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Nuclear fusion presents a promising clean energy source to mitigate future energy crises, with magnetic confinement fusion well-positioned to provide a baseload scenario to power future reactors. The unmitigated power exhaust of such reactors threatens its divertor region with intolerably high heat fluxes, leading to wall erosion and, subsequently, core fuel dilution and contamination. Novel power exhaust solutions are being developed to address the integration of a high performance fusion core plasma with well-protected divertor targets, should the standard Single Null configuration (SN) not scale favourably to a reactor device. This work aims to further the physics understanding of the power exhaust benefits in configurations with multiple X-points and increased scrape-off layer (SOL) connection length (L||), such as the Snowflake minus configuration (SF-), combined with neutral baffling. To further elucidate these mechanisms, a novel divertor geometry is developed with three nearby divertor X-points in the Tokamak à Configuration Variable (TCV), named the Jellyfish (JF), and the mean-field edge transport code EMC3-EIRENE is employed to interpret experimental results. The TCV Langmuir probes are extensively used to evaluate target conditions, employing an upgraded heat flux analysis.Configurations with multiple nearby divertor X-points exhibit a strong reduction in the outer target heat flux (up to 66%) and the ability to balance the strike-point distribution of heat flux, compared to a reference SN. Furthermore, an earlier detachment onset is observed as well as a local increase in radiated power in flux tubes with increased L||, as predicted by the simplified SOL model SPLEND1D. While this does not necessarily map to higher total divertor radiative losses for multiple X-point configurations, it can, at least, provide some control over the radial position of the spatial radiation distribution.Despite a radiating region located farther from the confined plasma than a reference SN, no change in core confinement is observed in multiple X-point configurations. Core effective charge measurements indicate an increase in core impurity penetration for the SF- compared to the SN and JF. Interpretative modelling using EMC3-EIRENE indicates that this increase is due to the impurity source location, rather than an intrinsic property of multiple X-point configurations. Increasing the divertor closure with gas baffles, achieved for the first time in the SF-, further enhances the target heat flux reduction, without significantly affecting the location of the inter-null radiation region or the core-divertor compatibility.Multi-spectral imaging exhibits radial striations in the emissivity of many spectral lines in the inter-null regions of multiple X-point configurations, indicative of channels of enhanced cross-field transport. Although comparisons with simulations using EMC3-EIRENE support enhanced cross-field transport for the SF-, additional transport physics is required in the model to obtain a quantitative match with experiment.Future work looks to experimentally study and simulate multiple X-point configurations under more reactor relevant conditions, moving to higher power and high confinement scenarios. The datasets collected in this thesis constitute a good starting point for power scans in simulation studies, with the promising power exhaust benefits motivating higher power experiments in TCV and in other devices.