INVESTIGATION OF AN ALTERNATE MEANS OF WAKEFIELD
SUPPRESSION IN THE MAIN LINACS OF CLIC
V. F. Khan , R.M. Jones and I. Shinton; The Cockcroft Institute, Daresbury, WA4 4AD, UK;
The University of Manchester, Manchester M13 9PL, UK.
Abstract
We report on suppression of long-range wakefields in
the CLIC accelerating structures. Strong detuning along
with moderate damping is employed. In these initial
simulations we focus on the CLIC_G structure and
enforce a moderate Q of 500. We maintain dipole
bandwidth of approximately 1 GHz as specified from
breakdown constraints. A circuit model, which enables a
rapid design, of manifolds slot-coupled to the main
accelerating cells, is described.
INTRODUCTION
The successor to the LHC [] will be a lepton collider.
The main linacs of the electron-positron machine will
either consist of superconducting (SC) Niobium cavities
or will operate at room temperature with a chain of
copper cavities. The former design, known as the
International Linear Collider (ILC) [2], aims a centre of
mass energy of 500 GeV with the potential to upgrade to
1.0 TeV. The latter design, aims at a 3.0 TeV centre of
mass collision through acceleration with normal
conducting (NC) linacs operating at a gradient of 100
MV/m. The SC design aims at a gradient of 31.5 MV/m.
In order to achieve efficient acceleration each design
incorporates multi-bunch acceleration. The NC scheme
entails an inter-bunch spacing of approximately 6 r. f.
cycles at an accelerating frequency of 12 GHz, whereas
SC design accelerates at a 1.3 GHz with bunches spread
from each other by 468 r. f. cycles. In either case, the
ultra relativistic beam excites a wakefield which has
intra-bunch (short range) and inter-bunch (long range)
electromagnetic fields represented as wakefieds. This
wakefield has a longitudinal component, which effects the
energy spread of the bunches and a transverse component
which dilutes the beam emittance and can give rise to a
BBU [] instability. In this work we treat the case of the
transverse component of the long-range wakefields. The
wakefield is more severe in NC CLIC linacs and we focus
our attention on these room temperature accelerators.
These wakefields, in the present baseline CLIC design
[4] are suppressed by waveguides which couple out the
fields from each accelerating cells. This results in strong
damping (Q~10) and entails dielectric damping materials
being closely located to the accelerating cells. We present
an alternate design which entails strong detuning of the
cell parameters and in moderate damping (Q ~ 300-500).
The latter is reflected through four manifolds running
along the walls of the accelerators. The broad principle of
the design is similar to that used in the NLC / JLC [5].
However, requirements for CLIC on the wakefield
suppression are more stringent, as the bunches are spread
from each other by 0.5 ns, compared to 1.4 ns [6] in the
NLC / JLC design. Our original design, with a specified
first dipole bandwidth of ~ 3 GHz, enabled the wakefields
to be adequately suppressed at all the trailing bunches.
However, electrical breakdown constraints imposed due
to e.m. field gradients contain the allowable iris range and
hence the bandwidth has been restricted to ~ 1 GHz. In
this paper we present initial results based on these design
restrictions. The next section describes the prescribed
design. The main
penultimate section includes a
calculation of the wake function for a structure with
attached manifolds. The paper concludes with a
discussion of future work in this area.
UNCOUPLED DISTRIBUTION
The present CLIC baseline design consist of a structure
with 24 cells with an iris range of ~ 3.0 mm to 2.0 mm.
Tapering the irises within the structure ensures that a
range of modes are excited which do not add coherently.
We enforce an erf distribution of the iris radius with cell
number. The characteristic kick factor weighted density
function together with an indication of modes for a
structure, effectively consist of four times the number of
cells is illustrated in Fig. 1.
2K
dn
df
Mode separation
Figure 1: The kick factor weighted density function
2Kdn/df (red curve) and mode separation (vertical lines).
The Gaussian distribution used in this design is not
necessarily the optimum distribution as other functional
forms may give rise to a more rapid decay of the
wakefield [7]. The fourier transform of the Gaussian
Kdn/df distribution provides an indication of the fall-off
of the wakefield [8]. However, as the tails of the Gaussian
distribution are truncated a more accurate calculation of
the uncoupled wakefield of this truncated Gaussian is
given by [8]
Wt  2Ke 2πσt  χ t, Δf 
2
1)
where K is the average kick factor and the χ factor is
defined by:




