Tuning of 2.998 GHz S-band hybrid buncher for injector upgrade of LINAC II at DESY

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Tuning of 2.998 GHz S-band hybrid buncher for injector upgrade of LINAC II at DESY Y.C. Nie n, C. Liebig, M. Hüning, M. Schmitz Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany

art ic l e i nf o

a b s t r a c t

Article history: Received 21 February 2014 Received in revised form 25 April 2014 Accepted 12 May 2014

The injector upgrade of LINAC II at DESY aims to improve its reliability and mitigate the radiological activation of components due to electron losses at relatively high energy of hundreds of MeV. Therefore, a 2.998 GHz hybrid buncher has been developed and will be installed in between an existing 2.998 GHz pre-buncher and LINAC II. It comprises a 1-cell standing-wave (SW) section for rapid electron acceleration and a 13-cells traveling-wave (TW) section for further beam bunching and acceleration. This paper focuses on its radio-frequency tuning procedure. The tuning strategy combines a nonresonant bead-pull measurement of complex electric field and a linear model for local reflection coefficient calculation. It is demonstrated that imaginary part of the local reflection coefficient represents the field distribution straightforwardly, based on which the structure can be tuned from cell to cell. During tuning, special attention has been paid to the field enhancement in the SW section to ensure its beam-capturing capability. Field amplitude and phase, global and local reflection coefficients have been analyzed for two different frequencies simultaneously, i.e. the intrinsic frequency of the structure and the target frequency, to avoid over-tuning. The tuning result is satisfying. For the target frequency, field unflatness of the TW section has been reduced from 7 9% to 7 4%, and field in the SW section has been enhanced significantly. Meanwhile, in the TW section, the deviation of phase advances between adjacent cells from the nominal value 1201 has been reduced from the range 7 51 to 721. By using ASTRA simulation, it has been verified that the residual detuning of the structure is acceptable in view of the beam dynamics performance. & 2014 Published by Elsevier B.V.

Keywords: Hybrid buncher LINAC tuning and detuning Complex field measurement Reflection coefficient Field unflatness Phase advance Electron bunching and acceleration

1. Introduction LINAC II at DESY consists of 12 S-band traveling-wave (TW) linac, working at 2.998 GHz [1]. Their radio-frequency (RF) stations are equipped with SLED cavities for pulse compression and increasing peak power by a factor in excess of four, i.e. from 20 MW up to 90 MW. Therefore, an average gradient of 18 MV/m or 90 MV/structure can be achieved. Presently, LINAC II accelerates electron bunches to 450 MeV before they are injected into the synchrotron accelerator DESY II. Subsequently, DESY II provides a 6.0 GeV beam for the third generation synchrotron radiation source PETRA III. Previously, LINAC II also served for DORIS III, a famous second generation storage ring light source. Moreover, it will play an important role in the recently proposed Accelerator Research and Development (ARD) facility Short INnovative Bunches and Accelerators at Doris (SINBAD) as a primary accelerator [2].

n

Corresponding author. E-mail address: [email protected] (Y.C. Nie).

It can be seen that the stable operation of LINAC II at DESY is of great importance . This partly relies on the performance of its injection system. At present, the injector of LINAC II is composed of the following main components: a 150 kV pulsed DC diode gun which is able to produce 6 A electron pulses of 4 ms duration, an electrostatic chopper that cuts the pulses into 2–30 ns length, a 2.998 GHz pre-buncher and two collimators downstream the chopper and pre-buncher, respectively. Even though such an injection system has been operated stably for many years, improvements need to be carried out, considering the following problems: 1) The pre-bunched 150 keV electron bunches from the injector are non-relativistic. After they are injected into the first section (section#1) of LINAC II, dephasing occurs in the first part of section#1 until the velocity of the electrons reaches the phase velocity (light speed in vacuum) of the accelerating structure. Due to the dephasing process, the electron bunches may transit the crest of the RF wave and locate at an accelerating but debunching phase in the following part of section#1. The not well-bunched or tailing electrons will be lost along LINAC II up

http://dx.doi.org/10.1016/j.nima.2014.05.043 0168-9002/& 2014 Published by Elsevier B.V.

Please cite this article as: Y.C. Nie, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.05.043i

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Table 1 Detail parameters of the hybrid buncher structure. Parameter

Value

Working frequency (GHz) 2.998 Number and working mode of SW cell 1, π Number and working mode of TW cell 13, 2π/3 Length (mm) and β of SW cell 24.8, 0.5 Length (mm) of TW cell 33.33 Buncher length (mm) 500 Radius of coupling iris (mm) 12.65 (coupling iris between SW and TW sections), 14.9 (coupling irises in TW section) SW cell radius (mm) 35 TW cell radius (mm) 41 Group velocity vg/c (%)  3.5 Filling time (ns)  50 Field gradient (MV/m)  15 Input electron energy (keV) 100 Output electron energy (MeV) 5

