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All issues Volume 13 (2026) EPJ Appl. Metamat., 13 (2026) 1 Full HTML
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EPJ Appl. Metamat.
Volume 13, 2026
Article Number 1
Number of page(s) 8
DOI https://doi.org/10.1051/epjam/2025008
Published online 23 January 2026

© C. Wang et al., Published by EDP Sciences, 2026

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

Metamaterials are novel artificial subwavelength structures exhibiting novel electromagnetic properties that cannot be achieved or are difficult to achieve with natural materials. For example, negative refractive, reversed Cherenkov radiation, reversed Doppler effect, and anomalous radiation pressure [1]. The design concept can be analogized to natural materials, where artificial subwavelength unit cells replace the molecules and atoms found in natural materials. By altering the shape, size, and arrangement of these subwavelength unit cells, novel electromagnetic properties are achieved. This design concept is illustrated in Figure 1 [2,3].

In 1967, the left-handed material (LHM) was first proposed theoretically by Soviet physicist V. G. Veselago [1]. However, due to the inability to conduct experimental verification, it did not receive significant attention from the scientific community. It was not until the 1990s that J. B. Pendry et al. proposed theories for constructing negative effective permittivity and negative effective permeability using periodic metal wire arrays [4] and metal split-ring resonator (SRR) arrays [5], respectively. In 2000, Smith et al. creatively combined metal wires and rectangular SRRs based on Pendry's theory, realizing LHMs and verifying them through electromagnetic wave transmission experiments [6]. In 2001, Shelby et al. experimentally demonstrated negative refraction in LHMs at microwave frequencies [7]. In 2003, Seddon and Bearpark experimentally confirmed the reversed Doppler effect in LHMs [8]. In 2017, Duan et al. employed real charged particles to experimentally verify reversed Cherenkov radiation in LHMs for the first time [9].

Due to the novel electromagnetic properties of LHMs, their theory, experiments, and applied research have garnered widespread attention among scientists and engineers [10–20]. The concept of LHMs has gradually evolved into the broader field of metamaterials. Research has expanded from microwave electronics into optics, acoustics, mechanics, thermodynamics, and other domains, yielding far-reaching impacts [3,21].

The klystron is a microwave vacuum electron device characterized by high power, high efficiency, and long lifespan. As a core electronic component, it finds extensive application in accelerators, colliders, radar systems, medical equipment, and plasma heating systems [22]. Loading metamaterials into klystrons represents a significant development direction, enabling low-voltage operation or miniaturization of klystrons.

To address low-voltage operation requirements, A. Galdetskiy from Russia's Istok Corporation proposed a low-voltage, high-power multibeam klystron based on a metamaterial-inspired resonator, as shown in Figure 2. Simulation results demonstrated that a 37-beam metamaterial-inspired klystron achieved 30 MW output power in the S-band at a cathode operating voltage of only 85 kV [23]. Research on the miniaturization of the metamaterial-inspired klystrons has been primarily concentrated in Duan's group at the University of Electronic Science and Technology of China [3]. The following sections will systematically introduce the relevant research progress of this group in the field of metamaterial-inspired klystrons.

thumbnail Fig. 1

Schematic diagram of natural material and metamaterial [3].
thumbnail Fig. 2

Design model of a 37-beam S-band metamaterial-inspired cavity and the gap of a partial channel with a sleeve and a helix [23].

2 Physical mechanism and challenges of klystrons

Transition radiation refers to the electromagnetic radiation generated when charged particles traverse the discontinuous interface between two different media, as shown in Figure 3a [3]. In a broad sense, transition radiation is not limited to charged particles passing through the interface of two distinct media. It can also be based on the transition time effect [24], such as the perturbations generated by charged particles passing through a resonant cavity [25,26]. The standing wave at the transit gap of the resonant cavity is utilized to perturb the charged particles, thus realizing the energy exchange, which is a typical application of transition radiation in vacuum electron devices [27,28], as illustrated in Figure 3b. In these vacuum electron devices, the charged particles interact with the electromagnetic waves at the transit gap of the resonant cavity to generate a high-power coherent microwave output. Here, taking a klystron as an example, when the electron beam passes through the transit gap of the input cavity, which is subjected to the input high-frequency signal field, the velocity modulation is achieved. As the beam travels through the drift tube, the electron velocity differences gradually evolve into the density modulation, leading to the formation of electron bunches. When the preliminarily bunched beam enters the next resonant cavity, the bunched electrons produce coherent transition radiation. This means that a high-frequency field within the cavity is excited. This field, in turn, imposes additional velocity modulation on the electron beam, further enhancing the density modulation. Finally, in the output cavity, the fully bunched electron beam interacts strongly with the enhanced high-frequency field. It results in most electrons being decelerated and transferring their kinetic energy to the electromagnetic wave, which is extracted through the output coupler. This is the physical mechanism of klystrons.

