Fig. 4-6 Pressure wave generation in liquid metallic target A compression field forms due to momentary nuclear spallation heat generated by an incident pulsed-proton beam. A pressure wave then forms, which propagates to the circumference.

Fig. 4-7 Generation of negative pressure in Hg In the process by which the pressure wave propagates, a negative pressure of several tens of MPa is created in the Hg. Therefore, the bubble formation (cavitation) is expected in the high negative pressure field, and the wave propagation characteristics of the bubble-dispersed Hg become a problem.

Fig. 4-8 Application of bubble dynamics To elucidate the wave propagation phenomenon in Hg that contains gas bubbles, bubble dynamics that simulates latent micro-bubbles was applied. For a bubble dispersed Hg, nonlinear characteristics of the pressure wave propagation are enhanced since shrinkage forms a hard spring because the pressure in the bubble is high.

This picture.(55.7KB)

Fig. 4-9 Pressure wave propagation characteristics in a bubble dispersed Hg Nonlinearity is stronger in a bubble dispersed Hg than in a bubble dispersed water because the surface tension of Hg is larger. As a result, the shock wave is formed in a bubble-dispersed Hg, even if the initial pressure is about 25 MPa and the bubble volume fraction level is 10-9.

A pulsed 1 MW incident beam to a mercury (Hg) target is planned for use in the Materials and Life Science Facility of J-PARC. In use, a pressure of several tens of MPa occurs in the target due to the thermal expansion of Hg resulting from the heat generated by nuclear spallation. Therefore, a pressure wave is created, which propagates to the surrounding structure, and imposes a load on the target vessel (Fig. 4-6). In the process by which the pressure wave propagates in the target vessel, a negative pressure (i.e. tensile stress) of several MPa in the neighborhood of the beam window results, and gas bubbles are generated (cavitation) (Fig. 4-7). When the gas bubbles are formed, the speed of sound decreases greatly and nonlinear effects appear in wave propagation. As a result, the pressure loading on the target vessel changes, too. To achieve a good design of the vessel, the behavior of wave propagation in the bubble-dispersed Hg must be understood. Therefore, bubble dynamics was applied. Bubble dynamics deals with wave propagation phenomenon in a bubble-dispersed liquid. Bubble dynamics assumes that the bubble density is low enough that an interaction can be ignored between bubbles (Fig. 4-8) . The literature contained no examples of research for bubble-dispersed Hg, although there was a research example concerning wave propagation in bubble-dispersed water. The behavior of bubbles in Hg is vastly different from those in water because the density and the surface tension of Hg are about one order larger than those of water, and the wave propagation in bubble-dispersed Hg shows marked nonlinear effects compared with bubble-dispersed water. For example, Fig. 4-9 shows the solution of a one-dimensional nonlinear wave equation with an initial condition of Gaussian pressure distribution peaked at 50 MPa. From this figure, it is understood that the nonlinear behavior of wave propagation in bubble-dispersed Hg results in a shock wave formation even if the volume rate b of the bubble is a minute amount, 10-9. Incidentally, the shock wave was not generated until a pressure of several GPa was reached when the Hg did not contain a bubbles. These analytical techniques can be applied to the design process when bubbles are generated in Hg. The bubble injection method is being considered as possible measures to attenuate the pressure wave.

Reference S. Ishikura et al., Bubble Dynamics in the Thermal Shock Problem of the Liquid Metal Target, J. Nucl. Mater., 318, 113 (2003).

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