mailing address at the time of finishing this paper, 1983:
Department of Applied Earth Sciences,
Stanford University, Stanford, CA 94305, USA
Parts of this paper were added while the author was Visiting Scholar at the
Los Alamos National Laboratory, Los Alamos, New Mexico, USA
METHODS
The radioactive inventories of all chemical elements are evaluated after an operation time at which either reactor type has produced 1 GW_{th}yr of energy. In view of the resulting long isolation times for the radioactive waste it is conservatively assumed that eventually (a) the entire long lived radioactive inventory enters into the biosphere, and (b) the radioactive elements have forgotten their origin and behave like the corresponding natural elements. The International Commission on Radiological Protection (ICRP) guidelines specify their permissible concentrations in drinking water. The evaluation uses two types of characteristic quantities. Both decrease over time, as given by the radioisotopes' specific half lives:
(1) Biological Hazard Potential (Figs. 4a, b)
The radiological data for bismuth and beryllium are unknown and had to be conservatively assumed.
Geochemical as well as fusion reactor material composition data are missing for most of the elements that have relevant longlived radioisotopes. On the basis of extrapolations, in this classification scheme
Isolation times of the order of a million years can be anticipated for fusion as well as fission reactor waste based on both types of characteristics, BHP as well as c_{p}. The BHP and c_{p} differences of fusion and fission reactor waste elements seem small in view of geochemical and biochemical parameter uncertainties and little known potential ranges of environmental conditions. Therefore, a fusion/fission comparison of effects like geochemical accumulation of the radioactive waste elements appears to be an extremely difficult and yet unsolved task.
Thus, the presently unknown environmental variabilities rather than the differences presented in this publication might determine which type of energy source is less hazardous.
The most hazardous part of the activity within a fission reactor is considered to be the fission products and the actinides in the irradiated fuel element. Their activity is practically invariably connected with the fission process. In contrast to that, the amount and composition of future fusion reactor radioactive waste will largely depend on the choice of the materials of which it is made.
This provides fusion valuable degrees of freedom with respect to the objectives and strategies of waste management, the choice of the blanket materials still being open. There are materials which could be used for the structure of reactor blankets which would produce only short lived activity (if trace impurities levels present in these materials producing long lived activity could be sufficiently reduced). On the other hand, those materials demand a largely unknown processing and manufacturing technology. At present, stainless steels are most likely chosen as structural material.
If stainless steel is employed as structural material in fusion reactors its activity will not differ much from the activity of the stainless steel of the core barrel of a fission reactor (cache, core barrel (cache) in Westinghouse nuclear reactor) since the thermal neutron flux is the main source of steel activation in both types of reactors and the fluxes are similar. Moreover, the weights of the core barrel on the one hand and the most active part of a fusion reactor, the wall surrounding the plasma (the "first wall"), on the other hand, are similar, i.e. 6 to 8 tons for reactors having a thermal power of 500 to 1000 MW.
The same is true for graphite, which is used in fusion as well as in some fission reactors to slow down the neutrons for their required fission reactions: In fission reactors the thermal neutrons fission uranium (or thorium) to produce energy. As mentioned above, in fusion reactors energy is produced with tritium as intermediate step: Thermal neutrons fission lithium to produce tritium which in turn is fused to produce the major amount of energy.
Fission and fusion reactors differ in their multiplication processes: In fission the fuel is multiplied by producing long lived actinides. In fusion the neutrons are multiplied in beryllium, bismuth or lead to produce enough tritium. The half lives of the involved activation products in both processes (Be, Bi, Pb in fusion and Am, Np, Pu in fission) are similar.
The volumes of high level fission and fusion reactor waste that have to be disposed of after the generation of the same amount of thermal energy in both types of reactors are about the same, roughly one cubic centimeter of solid material per kW yr, if the comparison is limited to the volume of the fuel elements on the one hand and that of the first wall on the other. This is one of the reasons why in this paper the activities and potential hazards will be normalized to (i.e. given for) one cubic centimeter of reactor material.
This paper will identify critical elements likely to be present in activated steels, in the moderator graphite and multiplier materials. Graphs will show which of the activated elements will dominate the groundwater hazard for what period of time after shutdown of the reactor, i.e. for how long they will need to be isolated from the biosphere.
INTOR has been designed at the headquarters of the IAEA (International Atomic Energy Agency) in Vienna, Austria, by a group of European, Japanese, US and USSR scientists during the past few years. It belongs to the group of intermediate devices that will be operable by the turn of the century, between the presentday fusion experiments like the Tokamak Fusion Test Facility in Princeton, New Jersey, USA, and the demonstration reactors that will show the technological feasibility to generate energy by fusion. In the blanket of INTOR a thermal power of 500 MW will be generated.
Figure 1. Simplified Cross Section Through INTOR (after Abdou et al.)
In Tokamaks the plasma is confined by magnetic forces to a horizontal torus. In Fig. 1 one can see the right half of a vertical cross section through the torus and its surrounding parts. The figure shows the first wall, blanket and shield. Through the openings in the blanket the plasma will be heated. The torus is built of an array of wedgeshaped sectors, one of which is shown in Fig. 2.
