N.Holtkamp and A.Jöstingmeier
Deutsches Elektronen-Synchrotron DESY
Notkestr.85, 22609 Hamburg, GERMANY
In a linear collider, the drive line is the power feed line which is used to excite the high power klystrons, along the linac tunnel. The drive line typically has to fulfill a number of requirements, e.g. phase stability, amplitude and phase control as well as power distribution. A concept, especially fitting the needs of a linear collider, is presented.
Following the multibunch energy compensation concept presented in another paper [1], amplitude and phase control are required at every klystron along the linac. In the proposed 500GeV center of mass S-Band linear collider [2] for example, 2500 klystrons will require approximately 400W drive power each. These klystrons are distributed along the 30km long accelerator. Therefore approximately every 12m the drive line has to deliver this amount of power with the appropriate phase and amplitude control within one pulse and with the required pulse to pulse stability. So far different ideas have been discussed to solve this problem. For example, a low power glass fiber could be used to drive a solid state preamplifer in front of every klystron, or a special drive klystron could power groups of klystrons. While the first version turns out to be a rather cost intensive one, it has certainly the greatest flexibility, because the low power rf can be manipulated in front of every klystron. The second version is certainly cheaper but also requires a widely distributed rf control network. Both systems involve a dedicated distribution system for the low power rf and consist of a large number of components which tend to fail or have to be replaced according to their lifetime. In this paper a technical solution will be discussed which is based on the idea of using a single high power drive line for many klystrons. This drive line would be powered by the same type of klystron used to feed the accelerating structures (150MW peak power) and is a passive system which should not require any maintenance. Such a drive line system has a number of implications but also many advantages.
The main problem of a very long drive line is dispersion and energy
propagation velocity. The rf pulse which fills the accelerating structure
and accelerates the beam is only 2.8 
s
( 
m) long. To excite every klystron in time, the drive pulse
has to travel with the speed of the
beam pulse, here the velocity of light, along the linac. At the same
time the pulse shape (amplitude and phase) is not allowed to
change (mainly due to dispersion and mode conversion), especially if phase or
amplitude modulation is used within each single rf pulse.
There are basically two concepts for realizing such a drive line. Either a transmission line which supports a TEM mode or a shielded waveguide without inner conductor may be used. Both approaches will be discussed.
The main advantage of a coaxial transmission line compared with any other waveguide is that it supports an almost dispersion-free TEM mode. The remaining dispersion is due to the finite conductivity which increases the series inductance of the line. Nevertheless, the increase in the inductance due to wall losses does not lead to a significant dispersion for practical lines.
Therefore the maximum length of such a drive
line is limited by damping. Fig. 1
shows the attenuation constant 
of a coaxial transmission line for
various geometries. Let us assume a radius of the outer conductor of 10cm
and a ratio a / b = 0.3. With these
parameters a damping of only 
dB/m is achievable if
the drive line is made of copper with a conductivity of
S/m. If we assume 150MW rf power the maximum electric
field strength is
about 3MV/m which is sufficiently small to avoid breakdown.
Up to this point of the discussion we have considered the drive line
as a pure transmission line. Nevertheless a coaxial line is also a waveguide
which supports TE and TM modes. Assuming a geometry as given above and a
frequency of 2.998GHz, ten propagating higher order modes exist.
Some of the power of the fundamental TEM mode is converted into higher order
modes at the output couplers and at the struts, see Fig. 2, which
are necessary to support the inner conductor.
Two serious effects arise from this mode conversion.
Obviously some of the power in the fundamental mode is lost if it is
converted into other modes with higher damping. The second more serious effect
gives rise to signal distortion if the fundamental mode is converted into
higher order modes and some of the power of these modes is converted back
into the fundamental mode at a position further along the waveguide. In order
to avoid signal distortion by conversion and reconversion the undesired
modes have to be suppressed (attenuated) to avoid reconversion.
Due to the large variety of traveling higher order modes
it seems to be impossible to
construct mode filters in order to suppress all of these modes.
Therefore the cross sectional dimensions of the coaxial
line have to be reduced down to the single mode operation regime in order to
obtain mode stability. This requirement limits the radii of the inner and the
outer conductor to 0.75cm and 2cm, respectively. On the other hand,
the damping of such a drive line amounts to 
dB/m which is
not acceptable because less than 2km could be fed only.
From the above discussion it can be concluded that a coaxial waveguide is not suitable for a long drive line because a low loss coaxial line with a large cross section tends to mode instability while a structure with reduced cross section has too excessive losses.