to 450 MeV, resulting in radiation damage and activation along the beamline. One solution is such that by adjusting the timing of the sloped SLED pulse, the bunches are injected when section#1 has not been completely filled and its first several cells still possess relatively higher field than later on, to speed up the acceleration of the electrons. However, the effect has been proved to be limited. 2) The gun cathode is made of a carburized thoriated tungsten plug, heated by a 3 kV, 1.2 kW bombarder. It is no longer commercially available nowadays, and it is not economical for DESY to build up its own infrastructure to produce it. Moreover, for electrical and cooling purposes, the gun is operated in an oil bath, which is isolated from the beamline vacuum only by a ceramic plate. Although it has been working safely for tens of years, the cost would be enormous and the shutdown time would be unexpected in case it is broken and oil polluted the vacuum system. For the above reasons, a new injection system for LINAC II has been designed and constructed. Its main components are [3,4]: an 100 kV DC triode gun with a commercially available cathode EIMAC Y796, which delivers 2–50 ns long pulses at a repetition rate of 50 Hz (therefore no chopper is required any more), a 2.998 GHz pre-buncher which is the same as the one in the old injector, a novel hybrid buncher consisting of both standing-wave (SW) and TW structures surrounded by a focusing solenoid, a magnetic chicane that serves as an energy filter and incorporates the electrons into the end of the old injector which will serve as a backup system, 6 distributed quadrupole magnets, and adequate diagnostic instruments like toroids, beam position monitors and fluorescent screens. For such an injection system, a primary beam transport simulation has been implemented using the code ASTRA [5,6]. The result shows that the hybrid buncher can improve beam bunching efficiency dramatically and can accelerate the electrons to about 5 MeV. Combining with the energy collimation in the magnetic chicane, the majority fraction of electron loss occurs at an energy below 10 MeV. This implies that the radiological activation of components will be eliminated substantially. In this paper, we will focus on the RF tuning of the hybrid buncher, one of the most crucial components in the new injector. The hybrid structure usually has a compact beamline, simplified RF power supply, and more importantly, potential to combine the advantages of both SW regime and TW regime. Its applications in LINAC accelerator and photoinjector have been reported [7–9]. In our case, a more detailed RF design of the hybrid buncher cavity

can be found in Ref. [4], and the main features are as follows. Working at 2π/3 mode, the TW section consists of 11 regular cells, one input coupler cell, and one output coupler cell, with a constant gradient around 15 MV/m. One upstream SW cell is coupled to the TW section in π mode, which is shorter compared to the TW cells to match the incoming beam with velocity β¼ v/c¼0.5 (c and v are the velocities of light and electrons in vacuum, respectively). Its radius is smaller compared to those of the TW cells, for the purpose of frequency matching between the SW section and the TW section, considering that the resonant frequency of the SW cell will be lowered while the frequency of the coupler cell will be increased after their combination. In principle, the radius of the coupling iris can be adjusted to vary the coupling strength between the SW section and the TW section and hence achieve a proper field ratio between the two sections. In our case, the optimal value was chosen to make the field in the overall structure basically flat. Listed in Table 1 are the detailed parameters of the hybrid buncher. Using a phase shifter, the transmitted RF power from the buncher can be fed into the following LINAC II to make full use of the klystron. Mechanical design of the buncher is shown in Fig. 1. It consists of one input port, one output port, and two bottom waveguide ports for the connection of vacuum pumps. Each cell can be tuned by the deformation of the cylindrical holes in the outer wall, the so called tuners. For the SW cell, there are four tuners separated by 901, with the same diameter of 6 mm. For the TW cells, each regular cell has four tuners separated by 901, and each of the two coupler cells has two tuners (space constrained by the waveguides) separated by 1801. The TW cells' tuning holes have the same diameter of 8 mm. All the tuning holes can only be pressed inwards the cavity gently by hammering a copper rod with a spherical head, and the deformations can hardly be recovered. It means that we can only increase the structure's frequency during the tuning process. Considering that both manufacturing error and the succeeding brazing process can result in fluctuation of the geometrical dimension which determines the resonant frequency of a cavity, the buncher was manufactured at a frequency several MHz lower than the future operating frequency 2.998 GHz on the basis of RF simulation. Referring to the tuning strategy of a traveling wave structure, the most used method is derived from a non-resonant perturbation theory of Steele [10] and a linear model of Khabiboulline et al. [11,12]. They are used for the overall bead-pull measurement of the complex electric field including its amplitude and phase, and the derivation of each cell's reflection coefficient, i.e. the so called local reflection coefficient, respectively. Such a method has been complemented during its applications to the tuning of 12 GHz Xband traveling wave accelerator of CLIC at CERN [13], 5.712 GHz Cband prototype for SPARC photo-injector energy upgrade [14], and 5.712 GHz cavity for Shanghai soft X-ray free electron laser test facility [15], etc. So far, the algorithm is feasible for tuning not only the regular cell, but also the input and output couplers of a traveling wave accelerator structure. However, in our case there are still several specific aspects which have not been studied or reported before: 1) Firstly, for the interest of vacuum condition, the two bottom waveguide ports will be connected with vacuum pumps. Therefore, shortcut plates need to be inserted into the waveguide where the field is such weak that it is terminated without obvious RF reflection. Meanwhile, five stub tuners are mounted on the output waveguide wall in succession to avoid RF reflection from the loaded output port. All the positions of the shortcut plates and stub tuners need to be optimized. Reflection from any port will cause standing wave component, and thus make the tuning complicated and even lead to a wrong tuning direction.

Please cite this article as: Y.C. Nie, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.05.043i

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Input port

Tuning holes

Output port

n-1

Bottom waveguide port #1 for vacuum SW cell

Cooling water pipes

3

Bottom waveguide port #2 for vacuum

n

n+1

An-1

An

An+1

Bn-1

Bn

Bn+1

TW cells

Fig. 2. Forward and backward waves traveling through three adjacent cells in a traveling wave structure.

