## 1 Introduction  
The expression (laser-)plasma wakefield acceleration refers to schemes of charged-particle acceleration exploiting the highly electric fields that are sustainable by plasmas [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. Electric fields in plasmas can exceed the so-called wave-breaking limit for a cold non-relativistic plasma [13; 14]:  
\[E_{wb}\sim 96\,\sqrt{n_{e}[10^{18}{\rm cm^{-3}}]}\,\,\,{\rm GV/m} \tag{1}\]  
where the electron plasma density is denoted by \(n_{e}\). The term wave-breaking indicates indeed a breakdown phenomenon, the one involving the fronts of the Langmuir waves [15]. Wave-breaking can be responsible for the onset of regions of high-amplitude electric fields, reaching extraordinary values as high as \(\lesssim\)\(TV/\,\)m [16; 17; 18]. Langmuir waves, also known as electron plasma waves, are collective oscillations of the electron plasma density. These oscillations can be induced by perturbing the plasma with an external excitation. The external excitation can be realized either through a laser pulse or by means of a bunch of charged particles. In fact, both a laser pulse and a bunch of charged particles can be associated with an electric field \(\vec{E}_{0}\). This driving field can act on the plasma electrons as a collectivity, generating a Langmuir wave in its wake. In the frequency domain, it is possible to establish a relationship between the pumping field \(\vec{E}_{0}\) and the wakefield \(\vec{E}\)[19]:\[\vec{E}(\vec{r},\omega)=\left(\frac{1}{\varepsilon(\omega,\vec{E}_{0})}-1\right): \vec{E}_{0}(\vec{r},\omega) \tag{2}\]  
where we have introduced the dielectric function of the plasma \(\varepsilon(\omega,\vec{E}_{0})\). The explicit dependence of the dielectric function upon the driving field is shown with the aim to remind that a non-linear response of the plasma, when excited by high-intensity drivers, must be expected. This also means that the effective driving field may not be directly provided by the pumping field \(\vec{E}_{0}\) (as for the case of an intense laser pulse) but rather a complicated non-linear function of the same field hidden within the dielectric function. Furthermore, the vectorial dependence is also explicitly shown since the plasma response may be anisotropic. Indeed, we have introduced the double dot product \":\" due to the fact that, at high intensity, the polarization of the excited wave can be different from that of the pumping field. The latter is particularly true when a high-intensity transversally polarized laser induces a longitudinal (in the direction of light propagation) plasma perturbation through the so-called ponderomotive force [13]. In the self-injection regime, the laser excites plasma wakefields above the wave-breaking threshold in such a way that electrons from the background plasma, concentrated in the region of wave-breaking, can be injected into the wakefield and accelerated spontaneously. Since \(1/\varepsilon\) tends to zero for some value of the exciting frequency \(\omega\sim\omega_{p}\), where \(\omega_{p}(\vec{E}_{0})\) is the non-linear plasma frequency, the wakefields are efficiently generated when the spectrum of the effective driver extends over the \(\omega_{p}\) range. Furthermore, Equation (2) also shows that a resonant plasma excitation (\(1/\varepsilon>>1\)) corresponds to a wakefield amplitude that can be orders of magnitude higher than the electric amplitude of the pumping field. In Figure 1, the laser-plasma wakefield (LWFA) accelerator at the CLPU facility (Salamanca, Spain) is shown. The present paper aims to be an overview of the performance of the latter accelerator and of the secondary source of X-rays based on it for a specific working point, i.e., for a particular case of operational conditions. Such conditions were determined by the needs of another experiment ongoing at the facility [20].