of water-absorber thickness. If the newly proposed Qs are adopted, then the estimated dose equivalents resulting from GCR exposures of crews on interplanetary missions at solar minimum could increase by as much as 15%-with a concomitant increase in estimated spacecraft-shielding requirements. Finally, the cellular track model of Katz was used to estimate RBE vs mission duration for mammalian cell cultures exposed to galactic cosmic rays. For mission durations shorter than 1 yr, the potential for cell damage was found to be significantly greater than current risk assessments using ICRP-26 Qs would indicate. For missions lasting more than 2 yr, the current Qs are conservative when compared with RBEs that assume high dose rate gamma rays as a reference radiation.
REFERENCES Adams J. H. (1987) Cosmic ray effects on microelectronics,
Mission
durotlon
(yeorsl
FIO. 3. Average RBE for ccl1 killing and ncoplastic transformations of C3HlOTl/2 calls, by galactic cosmic rays at solar minimum, as a function of mission duration. Results arc displayed for all killing and transformation using the Katz model and for the average RBE obtained from ICRP26. Aluminum shielding of 10 g cm-’ is assumed. NT 20/l-F
7. CONCLUDING
Part IV. Naval Rescarch Laboratory Memorandum Report 5901 (revised), Washington, DC. Anderscn H. H. and Ziegler J. F. (1976) Hydrogen Sropping Powers and Ranges in All Elements. Pergamon Prms, Nm York. Benton E. V., Heinrich W., Parnell T. A., Armstrong T. W., Dcrrickson J. H., Fishman G. J., Frank A. L.. Watts J. W. Jr and Wicgel B. (1992) Ionizing radiation exposure of LDEF: prc-recovery estimates (Edited by E. V. Benton and W. H&rich). Nucl. Troth RadioI. Meas. Xl, 75-100. Bowman J. D., Swiatccki W. J. and Tsang C. F. (1973) Abrasion and ablation of heavy ions. Lawrcncc Bcrkeley Laboratory Rcport, Berkeley, CA, LBL-2908. Cucinotta F. A., Katz R., Wilson J. W., Townsend L. W., Ncaly J. E. and Shinn J. L. (1991) Cellular track model of biological damage to mammalian all cultum from galactic cosmic rays. NASA Technical Paper, Washington, DC, NASA TP-3055.
L. W. TOWNSEND
72
Cucinotta F. A., Wilson J. W., Townsend L. W., Shinn J. L. and Katz R. (1992) Track structure model for damage to mammalian cell cultures during solar proton events. Nucl. Tracks Radial. Meas. 20, 177-184. International Commission on Radiological ProtectionICRP (1977) Recommendations of the commission. ICRP Publication 26. Pergamon Press, New York. International Commission on Radiological ProtectionICRP (1990) Recommendations of the commission. Draft report ICRP@/G-01. Katz R. (1986) Biological effects of heavy ions from the standpoint of target theory. Adv. Space Res. 6, 191-198. Katz R., Ackerson B., Homayoonfar M. and Sharma S. C. (1971) Inactivation of cells by heavy ion bombardment. Radial. Res. 41, 402-425. Linhard J., Scharff M. and Schiott H. E. (1963) Range concepts and heavy ion ranges (notes on atomic collisions II). Mat. Fys. Medd. Dun. Vid. Selsk. 33, l-42.
Norbury J. W., Cucinotta F. A., Townsend L. W. and Badavi F. F. (1988) Parameterized cross sections for coulomb dissociation in heavy ion collisions. Nucl. Instrum. Merh. B31, 535-537. Rudstam G. (1966) Systematics of spallation yields. 2. Nurursforschung 21a, 1027-1041. Townsend L. W., Nealy J. E., Wilson J. W. and Simonsen L. C. (1990) Estimates of galactic cosmic ray shielding requirements during solar minimum. NASA Technical Memorandum, Washington, DC, NASA TM-4167. Townsend L. W.. Shinn J. L. and Wilson J. W. fl99lb) Interplanetary crew exposure estimates for the August 1972 and October 1989 solar particle events. Radiuf. Res. 126, 108-110.
