Saturation conditions in elongated single-cavity boiling water targets

Introduction It is shown that a very simple model reproduces the pressure versus beam current characteristics of elongated single-cavity boiling water targets for 18F production surprisingly well. By fitting the model calculations to measured data, values for a single free parameter, namely an overall heat-transfer coefficient, have been extracted for several IBA Nirta H218O targets. IBA recently released details on their new Nirta targets that have a conical shape, which constitutes an improvement over the original Nirta targets that have a cylindrical shape [1,2]. These shapes are shown schematically in FIGURE 1. A study by Alvord et al. [3] pointed out that elevated pressures and temperatures in excess of the saturation conditions may exist in a water target during bombardment. However, as long as the rate of condensation matches the rate of vaporization, the bulk of the system should remain at saturation conditions. Superheated regions are therefore likely to form but also likely to disappear rapidly, typically on the scale of a few milliseconds. Even though the boiling process is generally quite complex, enhanced by radiation-induced nucleation, the presence of fast mixing mechanisms in the water volume justifies some simplifications to be made. Materials and Methods The simplified model assumes that the bulk of the target water has a constant temperature, which is the same as the inner wall temperature of the cavity, Tw. A second simplification is to neglect the temperature difference across the target chamber wall, which is only justified if the wall is thin. The boiling is not explicitly taken into consideration, including the rather complex boiling behaviour at the Havar window, except to acknowledge that it is the main mixing mechanism. Large temperature gradients can briefly exist in the water medium but they also rapidly disappear. A further assumption is that a single, overall convective heat-transfer coefficient can be applied, which is constant over the entire water-cooled surface. As the wall thickness is neglected, the heat-transfer surface is assumed to be the inner surface of the cavity, excluding the surface of the Havar window. One can then write down an energy balance between the beam heating and the convection cooling (Newton’s law of cooling), where Ib is the beam intensity, ΔE is the energy windows of the target (taken as 18 MeV), h is the convective heat-transfer coefficient, A is the inner cavity surface through which the heat has to be transferred from the target-water volume to the cooling water, and T0 is the cooling-water temperature. The saturated vapour pressure of water versus temperature is a characteristic curve, given by the steam tables [4]. Assuming the bulk of the system at saturation conditions, one gets from (1) and (2). The function f is represented by a polynomial. The only unknown in Equation (3) is the overall convective heat-transfer coefficient h. Our approach was to adjust h until a good fit with a set of measured data was obtained. It also has to be mentioned that subtle differences in the physical properties between 18O-water and natural water have been neglected. All in all, quite a few assumptions and simplifications are made in deriving Equation (3) and the system is, admittedly, much more complex. Nevertheless, the results obtained by applying Equation (3) are rather interesting. Results and Conclusion Measured data and corresponding calculations are shown in FIGURE 2 for three different conical targets and one cylindrical target. The extracted convective heat-transfer coefficients are pre-sented in TABLE 1 for the four cavities. As can be seen in FIGURE 2, while there are some differences between the data and calculated curves, especially towards lower beam currents, the overall agreement is remarkably good. It is possible that the better agreement towards higher beam intensities is related to more ebullient boiling and more rapid mixing, i.e. closer to the conditions that the model assumes. The values obtained for the overall convective heat-transfer coefficient are also remarkably similar. This tells us that, by and large, all the cavities perform in a similar way and the performance in terms of maximum operational beam current depends largely on the available surface to effectively remove the heat from. The values of h increase marginally if a smaller value is adopted for the cooling water. Note that the choice of T0 = 30 ᵒC used to obtain the results in TABLE 1 is typical for the room temperature closed-loop cooling system used at iThemba LABS, once it has stabilized under operational conditions. A study by Buckley [5] on a quite different target design reports a value of h = 0.49 W cm−2 ᵒC−1, which is reassuringly similar. That study describes a cylindrical target cavity with a volume of 0.9 cm3, 8 mm deep, cooled with 25 ᵒC water from the back, operated with a 15 MeV proton beam with an intensity of 30 µA. The Nb Nirta targets are typically filled with 18O-water to about 60% of the cavity volume (see refs. [1,2] for the recommended values). The elongated shape, in combination with the ebullient properties of the boiling water, prevents burn-through. All the targets deliver the expected saturation yield. The targets are self-regulating ─ no external gas pressure is required. While the thermosyphon targets seemingly take advantage of a superior concept, we are now questioning whether this is really so in practice? It is not clear to us that the much more complex thermosyphon targets deliver any operational and/or performance advantages compared to the simple elegance of these elongated, single-cavity boiling target designs