Ablative and Discharge Capillaries for Optical
Guiding and Velocity Control
Arie Zigler, B. Greenberg, and T. Palhan
Hebrew University, Jerusalem, Israel
D. Kaganovich,1 R. F. Hubbard, A. Ting, T. G. Jones, and P. Sprangle
Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375-5346
*LET Corp,, Washington, DC 20007
Abstract. To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA) it
is necessary to propagate an intense laser pulse long distances in a plasma channels while
maintaining a proper phase with the accelerated electrons. Using capillary discharge we have
demonstrated a method that allows controlling the laser group velocity in long, multistage
plasma channels. The control is achieved by modifying the index of refraction through variation
of plasma density using a segmented capillary discharge
INTRODUCTION
Propagation of high intensity laser pulses over substantial distances is limited by
the expansion of the laser spot size due to diffraction. Plasma channels are used to
overcome this limitation by modifying the index of refraction so that the pulse is
confined to a small spot size within the channel. A plasma channel is a plasma column
with an off-axis density maximum. Potential applications of channel-guided intense
pulsed lasers include laser-driven accelerators [1-4], harmonic generators and laserpumped x-ray lasers. Theoretical and simulation studies [5,6] show that stable laser
propagation and generation of a high quality electron beam in the GeV energy range
may be possible using plasma channels.
This paper reviews recent progress in generating plasma channels for optical
guiding. These techniques include laser generated methods [7-9] and various wall
guided [10,11] and capillary discharge techniques [12-17]. The paper also
summarizes recent experimental results on a new method for creating arbitrarily long
plasma channels with an axially-varying plasma density [17]. This method employs a
multi-stage capillary discharge with independently-controllable voltages on the
individual stages. Simulations have shown that the limitations on energy gain from
dephasing in a laser wakefield accelerator (LWFA) may be partially overcome with
proper density tapering [6]. The multi-stage discharge may also be useful for
generating the extremely long plasma column required for future plasma wakefield
accelerator experiments such as plasma 'afterburner' [18].
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
47
CHANNEL CREATION TECHNIQUES
Here we will review several techniques for plasma channels guiding and will
concentrate on the capillary discharges [12-17]. We will focus on the laser intensities
that are below those required for relativistic guiding. The first channel experiments
that demonstrated optical guiding used an axicon-focused laser to create the channel
[7]. In this process, elongated preformed plasma fibers are produced through the
radial hydrodynamic evolution of the breakdown spark produced in the line focus of
an axicon lens [7-9]. The heated electrons drive a radial expansion of the plasma into
the surrounding background gas, resulting in the formation of a shock wave. The
plasma remains essentially charge neutral, and an on-axis electron density minimum
follows the ion density, providing the desired refractive index profile for guiding [79]. However, this technique requires a careful timing and an extra laser. Generation
of long channel introduces several additional issues such as higher laser energy,
hydrodynamics stability, large gas target jet and differential pumping. The axicon
technique was combined recently with an electrical discharge to create the seed
ionization [9].
Propagation in hollow fibers and gas filled fibers offers an alternative to plasma
channels for guiding in some cases. Dorchies, et al. [10] demonstrated monomode
guiding over 100ZR (10 cm) of an ultrashort laser pulse (100 fsec) at intensities of 1016
W/cm2 without any inner wall glass breakdown. The propagating mode is believed to
have a much lower intensity at the wall of the fiber. The technique was previously
demonstrated for multi-mode guiding by Jackel, et al. [11]. In this case, the guiding
was believed to be due to multiple internal reflections. These techniques require very
high beam quality and are currently limited to single shot experiments.