Townsend L. W. and Wilson J. W. (1985) Tables of nuclear cross sections for galactic cosmic rays: absorption cross section. NASA Reference Publication, Washington, DC, NASA RP-1134. Townsend L. W. and Wilson J. W. (1986) Energy-dependent parameterization of heavy ion absorption cross sections. Radiar. Res. 106, 283-287. Townsend L. W., Wilson J. W., Cucinotta F. A. and Norbury J. W. (1986) Comparisons of abrasion model
et al.
difference in heavy ion fragmentation: optical versus geometric models.. Phys. R&J. C 34, 1491-1494. Townsend L. W.. Wilson J. W. and Norburv J. W. (1985) A simplified optical model description of heavy ion fragmentation. Canadian J. Phys. 63, 135-138. Townsend L. W., Wilson J. W., Shinn J. L. and Curtis S. B. (199 I a) Human exposure to large solar particle events _ in space. Adu. Space Res. (in p&s). Wilson J. W. (1983) Heavy ion transport in the straightahead approximation. NASA Technical Paper, Washington-DC, NASA TP-2178. Wilson J. W. and Townsend L. W. (1988) A benchmark for galactic cosmic ray transport codes: Radiat. Res. 114, 201-207. Wilson J. W., Townsend L. W. and Badavi F. F. (1987a) Galactic HZE propagation through the Earth’s atmosphere. Radial. Res. 109, 173-183. Wilson J. W., Townsend L. W. and Badavi F. F. (1987b) A semiempirical nuclear fragmentation model. Nucl. Instrum. Meth. B18, 225-231. Wilson J. W., Townsend L. W., Bidasaria H. B., Schimmerling W., Wong M. and Howard J. (1984) *ONe depth-dose relations in water. HIrh Phys. 46, 1101-1111. Wilson J. W., Townsend L. W., Buck W. W., Chun S. Y., Hong B. S. and Lamkin S. L. (1988b) Nucleon-nucleus interaction data base: total nuclear and absorption cross sections. NASA Technical Memorandum, Washington, DC, NASA TM-4053. Wilson J. W., Townsend L. W., Ganapol B. D., Chun S. Y., Hong B. S. and Buck W. W. (1988a) Charged particle transport in one dimension. Nucl. Sci. Engng 99, 285-287. Wilson J. W., Townsend L. W., Nealy J. E., Chun S. Y., Honn B. S.. Buck W. W.. Lamkin S. L.. Ganawl B. D.. Khan F. and Cucinotta F. A. (1989) BRYNTRN: a baryon transport model. NASA Technical Paper, Washington, DC, NASA TP-2887. Ziegler J. F. (1977a) The electronic and nuclear stopping of energetic ions. Appl. Phys. Lert. 31, 544-546. Ziegler J. F. (1977b) Helium Stopping Powers and Ranges in All EIemenrnl Muffer. Pergamon Press, New York.
0735-245x/92 S5.00 + .oO Pergamoo Rem pk
Part D
Printed in Great Britain
GALACTIC
COSMIC RAY TRANSPORT METHODS RADIATION QUALITY ISSUES
AND
L. W. TOWNSEND, J. W. wIlSON, F. A. ~ClNOTT.4 and J. L. SEWN Mail Stop 493, NASA Langley Research Center, Hampton, VA 23665-5225, U.S.A. (Received 4 M&I
1991)
Abstract-An overview of galactic cosmic ray @CR) interaction and transport methods, as implemented in the Langley Research Center GCR transport code, is presented. Representative results for solar
minimum, exo-magnetospheric GCR dose equivalents in water are presented on a component by component basis for various thicknesses of aluminum shielding. The impact of proposed changes to the currently used quality factors on exposure estimates and shielding requirements are quantified. Using the cellular track model of Katz, estimates of relative biological effectiveness (RBE) for the mixed GCR radiation fields are also made.