Figure 2. First wallblanketshield sector of INTOR (after Abdou et al.)
Figure 3. Blanket module of INTOR (after Abdou et al.)
The blanket itself is composed of modules, one of which is depicted in Fig. 3. The blanket has a thickness of 50 cm, therefore the height of the steelbox in Fig. 3 is 50 cm.
In principle, in an individual activation reaction the number Δn of waste nuclei ("daughters") generated during an operation time Δt of the reactor is proportional to both the number Φ Δt of the incident neutrons (per area of the neutron flux) and the number n of exposed nuclei ("mother" nuclei). The ratio Δn/(n Φ Δt) is called the neutron activation cross section σ. It has been determined directly by experiment or calculated with the help of a nuclear model which correlates the basic properties of the nucleus, such as the number of protons and neutrons and their individual sizes, with the size of the nucleus and the chance of a nuclear activation reaction.
The activation cross sections for most thermal neutron reactions used here are from the German Chart of the Nuclides. The rest of the cross sections have been taken from a compilation of Alley and Lessler. They were used in the PLOWSHARE project for calculating the activity induced in soil by peaceful nuclear explosions.
As the compilation gives σvalues for most of the nuclides, even radioactive ones, it is a useful data base for activation calculations of the kind presented in this article. On the other hand many of its σvalues have been determined using the above mentioned nuclear structure theory, and therefore a discussion of possible variations of the activities is necessary. This is greatly eased by a linearization of the activation calculations: Except in the reactions given in Table 2, the number n of mother nuclei will be assumed to change only insignificantly, i.e. Δn/n = σ Φ Δt is assumed to be small. As long as the cross section σ is of normal size, i.e. below 10^{23 }cm^{2} = 10 barn this is guaranteed by the technical constraints to the number Φ_{14} Δt of 14 MeV neutrons entering each squaremeter of the first wall. They keep Φ_{14} Δt below several MWyr/m^{2} and Δn/n below several percent. (q is a linear function of all parameters)
The neutrons penetrating the initially non radioactive blanket react with the stable nuclei, thus yielding a first generation of new nuclei, called daughters. Those, in turn, are exposed to the neutrons, they act as mothers for a second generation of daughters, and so on. The sequence of generations is called an activation chain.
Because of the exponential decay of radionuclides with time it is not possible to accumulate radioactive nuclei in any generation during a period Δt longer than roughly their half life T. Thus the number of radioactive daughternuclei cannot become larger than Δn = n σ Φ T, which is less than 1 millionth of the number n of mothers if the reaction cross section lies in the normal range and the half life is of the order of hours. Such radionuclides terminate the activation chain, i.e. in the next generation of the chain the number of particles will be negligible compared with the number of first generation daughters or even the number of atoms of a trace impurity.
An investigation of the chart of the nuclides shows that we can expect a very large fraction of all known longlived radionuclides (T > 10 yr) to appear in the blankets in the first generation of activation chains if we assume at least traces of each of the 83 elements to be present in the blanket materials. In a few cases the longlived radionuclide does not appear among the first generation of daughters but instead a shortlived radionuclide takes that place. But after its formation it decays entirely yielding the longlived waste nuclide. Therefore in the calculations these cases can be handled without loss of accuracy by neglecting the intermediate shortlived nuclide and assuming that the activation of the mother leads directly to the longlived waste nuclide. An example is the reaction Mo100(n,2n)Mo99 which has a half life of 2.8 days. All of the decays end in Tc99 which has a half life of 2.1 x 10^{5} yr. This reaction will therefore be referred to as Mo100(n,2n)Tc99.
Element  Concentration (mg of element per kg of steel) 
Al  5 10^{2} 
As  3 10^{2} 
B  10 
Co  5 10^{2} 
Cr  1.8 10^{5} 
Cu  10^{3} 
Fe  6.3 10^{5} 
Mn  2 10^{4} 
Mo  2 10^{4} 
Nb  5 10^{2} 
Ni  1.4 10^{5} 
P  2 10^{2} 
S  10^{2} 
Si  7 10^{3} 
Ta  2 10^{2} 
Ti  10^{2} 
V  2 10^{3} 
C  6 10^{2} 
N  10^{2} 
O  2 10^{2} 
Table 1b. Elements Present in Larger than Trace Amounts in Moderator Graphite
Element  Concentration (mg of element per kg of graphite) 
N  3 10^{1} 
O  3 10^{2} 
All other elements are arbitrarily taken to be present as traces of 1 mg per kg of structural, multiplier or moderator material. Furthermore beryllium is assumed to be used as oxide (beryllia) and lead, bismuth and graphite without additional metals or binders.