The other guiding techniques are based on the capillary discharge. They include
slow capillary discharges based on wall ablation [5,12-14], gas-filled slow discharges
[15], and fast z-pinch discharges [16]. The z-pinch discharge [16] produces an
imploding plasma column that has a concave electron-density profile in the radial
direction. This occurs just before a stagnation phase driven by a converging current
sheet and a shock wave. The main issues with the z-pinch approach are MHD stability,
jitter, timing, and experimental complexity. Recently, high intensity laser pulses have
been guided by [15] gas-filled slow capillary discharges. The capillary has a ceramic
liner, so the plasma originates from the gas fill. These discharges can survive for
many shots, which is a characteristic that may be required for the future accelerators.
In addition, a low Z gas can be used so that further ionization by the high intensity
guided pulse may be avoided. However, the need for the gas feed introduces
substantial experimental complexity.
The slow capillary ablative-wall discharges provide a very convenient technique for
guiding that can be operated in a very large range of densities (1016-1020 cm"3). The
timing between the laser and electron guiding can be accomplished quite easily due to
the relatively long (100 nsec) favorable conditions for the guiding, as shown on Fig. 1
of Ref. 14. The capillary can survive for several hundred shots and thus is well-suited
for systems such as the NRL T3 laser [13] that require several minutes between shots.
Modifications for more elaborate configurations such as bending [12] or staging [17]
are also relatively easy and have also been demonstrated in the past.
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MULTI-STAGE CAPILLARY DISCHARGE EXPERIMENTS
Background and Motivation
In most regimes of interest, the energy of the accelerated electrons in a LWFA is
limited by dephasing or phase slippage, which arises from the mismatch between the
electron velocity and the phase velocity vpw of the accelerating wake. This phase
velocity is approximately equal to the group velocity vg of the laser pulse and is
determined by the plasma density. Therefore, the dephasing limitation could be
improved by proper tailoring of the plasma density along the acceleration path.
Kaganovich, et al. [14] have shown that the density could be varied by tapering the
wall radius of a capillary discharge. However, increasing the wall radius causes an
undesirable increase in the laser spot size and would result in a corresponding decrease
in LWFA energy gain. In addition, the shape of the tapering is fixed by the geometry
of the capillary, thus limiting the control of plasma density.
In this work, we have demonstrated control of laser group velocity along the axis of
propagation using multi-stage capillary discharges [17]. The control is achieved
through modification of the index of refraction by varying the plasma density along
the plasma channel. We have used an autocorrelation measurement that compares the
propagation time through the plasma channel with the propagation time for the laser
pulse to traverse the same distance in a vacuum. This diagnostic method provides a
direct measure of the average plasma density in the channel during laser pulse
propagation.
The plasma channel has a constant diameter, so the scheme proposed here modifies
the index of refraction while preserving the high laser intensity as the beam
propagates. We made the capillary out of several segments, as shown in Fig 1. Each
segment is connected to separate capacitor that can be charged to a specified voltage.
Therefore, the current density along the capillary can be increased (or decreased) by
sequential discharge of the capacitors. Switches connected to each capacitor are used
to set the timing of the discharges. The external circuit parameters of each segment
can also be varied, thus providing additional control.
I
H.V. pulse
V2
Vi
FIGURE 1. Characteristic configuration for a segmented capillary discharge. The voltages in each
stage are specified independently, so that the plasma density can be tuned in each stage.
49
For each segment, hydrodynamic simulations of the time-dependent behavior of the
capillary discharge plasma reveal the existence of the on-axis density minimum
required for optical guiding. These simulations can be used to predict the plasma
density and discharge current for a given capillary voltage and wall radius. Power law
fits to simulation results [14] give a scaling law for the plasma density:
17
(1)
where Im is the maximum current in the discharge and Rc is capillary radius. The
plasma density can thus be controlled by varying the discharge voltage and current.