Fig. 1. Design of the 2.998 GHz hybrid buncher structure.

2) Secondly, for the hybrid buncher structure, field strength in the SW cell should be paid special attention to, since it must be strong enough to ensure a good capturing capability. Concerning with the interaction between the SW section and the TW section, proper tuning procedure must be arranged carefully. 3) Finally, we are interested in having a detailed study on the relationship between the field distribution and the local reflection coefficient. For example, to check if a lower imaginary part of the local reflection coefficient corresponds to a lower electric field in a certain cell, and if so, it will provide us a direct concept of how to tune the related cells. Such a comparison has not been reported before. In the following sections, we will present the tuning process and result analysis of the 2.998 GHz hybrid buncher, including tuning principle (Section 2), CST Microwave Studio (MWS) [16] simulation (Section 3), bead-pull measurement and tuning result (Section 4), tuning result evaluation in the viewpoint of beam dynamics behavior (Section 5), and summary (Section 6).

2. Tuning Principle

Variations of the field amplitude and phase with longitudinal length can be obtained as the perturbing object moving through the structure along the axis. Required tuning for each TW cell can be represented in terms of local reflection coefficient, which can be derived via Khabiboulline's linear model. In all the cells' centers, the field can be considered as a superposition of forward and backward waves, provided that the cavity is lossless. For a regular TW cell, its two opposite wave components and hence its local reflection can be calculated by taking into account the two adjacent cells before and after it, under proper approximation. For output coupler, its reflection can be reduced by tuning of the coupler cell itself and its adjacent cell. Usually, the input coupler is tuned at the end, for the purpose of minimizing the global reflection. In principle, for a TW cell, if the imaginary part of its local reflection coefficient is negative, it means its frequency is lower than the working frequency (or the average frequency of the structure) and correspondingly it has a lower field than average. As a result, its tuners should be pressed inwards to decrease the cell's volume and thus increase its frequency. In this way, the cell's field will be enhanced relatively and the field unflatness will be reduced. During this process, the integral frequency of the structure is upshifted. In detail, as illustrated by Fig. 2, for the TW section with N cells, the fields in the center of (n  1)-th, n-th, (n þ1)-th cells are treated as the superposition of two waves In  1 ðφn  1 Þ ¼ An  1 þ Bn  1 ; In ðφn Þ ¼ An þ Bn ; In þ 1 ðφn þ 1 Þ ¼ An þ 1 þ Bn þ 1

ð2Þ

To obtain both the amplitude and phase of the electric field, a non-resonant bead-pull measurement needs to be performed. On the axis of our hybrid buncher, the magnetic field is zero. According to Steele's non-resonant perturbation theory, when a perturbing object fulfills certain properties such as (a) if it is placed in a sinusoidally varying electric field, it sets up an electric dipole moment, but no magnetic dipole moment, and (b) it has a rotational symmetry about the axis, symmetry about a plane normal to the axis, and has an electric polarizability that is scalar in the directions of the axis and normal to it, the relationship between the reflection coefficient and the electric field can be expressed by the following equation at a given frequency ω¼ 2πf:

where φn  1, φn, and φn þ 1 are the phases of the field, and An  1, An, An þ 1 (Bn  1, Bn, Bn þ 1) are the forward (backward) waves in the (n  1)-th cell, n-th cell, (n þ 1)-th cell, respectively. As an approximation, for n ¼ 2…N  1, the cell is considered to be a symmetric two-port network, with a small reflection coefficient. So we have Sn11 ¼Sn22, Sn12 ¼Sn21 E1. Therefore the scattering matrix of the n-th cell can be simplified as " # Sn11 e  jφn Sn ¼ : ð3Þ n e  jφn S11

2P i ΔS11 ¼ 2P i ðS11p  S11a Þ ¼  jωkE2a

"

ð1Þ

where Pi is the input power, S11p is the reflection coefficient in the presence of a perturbing object, S11a is the reflection coefficient in the absence of the perturbing object, k is a constant depending on the electric property and the geometry of the perturbing object, and Ea is the electric field at the perturbed position. It means that the field amplitude is proportional to the square root of the amplitude of ΔS11, and its phase is half to the phase of ΔS11.

Hence, for three adjacent cells, we have Bn An þ 1

#

" ¼

Sn11 e  jφn n e  jφn S11

#"

An Bn þ 1

# " ;

Bn  1 An

#

" ¼

 jφ Sn11 1 e n  1  jφn  1 Sn  1 e 11

#"

An  1 Bn

#

ð4Þ where φn ¼|φn þ 1  φn|, φn  1 ¼ |φn  φn  1|, which are phase advances between (n þ1)-th and n-th cells, n-th and (n  1)-th cells, respectively. The phase advances φn and φn  1 are close to the nominal phase advance of the structure φ0 ¼ 2π/3, and their

