A COMPARISON BETWEEN PULSE COMPRESSION OPTIONS FOR NLC
*
S. G. Tantawi
#$
, R. D. Ruth, P. B. Wilson, SLAC, Stanford, CA
Abstract
We present a comparison, between options for pulse
compression systems that provide rf power to the main
linac of the Next Linear Collider (NLC). The parameters
which are compared are efficiency, number of
components and length of rf storage lines. Based on these
parameters we produce a cost model for each system as a
function of compression ratio, number of rf sources per
unit system, and storage line parameters. The systems
considered are Delay Line Distribution Systems (DLDS),
Binary Pulse Compression (BPC), and Resonant Delay
Lines (SLED-II). For all these systems we consider
possible improvements through the use of several modes,
active switches, and circulators.
1 INTRODUCTION
During the past few years high power rf pulse
compression systems have developed considerably. These
systems provide a method for enhancing the peak power
capability of high power rf sources while matching the
long pulse of that source to the shorter filling time of the
accelerator structure. In particular, future linear colliders,
such as the proposed NLC[1] require peak rf powers that
cannot be generated by current state-of-the-art microwave
tubes. The SLED pulse compression system [2] was
implemented to increase the gradient of the two-mile linac
at the Stanford Linear Accelerator Center (SLAC). One
drawback of SLED is that it produces an exponentially
decaying pulse. To produce a flat pulse and to improve the
efficiency, the Binary Pulse Compression (BPC) system
[3] was invented. The BPC system has the advantage of
100% intrinsic efficiency and a flat output pulse. Also, if
one accepts some efficiency degradation, it can be driven
by a single power source [4]. However, The
implementation of the BPC [5] requires a large assembly
of over-moded waveguides, making it expensive and
extremely large in size. The SLED II pulse compression
system is a variation of SLED that gives a flat output
pulse [6]. The SLED II intrinsic efficiency is better than
SLED, but not as good as BPC. However, from the
compactness point of view, SLED II is far superior to
BPC. Several attempts have been made to improve its
efficiency by turning it into a system using active
switching [7]. However, the intrinsic efficiency of the
__________________________________________________
*
This work is supported by Department of Energy Contract DE-AC03-
76SF00515.
#
Email: tantawi@slac.stanford.edu
$
Also with the Communications and Electronics Department, Cairo
University, Giza, Egypt.
active SLED-II system is still lower than that of the BPC.
The DLDS [8] is a similar system to BPC, but by sending
the rf upstream twords the gun it utilzes the return delay of
the electron beam to reduce the length of the over-moded
waveguide assembly. However it still uses more over-
moded waveguide than that required by SLED-II. To
further enhance the DLDS a variation on that system, the
Multi-moded DLDS (MDLDS) [9] was introduced, which
further reduces the length of the waveguide system by
multiplexing several low-loss rf modes in the same
waveguide. The system has an intrinsic efficiency of
100%, and the total over-moded waveguide length has
been reduced considerably.
We present a comparison, based on cost, for all various
compression schemes that are available for the Next
Linear Collider. In this comparison we do not describe the
systems involved at any level of detail. The reader is
referred to the cited references for details. However, it is
our purpose to give an accurate formulation for the system
efficiency, number of components, and length of delay
lines or storage lines for each of these schemes as a
function of compression ratio (the ratio of the source rf
pulse width to the compressed pulse width). This will
provide the basis for cost comparison. We will also
extrapolate on the potential to expand and/or improve
systems through the usage of
a.
Multi-moded structures,
b.
Active switching,
c.
Circulators.
2 COST MODEL
Basically, the rf sources available now or in the near
future will produce a pulse T of about 1.5
µ
s. The NLC
accelerator structure needs a pulse of 380 ns. Hence, a
pulse compression system which compresses the source rf
pulse by a factor C
r
=4 is required. The factor of 4 is the
minimum required compression ratio. If rf sources can be
improved to provide longer pulse lengths at the same peak
power, one might utilize a bigger ratio.