Experimental Setup for Autocorrelation Diagnostic
The autocorrelation experiments were carried out using a Ti sapphire laser at 800
nm wavelength, with 40 mJ, 160 fs pulses at a repetition rate of 10 Hz. The laser was
focused to a 20 jim radius spot into the capillary by means of a 20 cm focal length
lens, resulting in the intensity of 5xl016 W/cm2. The longitudinal plasma density
gradient was measured using a three-stage capillary with 6 cm total length and 0.5-mm
diameter. Each stage was connected to a separate capacitor. Changes in an individual
capacitor's voltage results in a change in the current through each stage and thus the
plasma density. For the purpose of simplicity, we have demonstrated the change in
the plasma density and resulting group velocity change by sequential bias of a
capillary as a single stage. Beam propagation and its group velocity modification
were measured using the experimental system configuration shown in Fig. 2.
Autocorrelation
Image camera
spleater
SRS
Forward
\_/image
|_| camera
Spectrometer
OMA
FIGURE 2. Experimental setup for the autocorrelation measurement of laser pulse group velocity and
average plasma density in the capillary.
50
The autocorrelation diagnostic offers a direct measure of the integrated plasma
density from the effective optical path length change. The transit time for a laser pulse
to cross a distance AL is AL/vg. From the dispersion relation, one can show that the
group velocity of the laser pulse is given by
(2)
where (Op is the average plasma frequency, co is the laser frequency, L0 is the capillary
length, and AL is the effective optical path change measured by the autocorrelator.
For the single segment experiment LQ = 1.65 cm, thus the plasma density ne can be
described by: ne[cm"3] = 2.12xl017 AL[|im].
Other Diagnostics and Results
The characteristics of the plasma channels were measured using time resolved
optical spectroscopy diagnostics, interferometry and autocorrelation. The electron
density distribution across and along the axis was studied using Stark broadening,
interferometry [13] and Raman scattering methods. The group velocity control of the
propagating beam was demonstrated by measuring the propagation time along the
capillary for the various current profiles along the capillary. Imaging of laser beam at
the entrance and exit of the created plasma channel was used for the study of laser
propagation in the channel.
The results obtained by the autocorrelation measurements of transit time through
the capillary for the various voltages on the capillary are presented in Fig. 3. The shift
of the bright vertical band in each image determines the path length change AL.
100 jim callibrated
3kV
4kV
5kV
FIGURE 3. Autocorrelation images for capillary voltages of 3, 4, and 5 kV.
Another verification of the plasma density value was derived from the Raman
spectrum. For our experimental parameters, the Raman reflectivity was found to be
relatively weak. The results obtained for low voltages were very noisy. The cause of
these phenomena is related to higher channel leakage at low voltages. This leakage
51
results in a portion of the laser beam striking the wall, thus generating additional
Raman scattering from wall that interferes with the Raman signal from the plasma.
The significant signal was obtained only for the high plasma density in the capillary
channel.
The results obtained by Raman, interferometry and autocorrelation methods are
summarized in Table I.
TABLE 1. Plasma Density from Different Techniques
Raman
Capillary Voltage (kV)
ne (cm 3)
3
4
5
2.4xl019±1019
Autocorrelation
ne (cm 3)
I.lxl019±1018
1.6xl019±1018
2.3xl019±1018
Interferometry
ne (cm 3)
9xl018±1018
1.5xl019±1018
2.2xl019±1018
The interferometric measurements represent the capillary plasma density in absence
of the intense laser pulse propagation and therefore do not include the additional
ionization caused by the laser. Thus, the density difference obtained from
autocorrelation and interferometry measurements can be used as an indicator for the
variation in Zeff. This variation was found to be modest for the relatively low
intensities of current experiment.
To demonstrate the guiding capability of the segmented capillary plasma channel,
the propagation of laser pulse through the capillary was studied using imaging
technique similar to Ref. 12. Images of the laser pulse guided through the segmented
capillary biased by the sequence of voltages were found to similar to those obtained
for the one stage capillary.
SUMMARY
In conclusion, we have demonstrated a new method that can allows control of the
plasma density and thus the group velocity of a high intensity laser beam as it
propagates in the plasma channel. The control is achieved by varying the discharge
voltage and current. By using segmented capillaries with different voltages in each
stage, the plasma density can be tailored along the path of propagation, and the plasma
channel can be arbitrarily long. A substantial enhancement of the energy of the
accelerated electrons in future LWFA experiments can be achieved by using a
properly-tapered density channel [6].
