The TW Hydrae Association is a cluster chain of Sco-Cen

The TW Hydrae Association (TWA) is a young local association (YLA) about 50 pc from the Sun, offering a unique opportunity to study star and planet formation processes in detail. We characterized TWA's location, kinematics, and age, investigating its origin within the Scorpius-Centaurus (Sco-Cen) OB association. Using Gaia DR3 astrometric data and precise ground-based radial velocities, we identified substructures within TWA, tentatively dividing them into TWA-a and TWA-b. Sco-Cen's massive cluster $\sigma$ Cen (15 Myr, 1,805 members) may have influenced TWA's formation. The alignment of $\sigma$ Cen, TWA-a, and TWA-b in 3D positions, velocities, and ages resembles patterns in regions such as Corona Australis, suggesting that TWA is part of a cluster chain from sequential star formation induced by massive stars in Sco-Cen. TWA's elongation in the opposite direction to that produced by Galactic differential rotation indicates its shape is still influenced by its formation processes and will dissipate in less than 50 Myr due to Galactic forces. These findings unveil the nature of YLAs and low-mass clusters in a new light. We propose that clusters such as $\epsilon$ Chamaeleontis, $\eta$ Chamaeleontis, and TWA were forged by stellar feedback from massive stars in Sco-Cen, while others--such as $\beta$ Pictoris, Carina, Columba, and Tucana-Horologium--are older and formed differently. Remarkably, all these YLAs and Sco-Cen are part of the $\alpha$ Persei cluster family, a vast kiloparsec-scale star formation event active over the past 60 Myr. This suggests that YLAs are the smallest stellar structures emerging from major star formation episodes and should be common in the Milky Way. Crucially, their formation in regions with intense stellar feedback may have influenced planet formation in these systems.