Isotope released fraction
calculations
Tania Melo Mendonca
CERN, EN-STI-RBS
Non steady-state diffusion:
Released fractions vs. Time in irradiation and diffusion chambers
n=1, 2, 3 for film, cylinder,
sphere respectively
Irradiation volume
t0
•
•
•
•
•
N0: isotopes produced at irradiation volume
N1: isotopes in LBE droplet entering diffusion chamber.
N2: isotopes still trapped in LBE droplet leaving diffusion
N3
N1
Diffusion chamber
Transfer line
Ndif
τi + τd
•
where a LBE droplet that contains them forms
τres: residence time of LBE droplet in diffusion chamber
N0
τi
N2
t0: N0 isotopes produced at irradiation volume
τi: time at which isotopes produced at t0 reach pores
•
•
chamber and entering loop.
N3: isotopes revisiting irradiation cell.
Ndif: released isotopes from LBE
•
D: isotope diffusion coefficient
•
(D=3.5x10-3 mm2/s Tl in LBE @600ºC)
r: radius of LBE droplet/jet
Released fractions as a function of the shape
and size
τi=0 ms (no time elapsed from irradiation until droplet/jet formation)
D= 3.5x10-3 mm2/s, Tl in LBE at 600ºC
Reference isotope 177Hg (T1/2=130 ms)
Solid: droplets, dashed: jets, dot: film
Reduction to ½ with
cylinder and 1/8 with
film
Reduction to ¼ for
150 μm and 1/20 for
200 μm
3
τres
Released fractions for different isotopes
τi=0 ms (no time elapsed from irradiation until droplet/jet formation)
D= 3.5x10-3 mm2/s, Tl in LBE at 600ºC
Radius of droplet: 100 μm
τres
4
Influence of temperature/diffusion coefficient
At 600ºC: D= 3.5x10-3 mm2/s for Tl in LBE
D=5x10-3 mm2/s for Au in Pb
(EURISOL-DS report)
5
T
[ºC]
D Tl in LBE
[x10-3 mm2/s]
200
0.6
300
1.1
400
1.8
500
2.2
600
3.5
700
4.4
T
[ºC]
D Au in Pb
[x10-3 mm2/s]
592
4.45
684
6.36
785
9.21
Influence of temperature on the released fraction
τi=0 ms (no time elapsed from irradiation until droplet/jet formation)
Radius of droplet: 100 µm
Reference isotope 177Hg (T1/2=130 ms)
Tl in LBE
Au in Pb
6
Non steady state process:
fraction of isotopes reaching pores (grid): N1
1
Radius of droplet: 100 µm
7
Residence time in diffusion chamber for irradiation
times up to 100 ms
Diffusion coefficient of Tl in LBE at 600ºC: 3.5x10-3 mm2/s
Radius of droplet: 100 μm
8
Residence time in diffusion chamber for irradiation
times up to 100 ms
Diffusion coefficient of Au in Pb at 600ºC: 5x10-3 mm2/s
Radius of droplet: 100 μm
~1.5x improvement for short -lived isotopes
9
Integrated release up to 100 ms in the irradiation
volume
Radius of droplet 100 μm
Reference isotope 177Hg (T1/2=130 ms)
3.1% at 270 ms
5% at 220 ms
10
Comparison with experimental values
Experimental values obtained from a Pb static target unit
Assumed 100 µm radius droplet and diffusion coefficient of Tl at 600ºC
11
Effusion efficiency
Characteristic effusion delay time
χ: mean number of collisions with surface of droplets and containment
Mean sticking time
Mean flight time
(Kirchner et al., NIM B70 (1992) 186)
12
Temperature dependence of sticking times
13
Temperature and shape dependence of effusion
efficiency
Diffusion chamber dimensions: 20 cm length, 12 cm height, 2 cm width
Configurations:
Droplets 100 μm radius with 300 μm separation between holes
Film with 200 μm thickness with 300 μm separation
0.86 at 600ºC vs. 0.81 at 200ºC for droplet configuration
0.72 at 600ºC vs. 0.66 at 200ºC for film configuration
Summary
177Hg
as reference isotope:
Release by diffusion is maximized for spherical shape (droplets) of 100 μm
radius.
Increase on radius or change in shape surface area will decrease released
fraction
Diffusion release fraction maximized in the interval 200-300 ms of residence
time in the diffusion chamber
Temperature (and diffusion coefficient) increase improve released fractions
Effusion efficiencies of the order of 86% at 600ºC for configuration with
10000 droplets (100 μm radius+0.3 μm distance)
Thank you!
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