Design and Optimization of a Broadband Stripline Kicker for Low Beam Emittance Ring Accelerators

Abstract

The performance and beam quality of the new fourth-generation synchrotron light source with ultra-low emittance are highly susceptible to coupled-bunch instabilities. These instabilities arise from the interaction between the bunched electron beam and the surrounding vacuum chamber installations. To mitigate these effects, the installation of a transverse bunch-by-bunch feedback system is planned. This system will comprise a button-type beam position monitor (BPM) for beam signal detection, a digital feedback controller, a broadband power amplifier, and a broadband stripline kicker as the primary actuator. One of the critical challenges lies in the development of the stripline kicker, which must be optimized for high shunt impedance and wide bandwidth while minimizing beam-coupling impedance. This work focuses on the comprehensive design of the stripline kicker intended for transverse (horizontal and vertical) bunch-by-bunch feedback in the Siam Photon Source II (SPS-II) storage ring. The stripline kicker design also incorporates features to enable its use for beam excitation in the SPS-II tune measurement system. The optimization process involves analytical approximations and detailed numerical electromagnetic field analysis of the stripline’s 3D geometry, focusing on impedance matching, field homogeneity, power transmission, and beam-coupling impedance. The details of engineering design are discussed to ensure that it meets the fabrication possibilities and stringent requirements of the SPS-II accelerator.

1. Introduction

Fourth-generation synchrotron light sources aim to produce high-brightness photon beams by employing ultra-low emittance electron storage rings. While these configurations significantly enhance spatial resolution and beam coherence, they also introduce new technical challenges, most notably in preserving beam stability. Among the most critical concerns are coupled-bunch instabilities, which arise from interactions between the stored electron beam and the surrounding electromagnetic environment, particularly the vacuum chamber and its associated structures.

As the SPS-II storage ring [1] is designed to operate with high beam current and stringent stability requirements, active suppression of such instabilities is essential. A widely adopted solution is the transverse bunch-by-bunch feedback system, which provides real-time correction by applying precise transverse kicks to individual electron bunches through a combination of fast beam position monitors (BPMs), digital feedback controllers, broadband power amplifiers, and transverse kickers. Stripline kickers are the most commonly used devices for this purpose due to their broad bandwidth, symmetric field structure, and mechanical simplicity. Their design strongly influences impedance characteristics, RF power handling, and overall feedback efficiency. Many accelerator facilities have developed stripline kickers tailored to their specific requirements with emphasis on impedance matching, shunt impedance, and power transmission efficiency [2,3,4,5,6].

This study presents the first design and optimization of a broadband stripline kicker developed for the SPS-II storage ring. The design approach combines analytical modeling with detailed three-dimensional electromagnetic simulations to optimize critical parameters: (i) characteristic impedance (~50 Ω) matching to ensure broadband power transfer and minimize the reflections of the applied RF power, and (ii) smooth electrode and chamber tapering to suppress reflections and beam coupling impedance. Engineering design aspects, including vacuum compatibility, fabrication feasibility, and mechanical integration, are also addressed. The resulting design meets the demanding requirements of a low-emittance, high-repetition-rate storage ring and offers insights applicable to future broadband kicker development in next-generation light sources.

2. Two-Dimensional Geometry Optimization and Simulation

The stripline kicker consists of a pair of parallel electrodes enclosed within a conductive circular beam pipe. The characteristic impedance was set to Z₀ = 50 Ω, as this value provides a practical balance between efficient power transmission and manageable energy losses [7]. Furthermore, 50 Ω is widely adopted as an industry standard, ensuring compatibility with commercially available RF components such as cables, feedthroughs, and terminations.

Electromagnetically, the stripline kicker behaves as a pair of coupled transmission lines that support two fundamental excitation modes: odd mode and even mode [7]. In the odd mode, the electrodes are driven with equal voltages of opposite polarity, producing a transverse electromagnetic field that generates a net deflecting force on the beam. This is the intended operating condition for transverse bunch-by-bunch feedback. In contrast, the even mode arises when an unperturbed beam induces image currents flowing in the same direction on both electrodes, producing a longitudinal electric field that may contribute to beam loading and longitudinal instabilities when the feedback system is inactive. Ideally, both modes should be impedance matched to 50 Ω to minimize reflections and power losses. However, due to inherent asymmetries in the field distributions and boundary conditions, perfect 50 Ω matching cannot be achieved for both modes simultaneously.

