1
GeV electron beams from a cm-scale accelerator
W.P. Leemans
1
, B. Nagler
1
, A.J. Gonsalves
2
, Cs. Tóth
1
, K. Nakamura
1,3
, C.G.R.
Geddes
1
, E. Esarey
1
, C.B. Schroeder
1
and S.M. Hooker
2
1
Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720,
USA.
2
Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road,
Oxford OX1 3PU, UK.
3
Nuclear Professional School, University of Tokyo, 22-2 Shirane-shirakata, Tokai,
Naka, Ibaraki 319-1188, Japan.
GeV electron accelerators are essential to synchrotron radiation facilities and free
electron lasers, and as modules for high-energy particle physics. Radiofrequency-
based accelerators are limited to relatively low accelerating fields (10-50 MV/m)
and hence require tens to hundreds of metres to reach the multi-GeV beam
energies needed to drive radiation sources, and many kilometres to generate
particle energies of interest to the frontiers of high-energy physics. Laser-
wakefield accelerators (LWFA)
1,2
– in which particles are accelerated by the field
of a plasma wave driven by an intense laser pulse – produce electric fields several
orders of magnitude stronger (10-100 GV/m) and so offer the potential of very
compact devices. However, until now it has not been possible to maintain the
required laser intensity, and hence acceleration, over the several centimetres
needed to reach GeV energies. For this reason laser-driven accelerators have to
date been limited to the 100 MeV scale
3-5
. Contrary to predictions that PW-class
lasers would be needed to reach GeV energies
6,7
, here we demonstrate production
of a high-quality electron beam with 1 GeV energy by channelling a 40 TW peak
power laser pulse in a 3.3 cm long gas-filled capillary discharge waveguide
8,9
. We
anticipate that laser-plasma accelerators based on capillary discharge waveguides
will have a major impact on the development of future femtosecond radiation
sources – such as x-ray free electron lasers – and become a standard building block
for next generation high-energy accelerators.
2
Although it is relatively straightforward to achieve acceleration gradients of 10-
100 GV/m in laser wakefield accelerators
1,2
, until recently the electron beams (e-beams)
from such accelerators were of relatively low energy (below 200 MeV) and had 100%
energy spread
10
. A breakthrough improvement in energy spread was obtained in 2004
by three groups
3-5
, including ours
4
. In that work intense laser pulses interacting with
millimetre-scale gas jets generated 70-200 MeV beams with percent-level energy
spread. Two of the groups
3,5
used a relatively large laser spot size r
s
such that the
diffraction distance (of the order of the Rayleigh range Z
R
= πr
s
2
/λ, where λ is the laser
wavelength and r
s
is the 1/e
2
radius of the laser intensity profile) roughly matched the
gas jet length, which set an upper bound on the acceleration length. This approach
produced, for example, 170 MeV e-beams with order 0.5 nC bunch charge using 30 fs,
30 TW laser pulses
5
. In contrast, in our previous experiments, precursor laser pulses
created a 2 mm long plasma channel (parabolic transverse density profile with a
minimum on axis, which functions like an optical fibre
2
) in a gas jet to guide the driving
laser beam
4,11,12
, enabling acceleration over many Z
R
. This allowed generation of 80-
150 MeV e-beams, with 0.3 nC bunch charge, using only 9 TW
4,12
.
To scale laser-driven accelerators to GeV electron energies and beyond, two
different approaches had been proposed: (1) operate in initially uniform plasmas
7,13
with
ever more powerful laser beams and large laser spot sizes, or (2) guide the laser beam
over cm-scale distances
2,14,15
. Without some form of guiding (e.g., self-focusing or
preformed channels) the laser-plasma interaction length is limited to the order of Z
R
,
which is a few millimetres for r
s
=25 µm. Relativistic self-guiding
2
can extend the
propagation distance of high-power pulses due to self consistent modification of the
plasma refractive index, but is limited by nonlinear effects such as the erosion of the
leading edge of the laser pulse. Obtaining GeV energies without a guiding channel
therefore requires the laser spot size to be large, so as to increase Z
R
, but this also
3
increases the required laser power to PW levels
6,7
. In addition, using large laser spot
sizes can result in an undesirable increase in the e-beam emittance.
A more efficient approach relies on channelling laser beams over cm-scale
distances, allowing smaller spot sizes. Theory and simulations indicate that such
channel guided accelerators
4
could produce GeV e-beams with only 10-50 TW of laser
power
14,15
, allowing the use of low-cost, compact high repetition rate lasers. However,
simply making the accelerator longer is not sufficient. Phase slippage occurs between
relativistic particles and the wake, because the wake has a phase velocity less than the
vacuum speed of light. The dephasing length, L
d
= λ
p
3
/λ
2
∝ n
p
-3/2
, over which electrons
outrun the wake and slip into the decelerating phase, must then be extended to increase
the accelerator length. Here λ
p
is the plasma wavelength and n
p
the plasma density.