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deviations, namely the phase shifts depend on the detuning of the related cells. Solving Eq. (4) yields ( ( Bn  1 ¼ Sn11 1 An  1 þ e  jφn  1 Bn Bn ¼ Sn11 An þ e  jφn Bn þ 1 ; : ð5Þ n  jφn An þ 1 ¼ e An þS11 Bn þ 1 An ¼ e  jφn  1 An  1 þ Sn11 1 Bn In order to obtain Sn11 and Sn11 1, as the first iteration we assume that Sn11 ESn11 1 E0, thus from Eq. (5), we have ( ( Bn ¼ e  jφn Bn þ 1 Bn  1 ¼ e  jφn  1 Bn ; : ð6Þ  jφn An þ 1 ¼ e An An ¼ e  jφn  1 An  1 Combining Eq. (6) with Eq. (2) leads to 8  jφn  1 > An ¼ In 2j1 sinIn eφ > > n1 > < jφ n  1  In e n  1 Bn ¼ I 2j sin φn  1 : > > > I n  I n þ 1 ejφn >B : ¼ nþ1  2j sin φ

ð7Þ

n

Substituting Eq. (7) into the first equation on the left-hand side of Eq. (5), the local reflection coefficient Sn11 of the n-th cell can be given by Sn11 ¼

Bn  Bn þ 1 e  jφn : An

ð8Þ

For our hybrid buncher structure, wall deformation of the SW cell or a TW cell will influence the overall field distribution pattern, due to their interaction. With respect to that the SW cell should have a sufficiently strong field to capture incoming electrons, it should be tuned with higher priority. A compromise needs to be considered between the field strength of the SW cell and the remaining frequency margin for the following TW cells' tuning. Combining all the above concerns, our tuning procedure is concluded as follows: 1. Establish all the positions of shortcut plates and stub tuners for minimum reflection from bottom waveguide ports and output port; 2. Tune the SW cell to enhance its field strength in comparison to the TW section; 3. Tune the regular TW cells from output side to input side; 4. Tune the output coupler and input coupler to make field flat and reflection small; 5. Check and assure the increment in frequency during steps 2–4 is around 500 kHz; 6. Repeat steps 2–5 until the structure's frequency reaches the target frequency calculated from Eq. (10), where the global reflection is small enough and the corresponding field's flatness is satisfying.

As a simplification, it is usually assumed that all the phase advances equals to the nominal phase advance φ0 φn  φn  1  φ

ð9Þ

For better distinguishing, the local reflection coefficient calculated using Eq. (9) is denoted by Sn(0) 11 . Comparison will be made between Sn11 and Sn(0) 11 later. Tuning of a structure aims to make its frequency be exactly the working frequency f0, its regular TW cell's phase advance be 2π/3, and at the same time its field on axis as flat as possible. Take into account the differences in air temperature, pressure, and humidity between laboratory and operating condition, the final tuning frequency ft, i.e. target frequency in laboratory can be calculated by the recently summarized empirical formulas: ft ¼

f0 ½1 þ 1:7  10  5 ðT str  40Þ

ε ¼ 1 þ 10  6

1 pffiffiffi ε

  158:3P air 0:75P 0 H air 10160 þ  0:294 T str þ 273 T str þ273 T str þ 273

ð10Þ



P 0 ¼ 2:8868ð1:098 þ

T air 8:02 Þ 100

ð0 rT air r 30 1CÞ

ð11Þ

ð12Þ

where Tair is the air temperature in 1C, Pair is the air pressure in mbar, Hair is the air humidity in %, Tstr is the temperature of the structure in 1C, ε and P0 are the relative dielectric constant and pressure, respectively, f0 is 2.998 GHz in vacuum when Tstr ¼ 40 1C. Take the air temperature into account, Eqs. (10)–(12) predict more precise results compared to the previous formulas in Refs. [12,14]. Under a typical condition where Tair ¼ 23.0 1C, Pair ¼ 1016.9 mbar, Hair ¼39.6, Tstr ¼40.4 1C, ft was calculated to be 2997.1 MHz by Eqs. (10)–(12). For the interest of comparison, under the same condition, ft would be 2996.9 MHz if equations in Refs. [12,14] were used. Before the tuning started, all the shortcut plates inserted in the bottom waveguides and the stub tuners for loaded output port matching should be optimized, in order to overcome the problem of reflection and hence mitigate the standing wave component. The ideal positions would lead to a relatively flat field distribution without obvious standing wave pattern, and low S11 parameter at the structure's manufacturing frequency.

3. MWS Simulation As for the 3D MWS simulations, Fig. 3(a) is a full-size model, and Fig. 4(a) is a simplified model. For the full-size model, two planes (X–Z, Y–Z) were used for symmetrical boundary setting, which meant that the two bottom waveguides shortcut plates were not included. The simulated 3D electric field at 2998 MHz is shown in Fig. 3(b), and the amplitude and phase of the longitudinal field Ez varying along with axis are plotted in Fig. 3(c). From Fig. 3, it can be seen that the hybrid buncher works at 2π/3 mode with the SW cell coupled in π mode. As a result, we can see a 1801 phase jump between the SW section and the following TW section, and each three TW cells integrate one RF period. Due to the reflection from the bottom waveguide ports, the field involves serious standing wave component, with an unflatness of 725%. The first three TW cells' phase advances are 1001, 1451, and 1071, respectively, and the following TW section undergoes such a low– high–low phase-advance (relative to the nominal value 1201) pattern periodically. In order to provide a reference position of the shortcut plates for experiment, a simplified simulation model was studied. It included the SW cell and four TW cells, one input port and one output port, and two bottom waveguides with a pair of shortcut plates inside each. Only four TW cells were included concerning with time consumption, since in this model only Y–Z plane could be treated as symmetrical boundary plane, and including more regular TW cells would not have apparent impact on the integral frequency and field distribution pattern. To save simulation time, the five stub tuners on the wall of the output waveguide were not included by setting the corresponding port as an ideal “waveguide port”. The optimized results are shown in Fig. 4(b). As it can be seen, the reflection now almost disappears, making the field unflatness as low as 74%. The phase advances between the four TW cells are 1131, 1201, and 1271, respectively. The residual field unflatness attributes to the simulation error and the original RF structure. Of interest is that the optimal position occurs periodically, e.g., ideal distances between the inserted plates and the buncher axis can be 72 mm, 139 mm, 206 mm, etc., separated by 67 mm, which is around 2/3 RF wavelength