In this work, the optimization was therefore focused on the odd mode, as it produces the transverse field required for bunch-by-bunch feedback. Matching the odd mode to 50 Ω ensures efficient power transfer, minimizes reflections, and maintains compatibility with standard RF components. The even mode, in contrast, is only excited by beam-induced image currents and generates a longitudinal field that can drive instabilities when the system is inactive. Since it is not externally driven, precise matching of the even mode is less critical; its impedance was instead kept close to 50 Ω to mitigate beam-induced effects rather than to define the kicker’s operational performance.

Stripline kickers commonly employ two electrode geometries: flat [3] and curved profiles [5,6]. Flat electrodes provide uniform field distribution in the transverse plane, whereas curved electrodes achieve improved impedance matching between odd and even modes. Since impedance matching is a critical parameter in stripline design for bunch-by-bunch feedback applications, SPS-II kickers adopt curved electrode profiles conforming to the inner contour of the circular beam pipe, as shown in Figure 1. Identical electrode geometry is used for both the horizontal (Figure 1a) and vertical (Figure 1b) kickers, with the two configurations differing by a 90° rotation.

Key geometric parameters, including the chamber radius $\left(R_g\right)$, electrode radius $\left(R\right)$, electrode span angle (${\alpha }_s$), and electrode gap angle (${\alpha }_g$) must be carefully optimized to achieve an odd-mode impedance of 50 Ω. The electrode radius was fixed and chosen based on a 1:10 linear taper from the elliptical storage ring vacuum chamber to the circular cross-section of the kicker. This taper minimizes impedance mismatch and helps preserve field uniformity across the transition region.

Two-dimensional electrostatic simulations were performed using Poisson Superfish [8] and the E-Static solver in CST Studio Suite [9] to optimize the transverse geometry. The Trust Region Framework (TRF) was applied to tune $R_s$, ${\alpha }_s,$ and ${\alpha }_g$ targeting an odd-mode impedance of 50 Ω ± 0.5 Ω, with the even-mode impedance relaxed to 50 Ω ± 10.0 Ω, while keeping R fixed. The optimized transverse geometric parameters are summarized in

Table 1. Optimized transverse geometric parameters obtained from Poisson Superfish and the CST E-Static solver.

Simulation	CST E-Static	Poisson Superfish
$\mathrm{Chamber}\mathrm{radius}({\mathrm{R}}_{\mathrm{s}}$)	34 mm	34 mm
$\mathrm{Electrode}\mathrm{angle}({\alpha }_s$)	105°	105°
$\mathrm{Electrode}\mathrm{angle}({\alpha }_g$)	14.75°	14.75°
Odd-mode impedance (Ω)	49.83	49.97
Even-mode impedance (Ω)	56.36	56.53

. The simulated electric field patterns for the odd and even modes are shown in Figure 2 (Poisson Superfish) and Figure 3 (CST E-Static solver). The results from both codes exhibit excellent agreement, with the calculated odd-mode impedances differing by less than 0.2 Ω for the same transverse geometry. The small discrepancy is attributed to differences in meshing and singularity treatment: Superfish employs a structured orthogonal grid, whereas CST uses tetrahedral and hexahedral elements with adaptive refinement. Peak fields at electrode edges are highly mesh-sensitive: coarse meshes underestimate E_max, while refinement strategies yield different peak values. Overall, Superfish proved efficient for rapid parameter scanning, whereas CST provided more detailed field visualization.

3. Three-Dimensional Geometry Design and Performance Optimization

The full stripline kicker consists of a vacuum chamber, a pair of electrode plates, and coaxial feedthroughs. The three-dimensional geometry of these components was carefully optimized using full electromagnetic simulations to maximize performance in terms of impedance matching, shunt impedance, and power transfer efficiency. For the SPS-II storage ring, the electron beam energy is 3 GeV, and the RF frequency is 500 MHz, corresponding to a bunch spacing of 2 ns (600 mm), equal to one full RF wavelength (λ). The stripline kicker is designed with an electrode length of 300 mm, enabling it to deliver the required transverse kick within 1 ns. This ensures that the excitation is confined to the targeted bunch without disturbing the adjacent bunches. The chosen length also enables energy transfer from the RF amplifier to the beam while maintaining a broad frequency response [10]. Before the full 3D optimization, a preliminary study was conducted to assess the kicker’s shunt impedance. This confirmed its transverse deflection efficiency and potential effects on beam dynamics.

3.1. Shunt Impedance Analysis

Transverse and longitudinal shunt impedances were evaluated using two approaches. The first involved an analytical model based on idealized transmission line theory, which provided quick estimates of frequency-dependent impedance. The second used detailed 3D electromagnetic simulations in CST Studio Suite, incorporating practical features such as tapered transitions and realistic termination boundaries.

