A system (100, 500) for separating carbon dioxide from other gases to form a solid, comprising: a single separation vessel (116, 516) having a process stream inlet and a light gas outlet, wherein the process stream inlet is in fluid communication with a process stream (112, 512) that includes carbon dioxide; a bed of particles (118, 518) positioned within the single separation vessel (116, 516), the bed of particles (118, 518) in fluid communication with the process stream (112, 512), wherein the process stream inlet is below the bed of particles (118, 518) and the light gas outlet is above the bed of particles (118, 518), wherein the process stream (112, 512) has sufficient pressure to flow through at least a portion of the bed of particles (118, 518); means for adding particles to a top portion of the bed of particles (118, 518); means for removing particles from a bottom portion of the bed of particles (118, 518); and an in-bed heat exchanger (120, 520) comprising one or more conduits at least partially submerged in the bed of particles (118, 518); an expansion device downstream from the single separation vessel (116, 516), the expansion device configured to cool the light gas stream by reducing the pressure, wherein the cooled light gas stream flows through an interior of the conduit of the in-bed heat exchanger (120, 520); means for separating solids from the expanded light gas stream to be used for cooling the in-bed heat exchanger; wherein the single separation vessel (116, 516) and in-bed heat exchanger (120, 520) are configured so that the temperature and pressure within the bed are sufficient to desublimate or condense and freeze at least a portion of the carbon dioxide from the process stream (112, 512) onto the bed of particles (118, 518) so as to form a solid and a separated light gas stream, wherein the single separation vessel (116, 516) and light gas outlet are configured so that the separated light gas stream produced from the process stream (112, 512) in the single separation vessel (116, 516) exits the single separation vessel (116, 516) through the light gas outlet, and wherein the solids produced from expansion and separated using the means for separating solids are introduced into the vessel (116, 516). a single separation vessel (116, 516) having a process stream inlet and a light gas outlet, wherein the process stream inlet is in fluid communication with a process stream (112, 512) that includes carbon dioxide; a bed of particles (118, 518) positioned within the single separation vessel (116, 516), the bed of particles (118, 518) in fluid communication with the process stream (112, 512), wherein the process stream inlet is below the bed of particles (118, 518) and the light gas outlet is above the bed of particles (118, 518), wherein the process stream (112, 512) has sufficient pressure to flow through at least a portion of the bed of particles (118, 518); means for adding particles to a top portion of the bed of particles (118, 518); means for removing particles from a bottom portion of the bed of particles (118, 518); and an in-bed heat exchanger (120, 520) comprising one or more conduits at least partially submerged in the bed of particles (118, 518); an expansion device downstream from the single separation vessel (116, 516), the expansion device configured to cool the light gas stream by reducing the pressure, wherein the cooled light gas stream flows through an interior of the conduit of the in-bed heat exchanger (120, 520); means for separating solids from the expanded light gas stream to be used for cooling the in-bed heat exchanger; wherein the single separation vessel (116, 516) and in-bed heat exchanger (120, 520) are configured so that the temperature and pressure within the bed are sufficient to desublimate or condense and freeze at least a portion of the carbon dioxide from the process stream (112, 512) onto the bed of particles (118, 518) so as to form a solid and a separated light gas stream, wherein the single separation vessel (116, 516) and light gas outlet are configured so that the separated light gas stream produced from the process stream (112, 512) in the single separation vessel (116, 516) exits the single separation vessel (116, 516) through the light gas outlet, and wherein the solids produced from expansion and separated using the means for separating solids are introduced into the vessel (116, 516).