Adsorption cell suitable for a thermal wave operated adsorption compressor comprising: • an elongated heat transfer fluid channel defining a heat transfer fluid flow path having an axis and a length; • at least one solid adsorption material housing extending in the heat transfer fluid channel defining an adsorption material chamber; • solid adsorption material that is accommodated in the solid adsorption material chamber and that is in direct heat transferring contact with heat transfer fluid that, in use, flows through the heat transfer fluid channel, wherein said solid adsorption material comprises a stack of units (68B, 150), each unit comprising: o a pill (68B; 150) of adsorption material, each pill (68B, 150) including a top, a bottom and at least one side; and each unit being associated with: o a cup (111; 158) from a heat conductive material, the pill (68B, 150) of the unit being at least partly surrounded by the associated cup (111; 158), each cup including: ▪ a cup bottom wall forming a heat conductive lamella extending between the pill (68B; 150) of the unit and a pill (68B'; 150') of an adjacent unit (68B', 150') in the stack of units, parts of the cup bottom wall being in abutting contact with associated parts of the bottom of the pill (68B, 150) of the unit (68B, 150) and parts of the cup bottom wall being in abutting contact with associated parts of the top of the pill (68B', 150') of the adjacent unit; and ▪ a jacket wall of which at least a part is in abutting contact with an inner side of the solid adsorption material housing; wherein the surface conformity and roughness of the associated parts of the bottom of the pill of the unit and of the associated parts of the top of the pill of the adjacent unit on the one hand and of the abutting parts of the cup bottom wall on the other hand are such that any gap between the abutting parts is less than 30 micron, preferably less than 10 micron. • an elongated heat transfer fluid channel defining a heat transfer fluid flow path having an axis and a length; • at least one solid adsorption material housing extending in the heat transfer fluid channel defining an adsorption material chamber; • solid adsorption material that is accommodated in the solid adsorption material chamber and that is in direct heat transferring contact with heat transfer fluid that, in use, flows through the heat transfer fluid channel, wherein said solid adsorption material comprises a stack of units (68B, 150), each unit comprising: o a pill (68B; 150) of adsorption material, each pill (68B, 150) including a top, a bottom and at least one side; and each unit being associated with: o a cup (111; 158) from a heat conductive material, the pill (68B, 150) of the unit being at least partly surrounded by the associated cup (111; 158), each cup including: ▪ a cup bottom wall forming a heat conductive lamella extending between the pill (68B; 150) of the unit and a pill (68B'; 150') of an adjacent unit (68B', 150') in the stack of units, parts of the cup bottom wall being in abutting contact with associated parts of the bottom of the pill (68B, 150) of the unit (68B, 150) and parts of the cup bottom wall being in abutting contact with associated parts of the top of the pill (68B', 150') of the adjacent unit; and ▪ a jacket wall of which at least a part is in abutting contact with an inner side of the solid adsorption material housing; wherein the surface conformity and roughness of the associated parts of the bottom of the pill of the unit and of the associated parts of the top of the pill of the adjacent unit on the one hand and of the abutting parts of the cup bottom wall on the other hand are such that any gap between the abutting parts is less than 30 micron, preferably less than 10 micron. o a pill (68B; 150) of adsorption material, each pill (68B, 150) including a top, a bottom and at least one side; and o a cup (111; 158) from a heat conductive material, the pill (68B, 150) of the unit being at least partly surrounded by the associated cup (111; 158), each cup including: ▪ a cup bottom wall forming a heat conductive lamella extending between the pill (68B; 150) of the unit and a pill (68B'; 150') of an adjacent unit (68B', 150') in the stack of units, parts of the cup bottom wall being in abutting contact with associated parts of the bottom of the pill (68B, 150) of the unit (68B, 150) and parts of the cup bottom wall being in abutting contact with associated parts of the top of the pill (68B', 150') of the adjacent unit; and ▪ a jacket wall of which at least a part is in abutting contact with an inner side of the solid adsorption material housing; wherein the surface conformity and roughness of the associated parts of the bottom of the pill of the unit and of the associated parts of the top of the pill of the adjacent unit on the one hand and of the abutting parts of the cup bottom wall on the other hand are such that any gap between the abutting parts is less than 30 micron, preferably less than 10 micron. ▪ a cup bottom wall forming a heat conductive lamella extending between the pill (68B; 150) of the unit and a pill (68B'; 150') of an adjacent unit (68B', 150') in the stack of units, parts of the cup bottom wall being in abutting contact with associated parts of the bottom of the pill (68B, 150) of the unit (68B, 150) and parts of the cup bottom wall being in abutting contact with associated parts of the top of the pill (68B', 150') of the adjacent unit; and ▪ a jacket wall of which at least a part is in abutting contact with an inner side of the solid adsorption material housing;