The calculations specify the (henceforth called "normalized") activities q (units: Ci/cm^{3}) generated in 1 cm^{3} of blanket material, i.e. 1 cm^{3} of steel, 1 cm^{3} of BeO, 1 cm^{3} of Bi, 1 cm^{3} of C and 1 cm^{3} of Pb:
q = n σ Φ Δt λ F
(see Notation section for meaning of n, σ, Φ, Δt , λ, F)
n = f N_{A} ρ w / M
(meaning of f, N_{A}, ρ , w, M)
Number n of mothers with high neutron capture cross sectionsThe cross sections influencing the generation of Sm151, 152, Eu150,152,154, Hf178*, Irl92*, 193, 194 are very large (Table 2): Mothers or daughters have a large tendency to capture the thermal neutrons. Instead of being the constant value n = f N_{A} ρ w / M, their numbers decrease rapidly during reactor operation, i.e. their n depends on the reactor operation time t: n = n(t). To simplify things, one can assign them an "effective" half life
T_{eff} = ln2/(σ Φ)
(meaning of σ, Φ, ln2)which is defined analogously to the radioactive decay time T = ln2/λ. T_{eff} is the time during which their number decreases by a factor of 2.
Table 2. Cross Sections and Effective HalfLives of Mothers Involved in Nonlinear Activation Calculations, i.e. when number of mother isotopes decreases by a factor of 2 during T_{eff}
(a: effective half life determined by reaction in next line)
(more cross sections, halflives, Annual Limits of Intake, Maximum Permissible Concentrations, concentrations in biosphere water bodies)
Mother (n,x) Daughter Cross Section
(barn)Eff. Half Life of Mother, T_{eff}
(yr)Sm150(n,g)Sm151 1.0 10^{2} 4.9 Sm152(n,2n)Sm151 2.1 2.3 10^{2} Sm151(n,g)Sm152 1.5 10^{4} 3.3 10^{2} Eu151(n,g)Eu152 5.9 10^{3} 8.3 10^{2} Eu151(n,2n)Eu150 6.1 10^{1} 8.1 10^{2} Eu153(n,2n)Eu152 7.6 10^{1} a Eu153(n,g)Eu154 3.9 10^{2} 1.3 Hf177(n,g)Hf178* 1. 10^{7} a Hf177(n,g)Hf178 3.7 10^{2} 1.3 Ir191(n,g)Ir192 9.2 10^{2} 5.4 10^{1} Ir192(n,g)Ir193 1.1 10^{3} 4.5 10^{1} Ir193(n,2n)Ir192* 5.9 10^{1} a Ir193(n,g)Ir194 1.1 10^{2} 4.5 To deal with this situation, I will use a similar simplification as the one mentioned above: When the number n of the mother is fairly constant, the number of daughter nuclei increases only during an operation time roughly equal to the half life of the daughter.
Similarly, in the case of rapidly depleted mother nuclei, I will assume the activation reactions come to an end when the mother has disappeared. This happens roughly after one half life T_{eff} of the mother.
So, the activities for the radionuclides in Tab. 2 have been calculated taking into account these effects by simplifying the number n(t) of mothers as
n(t) = f N_{A} ρ w / M ..... for reactor operation times t < T_{eff}
n(t) = 0 ..... for reactor operation times t > T_{eff}
Q is the activity of the entire blanket material, i.e. Q = Q_{1} for the first wall with volume V_{1}, and Q = Q_{m} for the neutron multiplier or moderator with volume V_{m}:
Q_{1} = V_{1} q
Q_{m} = V_{m} q
The metabolism of radionuclides in the socalled reference man has been formulated in models based on which the maximum permissible concentrations of radionuclides in drinking water for occupationally exposed workers (MPC) have been calculated. The International Commission on Radiological Protection (ICRP) recommends that the general public receive only 10% of the dose of the occupationally exposed population.
According to the definition of MPC, consumption of V = 0.8 m^{3} of water with a concentration 0.1 MPC will cause a radioactive burden ("population dose") of 0.5 rem which is supposed to be independent from the distribution of the water over the population: If one person drinks the whole 0.8 m^{3} she receives the dose of 0.5 rem. If she shares some of the water with another person her radiation burden is correspondingly less, (0.5  x) rem, while the other person receives the x rem.
The definition of the potential biological hazard (BHP)
BHP = Q/(0.1 MPC)
implies
The BHP is the volume of such a drinking water body carrying the radioactive inventory Q. Due to the low dose rates, the population dose, dose_{max}, is assumed to be independent from how many people are actually exposed to the inventory Q. In this sense, the BHP gives us a measure of the maximum dose, dose_{max}(Q), an inventory Q of a radionuclide can cause in a population:
dose_{max}(Q) = BHP/V 0.5 rem = Q/(0.1 MPC V) 0.5 rem.
Let us use BHP_{ref} = V = 0.8 m^{3}as a reference level against which to measure actual BHP's.
Thus, an actual BHP = n BHP_{ref} means a maximum population dose dose_{max} = n 0.5 rem.
The potential amount of contaminated drinking water BHP decreases exponentially with time t after shutdown of the reactor according to the radioactive decay law:
where BHP is the hazard potential of a radionuclide X at shutdown of the reactor and λ = ln2/T is the radioactive decay constant of X.
The isolation time t_{is}^{BHP} can be defined as the time t at which
BHP(t = t_{is}^{BHP}) = BHP_{ref}.
