CLIC 30 GHz Accelerating Structure
Development
W. Wuensch
CERN, Geneve23, 1211 Switzerland
Abstract. The main effects which limit accelerating gradient in CLIC (Compact Linear Collider)
main linac accelerating structures are RF breakdown and pulsed surface heating. Recent
highlights of the structure development program are presented, including demonstration of
higher accelerating gradients using tungsten and a complete redesign of the CLIC main linac
accelerating structure, based on reduced surface electric and magnetic fields and including new
power couplers and higher-order mode damping waveguides.
INTRODUCTION
The CLIC linear-collider design envisages the use of the rather high accelerating
gradient of 150 MV/m [1], which results in an accelerating structure input power of
130MW [2], These fields and powers are well above those used in existing, lower
frequency, RF structures. For reasons of beam stability, CLIC accelerating structures
also have quite stringent limits on short-range wakefields and the requirement that
long-range wakefields must be suppressed. Because of the challenges that each of
these design requirements presents, programs of high-gradient studies and dampedstructure studies have been carried out by the CLIC team. This has lead to a better
understanding of the interplay between high-gradient, structure wakefield and RF
efficiency issues. The status of this work is presented in this report. Recent progress in
overcoming RF breakdown induced damage and obtaining higher gradients with
tungsten is reviewed in section 2. A recent redesign of the CLIC main linac
accelerating structure, which takes into account the most recent ideas about highgradient limits, is outlined in section 3. Finally a simplified discussion of the
motivation of the very high fields in CLIC, and the consequences on the required
powers and pulse energies, is presented in section 4.
HIGH-GRADIENT TESTING
Accelerating gradients in the range of 150 MV/m, and with a pulse length of
150ns, were demonstrated using two copper X-band accelerating structures, one
tested at KEK and one tested at SLAC [3,4]. However, subsequent tests of prototype
copper 30 GHz accelerating structures at the CLIC test facility, CTF2, with pulse
lengths of only 16 ns have produced accelerating gradients of only 60 MV/m and
significant damage to the structures was observed [5]. The reasons for the very
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
506
different performances achieved in the tests are probably partially due to differences in
RF design, the X-band structures had a very small beam aperture, a/?i=0.11, and the
30 GHz structures had highly asymmetric power couplers. In addition there were
substantial differences between the conditioning procedures. The high-gradient test
area in CTF2 was not, until recently, instrumented as thoroughly as the test areas at
KEK and SLAC, and power production is still not interlocked to breakdown. It is clear
however, that the tens of thousands of structures that must survive many decades in a
linear collider must be extremely robust and cannot require heavily instrumented,
lengthy and delicate conditioning and re-conditioning procedures. In this way, the
conditions at CTF2 may be more representative of what may be encountered at a
future linear collider. In any case, the difficulties encountered with the damage to the
copper structures indicated that a very basic problem existed and that an innovative
new approach to structure design and construction had to be found.
One solution to the structure damage problem is to use an arc-resistant material
instead of copper in the areas of a structure where damage due to RF breakdown
occurs [6,7]. The arc-resistance of a material is a well established concept at DC, and
is a consequence of a high melting point and a low vapor pressure. A number of
refractory metals are arc resistant, but tungsten, with a DC conductivity only three
times worse than copper, is the most obvious candidate for a first test in an accelerator
application. In addition to arc resistance, it is possible that the highest field a surface is
capable of supporting is a function of material.
The program of testing new materials has begun with tungsten, and has had two
distinct phases. In the first phase, a series of simple and rapid tests were made by reusing a copper constant-impedance structure and replacing only the damaged iris of
the input coupler with a new iris. Each new iris to be tested was clamped between the
coupler and the structure, giving mechanical integrity and an RF contact. Vacuum was
provided by placing the clamped assembly inside a vacuum tank. In these tests only
relative material properties could be tested since the geometry of the structure was
unchanged. Achievable gradients were also limited because the rest of the structure
was in copper. However, maintaining the single-feed coupler guaranteed that the
potential for damage to the new irises under test remained very high.
The second phase of the tungsten testing program consisted of producing two
entirely new 30-cell structures with identical geometries, one made entirely of copper
and the other made from copper cells with all irises made of tungsten. The first
objective was to demonstrate an improved accelerating gradient due to the RF design
change. The second objective was to provide a direct comparison between tungsten
and copper of achievable gradient.