1. INTRODUCTION
estimate RBE (relative biological effectiveness) values for the mixed radiation fields will be described. Details of the GCR environment itself will not be described. They are discussed elsewhere in this issue (Benton er ul., 1992).
the Earth’s magnetosphere, the two main sources of radiation hazards to crews of manned space missions are energetic solar particle events (SPEs) and galactic cosmic rays (GCRs). For a SPE, the major concerns center upon acute effects resulting from very large radiation doses accruing in a short period of time (hours or days). Without adequate protective shielding, e.g. a storm shelter, crews could receive mission-threatening or life-threatening exposures (Townsend et al., 1991a, b). Details of methods used to describe SPE transport and interactions are given in a companion paper (Cucinotta er al., 1992). For GCR particles, the main source of concern is cumulative exposure to the HZE [high charge (Z), high energy (E)] component. These particles, classified as high-LET (linear energy transfer) radiations, deposit large quantities of energy per unit distance traveled in tissue and shield materials. Therefore, they may be much more damaging than conventional low-LET radiation such as X-rays or @Co gamma rays. In this paper, methods for accurately describing the interactions and transport of GCR particles through bulk materials, as implemented in the current version of the Langley Research Center (LaRC) GCR transport code, HZETRN, will be described. To illustrate the computer code capabilities, representative GCR dose equivalents in water will be presented on a component-by-component basis for several of the most prevalent ions in the incident GCR spectrum. An assessment of the impact on exposure estimates and possible GCR shielding requirements resulting from proposed changes to the radiation quality factors (ICRP, 1990) will be quantified. Finally, use of the cellular track model of Katz (Katz et al., 1971) to BEYOND
2. GALACTIC COSMIC RAY TRANSPORT THEORY As high energy galactic cosmic rays traverse bulk matter, such as a spacecraft, their radiation fields change composition through interactions with the materials in their paths. As a result of these interactions, the internal radiation environment within the spacecraft can differ appreciably from the incident external environment. These alterations in the incident radiation environment depend upon the thickness, geometry, and material composition of the target. They are described by transport models which relate the transmitted fluxes, as functions of spatial location, kinetic energy, and directions of particle motion, to the incident fluxes. The main interaction processes involved in the transport of these radiation fields through bulk matter are (1) ionization energy losses through collisions with atomic electrons; (2) nuclear elastic and inelastic collisions; and (3) nuclear break-up (fragmentation) and electromagnetic dissociation interactions. The latter are particularly important because fragmentations result in the production of reaction products which alter the elemental and isotopic composition of the transported radiation fields. The radioactive decay contributions of the transported fragments are ignored because their decay times are typically much longer than the time required for the radioactive fragment to exit the spacecraft or undergo a subsequent nuclear collision. 65
66
L. W. TOWNSEND
2.1. Heavy ion transport
Pi(E)=exp[-A,~Oe$$dE],
The overall propagation of these radiation fields is described by a Boltzmann equation, which can be derived from considerations of mass and energy conservation. Its solutions give values of particle fluxes and energies everywhere within and exiting the boundaries of the target medium. For GCR particles, the typically large ion kinetic energies allow one to neglect changes in particle direction because of collisions. This is called a straightahead approximation. The one-dimensional Boltzmann equation is then written (Wilson et al., 1984) g + aitE) [
GSitE)4itx, E) 1
In equation (I), 4, is the flux of type i ions at position x with motion along the x axis and energy E in units of A MeV, a,(E) is the corresponding macroscopic nuclear absorption cross-section in units of cm-‘, S,(E) is the change in E per unit distance (e.g. the stopping power per unit projectile mass), and a,(E) is the cross-section, in units of cm-‘, for producing ion i from a collision by ion j. Solution methods for equation (1) are usually optimized for the specific transport problem being investigated. For accelerator-beam studies, solutions can be obtained using analytic methods in a perturbation expansion (Wilson et al., 1984) 4,(x. E) = f b:“‘(x. E). n=cl
(2)
where n = 0 denotes the primary beam, n = 1 denotes secondaries produced by fragmenting of the primaries, n = 2 denotes tertiaries produced by fragmenting of the secondaries. etc. For the GCR transport problem, the incident GCR particles possess broad energy spectra; therefore, a different solution technique is required for computational efficiency (Wilson et al., 1987a). This is accomplished by using the first two terms of the perturbation expansion in an iterative procedure which effectively sums subsequent generations of reaction products to all orders. The result is
3,(x + h, E) =
z
$,(x. E ) $,(.~. 6).
(3)
where 3,(x. E) = %(-0$,(s,
E6= R;‘[;h
E).
+R,(E)]. + R,(E)].
(m = i,,j).
