Quasi-Optical Collider Concept
Michael I. Petelin
IAP, Nizhny Novgorod, Russia
Omega-P, Inc., New Haven, USA
Abstract. Electron (positron) accelerating structures are attractive to be fed with a wave flow
converging onto the structure axis. The feeding microwave pulse of RF breakdown- and fatiguesafe duration might be formed with a system of mirrors, part of them being corrugated.
MOTIVATION
Designing novel electron-positron colliders [1] implies radical enhancement of the
accelerating gradient and, as a result, faces dangers of
• dark current capture,
• RF breakdown,
• RF heating fatigue of metallic surfaces.
The dark current capture can be avoided by using a sufficiently high carrier
frequency [1]. As for the breakdown and fatigue [2-6], the RF produced metal plasma
does not appear within the structure if
(i)
0
and the RF produced mechanical stress at the metal surface is kept reversible if
]]*dt<K^JF
(2)
o
where j± is the current induced mostly by the RF electric field normal to the metallic
surface, j% is the current driven mostly by the tangential RF magnetic field, T is the
pulse duration, parameters K L and K^ are defined by characteristics of the metal and
the manufacturing technology. As the both dangerous effects are local in space and
integral in time, they can be excluded by optimization of the accelerator structure and
by using sufficiently short RF pulses.
As the distribution of RF energy deposition to the accelerator channel surface is
optimum if being uniform, the structure should be irradiated with a wave flow
converging to the channel axis so that all accelerating cells would be fed in parallel.
Thus we arrive to the configuration [7] shown in Figs. 1 and 2.
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
459
Radial Bragg reflector
Radial
Channel for
Channel
1. microwave
microwave energy
1.
storage and
and
storage
2. particle acceleration
acceleration
2.
FIGURE 1.
1. Quasi-optical
Quasi-optical feed
feed to
to ee++ -- ee"
collider
FIGURE
collider
E
H.
/
H.
E /
H.
E /
H
E
FIGURE2.
2. Radial
Radial Bragg
Bragg reflection
reflection cavity
cavity irradiated
irradiated with
with converging
converging wave
wave flow
flow
FIGURE
460
SYNTHESIS OF QUASI-OPTICAL ACCELERATING
STRUCTURE
The quasi-optically fed RF-energy-storage particle-acceleration structure (Figs. 1,
2) is deduced of the following specifications:
• the wave-particle coupling must be maximum,
• the RF energy must be efficiently accumulated within the accelerating channel
during the breakdown- and fatigue- safe period of time,
• the channel must provide a distributed out-filtering of spurious modes,
• the design must admit the simplest manufacturing technology.
Synthesis of Paraxial RF-Energy-Storage & Particle-Accelerating
Channel
RF Field Within the Channel
Inside the RF-energy-storage particle-acceleration channel Figs. (1-3), the RF
electric field
(3)
must have the axial component
0
P
FIGURE 3. Disk inner surface profile and radial distribution of RF field.
461
E
=e~
(4)
synchronous to the accelerated ultra-relativistic particles. Due to the + z symmetry of
the structure (Fig. 2), the RF field has the counter-propagating space harmonic e^ of
the same amplitude. Presence of other harmonics would reduce the RF field-particle
coupling resistance. Thus, the RF field takes the form of transverse-magnetic
1C—mode:
Eq = 2cos £,
where p = kr
£ p = psin £,
and £ = kz
H^ = /pcos £
(5)
are dimensionless radial and axial coordinates,
Channel Inner Walls
The channel surface being highly conductive, the RF electric field is
perpendicular to the surface
here Ap and A^ are components of an elementary vector tangent to the surface.
Integrated with use of (5), the equation (6) gives relation
p2 =p 0 2 -41nsin<;|
(7)
between longitudinal and radial coordinates of the inner wall surface, P0 is the inner
disc radius (Figs. 1-3).
The RF Field - Electron Coupling Parameter
The RF energy stored within the structure period is
2
w= J
_JC
1C
2
2
°°
?(P)
0
0
dV =2jdp27lp J dqp 2 cos 2 <;=
l + ln4 + ^
+1 +
2
^_
3
(8)
As the RF field (5) includes the accelerating space harmonic (4) of the unity
amplitude, for the structure elastance (R/Q) [1] we have
- 2
R, =
1
(9)
Buffer Groove
In Figs. 2, the axis-symmetrical groove nearest to the channel axis (in Fig. 3: the
region f)l < p < p2 conjugated with the narrow £2 «1 radial gap p > p 2 ) should
462
keep the optimum RF field structure (5) within the paraxial region. The RF electric
and magnetic energies accumulated in the cavity 0 < p < p 2 should be equalized,
which, with account of (5) and (7), gives a formula for the groove depth (^
(p 2 -Pi)fc«-5 ( 0 ) (pi).