All tests were made in the CTF2 and the results reported here were all produced
using 16 ns RF pulses (unless noted otherwise) at a repetition rate of 5 Hz. To improve
turn-around time, no in-situ bakeouts were made. It is clear that in-situ bakeouts, along
with clean assembly conditions, are desirable for achieving high gradients, and will
probably be part of an optimized linear collider assembly and installation procedure.
The emphasis of these test was however to determine the effects of materials and RF
design in as straight forward a way as possible. All structures were conditioned in the
same way, by raising power to maintain controlled levels of emitted breakdown
electron currents, vacuum activity and missing RF energy. The calibrations of field
507
levels were always confirmed by measurement of the acceleration of a 0.5 nC probe
beam.
In order to determine achievable gradient each new iris was RF conditioned after
after
installation. The conditioning curves, which plot the maximum stable
stable gradient as
as aa
function of number of RF pulses, for
for the coupler iris
iris tests for
for both aa copper
copper and
and aa
tungsten iris, are shown in Figure 1.
1. A saturation
saturation of the conditioning curve indicates
indicates
that
that the
the maximum
maximum gradient
gradient has
has been
been reached.
reached.
From
From the
the conditioning
conditioning curves
curves itit is
is clear
clear that
that the
the tungsten
tungsten iris
iris provided
provided an
an improved
improved
gradient
gradient compared
compared to
to the
the copper
copper iris.
iris. SEM
SEM (Scanning
(Scanning Electron
Electron Microscope)
Microscope)
micrographs
micrographs of
of both
both the
the copper
copper and
and the
the tungsten
tungsten irises
irises are
are shown
shown in
in Figure
Figure 2,
2, and
and
demonstrate
demonstrate quite
quite clearly
clearly the
the increased
increased arc
arc resistance
resistance of
of tungsten.
tungsten. The
The peak
peak surface
surface
electric
electric field
field of
of the
the damaged
damaged copper
copper iris
iris was
was estimated
estimated to
to be
be nearly
nearly 40%
40% higher
higher than
than
that
that of
of the
the original,
original, un-damaged,
un-damaged, geometry.
geometry. The
The tungsten
tungsten iris
iris showed
showed no
no change
change to
to its
its
geometry.
geometry. The
The micrographs
micrographs also
also show
show that
that the
the tungsten
tungsten iris
iris has
has been
been sprayed
sprayed with
with
copper
copper from
from the
the surrounding
surrounding structure,
structure, probably
probably the
the downstream
downstream iris.
iris. This
This iris
iris had
had aa
40%
40% lower
lower surface
surface electric
electric field
field than
than the
the coupler
coupler iris
iris and
and was
was clearly
clearly damaged
damaged after
after
the
the tungsten
tungsten test.
test. Microscopic
Microscopic zones
zones of
of melted
melted tungsten
tungsten are
are also
also visible
visible on
on the
the
tungsten
tungsten iris,
iris, but
but these
these zones
zones appear
appear to
to be
be benign
benign and
and aa normal
normal consequence
consequence of
of
conditioning.
conditioning. Although
Although the
the tungsten
tungsten iris
iris aa clearly
clearly higher
higher surface
surface field,
field, itit was
was not
not
possible
possible to
to conclude
conclude from
from these
these tests
tests whether
whether the
the tungsten
tungsten went
went to
to aa higher
higher because
because
the
the surface
surface is
is capable
capable of
of supporting
supporting aa higher
higher gradient,
gradient, or
or whether
whether the
the tungsten
tungsten went
went to
to
aa higher
gradient
because
it
maintained
its
shape.
higher gradient because it maintained its shape.
80
Accelerating gradient, [MV/m].
70
60
50
40
30
—A— Ground
Ground tungsten
tungsten
20
20
—*— Copper
Copper
10
10
00
0.0
0.0
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
5
Shots/10
Shots/10
2.5
2.5
3.0
3.0
3.5
3.5
4.0
4.0
FIGURE
FIGURE 1.
1. Conditioning
Conditioning histories
histories tungsten
tungsten and
and copper
copper irises
irises in
in the
the single-feed
single-feed input
input coupler
coupler set-up.
set-up.
508
FIGURE
copper (left)
(left) and
and tungsten
tungsten (right)
(right) irises
irises after
after conditioning.
conditioning.The
The
FIGURE 2.