Re erf  f  i42 t  / 2 2 


  t, f  
erf  f / 2 2 



2)
Here, f represents to the bandwidth of the Kdn/df
distribution.
 f  f 2
c

dn
K
2
K
N
e 2
3)
df
2
We chose a bandwidth of 3.0σ or ~5.0% of the central
frequency. In order to calculate the long-range behaviour
of the wake function wee utilise a circuit model which
includes TE-TM dipole modes coupled via TE modes to a
manifold through slot-cut in to each cell. This circuit
model includes a double band chain of L-C circuit
capacitively coupled to a transmission line [5]. The
wakefield is calculated by α-spectral method which
requires f parameters and the corresponding kick factors
to be obtained for each cell of the accelerating structure.
We parameterise the structure by choosing seven fiducial
cells and all the parameters of the other cells are obtained
by cubic spline interpolation. The procedure allows an
efficient determination of the wakefield. The parameters
are subsequently made functionally dependent on the
synchronous frequencies of each cells and thus allows a
rapid evaluation of the wakefield of new distributions.
The parameters of each cell are obtained through solving
eight coupled non-linear equations for each fiducial cell
subjected to infinite periodic boundary conditions. The
circuit equation describing a dipole mode of frequency f
coupled to the manifold at a phase advance per cell of ψ is
given by[5]:
1  η cos ψ/ f
1  η̂ cos ψ
2
0
/ f̂ 02
cos ψ - cos φ 




/ f f̂ sin ψ
(dashed) curves represent the coupled (uncoupled) dipole
modes.
All the points have been obtained with HFSSv11 operated
in to eigen mode module. The red points are used in
solving the coupled non-linear equation and the curves
are required to pass through these points. The additional
(black) points provide an indication as to the quality of
the fits and are not used in the parameter determination.
The field distribution of the lower zero and the lower pi
mode are illustrated in Fig. 3.
Manifold
Coupling slot
a)
b)
Figure 3: Electric field in CLCI_DDS at zero phase
advance (a) and pi phase advance (b), corresponding to
ω/2π = 14.37 GHz and 17.41 GHz respectively.
The dipole mode excited at the point where the light line
intersects the modal curves and synchronous point. This is
in the vicinity of a pi phase advance and the *** ** ** the
expected field in this region. The modes subsequently
travels down the accelerating structure and couples out to
the manifold through slots downstream. This allows the
coupled wakefield to be determined and this described in
the next section

  2 / α / F 2  f 2  f -2
f
-2

 η 2x

DISCUSSION
2
0 0
4)

 2 F 2 / F 2  f 2 πL/c 2 1  η̂ cos ψ f̂ 0-2  f̂ -2 sincφ
where all parameters are described in [5].
The corresponding Brillouin diagram of the first cell of
the CLIC_DDS design is illustrated in Fig. 2.
Application of the spectral function method structures to
be ***** designed which will suppress the wake function
in the CLIC main linacs. The initial design presented
here, is modified by a design to reduce the maximum
pulse temperature rise on the wall of the cavity and to
remotely located the HOM loads. Four-fold interleaving
of the erf distribution of frequencies of successive
structure is employed. This design can benefit from
additional optimisation. Further designs are anticipated
utilising different Kdn/df distribution and will benefit
from slightly increased bandwidth which are under active
consideration. Furthermore, we are now in a position to
perform an optimisation of provided manifold to cell
coupling and on means to further reduce the magnetic
field in the vicinity of the coupling slots where it is
maximum with respect to the whole structure.
ACKNOWLEDGMENTS
Figure 2: Brillouin diagram for the first cell of
CLIC_DDS. The points represent simulation and solid
Useful discussions have been conducted with W.
Wuensch, A. Grudiev, J. Wang and T. Higo regarding the
X-band structures. The research leading to these results
has received funding from European commission under
the FP7 research infrastructure grant agreement no.
227579. V. Khan is thankful to The Cockcroft Institute
for supporting to pursue PhD in accelerator physics field.
REFERENCES
[1] http://www.linearcollider.org
[2]
[3]
[4] H. Braun, et al, CLIC-Note 764, 2008
[5] R.M. Jones, et al, 2006, Phys. Rev. STAB, 9, 102001.
[6] J.W. Wang and T. Higo, SLAC-PUB-10370, 2004
[7] R.M.Jones, et al, 2000, SLAC-PUB-8609, LINAC00
[8] V.F. Khan and R.M. Jones, 2008, WEPP089, EPAC08