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).
Capillary discharges are widely used in many experiments devoted to laser-plasma interaction as a simple tool to create plasma with required parameters. One of the application of these experiments is laser-plasma accelerators (LPA) of charged particles. Such LPAs are able to accelerate electrons bunch to more that a GeV on the centimeters distances .
Essential part of these experiments is capillary discharge. It is used to create plasma waveguide in order to channel an accelerating laser pulse. The long (several decimetres) and thin (several microns) capillary is needed to achieve maximum acceleration but its fabrication is laborious and unreasonably expensive for the LPA experiments. Also capillary can be damaged by electric current pulse that is used to create plasma waveguide.
Additional heating of the plasma channel by a nanosecond laser pulse is used in order to avoid these limitations . Propagation of a heater laser through the plasma waveguide deepens it further in the vicinity of the capillary axis. Recent experiments show positive effect of such heating on the final acceleration of the electrons. This leads to a problem of choosing optimal parameters to achieve maximal acceleration.
Consistent numerical modeling of plasmadynamics and laser pulse propagation in plasma channel is required to maintenance and optimise the future experiments. The magnetohydrodynamic (MHD) code MARPLE  previously used for discharge simulations [3-5] was improved by taken into account additional heating due to laser radiation. Results of simulations that were done for the BELLA experimental facility will be presented at the conference.
The work was supported in part by the Competitiveness Program of MEPhI No.02.A03.21.0005, basic research program of the Project 3-OMN RAS, U.S. DOE under Contract No.DE-AC02-05CH11231, EU Reg.Dev.Fund Ns.CZ.02.1.01/0.0/0.0/15 008/0000162 and CZ.02.1.01/0.0/0.0/15_003/0000449 and by the MoEYaS of the Czech Republic No.LQ1606.
 W.Leemans et al. Phys. Rev. Lett. 113, 245002 (2014)
 N.Bobrova et al. Phys. Plasmas 20, 020703 (2013)
 G.Bagdasarov et al. Phys. Plasmas 24, 053111 (2017)
 G.Bagdasarov et al. Phys. Plasmas 24, 083109 (2017)
 G.Bagdasarov et al. Phys. Plasmas 24, 123120 (2017)
We present an experimental study of ion acceleration using the high repetition rate
petawatt BELLA laser  with an increased laser focal spot (compared to similar experiments) from micrometer thick metallic targets. Ion beams of unprecedented charge density with narrow and achromatic divergence were observed. A reduced curvature of the accelerating sheath field was found to account for these effects. The field dynamics inferred from 2D particle-in-cell simulations suggest an adiabatic treatment of the acceleration process. This is achieved by increasing the laser spot size w0 incident on the targets front side to values well above the target thickness ¹l << w0º. As the laser spot size is increased and hence, the virtual source size of the ion beam, the number of accelerated ions is escalated accordingly. By optimizing the target thickness, the contribution to the divergence by scattering of the hot plasma electrons propagating through the solid target could be adapted to yield proton beams with achromatic, narrow divergence. These findings are embedded in the first study of Target Normal Sheath Acceleration (TNSA) with statistical significance at petawatt laser power, consisting of several hundred target shots. We applied a tape drive target system [2, 3] that allows for conducting the experiments with Titanium tape of 5 _m thickness at repetition rates up to 0:5 Hz. Such ion beams are ideally suited for subsequent emittance preserving beam transport, with typically narrow acceptance, such as active plasma lenses  and many application in cell biology, high energy density - and material sciences.
This work was supported by the U.S. Department of Energy Office of Science Offices of
High Energy Physics and Fusion Energy Sciences, under Contract No. DE-AC02-05CH11231.
This research used computational resources (Edison, Hopper) of the National Energy Research
Scientific Computing canter (NERSC), which is supported by the Office of Science of the
U.S. Department of Energy under Contract No. DE-AC02-05CH11231. J.H.B. acknowledges
financial support from the Alexander von Humboldt Foundation.
 K. Nakamura, et al. Diagnostics, control and performance parameters for the bella high
repetition rate petawatt class laser. IEEE Journal of Quantum Electronics, 53(4):1–21,
 B. H. Shaw, et al. Reflectance characterization of tape-based plasma mirrors. Physics of
Plasmas, 23(6):063118, 2016.
 S. Steinke, et al. Multistage coupling of independent laser-plasma accelerators. Nature,
 J. van Tilborg, et al. Active plasma lensing for relativistic laser-plasma-accelerated electron
beams. Physical Review Letters, 115(18):184802, 2015.
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
 Benware B. R. et al 1998 Phys. Rev. Lett. 81 5804
 Bobrova N. A. et al 2001 Phys. Rev. E 65 016407
 Gonsalves A. J. et al 2007 Phys. Rev. Lett. 98 025002
 Esarey E. et al 2009 Rev. Mod. Phys. 81 1229
Laser-plasma accelerators (LPAs) rely on intense laser fields that create wakes in plasmas. Advancement in the field of LPAs depends on extending the laser-plasma interaction length. State-of-the-art accelerators make use of laser guiding by capillary discharge channels. The transverse density profile (channel depth) of such channels confines the laser, and the on-axis density determines the energy transfer to the wake. The transverse profile can be controlled by choosing the radius of the capillary, but laser-induced capillary damage occurs when the radius is reduced to achieve the required channel depth. Both the on-axis density and the transverse profile depend on the pressure inside the capillary before discharge. As the pressure is reduced to increase the interaction length, confinement of the laser beam is reduced. A scheme to improve laser guiding at low densities by locally heating the plasma with a secondary, nanosecond-scale heater laser has been implemented, and preliminary results are presented here. Heating of the plasma and modified confinement of the main laser pulse have been demonstrated.
We describe the first demonstration of a collisionally-excited optical field ionisation laser driven within a gas-filled capillary waveguide. Lasing on the 4d<sup>9</sup>5d - 4d<sup>9</sup>5p transition at 41.8 nm in Xe<sup>8+</sup> was observed to be closely-correlated to conditions under which the pump laser pulses were guided well by the waveguide. Simulations of the propagation of the pump laser radiation show that gain was achieved over essentially the whole 30 mm length of the waveguide.