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Output port

Input port TW cells SW cell

Bottom waveguide port#2

1.4

480

Amplitude 1.2

360 1.0 300 0.8

240 180

0.6

120 0.4

60

145

0

0.2

360-100 180

-60

0.0

Phase of Electric field φ (degree)

420

107

-120

Phase

-0.2 0

50

100

150

200

250

300

350

400

450

-180

500

Normalized amplitude of electric field Ez

1.4

480

1.2

420

1.0

360

Phase of Electric field φ (degree)

Bottom waveguide port#1

Normalized amplitude of electric field Ez

300

0.8

240 0.6

180

0.4

120

0.2

60 0

0.0 -60 -0.2

-120 -180

-0.4 0

50

100

150

200

Structure length along axis (mm) Fig. 4. MWS simulation results for a simplified hybrid buncher model: (a) the simplified model (right) derived from the full-size model (left) to save simulation time, and (b) the simulated longitudinal field amplitude and phase distribution.

Structure length along axis (mm) Fig. 3. MWS simulation results for a full-size hybrid buncher model: (a) the fullsize model, (b) the simulated 3D electric field distribution, and (c) the simulated longitudinal field amplitude and phase distribution.

owing to the operating electromagnetic mode. In the viewpoint of mechanical design, 139 mm is the best choice. The MWS simulated field distribution is in accordance with that of SUPERFISH in Ref. [4]. The overall field is relatively flat, and the ratio between the maximum field amplitudes in the SW cell and the first TW cell RE ¼Ez,max(SW)/Ez,max(TW) is approximately equal to 1. As expected, simulations show that the field ratio RE is very sensitive to the dimensions of the coupling iris. For instance, the strong dependency of it on the iris's radius is characterized in Fig. 5 over the range 11.95–13.15 mm. It can be seen that RE increases from 0.6 to 1.6 with an increasing radius from 11.95 mm to 13.15 mm. It implies that if the radius increases (decreases) 0.1 mm, the ratio will increase (decrease) nearly 10%, because the coupling between the two sections is strengthened (weakened). In addition, by comparing the simulation results for three different iris radius values (12.35 mm, 12.65 mm, and 12.95 mm) plotted in Fig. 4(b), it can be concluded that the field distribution in the TW section hardly changes with increasing (decreasing) coupling iris's radius and RE, and the four phase advances between the five adjacent cells are almost unaffected, although the absolute phases are different from each other. In particular, the phase jump in between the two sections is invariably 1801.

4. Tuning Procedure During the non-resonant bead-pull measurement for the 2.998 GHz hybrid buncher in laboratory, the perturbing object used was a cylindrical needle, with a diameter of 1 mm and length

Ez Ratio between the SW and TW sections

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

5

1.6

1.4

1.2

Design point (12.65mm, 1) 1.0

0.8

0.6 11.8

12.0

12.2

12.4

12.6

12.8

13.0

13.2

Radius of the coupler iris (mm) Fig. 5. Field ratio Ez,max(SW)/Ez,max(TW) as a function of the coupling iris's radius (design point is (12.65, 1)).

of 4 mm, fixed on a nylon string. Geometrical sizes of the perturbing object and string were chosen for the best signal to noise ratio after several times of comparison. Temperature of the structure was kept almost constant with the help of the so-called cooling water having a constant temperature of 40 1C. The measured data was acquired from a vector network analyzer through a computer code. In order to calculate the final tuning frequency, air temperature, pressure, and humidity were monitored regularly, as well as the structure's temperature, during the experiment. Shown in Fig. 6 is a typical field distribution before the final optimization of the shortcut plates in the bottom waveguides and the five stub tuners on the output waveguide wall. The field strength has been normalized to the mean peak value in the TW section. Influenced by the reflection waves and hence the standing