To achieve this pulse compression a storage system is
employed to store the rf power until it is needed. Different
portions of the rf pulse T are stored for different amount
of times. The initial portion of the rf pulse is stored for a
time period t
m
, the maximum amount of storage time for
any part of T. The maximum value for t
m
is
)1(
max
−=
rm
Ct
τ
(1)
where
r
C
T
=
τ
is the accelerator structure pulse width,
and C
r
is the compression ratio. The value given in by
Eq.(1) is typical for most systems with the exception of
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Proceedings of the 1999 Particle Accelerator Conference, New York, 1999
DLDS, which stores the energy for only half the time. The
realization of the storage system is usually achieved using
low-loss waveguide delay lines. These lines are usually
guides that propagate the rf signal at nearly the speed of
light. The maximum length required for these guides, per
compression system, is
2
max
r
gm
C
vtl =
,(2)
where
g
v is the group velocity of the wave in the delay
line. The total number of rf pulse compression systems
required for the accelerator system is given by
crkk
aa
c
CnP
PN
N
η
=
,(3)
where
a
N
is the total number of accelerator structure in
the linac,
k
P
is the klystron (or the rf power source) peak
power,
a
P
is the accelerator structure required peak
power,
k
n
is the number of klystrons combined in one
pulse compression system, and
c
η
is the efficiency of the
pulse compression system. Thus the total length of
waveguide storage line for the entire linac is given by
l
gm
k
aa
ck
lc
R
vt
P
PN
n
RNlL
2
1
max
η
==
. (4)
where
l
R
is a length reduction factor which varies from
one system to another and in general is also a function of
the compression ratio. The total number of klystrons in the
system is given by,
k
aa
cr
k
P
PN
C
N
η
1
=
.(5)
The cost of the rf system is divided into three different
parts: cost of the klystron tube, the klystron power source
and modulator, and the rf pulse compression and
transportation system. The cost of the klystron tubes is
given by
k
a
r
r
k
k
aa
cr
kk
k
C
C
A
P
PN
C
ANS
==
0
0
1
η
,(6)
where
0k
A is the cost per klystron at a compression ratio
0r
C . The exponent
k
a is a number that depends on the
details of manufacturing klystrons. For our present
discussion we will assume that this number is 0.4 and
0r
C =4 [10].
The cost of conventional modulators is also dependent
on the compression ratio. If the klystron pulse width is
increased the stored energy in modulator is increased and
hence its cost. A fraction
s
m
k of the modulator cost is due
to its energy storage elements [11]. The rest of the
fractional cost,
s
m
k−1 , is due to the rest of the system, in
particular the switching elements. Hence, a suitable model
for the modulator cost is
0
00
0
1
1
11
m
r
s
m
r
s
m
k
aa
cr
r
s
mmk
m
A
C
k
C
k
P
PN
C
C
kANS
+
−
=
−+=
η
, (7)
where
0m
A is the cost of the modulator per klystron at a
compression ratio
0r
C .
The cost of the rf pulse compression and power
transmission is divided into two parts: a part that is
dependent on the storage line length L and diameter D,
and a part that is dependent on the number of components
per pulse compression system n
c
. The storage line cost is
divided into two parts: the cost of the vacuum system,
which is a very weak function of diameter, and the cost of
the pipes, which is directly proportional to the diameter.
The cost model is, then, given by
() ()
++
−
=++=
cc
r
p
l
v
ll
r
g
ckk
aa
ccc
p
l
v
l
c
nA
C
DAAR
C
v
Pn
PN
nANLDAAS
1
2
)1(
τ
η
(8)
where
v
l
A is the cost of vacuum system per unit length,
p
l
A is the cost of waveguide pipe per unit length and
diameter, and
c
A is the cost per component. The total
cost of the rf system normalized to the cost of one klystron
0k
A is given by
()
++
−
+
+
−
+
=
r
c
p
l
v
ll
r
k
c
r
s
m
r
s
m
m
a
r
r
rck
a
s
mc
v
l
p
lmlkrr
C
n
DkkR
C
n
k
C
k
C
k
k
C
C
CP
P
kkkkkRnDCS
k
2
)1(1
1
),,,,;,,,(
00
η
. (9)
The parameters
p
lc
v
lm
k
k
k
k
,,, are the normalized cost
factors and are given by
c
g
v
l
v
l
k
c
c
k
m
m
A
vA
k
A
A
k
A
A
k
τ
=== ,,
00
0
, and
c
g
p
l
p
l
A
vA
k
τ
=
cm-1 (10)
The cost of the modulators and components are
normalized to the cost of a klystron at a compression ratio
0r
C . However, the cost of the delay line is normalized to
the cost of a component. This is done because of the
nature of the information available for the cost estimates
at this time [12].