ACKNOWLEDGMENTS
This work was supported by the Office of Naval Research, the Department of
Energy, and U.S.-Israeli Binational Science Foundation Contract 990017.
REFERENCES
1.
T. Tajima and J. M. Dawson, Phys. Rev. Lett. 43, 267 (1979).
52
2. P. Sprangle, E. Esarey, J. Krall, and G. Joyce, Phys. Rev. Lett. 69, 2200 (1992).
3. A. Modena, Z. Najmudin, A. E. Danger, C. E. Clayton, K. A. Marsh, C. Joshi, V. Malka, C. B.
Darrow, and C. Danson, IEEE Trans. Plasma Sci. PS-24, 289 (1996); D. Umstadter, S. Y. Chen, A.
Maksimchuk, G. Mourow, and R. Wagner, Science 273, 472 (1996).
4. F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R.
Marques, G. Matthieussent, P. Mine, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, Phys. Rev
Lett. 81, 995 (1998).
5. R. F. Hubbard, D. Kaganovich, B. Hafizi, C. I. Moore, P. Sprangle; A. Ting; and A. Zigler; Phys.
Rev. E 63, 036502 (2001).
6. P. Sprangle, B. Hafizi, J. R. Penano, R. F. Hubbard, A. Ting, A. Zigler, and T. M. Antonsen, Jr.,
Phys. Rev. Lett. 85, 5110,(2000).
7. C. G. Durfee III and H. M. Milchberg, Phys. Rev. Lett. 71, 2409 (1993).
8. T. R. Clark and H. M. Milchberg, Phys. Rev. Lett. 78, 2773 (1997). W. P. Leemans, P. Volfbeyn,
K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E.
Esarey, Phys. Plasmas 5, 1615 (1998).
9. E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff and M. C. Downer, Appl.
Phys. Lett. 77, 4112 (2000).
10. F. Dorchies, J. R. Marqutts, B. Cros, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F.
Amiranoff Phys. Rev.Lett 82, 4655, 1999.
11. S. Jackel, R. Burris, J. Grun, A. Ting, C. Manka, K. Evans, and S. Kosakowskii, Opt. Lett. 28,
1086(1995).
12. A. Zigler, Y. Ehrlich, C. Cohen, J. Krall, and P. Sprangle, J. Opt. Soc. Am. B 13, 68, (1996); Y.
Ehrlich, C. Cohen, A. Zigler, J. Krall, P. Sprangle, and E. Esarey, Phys. Rev. Lett. 77, 4186 (1996).
13. D. Kaganovich, A. Ting, C. I. Moore, A. Zigler, H. R. Burris, Y. Ehrlich, R. Hubbard, and P.
Sprangle, Phys. Rev. E 59, R4769 (1999).
14. D. Kaganovich, P. Sasorov, C. Cohen and A. Zigler, Appl. Phys. Lett. 75, 772 (1999).
15. D J Spence, A Butler and S M Hooker J. Phys. B: At. Mol. Opt. Phys. 34, 4103^112 (2001).
16. T. Hosokai, M. Kando, H. Dewa, H. Kotaki, S. Kondo, N. Hasegawa, and K. Nakajima Opt. Lett.
25, 10, 2000.
17. D. Kaganovich, A. Zigler, R. F. Hubbard, P. Sprangle, and A. Ting, Appl. Phys. Lett. 78, 3175
(2001).
18. S. Lee, T. Katsouleas, P. Muggli, W. B. Mori, C. Joshi, R. Hemker, E. S. Dodd, C. E. Clayton, K.
A. Marsh, B. Blue, S. Wang, R. Assmann, F. J. Decker, M. Hogan, R. Iverson, and D. Walz, Phys.
Rev. ST AB 5, 011001 (2002).
53