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WAKEFIELD AND SURFACE ELECTROMAGNETIC FIELD
OPTIMISATION OF MANIFOLD DAMPED ACCELERATING
STRUCTURES FOR CLIC
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V. F. Khan†*, A. D’Elia†*‡, R. M. Jones†*,
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A. Grudiev‡, W. Wuensch‡, G. Riddone‡, V. Soldatov‡§
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†
School of Physics and Astronomy, The University of Manchester, Manchester, U.K.
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The Cockcroft Institute of Accelerator Science and Technology, Daresbury, U.K.
‡
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CERN, Geneva, Switzerland.
§
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JINR, Dubna, Russia
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Email: Vasim.Khan@hep.manchester.ac.uk
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Abstract
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The main travelling wave linacs of the compact linear collider (CLIC) operate at a frequency of 12 GHz with a
phase advance per cell of 2π/3. In order to minimise the overall footprint of the accelerator, large accelerating
gradients are sought. The present baseline design for the main linacs of CLIC demands an average electric field
of 100 MV/m. To achieve this in practical cavities entails the dual challenges of minimising the potential for
electrical breakdown and ensuring the beam excited wakefield is sufficiently suppressed. We present a design to
meet both of these conditions, together with a description of the structure, CLIC_DDS_A, expressively designed
to experimentally test the ability of the structure to cope with high powers.
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Key words
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Beam dynamics, Breakdown, CLIC, CLIC_DDS, CLIC_G, DDS, HOMs, Linear collider, Manifold damped,
NLC, Wakefields.
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PACS: 29.20.Ej – Linear accelerator
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29.27.-a – Beams, charged particles- in accelerators
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77.22.Jp – Breakdown electrical, dielectrics
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1. Introduction
The aim of the CLIC project is to collide multiple bunches of electrons and positrons at a 3 TeV centre of
mass energy. In order to achieve high accelerating gradients within the cavities, normal conducting (NC) linacs
are employed [1-3]. The CLIC baseline design aims at an accelerating gradient of 100 MV/m [4-5] with an Xband frequency of 12 GHz. This frequency resulted from a detailed optimisation procedure based on various
simulations [4-5]. The curves representing the optimisation parameters are relatively flat in the vicinity of 12 to
15 GHz. The 12 GHz frequency was chosen as it is close to the frequency used in the next linear collider
(NLC) [6] programme and hence the wealth of knowledge developed over two decades can be capitalised upon.
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There are two phenomena which must be taken into account when designing these accelerating structures:
electrical breakdown and beam-excited wakefields. The former can be addressed both by carefully designing the
structure such that the surface e.m. fields are minimised and by paying attention to the surface morphology. As
for the wakefields, they have both short-range (along the bunch) and long-range (along the bunch train)
components. The short-range wakefield is a strong function of the iris aperture and is not the focus of this study.
Here we present a design for suppressing the long-range wakefield, whilst minimising the surface e.m. fields on
the walls of the accelerating structures. The method for damping the wakefields entails detuning each of the cell
frequencies, by tapering down the irises along the structure, and providing moderate (Q~1000) coupling to four
attached manifolds [6]. This method is similar to that adopted in the NLC, however, with stronger constraints
imposed due to the larger gradients required. This resulted in markedly different outer cavity wall design. The
design presented here is an alternative to the baseline design for the main linacs of CLIC, which relies on heavy
damping (Q~10 [5]) through strongly coupled waveguides attached to each cell. However, we maintain the same
number of cells in the CLIC_DDS_A design. Other wakefield suppression strategies are possible [7].
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In the CLIC damped and detuned structures (DDS), the focus of this work, both the fundamental
(accelerating) mode and the higher order dipole modes (HOMs) are calculated. In both cases, the
electromagnetic (e.m.) fields in single cells is calculated using codes which rely on representing the geometry
with a finite element based mesh. For a sufficiently fine mesh, an accurate representation of the e.m. fields is
obtained. The beam loaded accelerating field is calculated from an integral [8] representation of the energy flux
within the overall cavity, based on the field in individual cells. The transverse dipole field is calculated from a
circuit model [6, 9-11], designed to represent dipole mode slot-coupled to waveguide like manifolds. This
circuit model and its spectral function [6, 11] generalisation, provides a design tool to allow the influence of
geometrical modifications to be rapidly accounted for in the wakefield calculations. This unique tool has been
validated on several previous NLC structures and has proved to be an accurate prediction of the wakefield [6,
11].