In the following we will compare all available pulse
compression techniques based on the above-described
criteria. To make the comparison more specific for the
proposed NLC design we will make the following
assumptions:
a.
The operating frequency of the system is 11.424
GHz
b. The duration of the accelerator rf pulse is 380 ns.
c. The basic waveguide delay system uses the TE
01
mode.
d. The next higher order modes that can be used are
the two polarizations of the TE
12
, and the two
polarizations of the TE
22
mode. Hence in
calculating the efficiency of the compression
system, the theoretical attenuation as a function of
diameter for these modes is considered.
e. The efficiency of transmission from the klystrons
to the pulse compression system and from the pulse
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Proceedings of the 1999 Particle Accelerator Conference, New York, 1999
compression system to the accelerator structure is
about 90%. Hence the total efficiency of the rf
system is,
itc
ηηη
9.0=
; where
i
η
is the intrinsic
efficiency of the system, and
t
η
is the efficiency of
the delay lines. The maximum possible value is
achieved with the DLDS using the TE
01
mode in all
waveguides.
f.
The number of accelerator structures
a
N is 9936
for 1 TeV collider, and the power needed per
accelerator structure
a
P is 170 MW.
g. Based on [12], we will assume that the ratios
012.0=
c
k
,
5.0=
m
k
,
36=
v
l
k
,
4.1=
p
l
k
cm
-1
,
3/1=
s
m
k
,
4
0
=
r
C
h.
The maximum amount of energy per rf pulse
max
E that can be handled by rf components limits
the maximum number of klystrons,
k
n , that can be
combined to provide power to a single pulse
compression system; i.e.,
)/(
max
τ
rkk
CPEn ≤
.
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
4 6 8 10121416
Single Moded DLDS
M ulti-M oded DLDS (number of modes=3)
Active DLDS
M ulti-M oded BPC (A high power circulator and 3 modes)
M ulti-M oded SLED II (A high power circulator and 3 modes)
Active SLED II (One time Switching [7])
Multi-Moded DLDS (n
k
=4, number of modes =3)
Single-Moded DLDS (n
k
=4)
Relative Cost
Compression Ratio
n
k
=8
Fig. 1 Comparison between different pulse compression
schemes. The relative cost is normalized to the cost of a
single moded DLDS at a compression ratio of 4.
i. Because components vary in their complexity we
will give different weights to them. Hence in
counting the number of components
c
n
for each
system, we will assume that some complex
components are the equivalent of several simple
components.
Fig. 1 shows the relative cost for several systems vs
compression ratio. For each of these systems we
calculated a general expression for the number of
components, for the length reduction factor, and for the
efficiency as a function of compression ratio.
3 CONCLUSION
For most systems there is a considerable cost reduction
as one goes to higher compression ratios. This implies the
need for rf power sources that are capable of longer pulse
width.
The development of high power circulators, multi-
moded technology and active super-high-power switches
will result in a considerable cost reduction for the NLC
4 REFERENCES
[1] The NLC Design Group “Zeroth-Order Design Report
for the Next Linear Collider,” SLAC-Report-474, May
1996.
[2] Z. D. Farkas et. al., "SLED: A Method of Doubling
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Energy Accelerators, 1976, p. 576.
[3] Z. D. Farkas, "Binary Peak Power Multiplier and its
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[4] P. E. Latham, "The Use of a Single source to Drive a
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[5] Z. D. Farkas, et . al., "Two-Klystron Binary Pulse
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1208.
[6] P. B. Wilson, Z. D. Farkas, and R. D. Ruth, "SLED II:
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SLAC-PUB-5330.
[7] S.G.Tantawi, et al. "Active High-Power RF Pulse
Compression Using Optically Switched Resonant
Delay lines" IEEE TRANSACTIONS ON
MICROWAVE THEORY AND TECHNIQUES
IEEE, Aug. 1997. vol.45, no.8, pt.2, p. 1486-92
[8] H. Mizuno, Y. Otake, “A New Rf Power Distribution
System For X Band Linac Equivalent To An Rf Pulse
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Oct 1994. 3pp.
[9] S.G. Tantawi, et al. " A Multi-Moded RF Delay Line
Distribution System for the Next Linear Collider,” to
be published in the proc. of the Eighth Workshop on
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[10] Robert M. Phillips, private communications.
[11] Richard Cassel, private communications.
[12] Michael L. Neubauer, private communications.
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Proceedings of the 1999 Particle Accelerator Conference, New York, 1999