In Figs. 4a and b we will display the BHP's of 1 cm^{3} of first wall or neutron multiplier material, and so we will normalize the reference BHP accordingly by dividing BHP_{ref} by the volume of the first wall, V_{1}, or of the multiplier material, V_{m}:
bhp^{1}_{ref} = BHP_{ref} / V_{1} for the first wall
bhp^{m}_{ref} = BHP_{ref} / V_{m} for the neutron multiplier or moderator.
In the following figures (Figs. 4a and b)
Figs. 4a and b show that over millenia many BHP's are large enough (10^{6 ... 7} m^{3}) to represent the drinking water supply of a local population.
Furthermore, the MPC = 3 x 10^{5} Ci/m^{3} assigned to some radionuclides (symbols with !mark) in Figs. 4 and 5 is not based on their specific behavior in the human metabolism. It had to be used for those radionuclides according to the general rule given by the ICRP, stating that for nuclides for which no MPCvalues have yet been specified, the value 3 x 10^{5} Ci/m^{3}  given for an "unidentified" radionuclide  should be used. It can be expected that the ALIvalues that will be published in the future will correspond to higher MPCvalues for those nuclides.
In this paper, MPC is calculated from ALI as follows:
MPC = ALI/V
where
V = amount of drinking water of man (0.8 m^{3}/yr),
ALI = annual limit for intakes of workers (Ci/yr),
if ALI is given by Adams et al. or the ICRP. If ALI is not provided there, the old MPC value is taken. A source not used in these calculations is 10 CFR Part 20 "Standards for protection against radiation", Appendix B  Radionuclide Table  Index of Radioisotopes.
The specific activity of element X is the activity (Ci) of one gram of the activated element X. In the case of negligible isotopic dilution, the specific activity of an element X in drinking water is nearly the specific activity of that element in the reactor blanket. When in the reactor only one radioisotope of element X is generated, the specific activity S of X is
where the denominator, ρ w, is the weight of X in 1 cm^{3} of blanket material. If the activity of element X results from a number of radioisotopes, instead of q in the numerator of the specific activity S we have the sum over the q's of all radioisotopes.
The specific activity of non stable elements, such as Tc, or Pu239 is
S = N_{A} λ F / M,
where M is the weight of 1 mole of the non stable element, for example M_{TC99} = 99 g, M_{Pu239} = 239 g.
Now we can define c_{p}, the tolerable concentration of an element X from the reactor in drinking water of the public:
where the factor 10^{1} appears because the maximum permissible concentration of a radionuclide in drinking water of the public is 0.1 MPC.
Let us assume that the highest observed concentrations c_{e} of elements X in groundwater compiled in Drinking Water and Health, 1977 are sufficiently close to the saturation limits provided by the geochemical barriers.
The geochemical barrier is effective against a radioisotope X* of element X if at some time t after reactor shutdown
c_{p}(t = t_{is}^{c}) = c_{p} exp(ln2 (t_{is}^{c}/T)) = c_{e}
where c_{p} is the tolerable concentration of element X at shutdown (t = 0) of the reactor and T is the half life of the radioisotope X*. In that sense, the necessary isolation time of fusion reactor waste with a hazard below the limit BHP_{ref} can be defined as t = t_{is}^{c} that meets the isolation condition (*):
t_{is}^{c}= T ln (c_{e}/c_{p}) / ln2.
In Figs. 5, t_{is}^{c} is the abscissa of the intersection of a decay curve with the corresponding environmental level c_{e}.
The tolerable concentration c_{p} is independent from the size of the reactor, as long as the above discussed premises of the specific activity concept are met.
Obviously the activity Q and the potential biological hazard BHP depend on the size of the reactor, which is still subject to changes. Therefore, normalized values q and bhp have been calculated and plotted. To arrive at the potential hazard originating from an complete decomissioned fusion reactor, one needs to scale q and bhp by the number of cubic centimeters of blanket material present in the entire reactor.
As pointed out above, the total amount of first wall material is fixed
For example, the volume BHP_{Ni63} of drinking water that can potentially be contaminated by the inventory of Ni63 at shutdown of the reactor is of order 10^{8}  10^{9} m^{3} .
Figures 4 and 5 are combined plots, in the sense that they present
The hazards bhp and c_{p} at shutdown are plotted vs. their radioactive half lives T by placing the chemical symbol of the radioactive element (mother and daughter) at the locations {x = T, y = bhp} and {x = T, y = c_{p}}, respectively.
The plots of bhp(t) and c_{p}(t) show which radionuclide dominates the hazard at a given time after reactor shutdown. Obviously, these plots can be generated from the bhp(T) and c_{p}(T) plots by replacing each chemical symbol with a decay curve of the form given for BHP(t).
To avoid clutter, basically only the prominent decay curves were added to the bhp(T) and c_{p}(T) plots. The total bhp(t) or c_{p}(t) (summed over all activated elements) would look very much like the canvas of a tent being fixed below the prominent radionuclides like a canvas hanging from tent poles.
The reference level V is the upper (V/V_{1}) or lower (V/V_{m}) border of the shaded area in Figs. 4 a and 4b.
