An air separation unit having a rare gas recovery system, the air separation unit comprising a main air compression system, a pre-purification system, a heat exchanger system, and a rectification column system having a higher pressure column and a lower pressure column linked in a heat transfer relationship via a main condenser-reboiler, the rare gas recovery system comprises: a non-condensable stripping column configured to receive a stream of nitrogen rich shelf vapor from the higher pressure column, the non-condensable stripping column configured to produce a liquid nitrogen column bottoms and a rare gas containing overhead; a xenon-krypton column linked in a heat transfer relationship with the non-condensable stripping column via an auxiliary condenser-reboiler, the xenon-krypton column configured to receive a first stream of liquid oxygen pumped from the lower pressure column and a first boil-off stream of oxygen rich vapor from the auxiliary condenser-reboiler, the xenon-krypton column configured to produce a xenon and krypton containing column bottoms and an oxygen-rich overhead, wherein a portion of the xenon and krypton containing column bottoms is taken as a crude xenon and krypton liquid stream; the auxiliary condenser-reboiler configured to receive the rare gas containing overhead from the non-condensable stripping column and a second liquid oxygen stream as the refrigeration source, the auxiliary condenser-reboiler further configured to produce a condensate reflux stream that is released into or directed to the non-condensable stripping column, the first boil-off stream of oxygen rich vapor that is released into the xenon-krypton column and a non-condensable containing vent stream; characterized in that the rare gas recovery system further comprises a reflux condenser configured to receive the non-condensable containing vent stream from the auxiliary condenser-reboiler and a condensing medium, the reflux condenser further configured to produce a condensate that is directed to the non-condensable stripping column and a crude neon vapor stream that contains greater than about 50% mole fraction of neon; and a subcooler configured to subcool all or a portion of the liquid nitrogen column bottoms to produce a subcooled liquid nitrogen stream; wherein the condensing medium for the reflux condenser is a portion of the subcooled liquid nitrogen stream; wherein the non-condensable stripping column is configured to receive a portion of a liquid nitrogen condensate stream from the main condenser-reboiler; and wherein the second liquid oxygen stream is from the lower pressure column. a non-condensable stripping column configured to receive a stream of nitrogen rich shelf vapor from the higher pressure column, the non-condensable stripping column configured to produce a liquid nitrogen column bottoms and a rare gas containing overhead; a xenon-krypton column linked in a heat transfer relationship with the non-condensable stripping column via an auxiliary condenser-reboiler, the xenon-krypton column configured to receive a first stream of liquid oxygen pumped from the lower pressure column and a first boil-off stream of oxygen rich vapor from the auxiliary condenser-reboiler, the xenon-krypton column configured to produce a xenon and krypton containing column bottoms and an oxygen-rich overhead, wherein a portion of the xenon and krypton containing column bottoms is taken as a crude xenon and krypton liquid stream; the auxiliary condenser-reboiler configured to receive the rare gas containing overhead from the non-condensable stripping column and a second liquid oxygen stream as the refrigeration source, the auxiliary condenser-reboiler further configured to produce a condensate reflux stream that is released into or directed to the non-condensable stripping column, the first boil-off stream of oxygen rich vapor that is released into the xenon-krypton column and a non-condensable containing vent stream; characterized in that the rare gas recovery system further comprises a reflux condenser configured to receive the non-condensable containing vent stream from the auxiliary condenser-reboiler and a condensing medium, the reflux condenser further configured to produce a condensate that is directed to the non-condensable stripping column and a crude neon vapor stream that contains greater than about 50% mole fraction of neon; and a subcooler configured to subcool all or a portion of the liquid nitrogen column bottoms to produce a subcooled liquid nitrogen stream; wherein the condensing medium for the reflux condenser is a portion of the subcooled liquid nitrogen stream; wherein the non-condensable stripping column is configured to receive a portion of a liquid nitrogen condensate stream from the main condenser-reboiler; and wherein the second liquid oxygen stream is from the lower pressure column.