(4a) (4b)
(4d)
and v,, the range scale parameter relation is vi&(E) = v,R,(E),
(5)
with R,(E) the range of ion i with energy E, and A, is its mass number. The first term on the right-hand side of equation (3) represents attenuation of the incident primary ions. The second term on the righthand side represents production and attenuation of projectile ion secondaries. The distance h is usually chosen large enough to minimize the number of iteration steps while concomitantly minimizing the error resulting from neglect of tertiary production in h. Equation (3) can be used to propagate the solution a distance h beyond x. Taking the initial point on the boundary then allows propagation to any arbitrary depth within the interior. The computational algorithm represented by equation (3) has been verified to within 2% accuracy by comparison with an analytical benchmark (Wilson and Townsend, 1988).
2.2. Nucleon transport To characterize the radiation fields produced by primary and secondary nucleons (neutrons and protons) from incident galactic cosmic rays, a deterministic coupled neutron-proton transport code, BRYNTRN, has been developed (Wilson et al., 1989). Because of the high energies involved, the straightahead approximation is again introduced into the Boltzmann transport equation to yield
=xjx&,(E,
E’)4j(X, E’) dE’,
J
(6)
E
for protons. For neutrons, there is no stopping power contribution S(E) so that it becomes
=
1 I
1 E;.=R,-‘[h
er al.
I' j,CE, E’M,,x.
E’) dE’.
(7)
6
where the j, are differential cross-sections for elastic and non-elastic collision processes, and the remaining symbols are defined following equation (1). Solutions to equations (6) and (7), similar in form to equations (3) and (4), have been extensively described elsewhere (Wilson et al., 1989). These computational algorithms were verified to within 1% accuracy by direct comparison with an analytical benchmark solution for a continuous space proton input spectrum (Wilson et al., 1988a). A more detailed discussion of BRYNTRN can also be found in a companion paper (Cucinotta et al., 1992).
GCR TRANSPORT 3. INTERACTION
METHODS
PARAMETERS
AND RADIATION
For nucleon-nucleus collisions, equation replaced by (Wilson et al., 1988b)
3.1. Stopping power
c.&i,
In passing through a material, an ion loses a substantial fraction of its energy to electronic excitation of the material. For energies greater than a few MeV per nucleon, Betbe’s theory using the Born approximation is adequate provided appropriate corrections to Bragg’s rule, shell corrections, and effective charge are included (Wilson, 1983). Proton stopping powers are taken from the parametric expressions of Andersen and Ziegler (1976). A modification to their shell corrections, however, has been added to ensure a smooth transition to Betbe’s asymptotic formula. For alphas, the electronic stopping power is not derivable from proton stopping power at low energies because of the neglect of higher order Born terms. Instead, the parametric fits to experimental data, given by Ziegler (1977b) are used. Electronic stopping powers Sj for ions of charge greater than two are scaled to the proton stopping powers S, as s,=v,:$
E) -f
(10) is
(E)a,O’),
(11)
where uA(j) = 45Ap’(l - 0.018 sin @,),
(12)
and the angle eA is eA = 2.94 ln(A,) + 0.63 sin[3.92 ln(A,) - 2.329]- 0.176. The energy-dependent f(E)
(13)
amplitude is
= 1 - (0.3 e-O.u + 0.76 e-E/i34 x (0.4 + 0.9 e+‘30) sin 8r,
(14)
where 8 ,=1.44
(E<25MeV),
(15a)
and 8 r= 1.33 In(E) - 2.84
(otherwise).
(15b)
(8)
where vj = Zj /A,. At sufficiently low energies, the energy lost by the ion because of nuclear collisions becomes important. The nuclear stopping theory used herein is a modified form (Ziegler, 1977a) of the theory of Linbard et al. (1963). The total stopping power is obtained by summing electronic and nuclear components. 3.2. Nuclear absorption For nucleus-nucleus interactions, the macroscopic absorption cross-sections are obtained by using
where the pi are the elemental constituent-number densities for the target, and the u,~ are the microscopic nuclear absorption cross-sections for the nuclear collision pair. There are given by the energyindependent expression a,b,(i,j) = nri(Af’3 + A:” - 0.2 -A;’
61
QUALITY
- A,-‘)2, (10)
where r, = 1.26 fm and the Ak(k = i, j) are the atomic mass numbers for the colliding nuclei. Equation (10) accurately estimates these cross-sections at high energies but significantly underestimates them below 100 A MeV (Townsend and Wilson, 1986). Fully energy-dependent cross-sections, calculated by using fully energy-dependent, quantum-mechanical scattering models and validated by detailed comparisons with experimental data, have been published (Townsend and Wilson, 1985). These will be incorporated into the transport code in the future.
