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The possibility of utilizing plasma undulators and plasma accelerators to produce compact ultraviolet and X-ray sources, has attracted considerable interest for a few decades. This interest has been driven by the great potential to decrease the threshold for accessing such sources, which are mainly provided by a few dedicated large-scale synchrotron or free-electron laser (FEL) facilities. However, the broad radiation bandwidth of such plasma devices limits the source brightness and makes it difficult for the FEL instability to develop. Here, using multi-dimensional particle-in-cell (PIC) simulations, we demonstrate that a plasma undulator generated by the beating of a mixture of high-order laser modes propagating inside a plasma channel, leads to a few percent radiation bandwidth. The strength of the undulator can reach unity, the period can be less than a millimeter, and the number of undulator periods can be significantly increased by a phase locking technique based on the longitudinal tapering. Polarization control of such an undulator can be achieved by appropriately choosing the phase of the modes. According to our results, in the fully beam loaded regime, the electron current in the plasma undulator can reach 0.3 kA level, making such an undulator a potential candidate towards a table-top FEL.

We report on a proton acceleration experiment in which high-intensity laser pulses with a wavelength of 0.4 μm and with varying temporal intensity contrast have been used to irradiate water droplets of 20 μm diameter. Such droplets are a reliable and easy-to-implement type of target for proton acceleration experiments with the potential to be used at very high repetition rates. We have investigated the influence of the laser's angle of incidence by moving the droplet along the laser polarization axis. This position, which is coupled with the angle of incidence, has a crucial impact on the maximum proton energy. Central irradiation leads to an inefficient coupling of the laser energy into hot electrons, resulting in a low maximum proton energy. The introduction of a controlled pre-pulse produces an enhancement of hot electron generation in this geometry and therefore higher proton energies. However, two-dimensional particle-in-cell simulations support our experimental results confirming, that even slightly higher proton energies are achieved under grazing laser incidence when no additional pre-plasma is present. Illuminating a droplet under grazing incidence generates a stream of hot electrons that flows along the droplet's surface due to self-generated electric and magnetic fields and ultimately generates a strong electric field responsible for proton acceleration. The interaction conditions were monitored with the help of an ultra-short optical probe laser, with which the plasma expansion could be observed.