Graphite Sublimation Tests for the Muon Collider/Neutrino Factory Target Development Program

A passively cooled graphite target was proposed for a 1.5 MW neutrino production research facility because of its simplicity and favorable performance as a target material for neutrino production (Ref. 1). The conceptual design for the target in the Reference 1 study was a graphite rod 15 mm in diameter by 800 mm long. Figure 1 shows the graphite target rod supported by graphite spokes, which are mounted to a water-cooled stainless steel support tube. The target is radiatively cooled to the water-cooled surface of the support tube. Based on nuclear analysis results (Ref. 2), the time-averaged power deposition in the target is 35 kW. If this power is deposited uniformly along the axial length of the target, the volumetric power deposition in the target is about 250 MW/m3. The target surface temperature required to radiate the deposited power to a water-cooled tube is estimated to be about 1850 C, and the temperature at the center of the target is about 75 C hotter. The sublimation erosion rate (e), estimated assuming that the graphite is submersed in a perfect vacuum environment, can be derived from kinetic theory and is given by: e = psat (m/2π kT)1/2 where psat is the saturation pressure, m is the molecular weight, k is the Boltzmann constant, and T is the surface temperature. The saturation pressure given in Ref. 3 can be approximated by: psat = exp(-A/T + B) where A = 9.47 x 103, B = 24.2, and the units of psat and T are atmospheres and K, respectively. Using these equations, the saturation pressure and sublimation erosion rate are plotted in Fig. 2 as a function of temperature. The surface recession rate shown with units of mm/s in Fig. 2 assumes one-sided erosion. At the average power deposition value of 250 MW/m3, the surface temperature is 1850 C resulting in a sublimation erosion rate of only 2.2 mm/day. However, if the actual power deposition were peaked by a factor of two in the axial direction, then the surface temperature would be 2260 C and the surface recession rate would be 2.8 mm/day, which is clearly unacceptable. To establish the viability of a graphite target at the reference power levels and perhaps extend the power handling performance of radiatively cooled graphite targets, a helium cover gas at nominally one atmosphere pressure was proposed as a means to greatly reduce the net erosion rate. The mean free path for a graphite atom in a helium environment at a pressure of one atmosphere is less than 0.1 mm, which means that graphite that is sublimated from the target surface will travel on average less than 0.1 mm before it interacts with the helium. Given this small mean-free-path, it can be expected that a large fraction of the graphite that is sublimated will find its way back to the graphite surface and re-condense on the target, thereby greatly reducing the net erosion rate. The primary purposes for performing the tests described in this report are to (1) verify that we can reproduce the sublimation erosion rate expected for high vacuum conditions and (2) establish the reduction in net sublimation of graphite as a function of the gas (He) pressure in a chamber that roughly simulates the stainless steel support tube discussed above. Thus far, the first objective has been accomplished, but more work is required to accomplish the second. The experimental apparatus is described in Section 2 of this report and results obtained thus far are presented in Section 3 of this report