  The long proton beams present at CERN have the potential to evolve into a
train of microbunches through the self-modulation instability process. The
resonant wakefield generated by a periodic train of proton microbunches can
establish a high acceleration field within the plasma, facilitating electron
acceleration. This paper investigates the impact of plasma density on resonant
wakefield excitation, thus influencing acceleration of a witness electron bunch
and its corresponding betatron radiation within the wakefield. Various
scenarios involving different plasma densities are explored through
particle-in-cell simulations. The peak wakefield in each scenario is calculated
by considering a long pre-modulated proton driver with a fixed peak current.
Subsequently, the study delves into the witness beam acceleration in the
wakefield and its radiation emission. Elevated plasma density increases both
the number of microbunches and the accelerating gradient of each microbunch,
consequently resulting in heightened resonant wakefield. Nevertheless, the
scaling is disrupted by the saturation of the resonant wakefield due to the
nonlinearities. The simulation results reveal that at high plasma densities an
intense and broadband radiation spectrum extending into the domain of the hard
X-rays and gamma rays is generated. Furthermore, in such instances, the energy
gain of the witness beam is significantly enhanced. The impact of wakefield on
the witness energy gain and the corresponding radiation spectrum is clearly
evident at extremely elevated densities.