In the analytical method, the transverse and longitudinal shunt impedances, $R_{\perp }$ and $R_{\parallel },$ were estimated by using Equations (1) and (2) [2], which are simplified expressions for odd- and even-mode excitations, respectively.

$$R_{\perp }{T}^2\left(\omega \right)=2Z_e\left({\displaystyle \frac{g_{\perp }c}{R}}\right){\displaystyle \frac{{sin}^2\left. [\frac{\omega \left(L-L_t\right)}{c}\right]}{{\omega }^2}}{\displaystyle \frac{{sin}^2\left(\frac{\omega L_t}{c}\right)}{\left(\frac{\omega L_t}{c}\right)}}$$

(1)

$$R_{\parallel }{T}^2\left(\omega \right)=2Z_o{g}_{\parallel }^2{sin}^2\left[{\displaystyle \frac{\omega \left(L-L_t\right)}{c}}\right]{\displaystyle \frac{{sin}^2\left(\frac{\omega L_t}{c}\right)}{\left(\frac{\omega L_t}{c}\right)}}$$

(2)

where $T$ is the transit time factor,$g_{\perp }={\displaystyle \frac{V\left(x,y\right)}{\left(\frac{x}{R}\right)}}=1.09$ and $g_{\parallel }=V\left(0,0\right)=0.66$ are the geometry factors from the odd and even mode, respectively, as defined in [11], $\omega$ is the angular frequency, $c$ is the speed of light in vacuum, $L$ is the length of electrodes, $L_t$ is the taper length of electrodes, $R$ is the distance from the beam axis to the electrodes, $g_{\perp }$ is the transverse geometric factors, $g_{\parallel }$ is the longitudinal geometric factors, $Z_e$ is the even mode impedances, and $Z_0$ is the odd mode impedances of the stripline.

In comparison, the longitudinal shunt impedance of the stripline kicker was calculated from the real part of the longitudinal wake impedance $\left(R_e{Z}_{\parallel }\right)$, obtained from CST wakefield simulations. The relationship between the longitudinal beam impedance $\left(Z_{\parallel }\right)$ and the longitudinal shunt impedance at low frequencies is given by [11]:

$$R_{\parallel }{T}^2\left(\omega \right)=4Re{Z}_{\parallel }\left(\omega \right)$$

(3)

Similarly, the transverse shunt impedance can be derived from the longitudinal impedance using the relation:

$$Z_{\perp }{T}^2\left(\omega \right)={\displaystyle \frac{Z_{\left|\right|}}{{kR}^2}}$$

(4)

or directly from the transverse wake impedance ($Z_{\perp }$) as:

$$R_{\perp }{T}^2\left(\omega \right)={\displaystyle \frac{4Re{Z}_{\perp }\left(\omega \right)}{k}}$$

(5)

where $k=\omega /c$ is the wave number.

In the analytical approach, the transverse geometric parameters and impedances optimized using 2D CST simulations (Table 1) were employed together with longitudinal parameters of L = 300 mm. and Lt = 30 mm. For the 3D simulations in CST, the geometry corresponded to Model 3 described in Section 3.2. Figure 4 compares the calculated transverse (a) and longitudinal (b) shunt impedances of the stripline kicker as functions of frequency, showing the results from the CST 3D simulations alongside the analytical predictions. Overall, the CST results exhibit good agreement with the analytical model near the design frequency and confirm a broad effective bandwidth, demonstrating the kicker’s suitability for broadband feedback operation. However, for the transverse shunt impedance, the CST results exhibit a rapid rise near zero frequency, in strong contrast to the analytical model. This discrepancy is mainly attributed to a large DC component in the transverse wake potential introduced by the excited port, which cannot be accurately represented in the CST simulation. For the longitudinal shunt impedance, noticeable differences appear particularly at higher frequencies, which are mainly attributed to differences in the longitudinal geometry representation between the simplified analytical model and the detailed 3D CST simulations.

In the analytical approach within the operational frequency range of the bunch-by-bunch feedback system (DC to 250 MHz) and for an input power of 500 W, the transverse shunt impedance decreases from approximately 41.9 kΩ at DC to 20.3 kΩ at 250 MHz. This gradual reduction indicates that the kicker provides strong transverse deflection at low frequencies while maintaining sufficient impedance in the feedback bandwidth. Based on 3 GeV beam energy, together with this impedance range, the beam deflection is estimated to be between 2.16 µrad and 1.50 µrad per turn, as calculated using Equation (7).

$$R_{\perp }{T}^2\left(\omega \right)={\displaystyle \frac{{⌊V_{\perp }⌋}^2}{2P_{in}}}$$

(6)

$${\Delta y}^{\prime }={\displaystyle \frac{1}{ec{B}_0\rho }}\int F_{\perp }ds={\displaystyle \frac{V_{\perp }}{c{B}_0\rho }}={\displaystyle \frac{1}{c{B}_0\rho }}\sqrt{2P_{in}{R}_{\perp }{T}^2}$$

(7)

where $V_{\perp }$ is the transverse beam voltage (transverse kick) and $P_{in}$ is the input power. By using the magnetic rigidity, B₀ρ = p/e.