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The CLIC_DDS design is based upon the knowledge gained and documented from the NLC studies. However,
the geometrical change implemented in CLIC_DDS to minimise the pulsed temperature rise is based on the
baseline design of the CLIC main linacs which are waveguide damped (known as CLIC_G [4-5]). We report on
various stages involved in evolving CLIC_DDS so as to satisfy the stringent constraints imposed by the rf
breakdown and beam dynamics criteria. In order to rapidly realise the bandwidth necessary for the wakefield
suppression, detuned structures (DS) have been studied first. In all cases, we prescribe a Gaussian distribution
for suppression of the wakefields. We learned that a bandwidth of ~3.3 GHz is necessary to suppress the
wakefield to satisfy the beam dynamics criterion for an inter-bunch spacing of 6 rf cycles.
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The paper is structured such that the next section presents an overview of early designs for CLIC which fail to
subsequently satisfy both the electrical breakdown and beam dynamics constraints. This is followed by a design
to overcome these limitations. The final sections provide details on a structure which will be high power tested
and some concluding remarks.
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2. Means To Independently Satisfy RF Breakdown And Beam
Dynamics Constraints
In all cases, we utilise a finite element code HFSS [12] to model accelerating structures, calculate the fields
and eigen modes within the sructure. The single infinitely periodic cell is tuned by varying cavity radius (b) to
the accelerating frequency of 11.994 GHz for a given iris raius (a) and iris thickness (t). Dispersion curves are
obtained from the circuit model [13]. For a cell subjected to infinite periodic condition the dispersion relation
between frequency ω/2π and phase advance per cell ψ is:
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ωr
ω
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1  η cosψ
(1)
The resonating frequency (ωr) and coupling coefficient (η) of the neighbouring cells are obtained from the 0 and
π mode (simulation results).
ωr 
η
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2ω02ω2π
ω02  ω2π
(2)
ω 2π  ω02
ω02  ω 2π
(3)
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The calculation of group velocity (derivative of eq. 1 [14]) is followed by the calculation of the dipole mode
synchronous frequency. We model seven single cells to represent a structure of 25 cells. As the power absorbed
in the breakdown is strongly dependent on both surface e.m. fields and the fundamental mode group velocity
[15], we maintain a low group velocity by changing the iris thickness from 5.7 mm (cell 1) to 0.5 mm (cell 25).
The tapered iris radii and ticknesses in this structure result in a group velocity variation from 1.93 %c to 1.0 %c
Parameters of this large bandwidth DS are presented in Table 1. The ratio of average iris radius (<a>) to
accelerating wavelength (λ) for this structure is 0.142. It is important to minimise this ratio so as to reduce the
breakdown possibility [6].
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An optimal design, in terms of rapid damping of the dipole wakefield results in an iris radius taper down from
4.95 mm to 2.15 mm results in a dipole bandwidth of ~3.3 GHz [16]. The iris radius follows an erf distribution
with cell number. The bandwidth (∆f) in terms of the standard deviation of a Gaussian distribution (σ) is: ∆f =
3.6σ. The detuning spread in this structure is 20% of the central frequency. Once the synchronous frequencies
and kick factors are calculated using computational tool (uncoupled mode), we calculate the coupled mode
frequencies and kicks so as to account for the cell-to-cell interactions using a double band circuit model [13]. In
this structure, we observed an approximately 200 MHz shift in the coupled mode frequencies with respect to the
uncoupled mode due to the interactions of the fields coupled through irises. The representation of a Gaussian
distribution needs better sampling, 25 cells are clearly not sufficient for this purpose. In this case, wakefield
decay in a 25 cell structure is not adequate to meet the beam dynamics criterion. Hence, we interleave a number
of structures to satisfy the beam dynamics criteria. An 8-fold interleaving provides the necessary suppression of
the wakefield. The transverse long-range wakefield is calculated using the modal sum method as follows [17]
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N
WT (t)  2
K
p 1
p Exp


i 
iω p t 1 
  (t )
 2Q p 

(4)
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where ωp is the synchronous frequency, Qp is the quality factor of the synchronous mode and θ(t) is the
Heaviside step function. A comparison of the uncoupled and coupled mode frequencies is illustrated in Fig. 1.
