Support structure

The ladders are mounted on the forward and backward end-rings, which provide mechanical support and cooling. The positions of the ladders are fixed by cylindrical pins, which penetrate cylindrical holes in the heat-sinks and the end-rings. The end-rings are made of aluminum, which was chosen for its low mass, machinability, and thermal conductivity. Cooling tubes, in which 15 $^\circ$C water is circulating, are embedded in the end-ring. When the SVD electronics are turned on, thermal effects cause the ladder and end-ring to expand by estimated amounts 3 $\mu$m and 40 $\mu$m, respectively. To accommodate this expansion, a sliding mechanism is introduced to allow the ladder to move with respect to the end-ring in the longitudinal ($z$) direction. At the backward side, the pins and holes have the same diameter of 5 mm. On the other hand at the forward side, the diameters of pin and hole in the end-ring are 3 mm, but the diameter of the hole in the heat-sink is 5 mm. A spring-loaded attachment pushes the 3-mm pin to one side of the 5-mm hole in the heat-sink. This mechanism ensures that the forward end of the ladder is able to slide in the longitudinal direction but is not able to move in the transverse direction. The principle of this design is that the ladder end will slide before the ladder bows, thus preserving the essential planar nature of the ladder module. The precision of the machining and the assembly is about 50 $\mu$m and the position of DSSDs were measured with a precision of $\pm10~\mu$m. The end-rings are supported by the forward and backward support cylinders, which are made of 2.5-mm-thick CFRP. These support cylinders are connected by the outer cover, which is made of 0.5-mm-thick CFRP. The outer cover and the support cylinders form a single overall support envelope of considerable stiffness, $EI = 1 \times 10^4$ Nm$^2$. Based on ANSYS simulation, the gravitational sag at the center of the structure is expected to be about 10 $\mu$m. This structure is supported at three points on the forward (one point) and backward (two points) end plates of CDC. The backward end of the backward support cylinder is also fixed to CDC by means of a thin diaphragm, which rigidly constrains the $r$ and $\phi$ location of SVD, but allows easy motion in the $z$ direction. This longitudinal degree of freedom accommodates thermal expansion and contraction of SVD and CDC as well as changes in the length of CDC brought about by changes in atmospheric pressure. The beam pipe inside SVD is also supported by the CDC end plates through diaphragms that are independent of SVD. The beam pipe support is designed such that the heat load and any vibrations originating from the pipe and its cooling system do not affect the performance of the SVD system. The end rings, the end ring flanges, and the outer cover can all be divided into two (clamshell) halves in $r$-$\phi$. This makes it possible to assemble the SVD ladders in a tight space around the beam pipe.