For first wall materials the distance of an element bhp from the line V/V_{1}, i.e.
log d = log bhp  log (V/V_{1}) = log bhp/(V/V_{1})
gives the factor between the reference dose 0.5 rem and the population dose dose_{max}(q) due to that element:
dose_{max} / (0.5 rem) = BHP/V = bhp_{1}/ (V/V_{1})
thus
dose_{max} = bhp/(V/V_{1}) 0.5 rem
These are the populations doses dose_{max} listed in Tab. 4.
Detailed results are displayed in Tab. 3 (in the Appendix).
Figs. 4 display the biological hazard potentials in normalized form, i.e. for 1 cm^{3} of blanket material or fission fuel, such that they can be scaled according to design needs and data improvements, such as
Note: The fusion reactor is essentially a breeder reactor: The entire reactor fuel (tritium) is bred within the fusion reactor blanket and needs to be extracted from it by an elaborate and not yet developed reprocessing technology. Present day fission fuel reprocessing plants release the greater fraction of the tritium inventory from the fuel into the biosphere.Thus, apart from the operational safety associated with tritium (steel is permeable for hydrogen at the fusion reactor operating temperatures) the tritium bound physically (i.e. adsorbed on material surfaces) as well as chemically to the reactor materials poses a major disposal problem.
Instead of our burnup (30 GW_{th}d/t_{HM}) Kamil uses 41.2 GW_{th}d/t_{HM}.
(see also Nuclear Energy Agency, Organisation for Economic Cooperation and Development, Fig. 1.2 of "Physics and Safety of Transmutation Systems  A Status Report", Nuclear Science, ISBN 9264010823, OECD 2006, in cache)
At fusion reactor shutdown the bhp of Be10 in the multiplier (with a halflife T of approximately 2 million years) is 7 10^{1} m^{3}/cm^{3} (see Tab. 3A).
BHP 0.5 rem / V = BHP 0.5 rem / (0.8 m^{3}) = 4.4 10^{6}rem.
Figure 4b. Biological hazard potentials (ingestion pathway) bhp in 1 cm^{3} of reactor material generated together with an energy of 1 GW_{th}yr by fast (14 MeV) neutron activation. For activation products of Al, Bi, Cl, Er, Eu, La, Mo, Nb, Sm, Tb (marked by !) MPC values for unidentified radionuclides had to be used for same reason as in calculations for Fig. 4a. Irradiation data. For more information see caption of Fig. 4a.
Figure 5b. Maximum tolerable concentrations c_{p} of blanket materials in a combined plot as explained above. Only fast (14 MeV) neutron activation reactions considered. Irradiation data. For more information see captions of Figs. 4a and 5a.
Major results that can be extracted from Figs. 4 and 5 are presented in Tab.4 in nonnormalized form.
Table 4. Summary of Results: Evaluation of Relevant Radionuclides (T > 50 yr, Population Dose d_{max} > 50 rem) in fusion and fission reactors having produced 1 GW_{th}yr. Fusion reactor 1st wall load: 1 MW/m^{2} = 4.5 x 10^{17} neutrons per second, fission reactor fuel burnup: 30 GW_{t}d/t_{HM}. (Details in Tab. 3). Compare these findings with [Fetter et al., 1988, 1990].
Actinide 
for ALI, MPC 
Yes (+) or No ()
for c_{e} 
Reactor 

Li6(n,a)H3  12.3  10^{7}  + (^{3})  steel, mult., mod., fus.& fis. 
Ni62(n,g)Ni63  100  4 10^{7}  +  steel, fus.&fis. 
Ni64(n,2n)Ni63  100  1 10^{6}   (^{3})  steel, fus.&fis. 
Ag107(n,g)Ag108* 
130  6 10^{3}  +  steel, fus.&fis. 
Ir191(n,g)Ir192* 
240  1 10^{4}  +  steel, fus.&fis. 
Ho165(n,g)Ho166* 
1.2 10^{3}  2 10^{4}  +  steel, fus.&fis. 
Mo92(n,g)Mo93  3.5 10^{3}  6 10^{3}  +  steel, fus.&fis. 
Mo94(n,2n)Mo93  3.5 10^{3}  3 10^{4}    steel, fus.& fis. 
Mo92(n,2n)Nb91  1.0 10^{4}  6 10^{4}  +  steel, fus.& fis. 
Nb93(n,g)Nb94  2.0 10^{4}  2 10^{4}  +  steel, fus.& fis. 
Ni58(n,g)Ni59  7.5 10^{4}  1 10^{4}    steel, fus.& fis. 
Ni60(n,2n)Ni59  7.5 10^{4}  3 10^{2}    steel, fus.& fis. 
Mo100(n,2n)Tc99  2.1 10^{5}  5 10^{3}  +  steel, fus.& fis. 
Cl35(n,g)Cl36  3.0 10^{5}  5 10^{2}  +  mod,fus.& fis. 
Bi209(n,2n)Bi208  3.7 10^{5}  6 10^{8}  +  mult, fus.& fis. 
Be9(n,g)Be10  1.6 10^{6}  4 10^{6}    mult, fus. 
