omy, University of California, Los Angeles, California 90095, USA
2
Lawrence Livermore National Laboratory, Livermore, California 94551, USA
3
Stanford Linear Accelerator Center, Menlo Park, California 94025, USA
4
University of Southern California, Los Angeles, California 90089, USA
5
University of California, Santa Barbara, California 93106, USA
6
Manhattan College, Riverdale, New York 10471, USA
(Received 20 January 2008; published 27 May 2008)
First measurements of the breakdown threshold in a dielectric subjected to GV=m wakeelds produced
by short (30 330 fs), 28.5 GeV electron bunches have been made. Fused silica tubes of 100
m inner
diameter were exposed to a range of bunch lengths, allowing surface dielectric elds up to 27 GV=m to be
generated. The onset of breakdown, detected through light emission from the tube ends, is observed to
occur when the peak electric eld at the dielectric surface reaches 13:8
0:7 GV=m. The correlation of
structure damage to beam-induced breakdown is established using an array of postexposure inspection
techniques.
DOI:
10.1103/PhysRevLett.100.214801
PACS numbers: 41.75.Lx, 41.75.Ht, 52.25.Mq, 77.22.Jp
Particle accelerators with longitudinal elds orders of
magnitude larger than present systems are needed to make
continued explorations of particle physics at the energy
frontier feasible in the long term [
1
]. Such advanced ac-
celerators, which promise to dramatically reduce the size
and cost of high energy colliders, may also make relativ-
istic beams accessible to smaller laboratories, allowing
development of compact light sources such as free-electron
lasers and inverse Compton scattering devices [
2
]. Ultra-
high-eld accelerators may not, however, be created from
conventional metallic-resonant-cavity-based linear accel-
erators (linacs) by simply increasing drive power because
of breakdown limitations. The relationship between reso-
nant wavelength
r
and breakdown eld [
3
] can be used to
circumvent this constraint; existing linacs with
r
110 cm and tens of MV=m acceleration gradients should
support GV=m operation when scaled to
r
1 mm and
THz frequencies.
The power levels needed to yield GV=m elds in an
accelerating structure are available in the IR through opti-
cal region of the electromagnetic spectrum from laser
sources. Building laser accelerators using resonant struc-
tures at the optical scale presents many challenges [
4
],
which are presently being experimentally addressed.
These challenges include adherence to unprecedentedly
small spatial tolerances in the structure, as well as the
injection, propagation, and stable acceleration of beams
well below 1
m in both longitudinal and transverse di-
mensions [
5
]. It would be advantageous to operate struc-
tures in the more forgiving THz region, but no sources exist
at the powers needed to achieve GV=m elds.
The need for higher electromagnetic power at short
wavelengths has inspired research into beam-driven wake-
elds. In such schemes, electromagnetic power is radiated
by an ultrashort, intense driving electron bunch prop-
agating in a high impedance environment. This power is
then used to accelerate another witness bunch. With the
common enabling component of an ultrashort driving
bunch, large amplitude wakeelds may be excited in any
medium or structure that presents high beam impedance,
including resonant dielectric-loaded systems [
6
] and plas-
mas [
7
]. Indeed, with the recent advent of multi-
nanocoulomb,
t
< 100 fs relativistic beams, 50 GV=m
accelerating elds have been produced in an experimental
plasma wakeeld accelerator [
8
].
In this Letter, we present a study of the physical limita-
tions encountered driving >GV=m wakeelds in the sim-
ple hollow dielectric tube geometry of a dielectric
wakeeld accelerator (DWA) [
6
]; see Fig.
1
. In a DWA,
an ultrashort drive bunch traverses the evacuated central
region of the tube, creating Cherenkov wakeelds in the
dielectric that propagate outwards at the Cherenkov angle.
The Cherenkov elds are then reected by the dielectric or
cladding boundary back towards the center axis where a
witness bunch arrives and is accelerated. The DWA ap-
proach resolves the THz source problem by using radiated
elds from short electron bunches.
Prior to the present work, wakeelds observed in DWAs
were limited to long wavelength scales, equivalent to
frequencies in the 10 GHz range, and accelerating gra-
dients of at most 100 MV=m, by the length of the multi-ps
electron drive beams used [
6
,
9
,
10
]. The combination of
high charge, short bunch duration, and small spot size
available at the Stanford Linear Accelerator Center Final
Focus Test Beam (FFTB) facility [
11
] has enabled the
achievement of GV=m elds in this experiment; see
PRL 100, 214801 (2008)
P H Y S I C A L
R E V I E W
L E T T E R S
week ending
30 MAY 2008
0031-9007= 08=100(21)=214801(4)
214801-1
� 2008 The American Physical Society Table
I
. This combination of beam attributes is obtained
through both magnetic compression [
12
], to obtain bunch
lengths <100 fs, and the high 28.5 GeV beam energy,
which gives small beam sizes naturally through adiabatic
damping of the emittance.