3.3. Nuclear fragmentation At present there is no suitably accurate theory for predicting nuclear fragmentation (break-up) crosssections for all collision pairs at all energies of interest. Detailed quantum-me&a&al formulations based upon optical potential considerations are being developed (Townsend et al., 1985). These methods are too complex to use in a transport calculation and poorly represent light ion production because of an incomplete understanding of the complete fragmentation process. As an alternative, a semiempirical abrasion-ablation model has been developed (Wilson et al., 1987b). Although independent of the incident ion’s kinetic energy, as suggested by recent studies (Townsend et al., 1986), the model conserves fragment mass and charge, is physically realistic, has only a single adjustable parameter, and agrees very well with available experimental data. In the Langley semiempirical model, tbe classical, geometric abrasion-ablation model of Bowman et al. (1973) is modified to include frictional-spectator interactions (FSI) through the use of higher order corrections to the abraded prefragment excitation energies. In this method, the nuclear fragmentation cross-sections are given by o,, (Z,, A,) = F, exp[ - R IZ, - SA, + TA$3n]a(AA),
(16)
where according to Rudstam (1966) R = 11.8 Aj”“s, S = 0.486, T = 3.8 x lo-‘, and F, is a normalizing factor such that
$%d% A,>= u(M),
(17)
L. W. TOWNSEND
68
which ensures charge and mass conservation. The Rudstam formula for a(AA) is not used because his AA dependence is too simple and breaks down for heavy targets. Instead, the cross-section for removal of AA nucleons is estimated using a(AA)
= nb; - nb:,
(18)
where b, is the impact parameter at which Asbr nucleons are abraded by the collision and Aabl nucleons are ablated, in the subsequent prefragment de-excitation, such that Aa,,
+ Aab,(b~) = AA -!,
(19)
and similarly for b, Aabr(b,)+Aa,,(b,)=AA
+!.
(20)
et al.
absorbed per gram of target material) is computed from a D,(x, >E) = A, S,(E’)C#Q(X, E’) dE’. (24) 5E For risk assessment, the dose equivalent is obtained from H,(x, >E) = Ai
m QF, (E’)Si(E’M,(xt I
(21) where F is the fraction of the volume in the geometric overlap region between the colliding nuclei, and C, and C, are the maximum chord lengths of the intersecting surfaces in the projectile (p) and target (t). Expressions for F, given elsewhere (Wilson et al., 1987b), differ depending upon the relative sizes of the colliding nuclei and the nature of the collision (central vs peripheral). The number of ablated nucleons, Aa,,,, is computed from (22)
which assumes that a nucleon is ablated (evaporated) for every 10 MeV of excitation energy. In equation (22), E, represents excitation energy associated with the surface energy contribution from abrasion, and resulting from E Fs, represents the contributions frictional-spectator interactions. The only arbitrarily adjusted parameter in this model is a second order correction to the expression for the surface energy term. Because the dissociation of projectile and target nuclei by their interacting Coulomb fields may be important for some heavier nuclei at high energies,
alrae = anuc +a,,. Methods (Norbury however,
gem, crosscross-
(23)
CT,, have been developed and for use with this fragmentation model
for estimating
parameterized
ef al.. 1988). They are not currently m the GCR transport code.
4. DOSIMETRIC
E;u,(E’)&,(x,
E’) dE’,
(26)
and
Aabr=FAp[l -0.5exp(-C,il)-0.5exp(-C,/E.)]
the electromagnetic dissociation contributions, must be added to the nuclear fragmentation section, u,,,. to yield the total fragmentation section
(25)
where QF denotes the quality factor which relates absorbed dose to risk. These are LET-dependent quantities obtained from ICRP-26 (1977). For target fragments and nuclear recoils produced by protons, the absorbed dose and dose equivalent are given by
The number of abraded nucleons is estimated from the geometric overlap volume and the mean free path in nuclear matter, i. as
Aab,= (E, + EFsr): 10 MeV,
E’) dE’
E
used,
QUANTITIES
After the particle fluxes for each species (proton or HZE) have been determined, the dose (energy
H,+(x, >E)
E;’Q4 (E’)~jp(E’Mp,(E’)dE’ (27)
=q I
E
where Ei is the average recoil energy of the jth fragment. For propagating neutrons, all of the dose and dose-equivalent results from target nuclear recoils and fragments are computed using equations identical in form to (26) and (27).