Pi
dO)
If 52 is put equal zero, the closed region p < p 2 resembles a klystron resonator:
with maximum longitudinal RF electric field at the axis and maximum azimuthal RF
magnetic field at the radial periphery. On the other hand, such a closed cavity can be
regarded as the usual "pill-box" [1] profiled to maximize the elastance.
The narrow axis-symmetrical opening gap £2 ^ 0 in the "pill-box" wall results in
a small reduction of the elastance, but does not enlarge the RF electric or magnetic
field (and, so, the RF current) at any point of the metal surface (see Fig. 3). This gap
could be substituted with an azimuth-periodic system of metallic rods [8,9]. However,
to provide the same azimuth-average RF current, any rod of such a "fence" has to
carry a current of relatively high magnitude and, so, seems more vulnerable to the
fatigue. Besides, manufacturing the PEG structures [8, 9] for short-wave-driven
accelerators does not seem a simple problem.
Synthesis of Accelerating Structure Periphery
The peripheral part of the accelerating structure must be asymmetric to provide
• coupling with the converging wave flow within the feed sector,
• steep fading of the RF field in all radial direction outside the feed sector.
The gap between discs being less than half the wavelength, the proper grooving can
be synthesized basing on the radial cable mode approach: according to the Maxwell
equations in integral form, at junctions between two parallel wall sections the interwall voltage and the wall RF current are continuous:
E_A_=E+A+,
H_=H + ,
(11)
(12)
where A_ and A + are the channel widths at different sides of the junction.
Radial Bragg Reflector: Cascade of Mutually Phased Chokes
In radial directions outside the feed sector (Fig. 1), the RF field fading can be
provided by
• up-tapers situated at zeros of the RF magnetic field,
• down-tapers situated at zeros of the RF electric field.
Under this condition, any combination of an up-taper and a successive down-taper
results in M = A + / A _ times reduction of the RF field relative to the unperturbed
value. A cascade of such chokes provides an exponential fall of the RF field in the
radial direction: the Bragg back-scattering (stop band) effect.
463
Wave
Wave Matching
Matching Sector
Sector
As
As the
the accelerating
accelerating structure
structure is
is assumed
assumed to
to be
be fed
fed with
with the
the RF
RF flow
flow converging
converging
from
a
limited
angle
sector
(Fig.
1),
so,
reciprocally,
this
is
the
sector
from a limited angle sector (Fig. 1), so, reciprocally, this is the sector where
where the
the
operating
mode
must
radiate
at
its
free
oscillation:
in
the
feed
sector
operating mode must radiate at its free oscillation: in the feed sector
•• the
the RF
RF field
field fading
fading should
should be
be relatively
relatively slow,
slow,
•• all
radial
channels
should
have
all radial channels should have in-phase
in-phase output.
output.
As
As the
the RF
RF fields
fields in
in the
the inner
inner parts
parts of
of two
two neighboring
neighboring radial
radial channels
channels (Fig.
(Fig. 2)
2) are
are
0
counter-directed,
so
1)
the
phase
shifts
within
the
channels
must
differ
by
180
,
and
counter-directed, so 1) the phase shifts within the channels must differ by 180 , and
2)
2) the
the RF
RF fields
fields at
at the
the channel
channel outputs
outputs must
must be
be equal.
equal. The
The necessary
necessary difference
difference in
in
phase
phase shifts
shifts within
within two
two neighboring
neighboring channels
channels can
can be
be provided
provided by
by aa difference
difference in
in choke
choke
configurations
configurations (Fig.
(Fig. 2)
2) under
under the
the condition
condition that
that chokes
chokes are
are deep
deep enough:
enough: the
the parameter
parameter
(
)
2
M
2 j .. An
M must
must exceed
exceed 1(l ++ V2
An example
example of
of analytical
analytical synthesis
synthesis of
of the
the phase
phase shifter
shifter isis
presented
presented in
in Fig.
Fig. 4.
4.
1
0
1
6
4
2
0
2
4
6
8
10
x
0
FIGURE
FIGURE 4.