The criticality of these beam parameters for driving
ultrahigh eld wakes in a DWA can be seen from the
expression that describes the longitudinal decelerating
wakeeld within the driving electron beam, E
z;dec
, and its
relation to the peak surface electric eld E
r;surf
. While the
formal theory of DWAs is well developed [
13 16
], a
simple treatment based on the classic problem of
Cherenkov radiation in the presence of a dielectric bound-
ary [
17
] yields a more lucid, approximate form for E
z;dec
:

eE
z;dec
eE
r;surf
"
1
p
"
4N
b
r
e
m
e
c
2
a
8
" 1
q "
z
a
;
(1)
where e is the electron charge, a is the inner radius of the
hollow dielectric tube,
z
c
t
is the rms bunch length,
r
e
and m
e
c
2
are the classical radius and rest energy of the
electron, respectively, " is the dielectrics relative permit-
tivity, and N
b
is the number of bunch electrons. One could
simultaneously obtain the Table
I
beam parameters at the
FFTB. With such small beam dimensions, and a
50
m, decelerating elds up to 11 GV=m were produced
within the beam during these experiments. The peak radial
electric eld at the dielectric surface is, however, of pri-
mary interest in this breakdown study; values as high as
E
r;surf
27 GV=m were achieved.
While dielectric breakdown has been studied in detail at
both optical and cm wavelengths, only the laser-induced
breakdown studies use pulse times comparable to those
explored in this experiment. The beam-produced electro-
magnetic wave contains a fundamental wavelength of
4 b
a
"
1
p
634
m (f
c=
0:47 THz) and
higher harmonics. The length of this radiation pulse, as
experienced by the downstream end of the tube, is deter-
mined by the Cherenkov radiation group velocity and path
length through the media. Therefore, while
t
30330 fs depending on the level of compression, the pulse
of THz radiation produced by the 1 cm fused silica tube is
always
100 ps. Laser-induced breakdown of SiO
2
has
been studied extensively for wavelengths near 800 nm and
pulse lengths from 20 fs to 7 ns [
18
,
19
]. These studies have
consistently found a breakdown damage threshold of
1:1 GV=m for 100 ps pulses. Thresholds for
t
30 fs and 330 fs pulses were found to be about 18 GV=m
and 7 GV=m, respectively.
The fundamental mechanism for dielectric breakdown is
avalanche ionization. The manner in which avalanche
ionization is initiated and driven to the critical density
for damage varies with pulse length and photon energy.
For long pulse lengths * 10 ps, the background carriers
dominate the avalanche process and breakdown is insensi-
tive to wavelength [
20
]. For short pulse lengths &10 ps,
multiphoton or tunnel ionization provides the free elec-
trons that lead to the breakdown avalanche [
21 23
].
Comparisons between this experiment and previous la-
ser breakdown work is complicated by several factors: the
relative roles of tunneling and multiphoton ionization, the
THz pulse envelope, and possible background sources of
ionizing radiation. While the Keldysh parameter [
22
] at the
fundamental frequency is small, indicating that tunnel
ionization is dominant, multiphoton ionization will be-
come increasingly important for the higher harmonics. If
the THz pulse amplitude remains relatively constant for its
100 ps duration, breakdown should occur at about
1:1 GV=m as in the laser experiments at the same pulse
length. If, however, the pulse damps rapidly, possibly due
to absorption, dispersion, boundary losses, etc., and has a
large amplitude for much less than 100 ps, then the break-
down eld could be higher. It should also be noted that the
fused silica in this experiment is subject to additional low-
ux sources of ionizing radiation including: incoherent
optical and UV Cherenkov photons, stray 28.5 GeV elec-
trons, and background x rays.
With the above considerations in mind, the experiment
carried out at the FFTB was designed to assess the ability
of dielectric tubes to withstand the high elds generated by
TABLE I.
Experimental parameters.
Parameter
Value
Dielectric inner diameter (2a)
100
m
Dielectric outer diameter (2b)
324
m
Dielectric relative permittivity (")
3
Number of e
per bunch (N
b
)
1:4
10
10
RMS bunch length (
z
)
100
10
m
RMS bunch radius (
r
)
10
m
Beam energy
28.5 GeV
Maximum radial eld at dielectric surface
27 GV=m
Maximum decelerating eld (vacuum)
11 GV=m
Maximum accelerating eld (vacuum)
16 GV=m
FIG. 1 (color online).
Conceptual drawing of the dielectric
wakeeld accelerator (DWA). A drive beam excites wake-
elds in the tub