Fe54(n,2n)Mn53  3.7 10^{6}  5 10^{1}    steel, fus.& fis. 
Al27(n,2n)Al26  7.2 10^{6}  4 10^{4}    structure(^{4}) fus.& fis. 
Pb206(n,2n)Pb205  1.4 10^{7}  3 10^{4}    mult, fus. 
Am243  10^{4}  1 10^{8}  +  mult, fis. 
Pu239  2 10^{4}  3 10^{9}  +  mult, fis. 
Np237  2 10^{6}  1 10^{6}  +  mult, fis. 
Legend:
Two independent quantities can be used to characterize the activity levels Q and the resulting isolation requirements:
The potential population dose decreases with time t after reactor shutdown. After it has fallen below an acceptable limit, natural geochemical processes become relevant. The engineered radwaste repository may start to release the waste inventory at time t when those natural geochemical barriers succeed to sufficiently limit the exposure of an individual of the population.
The population doses of beryllium and bismuth are still unknown (see column "MPC unknown" in Tab. 4) because their radiological properties have as yet not been investigated. In view of the preliminary population doses, we can expect the neutron multiplier in a fusion reactor (about 10 m^{3} in INTOR) to pose a major long lived hazard, regardless of its eventually determined radiological properties.
Especially for the neutron multiplier materials the radiological and environmental properties need to be investigated to quantify the extent to which fusion reactor waste is less problematic than fission reactor waste.
Using the data presented in Figs. 4 and Figs. 5 in the way described we find a mimimum isolation time of fusion reactor waste of about half a million years.
ALI = Annual Limit of Intake of radionuclides by workers (Ci/yr), explanation
BHP = Biological Hazard Potential of entire reactor substructure (first wall, neutron multiplier, neutron moderator) at shutdown of the reactor (m^{3} drinking water), BHP and BHP(T) used interchangeably, first time used
BHP(t) = Biological Hazard Potential of entire reactor substructure (first wall, neutron multiplier, neutron moderator) t years after shutdown of the reactor (m^{3} drinking water), first time used
BHP_{ref} = V, first time used
bhp = ("normalized") biological hazard potential of 1 cm^{3} of reactor substructure at reactor shutdown (m^{3} drinking water contaminated by 1 cm^{3} of reactor substructure), bhp and bhp(T) used interchangeably, first time used
bhp(t) = ("normalized") biological hazard potential of 1 cm^{3} of reactor substructure t years after shutdown of the reactor (m3 drinking water contaminated by 1 cm^{3} of reactor substructure), first time used
bhp_{ref} = V/V_{1} for first wall material, = V/V_{m} for moderator/multiplier material, first time used
blanket material: 1 cm^{3} of blanket material means
c_{e} = upper limit of concentration found in environmental water body (g/L), first time used
charge = weight of the fission reactor fuel that produced 1 GW_{th} yr with a burnup of 30 GW_{th} d / t_{HM} (charge = 12.2 t_{HM}), first time used
c_{p} = tolerable concentration in drinking water at shutdown of reactor at reactor shutdown (g/L), first time used
c_{p}(t) = tolerable concentration in drinking water t years after shutdown of reactor (g/L), first time used
dose_{max}(Q) = population dose when radioactive inventory Q is released to a population, first time used
d_{spec} = specific ingestion dose coefficient, specified for
Δt = operation time of a blanket module (2 yr), first time used
F = conversion factor. F is the reciprocal of the number of decays per second equaling 1 Ci (F = 2.7 x 10^{11} Ci / (particles/sec)), first time used
f = fraction of mother isotope present in mother element, i.e. natural abundance of mother isotope, first time used
HM = the heavy metal constituting the fission reactor fuel. Here HM is enriched uranium, containing 3.7 % U235. first time used
λ = ln2/T (1/yr ), except when used in combination with F (q, where it is in 1/sec), first time used
ln2 = natural logarithm of 2 = 0.69
M = weight of 1 mole of mother element (g/mole), first time used
MPC = Maximum Permissible Concentration of radionuclides for workers, first time used
n = number of mother nuclei in 1 cm^{3} of blanket material (particles/cm^{3}), first time used
N_{A} = number of particles in 1 mole (particles/mole), first time used
normalized quantity = quantity calculated for 1 cm^{3} of blanket material, i.e. 1 cm^{3} of steel, 1 cm^{3} of BeO, 1 cm^{3} of Bi, 1 cm^{3} of C and 1 cm^{3} of Pb. Note that the specific activity of element X is its normalized activity, q, divided by ρ w, the number of grams of X in 1 cm^{3} of blanket material. first time used
Φ = neutron flux, only 14 MeVneutrons and thermal neutrons (Maxwellian distribution of energies for a moderator temperature of 25 C): Φ_{14} = 4.5 x 10^{13} cm^{2} s^{1} (for 14 MeV, "fast" neutrons) = Φ_{th} (for thermal neutrons), first time used
