[en] A plasma can sustain electric fields orders of magnitude larger than those attainable with the conventional radio-frequency (RF) technology typically used in particle accelerators, which are limited to ∼ 100 MV/m due to electrical breakdowns occurring at the metallic boundary of the accelerating structures. In a particle-beam-driven plasma-wakefield accelerator (PWFA), a charge-density wake sustaining field gradients in excess of GV/m is driven by the passage of a relativistic high-intensity particle bunch through a plasma. By harnessing the gradients of the wake, particles trailing behind the wakefield-driving bunch can be accelerated to GeV energies over meter distances, thus enabling a drastic reduction of the size of accelerator componenents and, consequently, potentially reducing the costs of future accelerator facilities. Despite this promise, however, for PWFA to be a viable technology, the quality of the accelerated bunches must match that achieved by RF-based state-of-the-art FEL linacs and particle colliders. Even though theoretical predictions suggest that PWFA schemes are capable of producing electric-field profiles with properties sufficient to preserve the longitudinal-phase-space structure of the accelerating beam, direct experimental demonstration has not yet been achieved. In the work presented in this thesis the diagnostic capabilities of a novel X-band transverse deflection structure (TDS) - featuring femtosecond resolution and a variablepolarisation of the streaking field - are exploited to investigate two mechanisms enabling the preservation of the energy spread of electron beams accelerated in a nonlinear plasma wake: optimal beam loading to preserve the correlated energy spread and a fully evacuated ion column to preserve the uncorrelated energy spread. By directly observing the longitudinal phase space of 1-GeV bunches accelerated 44 MeV in a nonlinear plasma wake, experiments performed at the FLASHForward facility (DESY, Hamburg) demonstrate that the longitudinal accelerating gradients are transversely homogeneous to within 0.8 % (1.5 %) at an interval of confidence of 68 % (95 %) and show variable amounts of beam loading depending on the exact shape of the current profile of the driver-trailing-bunch pair. The results presented in this work experimentally demonstrate the predicted suitability of PWFA for future applications requiring the preservation of high longitudinal beam quality. Furthermore, a reconstruction of the beam-plasma interaction in a particle-in-cell code has been accomplished, which illustrates the extreme sensitivity of the PWFA acceleration process to the phase-space distribution of the incoming beams. These achievements suggest that, while PWFA is capable of producing the desired field geometries, an improved control over the production of driver-trailing-bunch pairs will be required to demonstrate stable and quality-preserving acceleration at higher energy gains.