2. SEM
SEM images
images of
of the
the copper
tungsten
at aa higher
magnification –- the
theradii
radii are
arethe
thesame.
same.
tungsten image
image was
was taken
taken at
higher magnification
The
field in
in the
the cells
cells of
of the
the new
new 30-cell
30-cell structures
structures was
was reduced,
reduced,
The surface
surface electric
electric field
compared
the
structure
used
in
the
previous
tests,
by
reducing
the
iris
aperture,
from
compared the structure used in the previous tests, by reducing the iris aperture, from
4.00
mm
to
3.50
mm,
and
by
increasing
the
iris
thickness,
from
0.55
mm
to
0.85
mm.
4.00 mm to 3.50 mm, and by increasing the iris thickness, from 0.55 mm to 0.85 mm.
RF
design
issues
will
be
discussed
in
greater
detail
in
the
next
section.
The
surface
RF design issues will be discussed in greater detail in the next section. The surface
field
by adopting
adopting aa ‘mode
'mode launcher’
launcher' coupler
coupler
field enhancement
enhancement in
in the
the coupler
coupler was
was reduced
reduced by
[8].
[8].
The
disks, which
which formed
formed the
the cavity
cavity
The tungsten-iris
tungsten-iris structure was composed of copper disks,
cell
placed in
in counter-bores
counter-bores in
in the
the copper
copper
cell walls,
walls, and tungsten irises, which where placed
disks.
structure was
was assembled
assembled by
by
disks. These
These parts
parts are shown in Figure 3. The whole structure
clamping.
from diamond
diamond turned
turned disks
disks and
and
clamping. The
The all-copper structure was made from
assembled
were clamped
clamped on.
on. The
Thestructures
structures
assembled by
by vacuum
vacuum brazing, although the couplers were
were
structure was
was mounted
mounted on
on aa vacuum
vacuum cover
cover
were tested
tested inside a vacuum tank and each structure
plate
experiments to
to about
about an
an hour.
hour.
plate to
to reduce
reduce turn-around time between experiments
FIGURE 3.
3. Copper
Copper cells
FIGURE
cells with
with tungsten
tungsten iris
iris inserts.
inserts.
The conditioning
conditioning curves
curves of
The
of the
the two
two new
new structures,
structures, along
along with
with the
the copper
copperdata
datafrom
from
the
previous
test,
are
shown
in
Figure
4.
The
first
feature
to
emphasize
is
the previous test, are shown in Figure 4. The first feature to emphasize is that
that the
the
average accelerating
accelerating gradient
gradient improved
average
improved from
from 60
60 MV/m
MV/m to
to 100
100 MV/m
MV/m due
due to
to RF
RF
509
design changes
changes alone.
alone. A
A further
further improvement
improvement to
to 125
125MV/m
MV/m was
was obtained
obtained by
by the
the using
using
design
tungsten. ItIt should
should be
be noted
noted that
that the
the tungsten
tungsten conditioning
conditioning curve
curve may
may not
not yet
yet have
have
tungsten.
saturated,
but
the
experiment
was
suspended
due
to
lack
of
time
in
the
testing
saturated,
program. The
The maximum
maximum achieved
achieved accelerating
accelerating gradient
gradient in
in the
the first
first cell
cell was
was 152
152 MV/m
MV/m
program.
for the tungsten-iris structure
structure and
and 112
112 MV/m
MV/m for
for the copper
copper structure.
structure. Corresponding
Corresponding
for
surface fields
fields were
were 340
340 MV/m
MV/m and
and 270
270 MV/m
MV/m respectively.
respectively. AA visual
visual inspection
inspection
peak surface
of
of the tungsten-iris
tungsten-iris structure
structure confirmed
confirmed that
that the
the geometry
geometry of
of the
the irises
irises was
was unchanged.
unchanged.
A detailed
detailed analysis
analysis of
of the
the geometric
geometric and
and surface
surface changes
changes of
of the
the two
two structures
structures will
will be
be
at aa later
later date.
date.
made at
To
To investigate
investigate pulse
pulse length
length dependence,
dependence, the
the RF
RF pulse
pulse length
length was
was reduced
reduced to
to 88ns,
ns,
corresponds to
to the
the filling
filling time
time of
of the
the structure.
structure. The
The beneficial
beneficial effect
effect of
of the
the
which corresponds
reduced
reduced pulse
pulse length
length allowed
allowed aa direct
direct measurement,
measurement, using
using the
the tungsten-iris
tungsten-iris structure,
structure,
of
of aa 16.2
16.2 MeV
MeV energy
energy gain
gain of
of aa 0.5
0.5 nC
nC electron
electron bunch.
bunch. This
This corresponds
corresponds an
an average
average
accelerating
accelerating gradient
gradient of
of 152
152 MV/m
MV/m and
and aa gradient
gradient in
in the
the first
first cell
cell of
of 184
184MV/m.