Q' = Q/charge (first time used)
q = activity of 1 cm^{3} of blanket material (Ci/cm^{3}), i.e. of 1 cm^{3} of stainless steel, 1 cm^{3} of the neutron multiplier material, beryllium, bismuth or lead, and 1 cm^{3} of the neutron moderator material, graphite, first time used
ρ = density of blanket material (g/cm^{3}), steel: 7.7, beryllia: 2.5, Bi: 9.8, C: 2.3, Pb: 11.4. first time used
S = specific activity of an element X at reactor shutdown (Ci/g of the element), first time used
S(t) = specific activity of an element X at time t after reactor shutdown (Ci/g of the element), first time used
σ = activation cross section of mother isotope (cm^{2}), first time used
T = half life of radionuclide (yr), first time used
T_{eff} = effective half life of mother (yr), first time used
t = time after shutdown of reactor (yr), first time used
1 t_{HM} = 1 ton of heavy metal (HM), i.e. of fission reactor fuel first time used
t_{is} = necessary isolation time (yr), first time used
V = volume of drinking water consumed per year, (V = 0.8 m^{3}), first time used
V_{1} = volume of first wall (several m^{3}, in these calculations: V_{1} = 1 m^{3}), first time used
V_{m} = volume of neutron moderator or multiplier (several 10 m^{3}, in these calculations: V_{1} = 10 m^{3}), first time used
V_{HM} = volume of 1 ton of heavy metal (1 t_{HM}), assuming a HM density of 18.9 g/cm^{3} : V_{HM} = 5.3 10^{4} cm^{3} per t_{HM}, first time used for calculating biological hazard potential of 1 cm^{3} of fission reactor spent fuel.
w = weight of mother element in 1 g of blanket material (g/g), first time used
Adams, N. et al. "Annual Limits of Intake of Radionuclides for Workers", NRPBR82 Harwell; Didcot: Oxon, Great Britain, 1978.
Alley, W.E.; Lessler, E.M. Nuclear Data Tables 1973, 11, 621825.
Bell, M.J., ORIGEN  "The ORNL isotope generation and depletion code", ORNL  4628, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1973.
Council directive lying down basic safety standards for the protection of the health, Number 96/29/EUROATOM, 1996.
"Drinking Water and Health", National Academy of Sciences: Washington, D.C., 1977.
Fetter, S; Cheng E.T.; Mann, F.M., Longterm Radioactivity in Fusion Reactors, Fusion Engineering and Design 6, 123130, 1988 (in cache).
Fetter, S; Cheng E.T.; Mann, F.M., LongTerm Radioactive Waste from Fusion Reactors, Fusion Engineering and Design 13(2), 239246, 1990 (in cache).
Gasteiger, R. "Calculation of burnup data for spent LWRfuels with respect to the design of spent fuel reprocessing plants", KfK 2373 (in cache), Institut für Angewandte Systemanalyse, Projekt Wiederaufarbeitung und Abfallbehandlung, Gesellschaft für Kernforschung, Karlsruhe, Germany, November 1976, pages 48, 54.
Gruber, J. "Evaluation of the Activity Levels in Fusion Reactor Blankets"; HMIB202; HahnMeitnerInstitut für Kernforschung: Berlin, Germany, 1977.
Gruber, J. Contaminant accumulation during transport through porous media, Water Resour. Res., 26, 99  107, 1990. (updated version)
Gruber, J.; J.O. Leckie "Importance of secondary repositories in solute transport through porous media, in: Am. Assoc. of Petroleum Geologists Research Conf. Prediction of Reservoir Qualitiy through Chemical Modeling, Park City, UT, U.S.A., 21.  26. June, 1987.
Gruber, J. Models of Contaminant Migration: The Role of Chromatographic Models, 1996.
Gruber, J.; Schneider, J. "Transmutation und Aktivierung von Stainless Steel 316SS in einem thermischen FusionsreaktorBlanket"; HMIB212; HahnMeitnerInstitut für Kernforschung: Berlin, Germany, 1977.
Gruber, J.; Schneider, J.; Lehmann, B. "NUCCON  A Program for Calculating the Neutron Activation"; HMIB312; HahnMeitnerInstitut für Kernforschung: Berlin, Germany, 1979.
Gruber, J.; Schneider, J. "Hazardous Impurity Activity in Blanket Materials in 8th Symp. on Engineering Problems of Fusion Research: San Francisco, Calif., Nov. 1316, 1979 (IEEE Pub.No. 79 Cll 14415 NPS).
IAEA, Radiological Characterization of Shut Down Nuclear Reactors for Decommissioning Purposes, TECHNICAL REPORTS SERIES No. 389), 1998 (in cache).
ICRPPublication 2 "Radiation Protection Recommendations of the International Commission on Radiological Protection"; Pergamon Press: Oxford, Great Britain, 1959.
ICRPPublication 30, part 1 and 2 "Limits for Intakes of Radionuclides by Workers"; Pergamon Press: Oxford, Great Britain, 1978.
A free data source on the internet albeit not used in these calculations is 10 CFR Part 20 "Standards for protection against radiation", Appendix B  Radionuclide Table  Index of Radioisotopes.
Radiation Exposure: Data and Definitions.
