Coronal mass ejections (CMEs) are the primary sources of intense disturbances at Earth, where their geo-effectiveness is largely determined by their dynamic pressure and internal magnetic field, which can be significantly altered during interactions with other CMEs in interplanetary space. We analyse three successive CMEs that erupted from the Sun during September 4-6, 2017, investigating the role of CME-CME interactions as source of the associated intense geomagnetic storm (Dst_min=-142 nT on September 7). To quantify the impact of interactions on the (geo-)effectiveness of individual CMEs, we perform global heliospheric simulations with the EUHFORIA model, using observation-based initial parameters with the additional purpose of validating the predictive capabilities of the model for complex CME events. The simulations show that around 0.45 AU, the shock driven by the September 6 CME started compressing a preceding magnetic ejecta formed by the merging of two CMEs launched on September 4, significantly amplifying its Bz until a maximum factor of 2.8 around 0.9 AU. The following gradual conversion of magnetic energy into kinetic and thermal components reduced the Bz amplification until its almost complete disappearance around 1.8 AU. We conclude that a key factor at the origin of the intense storm triggered by the September 4-6, 2017 CMEs was their arrival at Earth during the phase of maximum Bz amplification. Our analysis highlights how the amplification of the magnetic field of individual CMEs in space-time due to interaction processes can be characterised by a growth, a maximum, and a decay phase, suggesting that the time interval between the CME eruptions and their relative speeds are critical factors in determining the resulting impact of complex CMEs at various heliocentric distances (helio-effectiveness).
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