It is well established that Si and SiC have very desirable thermophysical properties (principally, high thermal conductivity, and low thermal expansion) at cryogenic temperatures. Thus, cryocooled optics are a potentially good candidate for the first optical crystal of the third generation synchrotron machines, which will have very high heat flux levels. Currently, there is a great deal of interest, both experimental and analytical in such cryocooled crystals. The analytical studies involve cut micro- or capillary channel crystals. As opposed to machined channels, porous matrices provide significant advantages. Such matrices are known to effect superior heat transfer. They operate very quietly. Data available in the open literature suggest that surface heat flux levels up to approximately 8 kW/cm2 are possible. For cryogens for which the boiling heat transfer heat flux is a rather low value in conventional geometries, the enhancement available with such matrices is very significant. Cryogens are poor thermal conductors themselves. At cryogenic temperatures, the Si and/or SiC matrix itself becomes highly conductive: Thus, the matrix distributes the surface heat flux into the full volume effectively offsetting the poor conductivity of the coolant. In addition, the tortuous path of the coolant through the matrix increases the dwell time resulting in better heat transfer, however, at the expense of an increased pressure drop. In this study, a first optics crystal model of Si with a Si and/or SiC porous matrix as its heat exchanger and subject to prototypic synchrotron loads is analyzed, and the feasibility limits of the cooling possible with liquid nitrogen in single phase are delineated.