5. DOSE-EQUIVALENT
RESULTS
Utilizing the space radiation transport methods described in the previous sections, estimates of dose equivalent in water behind 0 gcrn-* and 10 gcrn-* thickness of aluminum shielding are displayed in Table 1. The input GCR spectra, for the solar minimum period, were obtained from the model promulgated by Adams (1987). No geomagnetic cutoffs are assumed, implying that these estimates are relevant for regions outside the Earth’s magnetosphere. The table includes separate entries for the seven most significant ion contributors to the total GCR dose equivalent. Note that particles heavier than helium (alphas), and their associated reaction products (secondaries and target fragments), account for approximately two-thirds of the total dose equivalent behind 10 g cm-* of aluminum shielding. Target fragments alone, however, account for only 4% of the total dose equivalent-about half the amount contributed by secondaries from heavy ion break-up processes. Contributions from mesons, antiparticles, and gamma rays are not yet incorporated into the transport code but are expected to be less than the target fragment contributions. As previously discussed in the section describing dosimetric quantities, the radiation risk (dose equivalent) is related to the absorbed energy (dose) by a
GCR
TRANSPORT
METHODS
AND RADIATION
69
QUALITY
Table 1. JXsc quivalent in water by GCR component* Incident
Primary ion dose
ion spccics
equivalent (cW
D
9.7
0
Mg Si Fe Rest
11.1 8.0 9.6 30.9 31.9
Total
119.2
E
Target Secondary ion dose quiialcnt (cW
fragment dose equivalent (cW
0 g cm- * Aluminum shield 0
Total dose eollivalent 9.7 7.0 4.9 11.1 8.0 9.6 30.9 37.9 119.2
0
4.9 7.0
P :
4.0 2.1 2.8
0 Mt? Si Fe Rest Total
4.8 3.2 3.7 8.7 11.9 41.2
IOg cmW2Aluminum shield 9.1 1.4 0.8
14.5 4.3 2.2
co.1
:,: 410 10.0 13.2 56.7
*Entries rounded to nearest 0.1 cSv.
multiplicative, LET-dependent quality factor Q. Current values, as specified by the International Commission on Radiological Protection (ICRP, 1977) are displayed in Fig. 1 as a function of LET. Recently, revised values of Q have been proposed (ICRP, 1990) based upon advances in risk assessment methods. These new Q values are also displayed in Fig. 1. To investigate the potential impact of the revised Q values on galactic cosmic ray risk assessments, we have used the HZETRN computer code to calculate annual dose equivalent in water as a function of absorber thickness (up to 30cm) for the solar minimum GCR spectrum beyond the Earth’s magnetosphere. The results are presented in Fig. 2. For water thicknesses up to lOcm, the dose-equivalent predictions using ICRP-60 quality factors are nearly 15% larger than those obtained with the ICRP-26 Q values. At 30 cm water thickness, this difference is reduced to 6%. At the spacecraft shield design level, this potential increase in Q (and therefore dose
equivalent) could double the required shield thickness (Townsend et al., 1990). 6. CELLULAR
TRACK MODEL
The Katz cellular track model has been described elsewhere (Katz et al., 1971; Katz, 1986). Here, for completeness, we will include a brief outline of its basic concepts and its extension to the mixed radiation fields of the GCR environment. Extensive details and applications can be found elsewhere (Cucinotta et al., 1991). Proceeding with the present discussion, the biological damage from propagating ions is caused by secondary electron (delta ray) production. Cell damage is separated into two types: a grain-count regime where random inactivations occur along the ion track, and a track-width regime where many inactivations occur and are said to be distributed like a “hairy rope”. Cellular response is described by four parameters: (1) m, the number of
40 r ----ICRP-60 -
RESULTS
----
ICRP-60
-
ICRP-26
ICRP-26
i
I
Ol
I
IO
loo
I loot
LET(keV/micron) FIQ.