Similarly, a comparison of the designed uncoupled and coupled mode kick factor weighted density function
Kdn/df is presented in Fig. 2. In this case, a non-smooth behaviour of Kdn/df is observed due to non-smooth kick
factors of the coupled mode. The envelope of the wakefield for an entire train of 312 bunches is illustrated in
Fig. 3. In this case, various damping Qs are artificially imposed. The wakefield in a DS with losses due to finite
conductivity (Qcu ~6000) is also shown. Wakefield suppression well beyond the beam dynamics requirements is
obtained. For this geometry, the surface e.m. field on the copper walls, on the other hand is too large. The
electrical breakdown constraints are not met.
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The motivation behind investigating a reduced bandwidth structure is also to enable the rf breakdown
constraints to be satisfied. This leads us to match the end cell iris dimensions to the CLIC_G structure, with a
tapering of Gaussian function. In this case, the ratio of <a>/λ reduces to 0.1 and the average group velocity also
reduces by ~20%, [18,19]. The structure now satisfies rf breakdown constraints. However, the structure
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bandwidth reduces significantly to ~0.9 GHz resulting in severe wakefields on the first two trailing bunches and
is illustrated by the blue curve in Fig. 4. For a moderate damping with reduced bandwidth, a possible way to
satisfy both the constraints is to increase the bunch spacing by a factor of 3 i.e. to 18 cycles (1.5 ns). In this case,
the rf-to-beam efficiency reduces down to an unacceptable value of 8 to10%. The other possible option is to rely
upon zero crossing scheme. When wakefield is calculated, an excursion of the envelope is calculated. However,
the wake experienced by the bunch may be small. In this case, the iris dimensions of the structure(s) are tuned in
such a way that the bunches see almost zero amplitude of the wakefield (and not the envelope). Wakefield in a
structure implemented with zero crossing is illustrated in Fig. 4, here the location of the dots represent bunches.
The envelope of wakefield for this structure in presented in Fig. 5 with several damping Qs.
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The CLIC project requires more than 140,000 [7] accelerating structures. In practice, it will be difficult to
maintain the zero crossing scheme for all structures. Meeting the mechanical tolerances to build these structures
is also challenging. A possible solution for a moderately damped DDS is to relax the bunch spacing, whilst
loosing a few percentage in overall efficiency and to choose a structure with a moderate dipole bandwidth. In
this manner a trade off between the bandwidth and efficiency is investigated in the next section.
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3. A structure Satisfying RF Breakdown And Beam Dynamics
Constraints
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After realising the necessary bandwidth range for satisfying the beam dynamics constraint by studying DS, a
conventional circular cell incorporated with manifold geometry was studied. The profile of a typical DDS cell is
presented in Fig. 6, where RM is the radius of the manifold and Rc is the radial distance of the manifold coupling
slot from the electrical centre of the cavity. This structure consists of 24 accelerating cells and is known as
CLIC_DDS_C. The taper in the iris radius ranges from 4 mm to 2.3 mm to provide a bandwidth of ~2.3 GHz.
The ratio of <a>/λ for this structure is 0.126. DDS_C incorporates manifolds, slot-coupled to the accelerating
cells. These coupling slots perturb the cell wall, and cause more current to flow in the vicinity of the slot,
leading to excessive surface magnetic fields (H-field). The average peak power requirement of an 8-fold
interleaved DDS_C is ~73 MW to maintain an average accelerating gradient of 100 MV/m. The bunch
population in this case is chosen to be 4.2 x 109. However, for this structure bunches can be populated up to 5.0
x 109. In this case, the input power requirement will increase to ~76 MW. The average rf-to-beam efficiency is
~23%. The enhancement of the H-field in the coupling slots results in a pulsed surface temperature rise of 72° K
for an rf pulse length of ~250 ns. The pulsed surface temperature rise along the structure length in each of the 8
structures of DDS_C is illustrated in Fig. 7. As can be seen, the structure observes nearly 30% (the tolerable
limit is 56° K [4, 5]) temperature rise towards the downstream end and fails to meet the rf breakdown constraint.