In a waveguide which does not support a TEM mode, signal distortion occurs
due to the non-linear frequency dependence of the propagation constant
. Different parts of the signal travel with different velocities
leading to a dispersed output signal, because
no unique signal velocity exists. Nevertheless,
for narrow band signals the transmitted signal is identical to the input
signal, apart from the amplitude and a time delay.
Let us assume an operating frequency of
3GHz, a bandwidth of 1MHz and a group velocity of 
.
In order to achieve
such a high group velocity the corresponding mode has to be far
above cutoff. With these parameters and L=2km, one obtains
corresponding to a transmission
time error of 
ps which is small compared to the rf pulse
length.
Nevertheless one has to keep in mind that delay lines with well-defined
length have to be inserted between the drive line and each individual
klystron feed, if the group velocity is smaller than the velocity of
light, in order to keep the drive pulse synchronous with the particles (see
Fig. 3).
The length of the first delay line is chosen to be 40m according to
m whereas the last accelerator feed is
directly connected to the drive
line. In between, the length of the delay lines has to be linearly decreased.
For practical reasons one would realize the delay
lines as coaxial cables
which unfortunately suffer from a high damping, typically 0.4dB/m. Hence
the first delay line leads to an additional damping of 16dB which is not
serious because the full klystron power of 150MW is available at the
beginning of the drive line. However no significantly smaller group velocity
is allowable due to the high damping of the delay lines.
If we consider the use of a circular waveguide as a drive line, it would be
desirable to use a TE 
mode due to the unique damping property
of these modes, namely, the attenuation decreases as 
for
high frequencies. This feature of the TE modes makes it possible
to construct a very low-loss drive line in the case of 
.
On the other hand, the circular waveguide
must have a radius of more than 30cm in order to achieve a group velocity
of . This however seems not practicable. Besides the fact that
such an overmoded waveguide in general generate mode instabilities, mode
conversion turns out to be especially crucial using TE modes because
of the degeneracy of the TE and the TM 
modes. In order to avoid
this problem a mode filter which suppresses modes with current flow directed
along the waveguide axis (TM modes) is necessary. Nevertheless such
a filter leads to a rather complicated structure of the drive line.
In conclusion it has to be stated that a circular waveguide exhibits excellent damping properties. Nevertheless this design is not suitable for a drive line because a small signal delay due to the frequency dependence of the propagation constant requires a large cross sectional dimension of the waveguide which directly implies mode instabilities.
In order to keep the group velocity close to the velocity of light it cannot be avoided to use a highly overmoded waveguide. Such a waveguide may be used if one can control the higher order modes.
In a ridge waveguide, see Fig. 4, the electromagnetic field is concentrated in the vicinity of the ridges whereas higher order modes extend throughout the cross section of the waveguide. These modes can be suppressed by suitable absorbers located at the side walls. Furthermore the fundamental mode of the ridge waveguide has a relatively low cutoff frequency due to the high capacitive loading associated with the ridges. This leads to a high group velocity compared with conventional waveguides.
A ridge waveguide with outside dimensions of
and a ridge radius of r=33mm is assumed. Due to the high field
strength in a drive line it is not recommended to use rectangular ridges
which may lead to discharge close to the edges. Instead, circular
ridges seem to be more suitable. Fig. 5
shows the transverse electric field of the fundamental mode
( 
). Again, for a 2km long drive line a coaxial
delay line of 32m has to be used at the first klystron feed
(see Fig. 3).
The attenuation of the dominant mode (7.11dB/km) is comparable to the above discussed coaxial drive line. Since the field distributions of all higher order modes are spread throughout the cross section of the waveguide these modes are strongly attenuated by losses at the side walls, whereas the damping of the fundamental mode is not significantly increased. If we insert two absorbers of 4mm thickness and a loss tangent of 0.2 at the side walls of the waveguide the attenuation of the fundamental mode is increased by only 3.29dB/km whereas the increase in damping for the higher order modes is much higher. The absorbers give rise to an attenuation of at least 35.1dB/km for the third higher order mode which seems to be strong enough in order to guarantee mode stability.
= 61.83 m-1.
A drive line concept for a linear accelerator has been presented which allows the simultaneous and synchronous excitation of a large number of high power klystrons. Various types of waveguides, namely, coaxial transmission lines, circular waveguides and ridge waveguides have been investigated. From the different types proposed here only the ridge waveguide fulfills all the necessary requirements which are low losses, low signal distortion due to dispersion and good suppression of higher order modes. From the calculation provided in this paper, it seems feasible to supply a 2-3km long subsection of the linear collider with a single drive line if one of the 150MW high power klystrons is used to generate the drive signal.