In the microwave frequency band, klystrons are large and heavy, which restricts their application scenarios. Consequently, exploring high-performance, miniaturized klystrons has become an urgent priority. When the metamaterial unit cell—complementary electric split ring resonator (CeSRR)—is loaded into the cylindrical cavity, it alters the electromagnetic wave distribution inside the CeSRR-loaded cavity. As shown in Figure 3c, a radial electric field is formed along the slot lines of the CeSRR, while surface currents are distributed on the metal bridges and the inner and outer rings [29]. Such a distribution of the electric field and surface currents leads to an increase in the equivalent inductance and capacitance of the CeSRR-loaded cavity. Thus, the resonant frequency decreases. This fact means that the miniaturization of the metamaterial-inspired resonant cavity can be achieved. Therefore, the innovative combination of metamaterials with klystrons not only enables the physical exploration of coherent transition radiation but also achieves miniaturization and high efficiency of klystrons, holding significant scientific and engineering value [30].

thumbnail Fig. 3

Schematic diagram of (a) narrowly-defined transition radiation and (b) broadly-defined transition radiation in a klystron [3]. (c) Metamaterial unit cell, metamaterial-inspired resonant cavity, and electric field and surface currents distribution of CeSRR [29].

3 Novel metamaterial-inspired extended interaction klystron

Based on the circular all-metal double-bridge CeSRR unit cells [31], Duan's group constructed a metamaterial-inspired extended interaction resonant cavity (MEIRC), as shown in Figure 4a. Its transverse dimension is approximately λ/4 (where λ is the wavelength in free space), whereas conventional extended interaction resonant cavities typically measure around λ/2, demonstrating significant miniaturization [32]. Based on this MEIRC, further studies are conducted on 2-gap MEIRC and 3-gap MEIRC with rod couplers to validate their miniaturization effects. The design model and assembled prototype of MEIRCs are shown in Figures 4b and 4c, respectively. Test results (resonant frequency, external quality factor) agree well with simulation results, demonstrating the feasibility of MEIRC's miniaturization.

Based on MEIRCs, a 3-cavity metamaterial-inspired extended interaction klystron (EIK) with coaxial input and waveguide output couplers is proposed [32,33], as shown in Figure 4d. The input signal is coupled into the 2-gap input cavity via the coaxial coupler, generating a high-frequency field with specific modes within the cavity. This high-frequency field modulates the velocity of the electron beam at the gaps, gradually forming a bunching core within the drift tube to achieve density modulation. Ultimately, in the 3-gap output cavity, the kinetic energy of the majority of electrons is converted into electromagnetic wave energy and coupled out.

Using computer simulation technology (CST), beam-wave interaction simulations are performed for the 3-cavity metamaterial-inspired EIK. Simulation results indicate that with the beam voltage of 30 kV, beam current of 3 A, axial magnetic flux density of 0.1 T, input signal frequency of 2.453 GHz, and input power of 1.1 W, the saturated output power reaches 56 kW, saturated electron efficiency is 62%, and saturated gain is 47 dB. More importantly, the diameter of the metamaterial-inspired interaction structure is approximately half that of a conventional EIK. As a power amplifier, metamaterial-inspired EIK features miniaturization and high efficiency, offering potential applications in future accelerators and microwave heating systems.

thumbnail Fig. 4

(a) Design model of 3-gap MEIRC. (b) Design model of the 2-gap MEIRC (left) and 3-gap MEIRC (right) with rod couplers. (c) Prototype of MEIRCs. (d) Schematic diagram of the 3-cavity metamaterial-inspired EIK [32].

4 Brand-new microwave metamaterial-inspired klystron

4.1 S-band metamaterial-inspired klystron

To explore the physical mechanism of coherent transition radiation in metamaterials through experiments, a compact S-band MW-level metamaterial-inspired klystron is proposed [34]. Each resonant cavity is loaded with two circular all-metal double-bridge CeSRRs, as shown in Figure 5a. The interaction structure of the metamaterial-inspired klystron, depicted in Figure 5b, exhibits miniaturization, with a volume approximately 0.44 times that of conventional interaction structures [35].

Based on the metamaterial-inspired interaction structure, the first S-band metamaterial-inspired klystron prototype was assembled after machining all components, as shown in Figure 5c. During the test, an electron beam of 120 kV/80 A was employed. At 2.852 GHz, the maximum observed pulse output power reached 5.51 MW, with a gain of 55.6 dB and an electron efficiency of 57.4%. This represents an improvement of nearly 10% in electron efficiency compared to conventional klystrons of the same type [36]. This compact metamaterial-inspired klystron holds potential application value in fields such as proton therapy facilities, tokamak systems, and accelerators.

thumbnail Fig. 5

(a) Design model of CeSRR and metamaterial-inspired resonant cavity (idler cavity). (b) Schematic diagram of metamaterial-inspired interaction structure. (c) Prototype of S-band metamaterial-inspired klystron [34].