MV/m.
140
140
Accelerating gradient [MV/m].
120
A^^mmm°^m
100
80
60
40
Single-feed
Single-feed coupler,
coupler, copper
copper
3.5
3. 5mm
mmcopper
copper
20
Tungsten
Tungsten iris
iris
0
0.0
5.0
5.0
10.0
10.0
15.0
15.0
5
Shots/10
Shots/105
20.0
20.0
25.0
25.0
30.0
30.0
FIGURE
FIGURE 4.
4. Single-feed
Single-feed copper
copper structure,
structure, 30-cell
30-cell copper
copper and
and 30-cell
30-cell tungsten
tungsten iris
iris structure
structure
conditioning
conditioning curves.
curves. The
The dip
dip in
in the
the tungsten
tungsten conditioning
conditioning curve
curve occurred
occurred after
after the
the structure
structure was
was opened
opened
to
to air
air for
for visual
visual inspection
inspection for
for damage.
damage.
In
In addition
addition to
to RF
RF breakdown,
breakdown, fatigue
fatigue damage
damage due
due to
to pulsed
pulsed surface
surface heating
heating
represents
represents aa second
second serious
serious limit
limit to
to accelerating
accelerating gradient
gradient [9].
[9]. A
A 30
30 GHz
GHz testing
testing
program
program has
has started
started in
in JINR,
JINR, Dubna,
Dubna, using
using aa free
free electron
electron maser
maser as
as aa power
power source
source
[10]
[10] to
to complement
complement and
and eventually
eventually extend
extend on
on previous
previous work
work made
made atat X-band
X-band [11].
[11].
After
After intentionally
intentionally damaging
damaging copper
copper test
test cavities
cavities in
in an
an initial
initial series
series of
of tests,
tests, an
an
investigation
investigation of
of different
different materials
materials will
will be
be made.
made.
510
RF-DESIGN STUDIES
The high-gradient testing program cannot yet give a definitive value of the
maximum achievable surface electric field because testing has not yet been made at
the full RF pulse length. However, from experience and quite reasonably, a reduced
peak surface electric field appears to be a crucial design criteria. Subjectively
combining the 150 ns copper X-band results and the 16 ns tungsten 30 GHz results
suggests that a design limit of 300 MV/m surface electric field can be set with
reasonable confidence. A definitive limit of allowable temperature rise cannot be
given either, as testing is only just beginning, but it is already clear that an RF design
should seek to reduce it as much as possible. For current design purposes an
'aggressive' design limit of 60°K has been chosen. The current redesign of the CLIC
main linac accelerating structure is based on maximizing RF-to-beam efficiency,
minimizing short-range wakefields and maintaining a high degree of long range
wakefield suppression under the constraints of a maximum surface electric field of
300 MV/m and a maximum temperature rise of 60°K.
It should be noted that the geometry of the structure may also play more subtle
roles, in the damage that an arc produces for example [6,11], but this is still unclear.
Features in accelerating structures that can cause enhanced levels of surface electric
and/or magnetic field are power couplers, higher-order-mode damping waveguides,
pumping holes and tuning dimples.
CLIC accelerating structures have quite stringent constraints on wakefields caused
by beam induced higher-order modes for reasons of beam stability [2]. Short-range
transverse wakefields must be limited through micron-precision alignment tolerances
and a limitation on the smallest beam aperture the structure can have. A large beam
aperture increases the peak surface electric field which can be reduced by utilizing a
relatively thick coupling iris and adopting an elliptical cross section.
Long-range transverse and longitudinal wakefields must be suppressed, by
approximately two orders of magnitude in twenty fundamental mode cycles for the
lowest dipole mode. This suppression is accomplished through a combination of
damping via waveguides and detuning via dimensional tapering along the length of the
structure. The validity of this technique has been demonstrated by direct measurement
in the ASSET facility at SLAC [12]. The boundaries of the damping waveguides are,
however, locations of a rather severe concentration of surface currents, which leads to
enhanced pulsed surface heating [9].
