1. 1 Gas-Filled Capillary Discharge Waveguides Simon Hooker, Tony Gonsalves & Tom Rowlands-Rees Collaborations Alpha-X Basic Technology programme (Dino Jaroszynski et al) LBNL (Wim Leemans et al.) Department of Physics University of Oxford

2. 2 Limitations to the laser-plasma interaction length DiffractionRefraction Diffraction limits the interaction length to the order of the Rayleigh range: Example: W 0 = 10 µm; = 1 µm  Z R = 0.3 mm For partially ionized plasmas refraction further limits the interaction length Spot size: 1/e 2 radius in intensity

3. 3 Gradient refractive index guiding - Plasma waveguides For non-relativistic intensities the refractive index of a plasma may be written: supports matched guiding of Gaussian beams with a constant spot size: Hence a parabolic electron density profile:

4. 4 Gas-filled capillary discharge waveguide: Overview Channels laser machined in sapphire blocks Channel 200 - 400 μm diameter Gas injected near each end of channel D. J. Spence et al. Phys. Rev. E 63 015401(R) (2001) Gas ionized by pulsed discharge –Peak current 100 - 500 A –Rise-time 50 - 100 ns

5. 5 Channels laser machined in sapphire blocks Channel 200 - 400 μm diameter Gas injected near each end of channel Gas ionized by pulsed discharge –Peak current 100 - 500 A –Rise-time 50 - 100 ns Gas-filled capillary discharge waveguide: Overview D. J. Spence et al. Phys. Rev. E 63 015401(R) (2001)

6. 6 Mechanism of Channel Formation – MHD Simulation No pinch effect is observed Plasma fully ionized for t > 50 ns Ablation of capillary wall found to be negligible Bobrova et al. Phys. Rev. E 65 016407 (2001)

7. 7 Discharge reaches a quasi equilibrium in which Ohmic heating of plasma is balanced by conduction of heat to wall: Solution of the heat flow equation yields a scaling relation for the matched spot size: Mechanism of Channel Formation – MHD Simulation Bobrova et al. Phys. Rev. E 65 016407 (2001)

8. 8 Guiding With Square Capillaries Transmission = 90% t = 115 ns Guided spot 27 × 32 µm 33 mm long, 400 μm square capillary 120 mbar H 2 Transmitted spots ~ same size as input spot

9. 9 Guiding With Square Capillaries (a) Input intensity 5.8  10 16 W cm -2 ; W ~ 28 μm (b) Exit: Unguided Output Spot t <0ns (c) Exit t =115ns

10. 10 Guiding experiments at LBNL (preliminary results) Energy meter Wedges Spectrometer OAP Capillary Waveguide Energy MeterLaser Guiding at 15 TW 50 μm input spot I ~ 5 ×10 17 Wcm -2 Beam 33 mm after focus (no waveguide) Beam at exit of 33 mm long waveguide I ~ 5 ×10 17 Wcm -2

11. 11 Transverse interferometry Nd:YAG camera 1.2 1.1 1.0 0.9 0.8 0.7 Electron Density (10 18 cm -3 ) Position in Capillary 60 mbar 140 ns

12. 12 Scaling of matched spot size However the optimum coupling for grazing-incidence guiding is, Matched spot scales as Plasma waveguide Grazing-incidence waveguide

13. 13 Summary Advantages Guiding of laser pulses with peak intensities of ~ 5 × 10 17 Wcm -2 over 33 mm demonstrated High pulse energy and peak intensity transmission Low coupling losses Long device lifetime demonstrated Should be able to be staged Disadvantages Guided spot size relatively large (> 20 µm) Spot size becomes even larger at low plasma densities