1. Quality factor as a function of LET according to ICRP-26 and ICRP-60.
Watrr
thicknear
(cm)
FIG. 2. Annual dose equivalent vs water-absorber tbickners for galactic cosmic rays at solar minimum. Results are displayed for ICRP-26 and ICRP-60 quality factors.
IO
L. W. TOWNSEND
targets per cell; (2) D,, the characteristic X-ray dose; (3) eo, the cross-sectional area of the cell nucleus within which the damage sites are located; and (4) K, a measure of the size of the damage site. The transition between the grain-count and track-width regimes takes place at Z*2/~f12 on the order of 4, where Z* is the effective charge number and fl is the velocity. The grain-count regime is at the lower values of Z*2/~f12 and the track-width regime is at the higher values. To account for the ability of cells to accumulate sublethal damage, two modes of inactivation are identified. For cells damaged by single ion traversals, the ion-kill (intratrack) mode occurs. The fraction of cells damaged in this mode is P = a/a,,, where a is the single-particle-inactivation cross-section. Cells not damaged in the ion-kill mode can be sublethally damaged by the delta rays from the passing ion and then inactivated in the gamma-kill mode by cumulative addition of sublethal damage due to delta rays from other passing ions. The surviving fraction of a cellular population N,, after irradiation by a fluence of particles F, is written as N - = II, x xi ) NCI where the ion-kill survivability
is
IT,= emaF, and the gamma-kill
survivability
where DX=-D,ht[l-(l-$--l,
is the X-ray dose at which this level is obtained. Equations (28x36) describe the cellular track model for monoenergetic particles. Katz (1986) has previously considered this model for mixed radiation fields. In order to apply this model to the mixed radiation fields seen in space, a replacement of the cross-section and particle fluence number (aF) with the GCR fluxes (r#~~(x, E)) and their corresponding crosssections is required. The ion-kill term, which will now contain a projectile source term (including projectile fragments) and a target fragment term, is written as aF = 1
dE,4j(xv
/ +
/
s
aF = c I (30)
(31)
a = a,[1 - exp( -Z*2/K/?2)]m.
(32)
where the effective charge number is _e-‘?58zq,
(33)
regime, where P > 0.98, we take
P = 1.
For cell transformation, the fraction formed cells per surviving cell is
of trans-
where N’/NA is the fraction of non-transformed cells, and a set of cellular response parameters for transformations m ‘, Dh , a;l , and K ’ are used. The RBE at a given survival level is given by
dE,$j(x, Ej)a*(Ej).
s
C dE,#j(x, Ej) [l - Pj(E,)Isj(E,) dEjdEa4m(x,Ea:Ej)
x 11- PmWI&(&).
(39)
Equations (37) and (39) are used in equations (29) and (30), respectively. The summations over all particle types in equations (37) and (39) represent the addition of probabilities from all ions in the radiation field that contribute to the end point under study. Estimates of biological damage to cell cultures from the GCR environment are detailed elsewhere (Cucinotta et al., 1991). In this work, we present estimates of RBE vs space-mission duration for C3HlOT1/2 cell cultures exposed to the GCR environment at solar minimum. In conventional dosimetry, the quality factor is defined to be independent of fluence. In the Katz model, however, the risk is fluence-dependent. From equations (35), (36), and (29), we see that the RBE values display a simple scaling with exposure time (mission duration). Here we find for N
(35) u
(38)
The gamma-kill dose fraction becomes
Dy=
where D is the absorbed dose. The single-particleinactivation cross-section is given by
RBE=%,
(37)
where the second term is the contribution of nuclear fragments produced locally in the biological medium. This may be written in terms of an effective-action cross-section a* for the passing ion, whose track is dressed by the local target fragments (nuclear stars), as
I
Di. = (1 - P)D
In the track-width
Ej)a,(E,)
C 1 dEmdEj4m(xvE, : Ejb,(E,), 0
is
dose fraction is
Z+=Z(l
(36)
(29)
xI = 1 - (1 - e-Ds/DO)m, The gamma-kill
et al.
