We introduce a complete semi-analytical model for a cavitated electron wake driven by an electron beam in a radially inhomogeneous plasma. The electron response to the driver, dynamics of electrons in a thin sheath surrounding the cavity, as well as accelerating and focusing fields inside the cavity are calculated in the quasistatic approximation. Our theory holds for arbitrary radial density profiles and reduces to known models in the limit of a homogeneous plasma. A free-propagating blow-out in an evacuated channel experiences longitudinal squeezing, qualitatively the same as observed in particle-in-cell simulations for the laser pulse-driven case [Pukhov et al., Phys. Rev. Lett. 113, 245003 (2014)]. Our model also permits qualitative interpretation of the earlier observed cancellation of the focusing gradient in the cavity [Pukhov et al., Phys. Rev. Lett. 113, 245003 (2014)]. In this work, we show the underlying mechanism that causes the radial fields in the vacuum part of a channel to become defocussing.
Based on a model of plasma wakefield in the strongly nonlinear (bubble) regime, we develop a lowest-order perturbation theory for the components of electromagnetic fields inside and outside the bubble using the assumption of small thickness of the electron sheath on the boundary of the bubble. Unlike previous models, we derive simple explicit expressions for the components of electromagnetic fields not only in the vicinity of the center of the bubble, but in the whole volume of the bubble (including areas of driving or accelerated bunches) as well as outside it. Moreover, we apply the results to the case of radially non-uniform plasma and, in particular, to plasma with a hollow channel. The obtained results are verified with 3D particle-in-cell (PIC) simulations which show good correspondence to our model.
Based on the already existing analytical theory of the strongly-nonlinear wakefield (which is called "bubble") in transversely inhomogeneous plasmas, we study particular behavior of non-loaded (empty) bubbles and bubbles with accelerated bunches. We obtain an analytical expression for the shape of a non-loaded bubble in a general case and verify it with particle-in-cell (PIC) simulations. We derive a method of calculation of the acceleration efficiency for arbitrary accelerated bunches. The influence of flat-top electron bunches on the shape of a bubble is studied. It is also shown that it is possible to achieve acceleration in a homogeneous longitudinal electric field by the adjustment of the longitudinal density profile of the accelerated electron bunch. The predictions of the model are verified by 3D PIC simulations and are in a good agreement with them.
We demonstrate both theoretically and experimentally the possibility of correlating the phase of a Cherenkov superradiance (SR) pulse to the sharp edge of a current pulse, when spontaneous emission of the electron bunch edge serves as the seed for SR processes. By division of the driving voltage pulse across several parallel channels equipped with independent cathodes we can synchronize several SR sources to arrange a two-dimensional array. In experiments carried out, coherent summation of radiation from four independent 8-mm wavelength band SR generators with peak power 600 MW resulted in the interference maximum of the directional diagram with an intensity that is equivalent to radiation from a single source with power 10 GW. Numerous scientific and technological applications stimulate interest in the generation of ultra-high power coherent radiation. Approaches that can be suggested to achieve this goal include the generation of radiation by a single source with an oversized electrodynamic system. In this case special methods (for example, 2D distributed feedback [1,2]) are required to produce spatially coherent radiation. Another method is the synchronization of a large number of moderate-power sources using a master oscillator [3][4][5]. DOIAt the same time for short-pulse sources, in particular, for sources based on Cherenkov superradiance (SR) of extended electron bunches moving in a slow wave structure (SWS) [6,7], there is an alternative opportunity, associated with the correlating the phase of a radiated pulse to the sharp edge of a current pulse. In fact, spontaneous emission of the bunch edge serves as the seed for SR processes. It gives rise to the stimulated emission including electron self-bunching and subsequent radiation of the short high-power electromagnetic pulse. If identical current pulses are sent simultaneously to several channels, identical SR pulses will be generated and the coherent summation of their amplitudes is possible. For two channel radiation sources such a possibility has been experimentally demonstrated in Ref. [8]. However the physical model describing the transformation of spontaneous Cherenkov radiation (i.e. the radiation from the unperturbed moving particles without the reverse effect of the field [9]) to stimulated radiation is still missing. The
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