In 2014, electron beams with energy up to 4.3 GeV were obtained using 9 cm-long capillary discharge plasma waveguides and laser pulses with peak power 310 TW . Although the laser power available was 1 PW, at that time it was not possible to increase the electron beam energy further since effective laser-guiding of the 60 micron focal spot at lower density was not possible. Usually the capillary radius would be reduced to increase the plasma channel depth and achieve matched guiding of the laser, but for PW laser pulses significant capillary damage would typically occur. The concept of inverse bremsstrahlung heating inside a capillary waveguide was proposed to address this problem . Results will be shown on the optimization of heating and laser-guiding, which has allowed for guiding of laser pulses with PW peak power and 60 micron radius over tens of centimeters, and the generation of electron beams with energy up to 8GeV.
The work was supported by the Office of Science, US DOE under Contract DE-AC02-05CH11231 and the NSF.  W. P. Leemans et al., Phys. Rev. Lett. 113, 245002 (2014).  N.A. Bobrova et al., Phys. Plasmas 20, 020703 (2013).
For several decades the capillary discharges have been under intensive investigations due to various promising applications, e.g. for the laser electron accelerators as well as for the X-ray lasers [1,2]. A major portion of the experiments were done with circular cross-section capillaries. An appropriate theoretical and numerical study of circular capillaries can be greatly simplified to a 1D model  assuming rotational and axial symmetries of the plasma flow in a long thin channel. On the other hand, studying capillaries with non-circular cross-section , which have been attracting substantially less attention, requires more complicated 2D models. Such capillaries, for example, square one, possess several advantages related to their fabrication as well as for plasma diagnostics
The aim of our work is to compare the plasma density and temperature distributions formed at the quasistationary stage of the discharge. We present the results of MHD simulations of hydrogen-filled capillary discharges with circular and rectangular cross-sections under almost the same conditions characterizing the initial configurations and the external electric circuit. The simulation parameters are choosen to correspond to the capillary discharge based waveguide for the laser wakefield accelerator .
 Leemans W. P. et al 2014 Phys. Rev. Lett. 113 245002
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 Gonsalves A. J. et al 2007 Phys. Rev. Lett. 98 025002
 Esarey E. et al 2009 Rev. Mod. Phys. 81 1229
High resolution x-ray emission spectra of plasma created by laser irradiation of rare-gas (Ar, Kr, Xe) clusters have been measured at laser intensities over 1019 W/cm2 and 30-fs pulse duration. To make these measurements possible, in addition to the effort to decrease a prepulse intensity using Pockels cell switches, micron-size clusters were produced using a specially designed conical nozzle. The Boltzmann equation and a detailed collisional radiative model are solved simultaneously as a function of time to model the time integrated x-ray spectra of the transient plasma. The results are quantitatively in good agreement with the experimentally observed x-ray emission spectra of Ar clusters.
A mathematical model of clusters forming in gas jets is proposed. This model concerns with the representation of the clusters by the moments of the distribution function of the clusters with respect to the radius. This model uses the kinetic theory of phase transitions presented by Frenkel for the kinetic of the clusters formation. The numerical results obtained with the help of this model are compared with the direct experimental measurements based on Mach-Zehnder interferometry and Rayleigh scattering.
Review of systematic investigations of x-ray radiation properties of different clusters heated by short-pulse high- intensive TI:Sa laser radiation is presented. The cluster targets were formed by the adiabatic expansion in vacuum of an Ar or CO2 gas puff produced by a pulsed valve with a Laval or conical nozzles. The gas jet pressure is varied form 15 up to 100 bar. Detailed theoretical modeling of cluster parameters have been done and compared with experimental measurements. High spectrally and spatially resolved x-ray spectra near resonance lines of H- and He- like ions of oxygen and Ar have been obtained and detailed spectroscopic analysis was consistent with a theoretical two-temperature collisional-radiative model of irradiated atomic clusters incorporating with an effects of highly energetic electronics. The role of laser prepulse for x-ray intensity emission and its spatial distribution were investigated in details. X-ray spectra radiation from plasma with electron density more than 1022 cm-3 was at first time observed. Big effect of fast electrons influence on the x-ray emission of He-like Ar spectra was demonstrated. Comparison with data under various experimental conditions clearly demonstrated that for increasing x-ray output form plasma the most essential to increase size of clusters and has reasonable value of ps prepulse.
This paper deals with a numerical simulation of the behavior of asthma flows produced when heating the inlet hole walls of hohlraum target by x-ray radiation. Results of 1D numerical calculation are presented for ablation plasma flows interaction with internal transverse magnetic field or with subcritical plasma contained in the target cavity. The calculations confirm the possibility of plasma flows suppression during the time of laser-pulse action.