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6

1.2

1.0

Normalized Ez amplitude

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wave component, the measured field unflatness could not reflect the actual detuning of the structure itself. Great efforts have been made to optimize the shortcut plates and stub tuners, in order to get rid of the reflection. During the process, their positions were swept gradually, and several iterations were executed to find the best locations. In accordance with the simulations in Section 3, the ideal positions of the shortcut plates in the bottom waveguides occurred periodically, and the differences in them between experiment and simulation were around 5 mm. Finally, the field was measured after the above initialization. The results before any tuning are plotted in Figs. 7 and 8, for two frequencies of 2995.4 MHz (the manufactured intrinsic frequency) and 2997.1 MHz (target tuning frequency), respectively. Each figure includes four small plots. For instance, Fig. 7(a) shows the amplitude of Ez, and the imaginary part of the local reflection coefficient Imag.Sn11 and Imag.Sn(0) 11 , along with the on axis position, Fig. 7(b) shows wrapped and unwrapped phases of ΔS11, as well as unwrapped phase of Ez, Fig. 7(c) plots the perturbed S11 parameter in phase diagram, and Fig. 7(d) is the deviation of phase advances between adjacent cells relative to the nominal value 1201. From Figs. 7 and 8(a), it can be seen that the field unflatness is about 79% for the TW section and the field of the SW cell is 35% lower than the mean value of TW cells. The disagreement between measurement and simulation mainly attributes to the manufacturing, brazing and installation errors. Especially for the SW cell, its field strength is quite sensitive to the dimension of the coupling iris as illustrated in Section 3. It is worth noting that the calculated Imag.Sn11 covering the range exceed 70.05. It varies on the same trend as the field amplitude longitudinally, which gives us a direct idea about which cell should be tuned and in which direction. For example, if an Imag.Sn11 is below 0, the corresponding cell has a relatively smaller field than others that have positive Imag.Sn11. It should be tuned by pressing its tuning holes inside to increase its frequency and hence strengthen its field. As a consequence, both of the related negative and positive Imag.Sn11 will move to the direction of 0, and the field unflatness will be reduced accordingly. Differences between Imag.Sn11 and Imag.Sn(0) 11 can be seen, since the phase advances between adjacent cells are not necessarily to be 1201. What could be found is that almost all the Imag.Sn(0) for 11 2997.1 MHz cluster under 0 in Fig. 8(a), indicating that the cells should be tuned by increasing their frequency. It is in accordance with the structure status, since its frequency at the moment is around 2995.4 MHz, which is 1.7 MHz lower than 2997.1 MHz. The measurement gives the real and imaginary parts of ΔS11, thus its wrapped phase can be easily solved. Then the unwrapped

phase of ΔS11 can be exported by subtracting 3601 once there is a phase jump from  1801 to þ 1801. Specifically, a 3601 phase jump on the boundary of the SW section and the TW section should also be introduced. Evidence of such a phase jump can be found, for instance, in Fig. 7(b), where a disturbance occurs in between the X-axis range of 115–125 mm, owing to the finite size of the perturbing needle passing through the boundary. At last, the unwrapped phase of Ez is computed by taking half of ΔS11. In Figs. 7 and 8(c), by comparing the phase diagrams of S11p, i.e. the variations of Imag.(S11p) with Real.(S11p), it can be observed that the three segments in Fig. 7(c) are much more uniform than that in Fig. 8(c). This phenomenon provides a straightforward criterion to identify the current intrinsic frequency of the structure. It is in effect the symbol based on which we figured out that the structure's manufacturing frequency was 2995.4 MHz (in Fig. 7 (c)) before tuning. As it can be seen from Fig. 7(d), the deviations of all cells' phase advances relative to 1201 scatter around 0, the average value of which is  0.41. It means that the average phase advance at 2995.4 MHz is 119.61 that is close to the nominal phase advance 1201. Notice that the phase shifts now are not negligible due to the detuning, which distribute in the range of 751, with one exception of about  101, even though their average value is as small as  0.41. On the other hand, from Fig. 8(d), we can see that the deviations of the phase advances have a tendency to be over 0, with an average value of þ1.51, which means the average phase advances at 2997.1 MHz is 121.51. It can be easily understood in the way that a RF wave of 2997.1 MHz propagating along the structure possesses a relatively bigger phase advance per cell, since the frequency of the structure itself is lower (2995.4 MHz) at the moment. Associating with Figs. 7 and 8(c), this feature provides another approach to distinguish the structure's frequency. Following the procedure described in Section 2, tuning of the SW cell and all the TW cells have been accomplished after 4 times iterations. The field unflatness was reduced greatly, and at the same time the structure's frequency has been tuned to be 2997.1 MHz. Again, the results after tuning are plotted in Figs. 9 and 10 for the two frequencies 2995.4 MHz and 2997.1 MHz, respectively. From Figs. 9 and 10(a), it can be seen that the field flatness has been improved from 79% to 74% for TW cells and the field of the SW cell becomes 20% lower than the mean value of TW cells from 35%. The above results can hardly be improved further. On one hand, the SW cell and TW cells which have lower field (e.g., no. 7, 10, 13) have been already tuned to saturation, since their tuning holes have been pressed to the maximum deformation inwards. On the other hand, the structure's frequency has been upshifted to be the target frequency 2997.1 MHz. The residual detuning is acceptable compared to the initial state, which will be verified by ASTRA simulation in view of beam dynamics performance in the next section. Once again, the calculated Imag.Sn11 has the same varying trends as the field. However the quantity has been reduced substantially, from the range  0.05 to þ0.05 to the range  0.02 to þ0.015, except one þ0.05 for the last regular cell. Difference between Imag.Sn11 and Imag.Sn(0) 11 is no longer as much as before, since the phase advances have been improved. In contrast with Fig. 8(a), it can be found that the Imag.Sn11 (0) is inversed, concentrating above 0, for 2995.4 MHz in Fig. 9(a), since the structure's frequency has been tuned to be higher than 2995.4 MHz now. Comparing Figs. 9 and 7(c), it is evident that the three segments become quite loose for 2995.4 MHz. Meanwhile, the segments in Fig. 10(c) for 2997.1 MHz are much better overlapped than those in Fig. 8 and 9(c), in accordance with the increment in the structure's frequency. Furthermore, Fig. 9(c) looks more regular than Fig. 8(c), as a result of tuning. In addition, from Fig. 10(d), it can be seen that most phase advance shifts relative to 1201 reside in the range of about 7 21

Please cite this article as: Y.C. Nie, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.05.043i

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Fig. 7. Bead-pull measurement results before tuning at 2995.4 MHz: (a) field amplitude and imaginary part of local reflection coefficient; (b) phases of ΔS11 and field; (c) perturbed S11 parameter; (d) phase-advance deviation per cell (average value is  0.41, i.e. the average phase advance is 119.61).