A major innovation for the geometry of waveguide damped structures has been the
introduction by a profiled convex outer cavity wall [2], in contrast to the usual, turned,
concave outer cavity wall. The convex outer wall blends the cavity to the damping
waveguides smoothly. This spreads out the surface currents so that the resulting
temperature rise is only about a factor of 2.3 higher than in an equivalent undamped
geometry. The convex geometry, called XDS for conveX Damped Structure, made
from straight line and elliptical segments is shown in figure 5. The corresponding
surface currents are shown in Figure 6.
511
FIGURE
electric
field
is
FIGURE5.
Lowsurface
surfaceelectric
electricand
andmagnetic
magnetic field
field geometry,
geometry, XDS.
XDS.
The
low
surface
FIGURE
5.5. Low
Low
surface
electric
and
magnetic
field
geometry,
XDS. The
The low
low surface
surface electric
electric field
field is
is
accomplished
through
a
thick
iris
with
an
elliptical
cross
section.
The
low
surface
magnetic
field
accomplished
through
a
thick
iris
with
an
elliptical
cross
section.
The
low
surface
magnetic
field
is
accomplished through a thick iris with an elliptical cross section. The low surface magnetic field is
is
accomplished
usual,
turned,
concave
accomplishedthrough
throughthe
theprofiled
profiledconvex
convexouter
outercavity
cavity walls,
walls, in
in distinction
distinction to
to
the
accomplished
through
the
profiled
convex
outer
cavity
walls,
in
distinction
to the
the usual,
usual, turned,
turned, concave
concave
outer
outercavity
cavitywall.
wall.
outer
cavity
wall.
FIGURE 6.Surface
Surfacecurrents
currentsofofthe
theXDS
XDSgeometry
geometry (1/4
(1/4 shown).
shown). The
The area
area of
of maximum
temperature
FIGURE
maximum
FIGURE6.
6.rise
Surface
currents
of
the
XDS
geometry
(1/4
shown).
The
area ofwaveguides.
maximum temperature
temperature
is
a
broad
area
in
the
cell
wall
situated
between
the
damping
rise
riseisis aa broad
broad area
area in
in the
the cell
cell wall
wall situated
situated between
between the
the damping
damping waveguides.
waveguides.
The inputand
and outputpower
power couplers are
are other features
features of aa structure
structure which are
a
The
The input
input and output
output power couplers
couplers are other
other features of
of a structure which
which are
are aa
source
of
a
concentration
of
both
surface
electric
and
surface
magnetic
fields.
source
source of
of aa concentration
concentration of
of both
both surface
surface electric
electric and
and surface
surface magnetic
magnetic fields.
fields.
Asymmetries in fields
fields due toto the
the input waveguide(s)
waveguide(s) result in
in enhanced surface
Asymmetries
Asymmetries in
in fields due
due to the input
input waveguide(s) result
result in enhanced
enhanced surface
surface
electric fields. Inductive
Inductive matching elements
elements result in
in concentrations of
surface
electric
electric fields.
fields. Inductive matching
matching elements result
result in concentrations
concentrations of
of surface
surface
magnetic
field.
An
electric
coupler
solves
both
of
these
problems
[8].
The
geometry
magnetic
magnetic field.
field. An
An electric
electric coupler
coupler solves
solves both
both of
of these
these problems [8]. The geometry
of theelectric
electric coupler isis shown
shown in Figure
Figure 1. In
In this coupler
coupler the
of
the maximum
maximum surface
surface
of the
the electric coupler
coupler is shown in
in Figure 7.
7. In this
this
512
electric
electric field
field isis on
on the
the matching
matching iris
iris and is about 80% of the value for a regular cell.
The
cell.
Themagnetic
magnetic field
field is
is about
about 5% higher than in a regular cell.
FIGURE 7. Electric
Electric coupler.
coupler.
FIGURE?.
DERIVATION OF
OF FIELD
FIELD AND
AND POWER
POWER LEVELS
DERIVATION
LEVELS
In order
order to
to better
better understand
understand how
how RF
RF breakdown
breakdown and
In
and pulsed
pulsed surface
surface heating
heating
become such
such important
important effects
effects for
for CLIC
CLIC accelerating
accelerating structures,
become
structures, aa simplified
simplified
explanation of
of the
the scale
scale of
of important
important accelerating
accelerating structure
explanation
structure parameters
parameters follows.
follows. A
A
150
MV/m
accelerating
gradient
is
required
for
the
CLIC
3
TeV
design
in
150 MV/m accelerating gradient is required for the CLIC 3 TeV design in order
order to
to
limit the
the over-all
over-all length
length of
of the
the facility
facility to
to 30
30 km
km [1].