Tucek, Kamil, Neutronic and Burnup Studies of Acceleratordriven Systems Dedicated to Nuclear Waste Transmutation, Doctoral Thesis, Royal Institute of Technology, Department of Physics, Stockholm 2004 (in cache).
O'Banion, K. Environ.Sci.Tech. 1981, 15(10), 11301136.
Ortoleva, P. et al. "Redox front propagation and banding modalitites", Physica, 19D, 334354, 1986.
SeelmannEggebert, W. et al. "Nuklidkarte", Verlag Gersbach und Sohn, 8 Mīnchen 34, Barer Str., Germany, 1974.

yr 
rem/Ci (10^{11} Sv/Bq) 
kg 
Ci/g H3 
H3  12.3  64 (1.7)^{(*)}  ^{1}  1.4 10^{4} (9.650 10^{3})^{(*)} 
Tritiated water, i.e. the H_{2}OHTO molecular array, released from a fusion plant undergoes thorough isotopical dilution in environmental water up to a point in time when it has filled an area that might be called "effectively closed area". This is so large that the tritiated water might recycle between various hydrogen compartments rather than leave the area. The following evaluation in terms of tolerable environmental tritiated water concentration c_{p} (units: g of tritiated water per liter of environmental biosphere water) is based on the specific activity concept. It can only be useful as a guide when applied to an effectively closed area.
The presented evaluation of the impact of tritium from fusion plants is incomplete in the sense that it will not provide any estimates of "effectively closed area" sizes.

Ci 
rem 
m^{3} Water/cm^{3} Blanket Material (^{1}) 
g HTO/L Water 
H3  1 10^{7}  6 10^{8}  1 10^{2}  7 10^{9} 
Comment:
(^{1}) The tritium inventory has been evenly distributed in 10 m^{3} of blanket material
Tritium activity per mol of H3, tpm:
tpm = N_{A} ln2 / T
where T = 12.3 yr
Total H3 inventory in blanket, Q
Q = tpm / (3 g/mol) M_{H3}
Population dose of inventory M_{H3}, d_{max}:
d_{max} = Q d_{spec}
Biological Hazard Potential of inventory M_{H3}, BHP:
BHP = Q d_{spec}
and biological hazard potential of 1 cm^{3} of blanket material (assumed tritiated volume of blanket material: 10 m^{3}), bhp:
bhp = BHP/(10 m^{3})
The specific activity of tritiated water, HTO, is
S = tpm / M,
where M (molecular weight of HTO) = 20 g,
S = 1.4 10^{3} Ci/(g HTO).
The tolerable concentration is defined as
c_{p} = (0.5 rem/V) 1/(S d_{spec}).
With the ingestion dose coefficient d_{spec} = 64 rem/Ci it follows that
c_{p} = 7 10^{9} g HTO per Liter of environmental water

yr 
10^{5} rem/Ci (10^{8} Sv/Bq) 
mole/t_{HM} 
Ci/g 
Am243  7.4 10^{3}  7.4 (20)  ^{ 0.24}  2.0 10^{1} 
Pu239  2.4 10^{4}  9.25 (25)  _{21.4}  6.2 10^{2} 
Np237  2.1 10^{6}  4.1 (11)  _{1.74}  7.0 10^{4} 
Pu242  3.7 10^{5}  8.9 (24)  _{1.05}  3.9 10^{3} 

Ci/t_{HM} 
rem 
m^{3} Water/cm^{3} HM 
g/L Water 
Am243  1.1 10^{1}  1.0 10^{8}  2.6 10^{2}  4 10^{9} 
Pu239  3.2 10^{2}  3.5 10^{9}  8.9 10^{3}  1 10^{8} 
Np237  2.9 10^{1}  1.4 10^{6}  3.6 10^{0}  2 10^{6} 
Pu242  1.0 10^{0}  1.1 10^{7}  2.7 10^{1}  2 10^{7} 
Q' = C_{OR} N_{A} ln2/T
where the unit of Q' is Bq/t_{HM} when the unit of T is sec. (Conversion from Bq to Ci: 1 Ci = 3.7 10^{10} Bq)
The activity per cm^{3} of fission reactor fuel is
q = Q'/V_{HM}
where the volume of 1 ton of heavy metal is V_{HM} = 5.3 10^{4} cm^{3}/t_{HM}
BHP = V / (0.5 rem) dose_{max}
and the biological hazard potential due to the actinides contained in 1 cm^{3} of fission reactor fuel is
bhp = BHP/(charge V_{HM})
The above given definition of the tolerable concentration c_{p} of a radioactive element in water of the biosphere environment is
c_{p} = 0.1 MPC / S,where
S for non stable elements has been defined above (the actual values have been entered into the last column of the Data Table)
0.1 MPC = permissible actinide intake / V
permissible actinide intake = 0.5 rem / d_{spec}.
Substituting these in the definition of c_{p}, we find for the tolerable concentration in biosphere water
c_{p} = 0.5 rem/ (V d_{spec} S)
The resulting tolerable concentrations c_{p} have been entered into the last column of the Results table.