A light water reactor, in particular a boiling water reactor, includes a reactor pressure vessel having an interior, a core disposed in a lower half of the pressure vessel, fuel assemblies disposed in the core, and a column of water covering the core and acting as a coolant and a moderator. The column has an initial level range during normal operation. A passively operating safety device is provided. Fluid lines are connected between the safety device and the interior of the pressure vessel. The fluid lines automatically transmit an actuation criterion to the safety device, with at least a drop of a level in the pressure vessel to a value below the initial level range serving as the actuation criterion.
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