Be Target Calculation
1.4 stars/inc. proton (probably a bit high...we used a
thicker target than is now contemplated).
.050 Be7/star (Be7 cross section = 10mb from Cossairt's book;
Be9 total inelastic cross section = 199 mb (PDG))
---> .07 Be7/inc. proton (greater than Chandra's .029 and Gerry's
.01)
Equilbrium conditions ---> As many Be7's are made as decay
25e12 protons/sec*.07 Be7/proton /3.7e10 decay/sec/Ci
= 47.5 Ci
Radiation hazard from target: assume a point source
Radiated energy = .1 (Branching fraction) * .478 MeV * 1.75e12
decays/sec = 8.4e10 MeV/sec
Incident flux in 1 cm^2 at 2 ft = 2.7e-4/cm^2*8.4e10 MeV/sec 1/4 pi
= 1.8e6 MeV/sec/cm^2
Absorption length in lung tissue for .5 MeV gamma = 10 g/cm^2
Dose = 1.8e6 MeV/sec/cm^2/10g/cm^2 /6.24e7 MeV/gm/Rad 1/2
= 1.44e-3 Rad/sec = 5.1 Rad/hr (target unshielded at 2 ft)
Note: for eq. 5.10 in D. Cossairt's book (a rule of thumb) with the
Source strength given above, you would
get 2.44 Rad/hr with the above source strength and Chandra's
approximation gives 3.2 Rad/hr
Absorption length in iron for .5 MeV gamma = 11.9 g/cm^2 = 1.51 cm
Horn calculation (for shielding purposes only the 1.27 MeV gamma from Na22
needs to be followed)
Inner conductor -- Narumon's mars calculation
Average 6e-4 stars/cc/inc. prot.
Na22 cross section 10 mb; Be7 Cross section 10 mb
Total inelastic cross section 247 mb
--> .04 Na22 and .04 Be7 / inc. prot.
Inner conductor volume = 3 mm at 1.1 cm for 200 cm
= 471 cc
Equilbrium assumption better for prot/year than prot/sec
Incident flux = 5e20 prot/year / 3.15e7 sec/year = 1.59e13 prot/sec
activation of inner conductor =
6e-4 stars/cc/inc. prot * 1.59e13 prot/sec * .04 Na22/star * 471 cc
1.8e11 Na22/sec (produced or decays) = 4.86 Ci
Radiation hazzard from 1.27 MeV gamma at 2 ft (assuming a point source)
Energy released = 1 (branching fraction) * 1.27 MeV * 1.8e11 d/sec
= 2.28e11 MeV/sec
Flux/cm^2 at 2 ft = 2.7e-4/cm^2 * 2.28e11 MeV/sec/4 pi
= 4.9e6 MeV/sec/cm^2
Absorption length for lung tissue at 1.25 MeV = 15.9 g/cm^2
Dose = 4.9e6 MeV/sec/cm^2 / 15.9 g/cm^2 /6.24e7 MeV/g/Rad 1/2
= 2.5e-3 Rad/sec = 8.9 Rad/hr
Outer Conductor -- Mars again (scaled to 1 ft.)
Average 7.5e-6 stars/cc/inc. prot.
Outer conductor volume = 1" at 1' for 200 cm = 1e5 cc
Activation of outer conductor =
7.5e-6 stars/cc/prot * 1e5 cc * 1.59e13 prot/sec * .04 Na22/star
4.8e11 Na22/sec (produced or decay)
Energy released = 1 * 1.27 MeV * 4.8e11 d/sec = 6.1e11 MeV/sec
Flux/cm^2 at 2 ft = 2.7e-4/cm^2 * 6.1e11 MeV/sec/4 pi
= 1.31e7 MeV/cm^2/sec
Dose = 1.31e7 MeV/sec/cm^2/15.9 g/cm^2/6.24e7 MeV/g/Rad 1/2
= 6.6e-3 Rad/sec = 24 Rad/hr
Total Na22 dose = 33 Rad/hr at 2 ft.
to reduce to .1 Rad/hr you need log 33/.1 absorption lengths
= 5.8 absorption length *18.7 g/cm^2 /7.87 gm/cc = 13.8 cm = 5.42"
Weight of 4' x 4' x 12' box with 5.42" skin
= 2.04e5 in^3 = 3.35e6 cc = 2.63e7 g = 2.63e4 kg = 5.8e4 lbs
= 29 tons