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An accurate determination of the dipole properties of this structure is facilitated by the circuit model [6, 9] and
spectral function method [6, 11]. This is necessary in order to accurately predict the wakefield for a multi-cell
structure, slot-coupled to wave guide like manifolds. The lowest dipole bandwidth in this structure is: ∆f = 3.6σ
= 2.33 GHz and the detuning spread is 13.7% of the central frequency. The dispersion relation for a manifold
damped single infinitely periodic cell is defined as [6, 9]
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



πP
 1  η cos  1  η̂ cos  η2

1  η̂ cos  f̂ 02  f 2 sinψ0n

sin cos  cosψ   Γ 2
 2
2 
2
2 
c
ψ 0n
f

f
f̂

f
f
f̂


 0
 0 0
 0

(5)
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where f0 and η are the resonating frequency and coupling coefficient of the TE mode respectively and 𝑓̂0 and 𝜂̂
of the TM mode, Γ coupling of the manifold with cell, φ phase advance per cell, ψ local phase advance per
waveguide section and P is the period of the cell. Here, the cross coupling term between TE and TM modes for a
thin iris [20], can be approximated as   ˆ . The dispersion curves of the first three dipole modes in a typical
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DDS_C cell are illustrated in Fig. 8. We utilise the spectral function method to calculate the impedance of the
structure [6, 11]
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S(ω)= 4 Im {Z(ω+jε)}
4
(6)
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where ε is an infinitesimal displacememnt and Z(ω) is the impedance of the structure and is define as [6, 11]
Zω 
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1
2π 2
N

K sn K sm ωsn ωsm exp[ 
n, m
~
jω
P]n  m  H nm
c
(7)
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Here N is the number of cells in a structure, K’s and ω’s are the synchronous kicks and frequencies respectively.
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The matrix H nm contains various circuit parameters involved and is defined in [6, 11].
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The wakefield is calculated by taking inverse Fourier transform of the spectral function. The spectral function of
an 8-fold interleaved DDS_C is illustrated in Fig. 9 and the corresponding wakefield in Fig. 10. As the dipole
bandwidth in this case is moderate, the wakefield decay should be rapid enough to meet the beam dynamics
criterion. In order to meet the beam dynamics constraint, the inter-bunch spacing in this case is relaxed to 8 rf
cycles (0.67 ns) from the base-line 6 rf cycles. It is inevitable to relax the bunch spacing in a structure with
moderate bandwidth. In this way, the beam dynamics criterion is satisfied at the cost of few percentage loss in
the efficiency. The wakefield in this case is damped beyond the beam dynamics limit which is shown by dashed
line in Fig. 10. Though the wakefield suppression in this structure is adequate, DDS_C needs further
optimisation to meet the rf breakdown criteria, this is discussed in the next section.
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The H-field in a standard circular cell is uniformly distributed along the surface of the cell. When the surface
is perturbed, to incorporate for manifold coupling, the field in this region gets enhanced. For a circular undamped cell of iris radius 4 mm, the normalised H-field (with respect to the accelerating field) on the cell wall is
~3.8 mA/V. When the cell wall is perturbed by a coupling slot of width 3 mm, the enhancement in the H-field
peaks up to 6 mA/V i.e. nearly 60% enhancement. The pulsed temperature rise is proportional to the square of
the H-field [21]. Reducing the iris radius also reduces the H-field, however, it also affects the dipole bandwidth.
In this case it is necessary to re-distribute the H-field on the cavity wall, and insert the manifold coupling slot at
a location where the field is minimum. This re-distribution reduces the field enhancement. In order to study the
field distribution in the absence of manifold slots i.e. an undamped cell, a range of cells with modified walls
have been studied and are illustrated in Fig 11. The modified cavity shape is defined in terms of an ellipse ε with
A and B as semi-major and semi-minor axis respectively [22]. For B = 0, ε = ∞ and the cell wall is rectangular
and a circular wall corresponds to ε = 1. The variation of the normalised H-field along the contour of an
undamped cell is presented in Fig. 12. The dashed line in this figure represents an approximate location where
manifold slot will be introduced. A manifold of slot width 2.5 mm was introduced. The field enhancement for
selected shapes is illustrated in Fig. 13. As can be seen, for an elliptical cell of ε = 1.38, the field enhancement
is a minimum. There is no field enhancement in the vicinity of the coupling slots compared to the peak field
within this cell. The peak normalised H-field on the cell contour is now ~4.4 mA/V. However, there is still some
field enhancement towards the tip of the manifold slots which is ~5 mA/m.
