Summary of Recent Target Studies Page: 4 of 13
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reduces peak heat load on target, and a ventilation system that
blows air down into the prevault/tunnel area, will help prevent
future releases of such gases.
Although the quality of the data is relatively poor, and information
on the detailed thermodynamic properties of rhenium is not always
available, it is important to try to develop a comparison between
the measured yield reduction and expected density depletion in the
powdered rhenium. The simple model of Ref. 3 may be used to
estimate the temperature of the material implied by the measured
amount of reduction in yield. The model assumes that the density
reduction is the result of the formation of a channel of liquid metal
in the target material. Typically the dependence of density of
liquid metals on temperature takes the form
dp/dT = -K p (1)
where the constant K is in the range 0.5 to 2 x 10'4. No data
exist for the density variation of liquid rhenium with temperature,
but the central value in the range (1 x 10-4) corresponds to copper.
Calculations have been made for this value of the constant K [Ref.
3]. If we use this value of K, a yield reduction of 8% implies a
central density reduction of 16% in a thin target. Thick-target
effects modify this result slightly. For example, if the absorption of
the incident proton beam is 50% through the entire target,
absorption to the center of the target is about 25%. Taking this
into account, the indicated density reduction is about Ap/p = -21%.
A density reduction of this magnitude corresponds to a temperature
rise beyond the melting point of 2100'C (from eq. 1). Since the
melting point of Re is 31800C, this result implies melting begins
about 60% into the pulse. The final temperature is 5280*C.
From another point of view, energy deposition in rhenium for 1.6 x
1012 protons should be about 1070 J/g for a o = 0.14 mm beam
spot. The melting point energy for rhenium (about 613 J/g) then
indicates melting begins about 57% of the way into the pulse. The
agreement between the two calculations, while certainly not
conclusive, suggests that the target material behaved about as one
Finally, it is interesting to note that, even with energy deposition
far exceeding the theoretical limit for melting the target, the
reduction in total yield was not significant (Table I). One can
conclude that the practical limit to target energy density due to
short-term density depletion is significantly higher than the melting
point of the material. Other limiting effects, such as shock-wave
damage, long-term radiation damage, and especially production of
airborne radionuclides, may ultimately play a more significant role
in limiting permissable energy density on target.
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Bieniosek, F. & O'Day, S. Summary of Recent Target Studies, report, February 4, 1993; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc1014573/m1/4/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.