[1]. In
In order
order to
to achieve
limit
achieve an
an adequate
adequate
luminosity
for
physics,
extremely
low-emittance
beam
trains
with
an
average
luminosity for physics, extremely low-emittance beam trains with an average current
current
of about
about one
one ampere
ampere and
and with
with aa 100
ns pulse
pulse length
of
100 ns
length must
must be
be accelerated
accelerated at
at aa repetition
repetition
rate of
of 100
100 Hz.
Hz. The
The current
current is
is strongly
rate
strongly influenced
influenced by
by the
the value
value of
of the
the lowest
lowest feasible
feasible
emittance.
Acceleration
of
a
1
A
beam
by
a
gradient
of
150
MV/m
requires
emittance. Acceleration of a 1 A beam by a gradient of 150 MV/m requires aa peak
peak
power transfer
transfer to
to the
the beam
beam of
of 150
MW per
per meter
meter of
of linac
power
150 MW
linac and
and aa pulse
pulse energy
energy of
of 15
15JJ
per
meter
of
linac
(ignoring
inefficiency
for
the
moment).
Irrespective
of
per meter of linac (ignoring inefficiency for the moment). Irrespective of the
the
mechanism, accelerating
accelerating aa linear-collider
linear-collider beam
beam at
mechanism,
at aa gradient
gradient as
as high
high as
as 150
150 MV/m
MV/m
requires coping
coping with
with extraordinary
extraordinary power
power and
and energy
requires
energy densities.
densities.
The peak input power required for an individual accelerating structure is
The peak input power required for an individual accelerating structure is
determined by its R/Q, which is proportional to accelerating gradient squared divided
determined
by its R/Q, which is proportional to accelerating gradient squared divided
513
by power flow. The main motivation for the original choice of an operating frequency
of 29.985 GHz [13] was, staying with a 'classical' RF accelerating structure, to
minimize peak power by maximizing R/Q with operating frequency (R/Q is
proportional to f2 for a given geometry). The upper frequency is limited by short range
transverse wakes which cause an unacceptable degradation of the stability of the
beam. Transverse wakefield amplitudes are fixed by fabrication and alignment
tolerances of a few microns, which is considered the current state of the art of
manufacturing. Another argument made in favor of a high operating frequency was
that it should increase the feasibility of achieving high accelerating gradients. The
result of choosing 29.985 GHz is that the peak power input to individual accelerating
structures is of the order of 100 MW. With a pulse length of 100 ns this results in a
pulse energy of 10 J. It is the combination of the 150 MV/m gradient combined with
an associated power flow of more than 100 MW and a pulse energy greater than 10 J
that define many of the design challenges of CLIC accelerating structures.
Selected RF parameters for CLIC accelerating structures [2], with losses now
considered, are summarized in Table 1.
TABLE 1. Selected CLIC accelerating structure parameters.____________________
Parameter____________________Value_______________Units________
Operating frequency
29.985
GHz
Average accelerating gradient
150
MV/m
Section input power
132
MW
Total RF pulse length
130
ns
Pulse energy_____________________16.5__________________J_________
Pulsed surface heating becomes a problem because the fraction of the more than
10 J pulse energy absorbed by cavity wall losses heats only a very small volume of
material. Losses are confined to the skin depth, and initially little heat diffusion takes
place because the pulse length is so short, so the corresponding temperature rise is
high. Breakdown level is a problem because an accelerating gradient of 150 MV/m
necessarily results in a surface electric field of about 300 MV/m. Damage due to RF
breakdown is a problem because the arc that is formed during a breakdown absorbs a
large fraction of incident power, often greater than 90%. A localization of this
absorbed energy can be quite serious since the destructive potential (total energy) of a
single 10 J pulse is sufficient to liquefy more than two cubic millimeters of copper [6].
ACKNOWLEDGMENTS
It is a pleasure to acknowledge the role of my colleagues in this work, particularly
D. Allard, C. Achard, H. Braun S. Dobert, S. Leblanc, J-Y. Raguin, W. Schnell, I.
Syratchev, M. Taborelli and I. Wilson. They are thanked for all their ideas, discussion,
efforts, and goodwill.
514
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