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The iris thickness was also optimised to minimise the surface electric field (E-field). The new structure
incorporating an elliptical outer wall and modified iris thickness is known as DDS_E. A change in iris thickness
primarily affects four rf parameters: 1) the surface E-field, 2) the fundamental mode group velocity (vg), 3) shunt
impedance (R), which affects the input power requirement and hence efficiency of acceleration (rf-to-beam
efficiency) and 4) dipole bandwidth. Several structures with a range of iris thicknesses were studied by
comparing their rf properties such as surface E-field, input power requirement, rf-to-beam efficiency and dipole
bandwidth. In this process, the rf properties of the structures (DDS_E) were compared with a reference
structure. The cavity wall of the reference structure is elliptical with iris radii and thicknesses retained from
DDS_C. A comparison of the rf properties of the reference structure with various other structures is shown in
Fig. 14. In this optimisation we realised that beyond the average iris thickness of 2.65 mm, surface E-field
remains almost invariant. The input power is reduced and hence the efficiency of acceleration increases.
However, the dipole bandwidth is reduced. Considering the trade-off between the efficiency and dipole
bandwidth, an average iris thickness of 2.65 mm was optimised which gives a taper in the iris from 4 mm to 1.3
mm. This demands an average input power for the 8-fold interleaved DDS_E of 69.5 MW. The overall average
rf-to-beam efficiency in this case is 24%. The maximum surface E-field is 251 MV/m and the pulsed
~
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temperature rise is 52° K, which is reduced by ~28% compared to DDS_C. As the fields on the cell walls were
reduced due to modifications in the geometry, the coupling of the dipole modes also reduced. This affects the
wakefield suppression adversely. However, the wakefield is still suppressed beyond the beam dynamics limit. A
comparison of the wakefield in DDS_C and DDS_E is presented in Fig. 15. A test structure, which is the first
out of eight-fold interleaved structures of DDS_E is being fabricated. The properties of the test structure are
discussed in the next section.
4. Structure Optimised For High Power Testing
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In order to test the high power performance of DDS_E, a test structure known as DDS_A has been designed.
HOM couplers are omitted as the purpose of this structure is to evaluate the ability of the accelerator to sustain
high powers. The first structure (out of eight DDS_E) is used because it has the largest aperture compared to
other interleaved structures (and is also the reason why it needs relatively more input power). Therefore, the
breakdown rates in this structure are expected to be severe compared to the remaining interleaved structures. In
order to make the design of the structure easy as far as the mechanical and cost point of view is concerned, the
manifold dimensions are kept constant throughout the structure. The consequence of which is poor coupling of
the dipole modes to the manifold, hence the wakefield is non-optimal in this case. As the primary aim of this
non-interleaved structure is to test the high power performance, we do not expect wakefield to be damped
adequately. Detailed geometric parameters of DDS_A are presented in Table 2. In [23], a new local quantity (Sc)
is defined, and is termed as modified Poynting vector, to calculate the complex power flow from the structures.
It provides the limit on the rf gradient in presence of electrical breakdown. The maxima in the E, H and Sc fields
in DDS_A cells are presented in Fig. 16 [22]. The fundamental mode rf parameters of the single cells are
illustrated in Fig. 17 and overall structure properties both in beam loaded and unloaded conditions are presented
in Fig. 18.
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The spectral function of DDS_A is illustrated in Fig. 19. The Q of the dipole modes is calculated by fitting a
Lorentzian [17] to the peaks in spectral function. The average dipole Q in this structure is ~1650 and is
illustrated in Fig. 20. The wakefield in DDS_A is illustrated in Fig. 21.
