A cryogenic trap system (500; 600) for a system comprising a helium circuit, the cryogenic trap system comprising: an enclosure (540; 640) having a first end, a second end opposed to the first end, and an interior surface that forms an interior of the enclosure; an inlet (570; 670) for a gas in the helium circuit to enter the interior of the enclosure; an outlet (574; 674) for the gas to exit the interior of the enclosure; and at least one helical cryocondensation surface in the interior of the enclosure, wherein the at least one helical cryocondensation surface: extends axially from at least proximate the first end of the enclosure at least toward the second end of the enclosure, and is thermally conductively coupled to a cold source, wherein respective ones of a plurality of portions of the at least one helical cryocondensation surface are conductively thermally coupled to a plurality of respective portions of the at least one cold source at a plurality of different temperatures, and the at least one helical cryocondensation surface exhibits a temperature gradient as the interior of the enclosure is traversed from the first to the second end, wherein the at least one cryocondensation surface extends radially in the interior of the enclosure and comprises at least one helical cryocondensation surface on an exterior surface of a helical member (528; 630) that axially extends along a majority of the enclosure, characterized in that the helical member is in a form of a helical plate having a pair of opposed exterior surfaces wherein the at least one helical cryocondensation surface comprises at least one of the opposed exterior surfaces, or, the helical member comprises a helical textile and the at least one helical cryocondensation surface comprises a respective exterior surface of a plurality of strands of the helical textile. an enclosure (540; 640) having a first end, a second end opposed to the first end, and an interior surface that forms an interior of the enclosure; an inlet (570; 670) for a gas in the helium circuit to enter the interior of the enclosure; an outlet (574; 674) for the gas to exit the interior of the enclosure; and at least one helical cryocondensation surface in the interior of the enclosure, wherein the at least one helical cryocondensation surface: extends axially from at least proximate the first end of the enclosure at least toward the second end of the enclosure, and is thermally conductively coupled to a cold source, extends axially from at least proximate the first end of the enclosure at least toward the second end of the enclosure, and is thermally conductively coupled to a cold source, wherein respective ones of a plurality of portions of the at least one helical cryocondensation surface are conductively thermally coupled to a plurality of respective portions of the at least one cold source at a plurality of different temperatures, and the at least one helical cryocondensation surface exhibits a temperature gradient as the interior of the enclosure is traversed from the first to the second end, wherein the at least one cryocondensation surface extends radially in the interior of the enclosure and comprises at least one helical cryocondensation surface on an exterior surface of a helical member (528; 630) that axially extends along a majority of the enclosure, characterized in that the helical member is in a form of a helical plate having a pair of opposed exterior surfaces wherein the at least one helical cryocondensation surface comprises at least one of the opposed exterior surfaces, or, the helical member comprises a helical textile and the at least one helical cryocondensation surface comprises a respective exterior surface of a plurality of strands of the helical textile.