-_1
NO
1,
w
GCR TRANSPORT
METHODS
AND RADIATION
QUALITY
71
lasting more than 2 yr, the current Qs are probably slightly conservative. Comparisons of Q vs RBE, as a function of shield thickness, are made in Table 6 of Cucinotta et cl. (1991). There it is noted that Q decreases much more rapidly than RBE as shield thicknesses are increased. Further radiobiological studies are clearly in order. sions
with
aF41,
(41)
Do ,__~l/m~-1+‘L”N*
(42)
that RBE
Then. scalinn the RBE as a function of duration in deep space ti the 1 yr value for a duration period of I (with F = nr) gives RBE(r) = (r/r,)l-’
+(“m)‘RBE(r,).
(43)
As a result, a one-hit (m 3: 1) system RBE becomes fluenceindependent as expressed by RBE(r) = RBE(r,);
(44)
a two-hit (m = 2) system is expressed by
and a three-hit (m = 3) system is expressed by
w Results of this scaling approximation, for cell death (loss of reproduction capability) and neoplastic transformation for C3HlOT1/2 cells in deep space behind 10 g cm-’ of aluminum shielding, are shown in Fig. 3 as a function of mission duration. Clearly, the usual assumption that the risk coefficients (Q or RBE) are fluence-independent may not be valid. For shorter duration missions (less than 1 yr), the risk of mammalian cells inside a spacecraft from GCR particles may be significantly larger than the risk estimated with current quality factors (ICRF’, 1977). For mis-
C3H10Tl/2
g .z c f
loo
Cells
---Cell tronsformotion ---Cell killing ICRP-26
REMARKS
A brief description of the Langley Research Center galactic cosmic ray transport code (HZETRN) has been presented. Included in the discussion were descriptions of the input physical interaction parameters (transport coefficients) as presently modeled. Methods used to convert the transported fluxes/fluences into absorbed doses and dose equivalents were also presented. To illustrate the capabilities of the computer code as a research and design tool, estimates of GCR dose equivalent in water behind and 10 g cms2 aluminum shielding were ogcm-’ presented on an input spectrum component-bycomponent basis. Dose-equivalent estimates using current (ICRP-26) and proposed (ICRP-60) quality factors were presented as a function of water-absorber thickness. If the newly proposed Qs are adopted, then the estimated dose equivalents resulting from GCR exposures of crews on interplanetary missions at solar minimum could increase by as much as 15%-with a concomitant increase in estimated spacecraft-shielding requirements. Finally, the cellular track model of Katz was used to estimate RBE vs mission duration for mammalian cell cultures exposed to galactic cosmic rays. For mission durations shorter than 1 yr, the potential for cell damage was found to be significantly greater than current risk assessments using ICRP-26 Qs would indicate. For missions lasting more than 2 yr, the current Qs are conservative when compared with RBEs that assume high dose rate gamma rays as a reference radiation.
REFERENCES Adams J. H. (1987) Cosmic ray effects on microelectronics,
Mission
durotlon
(yeorsl
FIO. 3. Average RBE for ccl1 killing and ncoplastic transformations of C3HlOTl/2 calls, by galactic cosmic rays at solar minimum, as a function of mission duration. Results arc displayed for all killing and transformation using the Katz model and for the average RBE obtained from ICRP26. Aluminum shielding of 10 g cm-’ is assumed. NT 20/l-F
7. CONCLUDING
Part IV. Naval Rescarch Laboratory Memorandum Report 5901 (revised), Washington, DC. Anderscn H. H. and Ziegler J. F. (1976) Hydrogen Sropping Powers and Ranges in All Elements. Pergamon Prms, Nm York. Benton E. V., Heinrich W., Parnell T. A., Armstrong T. W., Dcrrickson J. H., Fishman G. J., Frank A. L.. Watts J. W. Jr and Wicgel B. (1992) Ionizing radiation exposure of LDEF: prc-recovery estimates (Edited by E. V. Benton and W. H&rich). Nucl. Troth RadioI. Meas. Xl, 75-100. Bowman J. D., Swiatccki W. J. and Tsang C. F. (1973) Abrasion and ablation of heavy ions. Lawrcncc Bcrkeley Laboratory Rcport, Berkeley, CA, LBL-2908. Cucinotta F. A., Katz R., Wilson J. W., Townsend L. W., Ncaly J. E. and Shinn J. L. (1991) Cellular track model of biological damage to mammalian all cultum from galactic cosmic rays. NASA Technical Paper, Washington, DC, NASA TP-3055.
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