Advances in the generation of relativistic intensity pulses with wavelengthsin the X-ray regime, through high harmonic generation from near-criticalplasmas, opens up the possibility of X-ray driven wakefield acceleration. Thesimilarity scaling laws for laser plasma interaction suggest that X-rays candrive wakefields in solid materials providing TeV/cm gradients, resulting inelectron and photon beams of extremely short duration. However, the wavelengthreduction enhances the quantum parameter $\chi$, hence opening the question ofthe role of non-scalable physics, e.g., the effects of radiation reaction.Using three dimensional Particle-In-Cell simulations incorporating QED effects,we show that for the wavelength $\lambda=5\,$nm and relativistic amplitudes$a_0=10$-100, similarity scaling holds to a high degree, combined with$\chi\sim 1$ operation already at moderate $a_0\sim 50$, leading to photonemissions with energies comparable to the electron energies. Contrasting to thegeneration of photons with high energies, the reduced frequency of photonemission at X-ray wavelengths (compared to at optical wavelengths) leads to areduction of the amount of energy that is removed from the electron populationthrough radiation reaction. Furthermore, as the emission frequency approachesthe laser frequency, the importance of radiation reaction trapping as adepletion mechanism is reduced, compared to at optical wavelengths for $a_0$leading to similar $\chi$.
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