Reactor (2; 52; 62) for carrying out a chemical reaction in a process fluid using multiphase alternating current for heating the process fluid, wherein the alternating current has a number M of phases, wherein M is an integer greater than one, comprising a reactor container formed by a thermally insulating reactor wall (4; 54; 64); at least one group comprising a plurality of reaction tubes (6u, 6v, 6w; 56; 66), wherein each group comprises M reaction tubes, wherein each of the reaction tubes has an electrically heatable heating portion extending with a respective heating length between a first and a second removal region (22, 23) of the respective reaction tube, wherein the heating portions are arranged, at least for 95% of their heating length, within the reactor container and each have a feed region in a region extending from 20% to 80% of their heating length; electrically conductive feed elements, wherein each group is assigned M feed elements which are electrically conductively connected to the feed regions of the group, wherein different phases of the alternating current are fed or can be fed into different feed elements assigned to a group; electrically conductive first and second removal elements (34, 35), wherein each group is assigned M first removal elements and M second removal elements which are electrically conductively connected to the first removal regions and/or the second removal regions of the group; at least one electrically conductive first star bridge and at least one electrically conductive second star bridge, wherein each group is assigned to a first and a second star bridge, wherein, for each group, the first removal elements assigned to the group are electrically conductively connected to the first star bridge to which the group is assigned, and the second removal elements assigned to the group are electrically conductively connected to the second star bridge to which the group is assigned. a reactor container formed by a thermally insulating reactor wall (4; 54; 64); at least one group comprising a plurality of reaction tubes (6u, 6v, 6w; 56; 66), wherein each group comprises M reaction tubes, wherein each of the reaction tubes has an electrically heatable heating portion extending with a respective heating length between a first and a second removal region (22, 23) of the respective reaction tube, wherein the heating portions are arranged, at least for 95% of their heating length, within the reactor container and each have a feed region in a region extending from 20% to 80% of their heating length; electrically conductive feed elements, wherein each group is assigned M feed elements which are electrically conductively connected to the feed regions of the group, wherein different phases of the alternating current are fed or can be fed into different feed elements assigned to a group; electrically conductive first and second removal elements (34, 35), wherein each group is assigned M first removal elements and M second removal elements which are electrically conductively connected to the first removal regions and/or the second removal regions of the group; at least one electrically conductive first star bridge and at least one electrically conductive second star bridge, wherein each group is assigned to a first and a second star bridge, wherein, for each group, the first removal elements assigned to the group are electrically conductively connected to the first star bridge to which the group is assigned, and the second removal elements assigned to the group are electrically conductively connected to the second star bridge to which the group is assigned.