In
the linear wakefield regime (laser intensity I approximately 10
18
W/cm
2
,
or less), the
energy gain over this length is proportional to I/n
p
such that higher energy gains require
lower plasma densities (n
p
~10
18
cm
-3
)
14,15
. Matching acceleration length to L
d
also has
been essential for the production of low energy spread e-beams
3-5
.
Previously we created plasma channels
16
in a gas jet with the ‘ignitor-heater’
technique, in which a plasma column is first ionized and then heated by two precursor
laser pulses
4,11,17
. Due to the inefficiency of laser heating at low densities, suitable
plasma channels could only be produced at relatively high densities (>10
19
cm
-3
).
Together with the small diameter (few mm) of the supersonic gas jets nozzles, this
limited the acceleration length and restricted the energy of the e-beams to the 100 MeV-
level energy range.
In the experiments reported here we overcame the limitations inherent to laser-
induced channels in gas jets by employing a gas-filled
capillary discharge waveguide
8,9
to produce longer (few cm) and lower density plasma channels. The experiments used
4
the 10 Hz repetition rate TREX amplifier of the LOASIS Ti:sapphire laser system,
operating at a wavelength of 810 nm and delivering 40 fs full width half maximum
(FWHM) pulses with a peak power of up to 40 TW (Fig.1). The laser pulses were
focused by a 2 m focal length off-axis parabola (f/25) to r
s
= 25 µm at the capillary
entrance. The capillary waveguide
8
was laser-machined in sapphire blocks and was 33
mm long and approximately 300 µm in diameter. Hydrogen gas was introduced into the
capillary, and a discharge struck between electrodes located at each end of the capillary
ionized the hydrogen and formed the plasma channel
18
. Measurements
8,19
and
modelling
18,20
have shown that the plasma channel is essentially fully ionized and
approximately parabolic. Previous experiments
9
demonstrated that waveguides of this
type are able to channel laser pulses with I~10
17
W/cm
2
over lengths of 30-50 mm,
although these intensities were too low to generate large amplitude plasma wakes.
Laser guiding was optimized by tailoring the channel through the initial gas
density and the delay between the onset of the discharge current and the arrival of the
laser pulse. Under optimum conditions the on-axis density was 2–4×10
18
cm
-3
. Figure
2 shows the laser beam profile at the waveguide exit for 40 TW laser pulses with an
input intensity of order 10
18
W/cm
2
. This intensity is sufficiently high for large
amplitude wake generation, self-trapping, and high-gradient electron acceleration. High-
quality guiding was obtained at four times the peak power and over fifteen times the
length of the ignitor-heater experiments
4,11
. The laser pulse energy transmission was
observed to decrease from near 100% for input powers below 5 TW to less than 70%
for input powers around 40 TW, consistent with laser energy transfer to the wake and
electron beams.
The electron bunch energy was measured by a 1.2 T single-shot magnetic
spectrometer that deflected the electrons onto a 1.2 m long phosphor screen, covering
energies up to 1.1 GeV. The e-beam divergence and energy spread were calculated from
5
the raw data using the imaging properties of the spectrometer, obtained from detailed
magnetic field maps and a second order electron transport model
21
. The divergence was
determined from the beam size in the undeflected plane, taking into account the
transverse defocusing properties of the magnet. The energy spread was calculated by
deconvolving the effect of finite divergence from the measured beam profile. The
charge was obtained from the phosphor screen that was cross-calibrated against an
integrating current transformer.
Figure 3 shows the energy spectrum of (a) a 0.52 GeV and (b) a 1.0 GeV beam,
obtained with ~25 TW and ~40 TW laser pulses, respectively. In both cases the e-beams
had percent-level energy spread and a divergence of 1.2-2.0 mrad (see Fig. 3 c-f). The
measured energy spread at 1 GeV is comparable to the resolution of the spectrometer so
that the actual energy spread may have been even lower. The bunch charge ranged
between 50-300 pC. Tuning of laser power and pulse length as well as plasma density
was found to affect beam charge, and hence higher charge is expected with further
optimization. The e-beam energy fluctuated from shot-to-shot, due in part to the self-
trapping mechanism being sensitive to small variations in the laser and plasma
parameters
12
. At 40 TW, the highest energies were over 1 GeV, and narrow energy
spread beams were frequently produced near 0.5 GeV, with significantly more charge
than at 25 TW.
The dynamics of trapping, dephasing, beam loading
12,22
and hosing
23
may be
responsible for the second spatially-displaced bunch observed near 0.8 GeV in Fig. 3b.
Such features are observed in numerical simulations, owing to trapping of a second
electron bunch in a wake bucket behind the first
12,22
; and these issues are being further
explored.