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The calculations involved in optimising the structure for fundamental as well as dipole mode properties are
based on single infinitely long periodic cells. However, wakefield calculations do involve circuit parameters to
account for the coupled mode interactions. In order to build a realistic structure, we need to design matching
cells at the either ends of the structure (regular cells) to match the impedance of the structure to minimise the
reflection. Instead of a conventional rf power coupler, CLIC_DDS_A will be powered using a mode launcher
[24, 25]. In order to minimise the overall reflection in the structure, we design matching cells, at either ends of
the structure. The matching procedure begins with designing the cells as indicated in Fig. 22. Here, the geometry
in the middle is the first (or last) regular cell provided with matching cells at the either ends and beam pipes at
the extreme ends. This, in principle, is similar to a constant impedance structure. The matching parameters such
as matching iris a, matching cavity radius b and matching gap length L are varied to minimise the reflection
(S11) at the operating frequency. In this way, both the end cells are designed. However, the real geometry is not
the constant impedance but constant gradient type, hence the matching parameters (a, b and L) need to be fine
tuned for a real tapered structure. After defining a complete 3D structure of 24 regular cells + 2 matching cells
in simulation software (HFSS [12]), we fine tune the matching parameters for the whole structure using the
Kroll method [26]. This time we minimise the standing wave ratio (SWR) in the structure. In this way, the
complete structure is tuned including the matching cells. The accelerating field in the fully tuned structure is
illustrated in Fig. 23. The extreme peaks in this plot correspond to the matching cell accelerating fields. These
peaks are dissimilar to the regular cell peaks due to the fact that the matching cell lengths are different compared
to the regular cell lengths. The erf tapering of the regular cells is evident in the fully tuned structure accelerating
field. The accelerating field phase advance per cell is also illustrated in Fig. 23. Here, a nearly triangular shape
profile reflects the 120° phase advance. The maximum deviation in the phase advance per cell is no more than
6°. The discrepancy from a perfect triangular shape can be understood in the following ways: i) difference in the
extreme (regular) irises due to error function tapering, ii) use of only 9 cells to represent full structure of 24
cells, iii) difference in the cell lengths of the matching cells compared to regular cell length. The S parameters
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of the fully tuned structure are presented in Fig. 24. In this case, the simulation results of S11 = -54 dB (2.24 x
10-6) has been achieved at the operating frequency. The quality factor as a function of frequency is presented in
Fig. 25.
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The fabrication of the DDS_A cells is in progress and the test cells (discs) are shown in Fig. 26. A complete
CAD drawing of DDS_A, consisting of 24 regular cells and 2 matching cells is illustrated in Fig. 27. The overall
parameters of the DDS_A are summarised in Table 3.
5. Final Remarks
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Though the rf breakdown and beam dynamics constraints are stringent in the CLIC main linacs, a design
incorporated with a relaxed bunch spacing, moderate bandwidth and modified outer cell wall meets the design
constraints provided eight-fold interleaving of dipole frequencies is employed.
Acknowledgements
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We acknowledge illuminating discussions with J. Wang, Z. Li, T. Higo, R. Zennaro and I. Syratchev on linac
structures and beam dynamics. Research leading to these results has received funding from European
commission under the FP7 research infrastructure grant no. 227579.
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R. M. Jones, et. al., 2009, Influence Of Fabrication Errors On Wake function Suppression In NC XBand Accelerating Structures For Lepton Colliders, new Journal Of Physics, 11 (2009) 033013.
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K.L.F. Bane and R. Gluckstern, 1992, The Transverse Wakefield Of A Detuned X-Band Accelerator
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R. M. Jones, 2007, Fundamentals Of Collective Effects, Wakefields And Impedances, Contribute To
Cockcroft Institute Accelerator Course, U.K.
R. M. Jones, et. al., 2006, Dipole Wakefield Suppression In High Phase Advance Detuned Linear
Accelerators For The JLC/NLC Designed To Minimise Electrical Breakdown And Cumulative BBU,
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V. F. Khan and R. M. Jones, 2008, Wakefield Suppression In The CLIC Main Linacs, Proceedings Of
The European Particle Accelerator Conference, EPAC’08, Italy.