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Fig. 8. Bead-pull measurement results before tuning at 2997.1 MHz: (a) field amplitude and imaginary part of local reflection coefficient; (b) phases of ΔS11 and field; (c) perturbed S11 parameter; (d) phase-advance deviation per cell (average value is þ1.51, i.e. the average phase advance is 121.51).

(with three exceptions þ 7.51, þ41, and  51), centering at 0. The average phase shift is  0.21, which means the average phase advance has been downshifted from 121.51 (see Fig. 8(d)) to

119.81 for 2997.1 MHz. As a comparison, from Fig. 9(d), we can see that the phase advance shifts have a tendency to be under 0, with an average value of  2.51, which implies the average

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Fig. 9. Bead-pull measurement results after tuning at 2995.4 MHz: (a) field amplitude and imaginary part of local reflection coefficient; (b) phases of ΔS11 and field; (c) perturbed S11 parameter; (d) phase-advance deviation per cell (average value is  2.51, i.e. the average phase advance is 117.51).

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phase advance at 2995.4 MHz has been downshifted from 119.61 (see Fig. 7(d)) to 117.51, since the frequency of the structure itself is no longer 2995.4 MHz, but 2997.1 MHz.

As for the global reflection coefficients measured at the input port, before tuning they were  24 dB and  17 dB at 2995.4 MHz and 2997.1 MHz, respectively. After tuning, they have been

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improved to be 34 dB and  38 dB, respectively, as shown in Fig. 11.

5. Tuning results evaluation In this section, the above tuning results will be evaluated by ASTRA simulations in the viewpoint of beam dynamics. For this purpose, end-to-end beam transport simulations from the cathode to LINAC II have been performed. The emission current at the cathode is supposed to be 6 A, and the pulse length from the gun is 2 ns with the energy of 100 keV (βE0.54). The 2.998 GHz prebuncher introduces a velocity modulation to the electron pulse from the gun and hence divides the 2 ns pulse into 6 microbunches with a spacing around 50 mm (one βλ, where λ is the wavelength of the 2.998 GHz RF wave, 100 mm). After drifting 150 mm, the pre-bunched bunches enter the hybrid buncher. They are hence accelerated by the SW section and further bunched and accelerated by the following TW section. The wave phase of the hybrid buncher has been optimized to make the bunch length shortest. Here, the wave phase refers to the phase at the time when the electrons start to be emitted at the cathode, denoted by Φ0. In the case of the ideal (flat) field distribution, Fig. 12 shows variations of the momentum gain rate dPz/dz and relativistic velocity β¼ v/c along with the longitudinal position for the synchronous electron in the center of one bunch, from the entrance of the pre-buncher to the exit of the hybrid buncher. It can be seen that the synchronous electron has been neither accelerated nor decelerated after the pre-buncher. In contrast, in the hybrid buncher, it is accelerated rapidly by the SW cell on the crest from β¼ 0.54 to 0.75, and to 0.995 at the end of the TW section. Correspondingly, the evolution of the momentum gain in the TW section implies that the bunch undergoes a dephasing process while being both accelerated and bunched over the first several cells, and then becomes approaching the crest of the wave mainly for accelerating. Such a combination is ideal to produce well-bunched relativistic electron bunches for the downstream LINAC II. For simplification, the field unflatness is represented by using RE ¼0.8, ignoring the field unflatness within the TW section and assuming the phase advances are all nominal. Shown in Fig. 13 are comparisons of the rms bunch length sz, mean momentum Pz, bunch charge Q and energy spread ΔE/E versus wave phase Φ0 between the flat-field case RE ¼1 and unflat-field case RE ¼0.8. In the two cases, the optimal wave phases that give the shortest

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Y.C. Nie et al. / Nuclear Instruments and Methods in Physics Research A ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Fig. 12. Momentum gain rate and velocity of the synchronous electron versus longitudinal position, from the entrance of the pre-buncher to the exit of the hybrid buncher.

bunch are almost the same, which are around  421. In the case of RE ¼0.8, the dephasing process mentioned above becomes faster than that in the case of RE ¼1 due to the lower electron velocity after the SW cell. As listed in Table 2, the unflat field degrades the bunch length and energy spread by about 6%, whereas the momentum and bunch charge are only slightly influenced. It can hence be concluded that the residual unflatness after tuning of the hybrid buncher is acceptable.