3.2. Tapered Transition Region Analysis

The full 3D geometry design aims to reduce beam coupling impedance and improve impedance matching between the stripline electrodes and the coaxial feedthrough. This minimizes RF heating caused by power losses in the kicker structure by effectively reducing longitudinal and vertical discontinuities seen by the electron beam. The elliptical beam chamber, originally 40 mm wide and 16 mm high, is tapered into a circular stripline chamber using a 1:10 linear transition slope to ensure a smooth field transition.

At both ends of the stripline region (section A), the effects of different electrode and chamber geometries were carefully investigated. The central region (section B) maintains a fixed geometry defined by parameters obtained from 2D optimization (Table 1): the electrode span angle ${\alpha }_s$ = 105°, chamber radius $R_g$ = 34 mm, electrode radius $R=$14 mm, and electrode gap angle ${\alpha }_g$ = 14.75°. Three different transition designs were considered for section A:

• Model 1: A constant α_s without any taper, resulting in a sharp transition between regions.
• Model 2: A tapered electrode design, where α_s gradually increases to form a curved electrode profile that transitions smoothly into the fixed geometry of section B.
• Model 3: Similar to Model 2, but with the addition of a tapered vacuum chamber. In this model, the inner diameter at both ends of the stripline chamber is tapered, matching the reduced cross-section of the tapered electrode region and further enhancing impedance matching.

Three transition configurations of the stripline kicker were evaluated using full 3D electromagnetic simulations, as illustrated in Figure 5. Their impact was analyzed in terms of longitudinal wake impedance (Figure 6), S-parameter response (Figure 7), and time-domain reflectometry (TDR, Figure 8). Model 1, which employs no taper, exhibited the highest impedance and pronounced resonances across the frequency range. These effects arise from abrupt discontinuities at both electrode ends, which increase field distortion and enhance beam coupling impedance. The S-parameter results confirm this through strong reflections, while the TDR analysis reveals the largest reflection peaks. Model 2, with tapered electrodes, demonstrated clear improvement over Model 1. The smoother electrode transitions reduced field discontinuities, thereby lowering the wake impedance. However, the S-parameter and TDR responses indicated that electrode tapering alone was insufficient to achieve optimal matching, as residual reflections persisted at the chamber interfaces. Model 3, which incorporates tapering of both the electrodes and the vacuum chamber, delivered the most favorable performance. The additional chamber taper further smoothed the field distribution at the electrode–chamber junction. Since Models 2 and 3 share nearly identical gap widths and tapered electrode geometries, their longitudinal wake impedance responses are similar. However, the advantage of Model 3 becomes evident in the S-parameter results (Figure 7), which show improved impedance matching and consistently lower reflection levels, maintaining S11 < –20 dB below 1 GHz. The TDR analysis (Figure 8) further confirms this, revealing the smallest and most regular reflection profile.

Overall, these results establish Model 3 as the optimal transition design. By combining electrode and chamber tapering, it minimizes impedance discontinuities, reduces longitudinal beam coupling impedance, and achieves superior RF power matching, thereby providing the best overall electromagnetic performance.

An additional study was conducted to evaluate power reflection and transmission at the transition region between the coaxial feedthroughs and the stripline electrodes. Based on the results from the tapered transition design, the Model 3 geometry was selected for further analysis.

This simulation assumed an ideal 50 Ω vacuum feedthrough and focused on optimizing the transition between the feedthrough pin and the tapered electrode. We studied two key geometric parameters: the taper length $\left(L_t\right)$ and the radial gap height ($r_g$). These parameters were carefully adjusted to ensure smooth electromagnetic field transition, minimize signal reflections, and maximize power transfer efficiency. Figure 9 shows the simulated results of the longitudinal wake impedance and the S-parameter magnitude for varying taper lengths. As $L_t$ increases, the longitudinal wake impedance is reduced, especially at higher frequencies. The S-parameter results also show that longer $L_t$ values improve impedance matching (i.e., lower reflection), although the additional improvement becomes not practically significant for $L_t>$30 mm. According to Equation (1), increasing $L_t$ reduces the transverse shunt impedance, which directly lowers the kicker’s deflection efficiency. To balance these trade-offs, a taper length of $L_t=$30 mm was selected as the optimal compromise.

