In this paper we extend our previous analysis of cold beam tube vacuum in a superconducting proton collider to include ion desorption in addition to thermal desorption and synchrotron radiation induced photodesorption. The new ion desorption terms introduce the possibility of vacuum instability. This is similar to the classical room temperature case but now modified by the inclusion of ion desorption coefficients for cryosorbed (physisorbed) molecules which can greatly exceed the coefficients for tightly bound molecules. The sojourn time concept for physisorbed H{sub 2} is generalized to include photodesorption and ion desorption as well as the usually considered thermal desorption. The ion desorption rate is density dependent and divergent so at the onset of instability the sojourn time goes to zero. Experimental data are used to evaluate the H{sub 2} sojourn time for the conditions of the Large Hadron Collider (LHC) and the situation is found to be stable. The sojourn time is dominated by photodesorption for surface density s(H{sub 2}) less than a monolayer and by thermal deposition for s(H{sub 2}) greater than a monolayer. For a few percent of a monolayer, characteristic of a beam screen, the photodesorption rate exceeds ion desorption rate by more than two orders …