R. Jones, 2004, A Study Of Higher Band Dipole Wakefields In X-Band Accelerating Structure For The
NLC/GLC, Proceedings Of The Linac Conference, LINAC’04, SLAC-PUB-10682, Germany.
7
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304
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306
307
308
309
310
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313
314
315
316
317
318
319
320
321
322
323
18. V. F. Khan and R. M. Jones, 2008, Beam Dynamics And Wakefield Simulations For The CLIC Main
Linacs, Proceedings Of The Linear Accelerator Conference, LINAC’08, Canada.
19. V. F. Khan and R. M. Jones, 2008, An Alternate Design For The CLIC Main Linac Wakefield
Suppression, Proceedings Of The X-Band And beam Dynamics Workshop, XB’08, U.K.
20. R. M. Jones, 2005, Fundamentals Of Wakefields and Impedances: From Physical-Mathematica
Analysis To Practical Applications, Contributed to the U.S. Particle Accelerator School, USA.
21. I. Wilson, 1987, Surface Heating Of The CLIC Main Linac Structure, CLIC-Note-57, Switzerland.
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Proceedings Of The International Particle Accelerator Conference, IPAC’10, Japan.
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Accelerating Structures, Phy. Rev. STAB. 12,102001(2009).
24. I. Syratchev, 2002, Mode Launcher As An Alternative Approach To The Cavity – Based RF Coupler
Of Periodic Structures, CLIC Note 503, Switzerland.
25. C. D. Nantista, et. al, 2004, Low Field Accelerator Structure Couplers And Design Techniques, Phys.
Rev. STAB, 7, 072001.
26. N. M. Kroll, et. al, Application Of Time Domain Simulation To Coupler design For Periodic
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Structure, Talk Presented In The Second CLIC Advisory Committee, CLIC-ACE, Switzerland.
Fig. 1
324
325
Fig. 2
326
8
327
Fig. 3
328
329
330
331
Fig. 4
332
333
Fig. 5
334
9
335
336
337
Fig. 6
338
339
Fig. 7
340
341
Fig. 8
10
342
343
344
Fig. 9
345
346
347
Fig. 10
348
11
349
350
Fig. 11
351
352
353
354
Fig. 12
355
12
356
357
Fig. 13
358
359
360
361
362
Fig. 14
363
13
364
365
Fig. 15
366
367
Fig. 16
368
369
370
371
372
373
374
375
14
376
377
Fig. 17
378
379
Fig. 18
380
381
382
15
383
384
Fig. 19
385
386
387
Fig. 20
388
389
390
391
392
393
394
16
395
396
397
Fig. 21
398
399
400
Fig. 22
401
402
403
404
405
406
407
17
408
409
410
Fig. 23
411
412
Fig. 24
413
414
415
416
417
Fig. 25
18
418
419
420
Fig. 26
421
422
423
424
Fig. 27
19
425
426
Figure captions
427
Fig. 1: A comparison of uncoupled and coupled mode frequencies
428
Fig. 2: A comparison of uncoupled and coupled mode kick factor weighted density function
429
430
Fig. 3: A comparison of uncoupled and coupled mode frequencies. Dashed line represents tolerable limit on
wake.
431
Fig. 4: Amplitude of wake in a reduced bandwidth structure. Dots reprsent the location of the bunches.
432
Fig. 5: Envelope of wake in a reduced bandwidth structure. Dashed line represents tolerable limit on wake.
433
Fig. 6: Quarter symmetry cross section view of a DDS_C cell
434
Fig. 7: Pulsed temperature rise in each of the structures of DDS_C.
435
436
437
438
Fig. 8: Dispersion curves of first three dipole modes in an infinitely periodic single cell of DDS_C. Solid curves
represent circuit model prediction and the dots HFSS simulation results. Red dots are used to predict the curve
and the black dots additional points to show how good the prediction is. Dashed curves indicate the dipole
modes in absence of manifold coupling. Dashed line indicates the light line.
439
Fig. 9: Spectral function of 8-fold interleaved DDS_C structure.
440
Fig. 10: Envelope of wakefield in 8-fold interleaved DDS_C structure.
441
Fig. 11: Various contours to study H-field in an un-damped cell.
442
Fig. 12: A comparison of normalised H-field in various geometries of an un-damped cell.