For the gap height $r_g$, the simulated results in Figure 10a show only a minimal effect on longitudinal impedance. Thus, the optimization was based primarily on the S-parameter results in Figure 10b. In the frequency range below 1 GHz, varying $r_g$ between 15.0 and 21.0 mm yields S11 < −20 dB. Three representative cases ($r_g$ = 17.5 mm, 18.5 mm, and 19.5 mm) are shown, with the best performance obtained at $r_g$ = 18.5 mm.

Table 2. Final key geometric parameters obtained from the 2D and 3D optimizations.

Parameter	Tapered Transition Region (Section A)	Central Region (Section B)
Electrode radius (R)	14 mm	14 mm
$\mathrm{Chamber}\mathrm{radius}(r_g,R_g$)	18.5 mm	34 mm
$\mathrm{Electrodes}\mathrm{span}\mathrm{angle}({\alpha }_s$)	30°	105°
$\mathrm{Electrode}\mathrm{gap}\mathrm{angle}({\alpha }_g$)	7°	14.75°
Electrode thickness	2 mm	2 mm
Electrode length	30 mm	240 mm

presents the final key geometric parameters obtained from the combined 2D and 3D optimization studies. With these parameters, the odd-mode impedance is 49.83 Ω, meeting the design requirement of 50 Ω ± 0.5 Ω, while the transverse shunt impedance reaches 20.3 kΩ at 250 MHz, exceeding the minimum requirement of 20 kΩ. This value is sufficient to provide a beam deflection angle of approximately 1.5 µrad per turn, fulfilling the functional specifications of the kicker. These optimized parameters will serve as the basis for the subsequent mechanical design of the stripline kicker.

4. Mechanical Design

The stripline kicker was mechanically designed as two independent units, one for the horizontal plane and one for the vertical plane, which were later assembled together to form the complete system, as shown in Figure 11a. The detailed component layout of a single kicker unit is illustrated in Figure 11b.

The tapered electrodes (1), including their transition sections, are 300 mm long and are mounted inside the stripline vacuum chamber (2), which has an inner diameter of 68 mm. At both ends, the feedthrough housing (3) is welded to the stripline chamber and connected to the tapered chamber section (4). UHV-compatible coaxial feedthroughs (5) are installed on the feedthrough housings and connected to the ends of the tapered electrodes to interface with the RF components. For high-power and high-frequency reliability under UHV conditions, commercial EIA 7/8” vacuum feedthroughs manufactured by Kyocera were selected. The complete kicker assembly is connected to the standard storage ring vacuum chamber via flanged interfaces, ensuring smooth mechanical integration and electromagnetic continuity.

The electrodes are fabricated from oxygen-free high-conductivity (OFHC) copper to minimize RF losses and provide excellent electrical performance. The stripline chamber is made of AISI 316LN stainless steel, selected for its UHV compatibility, mechanical robustness, and corrosion resistance. Both the chamber and the curved electrode profiles can be manufactured with high precision using wire-cut Electrical Discharge Machining (EDM), which allows complex geometries to be cut directly from solid copper or stainless-steel blocks. The machining tolerance is expected to be better than 50 µm. To achieve precise assembly, the following procedure is followed:

1.

The tapered electrodes are inserted into the stripline vacuum chamber and accurately positioned using a dedicated assembly jig.

2.

The feedthrough housings are welded to the stripline chamber using TIG welding.

3.

Flange-mounted feedthroughs are installed and fastened to the electrodes with screws.

4.

The assembly jig is removed, and the tapered chamber is welded to the feedthrough housing.

During the bunch-by-bunch feedback operation, the downstream feedthroughs deliver RF power from the drive amplifier to the kicker, while the upstream feedthroughs are terminated with matched 50 Ω resistive loads to ensure proper termination and minimize reflections.

5. Conclusions

A stripline kicker was designed for the transverse bunch-by-bunch feedback system of SPS-II. The 2D cross-sectional geometry was carefully optimized to achieve a 50 Ω characteristic impedance in both odd and even modes, verified through both analytical calculations and electrostatic simulations. The final 3D design incorporates tapered electrodes and vacuum chamber transitions, effectively reducing beam coupling impedance and minimizing power reflections. The simulation results confirm that the kicker provides sufficient transverse shunt impedance for effective beam deflection while maintaining low longitudinal impedance to avoid instabilities. These results demonstrate that the proposed kicker design meets the stringent requirements of a low-emittance, high-repetition-rate storage ring. Future work will focus on a prototype fabrication and RF bench testing to validate electromagnetic performance under operational conditions.