6. Summary We have presented the tuning of the 2.998 GHz hybrid buncher, constructed for the new injection system of DESY LINAC II. Combining the existing tuning method of a traveling wave structure with our special considerations for the SW section, a tuning procedure has been established and followed. In particular, during the whole tuning process, the intrinsic frequency of the structure and the target frequency calculated by an empirical formula were monitored simultaneously, for the convenience of comparison and avoiding over-tuning. It has been demonstrated that the imaginary part of the local reflection coefficient Imag.Sn11 always varied in accordance with the field amplitude, according to which the structure was tuned. Even though Imag.Sn(0) did not 11 necessarily fit with the field distribution completely, it could reflect the distance between the structure's frequency and the target frequency. Eventually the hybrid buncher was successfully tuned. For the TW section, the field flatness has been improved to be better than 74% from 79%. For the SW cell, its field has been enhanced apparently, which was 35% and 20% lower than the mean field of the TW section before and after tuning, respectively. Meanwhile, the phase advances have been improved gradually. For 2997.1 MHz, the average phase advance changed from 121.51 to 119.81, and correspondingly the phase shift was improved from the range 751 to 7 21 with very few exceptions. The Imag.Sn11 has been reduced dramatically, from 0.05 to þ0.05 to  0.02 to þ0.015. Meanwhile, the global reflection coefficient decreased more than 20 dB detected at the input port after the tuning. The residual detuning of the structure is still visible but tolerable. This has been verified by ASTRA simulation in the viewpoint of beam dynamics performance. An even better field distribution would depend on: (a) higher machining precise, especially for the coupling iris between the SW and TW sections, and (b) more complicated tuners, for example, the tuning holes can be modified for more deformation at stronger field region and even for both directions in pushing and pulling. However, both of

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Y.C. Nie et al. / Nuclear Instruments and Methods in Physics Research A ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Fig. 13. Comparisons of rms bunch length and mean momentum (left), bunch charge and energy spread (right) versus wave phase between the flat-field case and unflatfield case.

Table 2 Beam dynamics comparisons between the flat-field and unflat-field cases. Cases

Parameters rms Bunch length Momentum Pz sz (mm) (MeV/c)

2.35 RE ¼ 1 RE ¼ 0.8 2.52

5.32 5.35

Bunch charge rms Energy Q (nC) spread ΔE/E (%) 1.63 1.61

2.82 2.99

the two ways lead to more construction cost, therefore a tradeoff should be considered. Acknowledgments The authors acknowledge useful discussions with Dr. K. Flö ttmann about the ASTRA simulation. Many thanks to the engineering staffs in MIN group for their supports during the experiment. The work is funded through the PETRA III Project at DESY. References [1] R. Brinkmann, G. Materlik, J. Rossbach, A. Wagner (Eds.), Conceptual design of a 500 GeV e þ /e  linear collider with integrated X-ray laser facility, in: Proceedings of DESY 97-48, ECFA 97-182, 1997. [2] R. Assmann, SINBAD. LAOLA Collaboration Meeting, Wismar, Germany, 2013.

[3] M. Hüning, M. Schmitz, Recent changes to the e þ /e  injector (LINAC II) at DESY, in: Proceedings of LINAC2008, Victoria, BC, Canada, 2008. [4] M. Hüning, C. Liebig, M. Schmitz, An electron linac injector with a hybrid buncher structure, in: Proceedings of LINAC2010, Tsukuba, Japan, 2010. [5] C. Liebig, M. Hüning, M. Schmitz., A new injection system for an electron/ positron LINAC, in: Proceedings of IPAC2012, New Orleans, Louisiana, USA, 2012. [6] ASTRA code, 〈http://www.desy.de/  mpyflo/Astra_for_WindowsPC〉. [7] S.V. Kutsaev, N.P. Sobenin, A.Yu Smirnov, et al., Design of hybrid electron linac with standing wave buncher and traveling wave structure, Nucl. Instrum. Methods Phys. Res. A 636 (2011) 13–30. [8] B. Spataro, A. Valloni, D. Alesini, et al., RF properties of a X-band hybrid photoinjector, Nucl. Instrum. Methods in Phys. Res. A 657 (2011) 99–106. [9] J.B. Rosenzweig, A. Valloni, D. Alesini, et al., Design and applications of an Xband hybrid photoinjector, Nucl. Instrum. Methods Phys. Res. A 657 (2011) 107–113. [10] C. Steele, A nonresonant perturbation theory, IEEE Trans. Microw. Theory Techn. MIT-14 (2) (1966) 70–74. [11] T. Khabiboulline, M. Dohlus, and N. Holtkamp, Tuning of a 50-cell constant gradient S-band travelling wave accelerating structure by using a nonresonant perturbation method, Technical report, DESY M-95-02, 1995. [12] T. Khabiboulline, V. Puntus, M. Dohlus, et al., A new tuning method for traveling wave structures, in: Proceedings of PAC1995. [13] J. Shi, A. Grudiev, W. Wuensch, Tuning of X-band traveling-wave accelerating structures, Nucl. Instrum. Methods Phys. Res. A 704 (2013) 14–18. [14] D. Alesini, A. Citterio, G. Campogiani, et al., Tuning procedure for traveling wave structures and its application to the C-Band cavities for SPARC photo injector energy upgrade, J. Instrum. 8 (2013) 10010, http://dx.doi.org/10.1088/ 1748-0221/8/10/P10010. [15] W.C. Fang, D.C. Tong, Q. Gu, Z.T. Zhao, Design and experimental study of a Cband traveling-wave accelerating structure, Chin. Sci. Bull. 56 (2011) 18–23. [16] CST MWS software, 〈https://www.cst.com〉.

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