443
Fig. 13: Filed enhancement in various geometries due to manifold slot.
444
445
Fig. 14: A comparison various rf properties as function of iris thickness. The rf properties of DDS_E with iris
thickness of DDS_C were attributed to 100% to compare the effect of iris thickness variation.
20
446
Fig. 15: A comparison of wakefield suppression in DDS_C and DDS_E.
447
Fig. 16: Maxima of fields in single cells (1/8th symmetry) of DDS_A.
448
Fig. 17: RF parameters of DDS_A.
449
450
451
Fig. 18: Overall rf properties of DDS_A. Lower and upper black dashed lines indicate allowable temperature
rise and E-field respectively. The black line in the middle represents the average beam loaded accelerating
gradient.
452
Fig. 19: Spectral function of DDS_A.
453
Fig. 20: Dipole Q of DDS_A
454
Fig. 21: A Envelope of wakefield of DDS_A
455
Fig. 22: Matching cell design geometry
456
Fig. 23: RF properties of fully tuned structure. Left: Accelerating field, Right: Phase advance per cell
457
Fig. 24: Final S parameters
458
Fig. 25: Quality factor as a function of frequency
459
Fig. 26: DDS_A discs.
460
Fig. 27: DDS_A: Full structure of 24 regular cells + 2 matching cells.
Tables
461
462
Table 1: Single cell parameters of the large bandwidth structure
Cell
Number
1
5
9
13
17
21
25
a
mm
4.95
4.53
4.23
3.95
3.65
3.26
2.15
463
464
b
mm
11.23
10.79
10.53
10.34
10.16
9.99
9.69
t
mm
5.72
4.83
4.19
3.65
3.24
2.4
0.5
vg/c
mm
1.93
1.86
1.73
1.62
1.47
1.3
1.03
fsyn
GHz
15.00
15.56
15.97
16.35
16.75
17.25
18.37
Table 2: Single cell parameters of DDS_A
Cell
Number
1
2
5
9
13
17
21
a
mm
4.00
3.85
3.61
3.39
3.21
3.02
2.8
b
mm
11.05
10.95
10.78
10.64
10.52
10.41
10.29
t
mm
4.0
3.88
3.55
3.13
2.76
2.39
1.94
vg/c
mm
2.07
1.85
1.62
1.51
1.42
1.34
1.22
21
Q
5020
5091
5325
5604
5838
6061
6307
R’/Q
kΩ/m
10.18
10.65
11.72
12.90
13.95
15.05
16.42
fsyn
GHz
15.91
16.07
16.38
16.67
16.93
17.18
17.50
Ksyn
V/pC/mm/m
46.66
50.22
57.23
63.86
69.58
74.88
81.11
23
24
2.63
2.50
10.21
10.16
465
466
1.65
1.47
1.11
1.00
6451
6534
17.41
18.13
17.73
17.89
Table 3: Summary of DDS_A parameters
Parameters
Units
Accelerating mode properties
<a>/λ
-First, last iris radius (a)
mm
First, last iris thickness (t)
mm
First, last (Q)
-First, last (vg/c)
%
First, last shunt impedance (R’)
MΩ/m
Filling (tf), rise (tr) time
ns
Pulse length (tcp)
ns
No. of bunches (Nb)
Bunch population (nb)
109
Peak input power (Pin)
MW
Maximum loaded, unloaded Eacc
MV/m
Maximum Esur
MV/m
Maximum ∆Tsur
°K
Maximum Sc
MW/μm2
RF-beam-efficiency (η)
%
Pin (tpp)1/3/Cin [27]
MWns1/3/mm
Luminosity per bunch crossing [27]
1034 (m-2)
Figure of merit [27]
arb. uni.
Lowest dipole mode properties
Dipole bandwidth (∆f)
GHz
Standard deviation of Gaussian (σ)
-Detuning spread (∆f/fc)
%
467
22
CLIC_DDS_A
0.13
4.0, 2.5
4.0, 1.47
5020, 6534
2.01, 1.0
51, 118
45.4, 23
251
312
4.2
70.8
105, 132
220
51
6.75
23.5
16.93
1.36
7.6
2.0
∆f/3.48
11.8
85.41
87.95