4. The
The 180
180 ° phase
phase shifter:
shifter: two
two neighboring
neighboring radial
radial channels
channels (below)
(below)
fed
fed with
with counter-phased
counter-phased RF
RF fields
fields provide
provide in-phase
in-phase output
output (upper
(upper curves),
curves), M=7.5.
M=7.5.
Mode
Mode Filtration
Filtration
The
The system
system of
of mutually
mutually phased
phased chokes
chokes is
is similar
similar to
to that
that proposed
proposed by
by T.
T. Shintake
Shintake
[10]
[10] to
to absorb
absorb high
high order
order modes:
modes: the
the quasi-optical
quasi-optical structure
structure (Fig.
(Fig. 2)
2) is
is produced
produced of
of that
that
described
described in
in [10]
[10] ifif the
the conductive
conductive ceramic
ceramic is
is substituted
substituted with
with the
the “free
"free space”
space" which,
which,
with
with account
account the
the short
short pulse
pulse operation,
operation, would
would be
be realized
realized as
as aa reasonably
reasonably broad
broad
surrounding
surrounding vacuum
vacuum volume
volume conjugated
conjugated with
with the
the quasi-optical
quasi-optical wave
wave feeder.
feeder. The
The
volume
volume should
should contain
contain detectors
detectors of
of dipole
dipole modes
modes radiated
radiated by
by the
the accelerated
accelerated bunches:
bunches:
this
this signal
signal should
should be
be used
used to
to align
align the
the particle
particle focusing
focusing system.
system.
464
Experiment
As a primary verification of the theory,
theory, an
an axis-symmetrical
axis-symmetrical radial-Braggradial-Braggreflection
cell of
of the
the quasi-optical
quasi-optical structure
structure was
was
reflection cavity (Fig. 5) corresponding to one cell
manufactured.
was calculated
calculated analytically
analytically and,
and, with
with aa
manufactured. The corrugated disc profile was
minor difference,
(modified E
E011
mode, dependence
dependence
difference, numerically. For the operating (modified
on) mode,
of the Q-factor
Q-factor on the gap between the corrugated disc and the
of
the wall
wall proved
proved to
to be
be in
in aa
reasonable agreement with calculations.
reasonable
FIGURE 5.
5. One-cell
FIGURE
One-cell model
model of
of the
the RF-energy-storage
RF-energy-storage particle-acceleration
particle-accelerationstructure:
structure:drawing
drawingand
and
photo.
photo.
QUASI-OPTICAL FEEDER
QUASI-OPTICAL
FEEDER TO
TO THE
THE ACCELERATING
ACCELERATING
STRUCTURE
STRUCTURE
As the
the RF
RF field
field intensity
As
intensity fades
fades in
in the
the radial
radial direction
direction from
from the
the accelerating
accelerating
structure,
the
RF
breakdown
and
fatigue
limitations
(1)
and
(2)
allow
structure, the RF breakdown and fatigue limitations (1) and (2) allow an
an RF
RF pulse
pulse
compression which
which would
would be
compression
be especially
especially simple
simple ifif the
the simplest
simplest wave
wave mode
mode -- the
the
Gaussian beam
beam -– were
were used
used through.
Gaussian
through. The
The primary
primary phase
phase controlled
controlled pulse
pulse could
could be
be
compressed by
by aa succession
succession of
compressed
of mirrors
mirrors (Fig.6),
(Fig.6), aa part
part of
of them
them being
being corrugated.
corrugated. In
In
particular, an
an inverse
inverse 33 dB
particular,
dB wave
wave splitter
splitter grating
grating (the
(the quasi-optical
quasi-optical magic
magic Y)
Y) [7]
[7]could
could
be used
used as
as the
the wave
wave beam
be
beam combiner-commutator.
combiner-commutator. The
The final
final chirped
chirped pulse
pulse
compression,
with
additional
power
gain
near
4,
could
be
performed
by
a
compression, with additional power gain near 4, could be performed by a multi-mirror
multi-mirror
open resonant
resonant cavity
cavity (the
open
(the quasi-optical
quasi-optical SLED)
SLED) [7].
[7]. The
The magic
magic Y,
Y, with
with aa dummy
dummy load
load
in
one
of
elbows,
could
be
used
also
to
isolate
the
RF
amplifiers
of
reflections
in one of elbows, could be used also to isolate the RF amplifiers of reflections from
from
doubled accelerator
accelerator sections.
doubled
sections.
