SLAC proposed a rotatable collimator design for the LHC Phase II collimation upgrade. There are 20 facet faces on each cylindrical jaw surface and two jaws are rotatable in order to introduce a clean surface in case of a beam hitting a jaw during operation. When the beam crosses the collimator, it will excite broad-band and narrow-band modes. The longitudinal modes can contribute to beam energy loss and power dissipation on the vacuum chamber wall. In this paper, the parallel finite element eigensolver Omega3P is used to search for all the longitudinal trapped modes in the SLAC collimator design. The power dissipation generated by the beam in collimators with different vacuum chamber and RF contact designs is discussed. It is found that a wider RF foil connecting the jaw and the vacuum flange can reduce efficiently the beam heating caused by the longitudinal modes. Show Partial Abstract