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

Limitations to the laser-plasma interaction length

Diffraction Refraction

Diffraction limits the interaction length to the order of the Rayleigh range:

2

0R

WZ

Example: W0 = 10 µm; = 1 µm

ZR = 0.3 mm

For partially ionized plasmas refraction further limits the interaction length

2

20

1 e

e

N e

m

Spot size:

1/e2 radius in intensity

3

Gradient refractive index guiding - Plasma waveguides

For non-relativistic intensities the refractive index of a plasma may be written:

2( ) (0) /e e e chN r N N r r

supports matched guiding of Gaussian beams with a constant spot size:

1/ 42ch

Me e

rW

r N

Hence a parabolic electron density profile:

2 2

2 20 0

11 1

2e e

e e

N e N e

m m

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

H2 gas

vacuum vacuumbellows

channel

+V 0V

electrode

laser

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

• Channels laser machined in sapphire blocks

• Channel 200 - 400 μm diameter

• Gas injected near each end of channel

H2 gas

vacuum vacuumbellows

channel

+V 0V

electrode

laser

• Gas ionized by pulsed discharge

– Peak current 100 - 500 A

– Rise-time 50 - 100 ns

Gas-filled capillary discharge waveguide: OverviewD. J. Spence et al. Phys. Rev. E 63 015401(R) (2001)

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

Discharge reaches a quasi equilibrium in which Ohmic heating of plasma is balanced by conduction of heat to wall:

210e

d dTr E

r dr dr

Solution of the heat flow equation yields a scaling relation for the matched spot size:

5

1/ 4-3

[μm][μm] 1.5 10

[cm ]M

e

aW

N

Mechanism of Channel Formation – MHD SimulationBobrova et al. Phys. Rev. E 65 016407 (2001)

8

Guiding With Square Capillaries

Transmission = 90%t = 115 nsGuided spot 27 × 32 µm

• 33 mm long, 400 μm square capillary

• 120 mbar H2

• Transmitted spots ~ same size as input spot

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Guiding With Square Capillaries

(a) Input intensity 5.8 1016 W cm-2; W ~ 28 μm

(b) Exit: Unguided Output Spot t <0ns

(c) Exit t =115ns

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Guiding experiments at LBNL (preliminary results)

Energymeter

Wedges

Spectrometer

OAP

CapillaryWaveguide

Energy Meter Laser

Guiding at 15 TW

50 μm input spot

I ~ 5 ×1017 Wcm-2

Beam 33 mm after focus

(no waveguide)

Beam at exit of 33 mm long waveguide

I ~ 5 ×1017 Wcm-2

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Transverse interferometry

Nd:YAG

camera

1.2

1.1

1.0

0.9

0.8

0.7

Ele

ctro

n D

ensi

ty (

1018

cm

-3)

Position in Capillary0( ) ( )

L

y y dxc

60 mbar140 ns

12

10

100

1000

1.0E+15 1.0E+16 1.0E+17 1.0E+18 1.0E+19

Electron density (cm-3

)

Mat

ched

sp

ot

size

(mm

)

Scaling of matched spot sizeMatched Spot vs. Capillary Size

15

20

25

30

35

40

45

0 100 200 300 400

Square capillary size (μm)

Mat

ched

sp

ot

(μm

)

Data - 120mbar

Heat Conduction Model

Matched Spot vs. Pressure

20

25

30

35

40

45

50

0 50 100 150

Pressure (mbar)

Mat

ched

sp

ot

(μm

) Data - 180μm capillary

Heat Conduction Model

However the optimum coupling for grazing-incidence guiding is,

0.645MW a

Matched spot scales as

5

1/ 4-3

[μm][μm] 1.5 10

[cm ]M

e

aW

N

Plasma waveguide

Grazing-incidence waveguide

13

Summary

Advantages

• Guiding of laser pulses with peak intensities of ~ 5 × 1017 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