A system for welding an elongate element along a longitudinal direction thereof to a surface of a component, wherein the elongate element and the surface each comprise thermoplastic material, the system comprising: - a support element comprising a support surface adapted to support a component thereon, - a magnetic field generating arrangement disposed on a side of the support element opposite the support surface and adapted to generate a predefined magnetic field above the support surface, - a carriage comprising at least one first contact means and at least one second contact means, wherein the at least one first contact means is spaced from the at least one second contact means such that the at least one first contact means and the at least one second contact means are operable to - contact an elongate element, which has a suitable cross-sectional shape and is placed on a surface of a component supported on the support element, at spaced locations and thereby support the elongate element against movement along the surface of the component in directions perpendicular to the longitudinal direction of the elongate element, and - allow movement of the carriage along the longitudinal direction of the elongate element, - a superconducting element having a defined transition temperature below which the superconducting element exhibits superconductivity and being fixedly connected to the carriage, - an element cooling device operable to cool and maintain the superconducting element below its transition temperature, - movement means operable to linearly move the carriage, and - at least one welding device operable to weld the elongate element to the surface of the component, wherein the predefined magnetic field is configured such that a linear path along the support surface at a distance above the support surface is defined for the superconducting element when the superconducting element has a temperature below its transition temperature, so that the movement means is operable to move the carriage along a path corresponding to the defined linear path of the superconducting element. - a support element comprising a support surface adapted to support a component thereon, - a magnetic field generating arrangement disposed on a side of the support element opposite the support surface and adapted to generate a predefined magnetic field above the support surface, - a carriage comprising at least one first contact means and at least one second contact means, wherein the at least one first contact means is spaced from the at least one second contact means such that the at least one first contact means and the at least one second contact means are operable to - contact an elongate element, which has a suitable cross-sectional shape and is placed on a surface of a component supported on the support element, at spaced locations and thereby support the elongate element against movement along the surface of the component in directions perpendicular to the longitudinal direction of the elongate element, and - allow movement of the carriage along the longitudinal direction of the elongate element, - contact an elongate element, which has a suitable cross-sectional shape and is placed on a surface of a component supported on the support element, at spaced locations and thereby support the elongate element against movement along the surface of the component in directions perpendicular to the longitudinal direction of the elongate element, and - allow movement of the carriage along the longitudinal direction of the elongate element, - a superconducting element having a defined transition temperature below which the superconducting element exhibits superconductivity and being fixedly connected to the carriage, - an element cooling device operable to cool and maintain the superconducting element below its transition temperature, - movement means operable to linearly move the carriage, and - at least one welding device operable to weld the elongate element to the surface of the component,