465
rr~rr~rr~~r—
phase-controlled RF
RF sources
phase-controlled
beam combiners-commutators
combiners-commutators
beam
Chirped pulse
pulse compressors
compressors
Chirped
«"
acceleration sections
acceleration
FIGURE 6.
6. Feeding
Feeding quasi-optical
quasi-optical accelerator
accelerator with
with delay
delay line
line distribution
distribution system.
system.
FIGURE
In Fig.
Fig. 66 one
one accelerating
accelerating section
section is
is fed,
fed, at
at aa moment
moment of
of time,
time, through
through aa 3-stage
3-stage
In
DLDS and
and QO
QO SLED,
SLED, with
with 88 amplifiers
amplifiers feed
feed simultaneously.
simultaneously. The
The total
total power
power gain
gain in
in
DLDS
such aa scheme
scheme would
would be
be near
near 30.
30. At
At millimeter
millimeter waves
waves the
the whole
whole system
system might
might be
be
such
reasonably compact.
compact.
reasonably
SUMMARY
SUMMARY
Optimized under
under the
the RF
RF breakdown
breakdown and
and fatigue
fatigue limitations,
limitations, the
the electron-positron
electron-positron
Optimized
collider turns
turns into
into aa design
design featured
featured with
with the
the wave
wave flow
flow focusing
focusing onto
onto the
the accelerating
accelerating
collider
channel axis,
axis, all
all cells
cells being
being filled
filled in
in parallel
parallel during
during aa common
common safe
safe period
period of
of time.
time. A
channel
A
necessary beam
beam luminosity
luminosity is
is assumed
assumed to
to be
be provided
provided with
with aa sufficiently
sufficiently high
necessary
high pulse
pulse
repetition rate.
rate.
repetition
The
cell
profile is
is synthesized
synthesized to
to maximize
maximize the
the structure
structure elastance
elastance (R/Q)
(R/Q) and,
and, to
The cell profile
to
reduce
(at
a
fixed
accelerating
gradient)
maximums
of
RF
electric
and
magnetic
fields
reduce (at a fixed accelerating gradient) maximums of RF electric and magnetic fields
at the
the metal
metal surfaces.
surfaces. The
The accelerating
accelerating structure
structure periphery
periphery is
is synthesized
synthesized to
at
to match
match the
the
structure
with
the
converging
wave
flow
and
to
out-filter
spurious
modes;
the latter
latter
structure with the converging wave flow and to out-filter spurious modes; the
effect can
can be
be used
used to
to align
align the
the beam
beam focusing
focusing system.
system.
effect
At
the
pre-breakdown
stage,
presence
of field-emitted
field-emitted and
and secondary-emitted
secondary-emitted
At the pre-breakdown stage, presence of
electrons
within
the
quasi-optical
accelerator
does
not
change
the
phase
electrons within the quasi-optical accelerator does not change the phase velocity
velocity of
of the
the
466
space harmonic synchronous to the accelerated particles. If the breakdown occurs, the
structure operating as a resonant cavity turns mismatched, reflects the incident wave
flow and, thus, is self-protected.
An important advantage of the quasi-optical accelerating structure is its robust
design: the RF field exposed surfaces are not welded or brazed.
Feeding the accelerating structure can be provided with a high-filtration quasioptical DLDS. In front of any pair of accelerating sections there is a chirped pulse
compressor and an isolator. Any wave combiner-commutator of the DLDS and any
isolator represents a specially corrugated mirror (magic Y). The total power gain can
amount up to ~30.
ACKNOWLEDGMENTS
The main idea of the research was initiated by discussions with SLAC people:
David Whittum, Sami Tantawi, George Caryotakis etc. Some hints by Protvino, CLIC
and KEK teams are also compiled into the project.
The theoretical and experimental studies are supported by DOE grants. Original
results by S. V. Kuzikov, A. D. Yunakovsky, M. L. Tai, A. L. Vikharev, V. G.
Pavelyev, Y. L. Bogomolov, Y. Y. Danilov and D. Y. Shegolkov cited in this review
will be published in the nearest time.
Discussions with Jake Haimson, Walter Wuensch, Slava Yakovlev and David
Sutter at the AAC-2002 were very helpful to ascertain main merits of the quasi-optical
accelerator concept.
Special appreciation is given to Jay L. Hirshfield for his encouraging and
stimulating discussions.
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3.
4.
5.
6.
7.
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