4.2 714 MHz metamaterial-inspired klystron

To further leverage the miniaturization advantages of metamaterials, the CeSRR is modified. Since the subwavelength characteristics of the CeSRR are closely related to its slot-line length, a single-bridge CeSRR with a longer slot-line length is constructed, as shown in Figure 6a. A metamaterial-inspired resonant cavity based on the single-bridge CeSRR is constructed as shown in Figure 6b. The inner radius of the single-bridge CeSRR is only about 0.15 λ. The cold-tested results of the metamaterial-inspired input cavity confirm the feasibility of miniaturizing the resonant (Fig. 6c) [37].

Based on the metamaterial-inspired resonant cavity with single-bridge CeSRRs, the metamaterial-inspired klystron is constructed, as shown in Figure 6d. The radius and length of the metamaterial-inspired interaction structure are 1/2 and 2/3 of the conventional counterparts, respectively [38]. A beam-wave interaction simulation is conducted. Under a beam voltage and current of 100 kV and 40 A, respectively, an input power of 50 W and a uniform axial magnetic flux density of 720 G, the output power reached 2.28 MW at 714 MHz, corresponding to an electron efficiency of 57% and a gain of 46.59 dB [37,39].

thumbnail Fig. 6

Design model of (a) single-bridge CeSRR and (b) metamaterial-inspired resonant cavity. (c) Prototype of the metamaterial-inspired input cavity and test platform. (d) Schematic diagram of 714 MHz metamaterial-inspired klystron [37].

4.3 324 MHz metamaterial-inspired klystron

To address the issues of large volume and heavy weight associated with the MW-level 324 MHz long-pulse klystron required for the China Spallation Neutron Source (CSNS) linac application, Duan's group researched a MW-level 324 MHz metamaterial-inspired klystron [40]. By loading double-bridge CeSRRs onto the drift tube on one side of the cavity, the cavity's inner diameter is reduced to approximately 0.3 λ. Simultaneously, the second harmonic bunching technology is employed to enhance electron efficiency. The metamaterial-inspired high-frequency structure is illustrated in Figure 7. Beam-wave interaction simulations indicate that under a beam voltage of 110 kV and current of 47.23 A, the metamaterial-inspired klystron generates an output power of 2.97 MW at 324 MHz, corresponding to an electron efficiency of 57.2% and a gain of 50.6 dB. Furthermore, vacuum breakdown and thermal analysis confirmed the reliability of applying miniaturization techniques to P-band MW-level klystrons.

Based on the 324 MHz metamaterial-inspired high-frequency structure, the first P-band metamaterial-inspired klystron has been developed. The overall volume and weight of the high-frequency structure have been reduced by approximately 66% and 32%, respectively, compared to conventional klystrons [41]. Experiment results demonstrate that under a beam voltage of 102 kV and beam current of 49 A, the metamaterial-inspired klystron achieves saturated peak output power exceeding 2.416 MW within the 323.4–324.3 MHz frequency band, with saturated electron efficiency surpassing 48% and saturated gain exceeding 49 dB. The 48 h reliability test results indicate that the fluctuation of the saturated peak output power remains between −0.5% and +6% [29,42]. It has met the requirements for next-generation CSNS linear accelerator applications.

thumbnail Fig. 7

Schematic diagram of 324 MHz metamaterial-inspired high-frequency structure [40].

4.4 X-band metamaterial-inspired klystron

Although the single-bridge CeSRR exhibits stronger subwavelength characteristics, its mechanical strength is insufficient. Therefore, to balance miniaturization and mechanical strength, a four-groove CeSRR (FGCeSRR) is constructed, as shown in Figure 8a. A metamaterial-inspired resonant cavity based on the FGCeSRR is constructed as shown in Figure 8b. Simulation results indicate that at 9.5 GHz, the cavity radius loaded with FGCeSRR is approximately 0.9 times that of the cavity loaded with double-bridge CeSRR, demonstrating the more pronounced miniaturization characteristics of the cavity loaded with FGCeSRR [43].

Based on the FGCeSRR-loaded resonant cavity, an X-band metamaterial-inspired klystron is proposed, as shown in Figure 8c. The radius and length of the interaction structure of the metamaterial-inspired klystron are approximately 0.8 and 0.79 times those of the conventional interaction structure, respectively, reducing its volume by about 50%. Through beam-wave interaction simulations, it is found that under conditions of beam voltage of 45 kV, beam current of 8 A, and a uniform axial magnetic flux density of 0.5 T, the output power reaches 187 kW at 9.5 GHz, with a gain of 49.7 dB and an electron efficiency of 52%. This compact and high-efficiency metamaterial-inspired klystron holds promise for future radar applications.

As discussed in the previous sections, all the metamaterial-inspired klystrons operating in different frequency bands can achieve miniaturization, and the majority of them also exhibit higher efficiency than conventional klystrons. To provide a concise overview, the device performance of the metamaterial-inspired klystrons and their conventional klystrons is summarized in Table 1.

thumbnail Fig. 8

Design model of (a) FGCeSRR and (b) metamaterial-inspired resonant cavity with FGCeSRR. (c) Schematic diagram of X-band metamaterial-inspired klystron [43].
Table 1

Comparison of parameters of the metamaterial-inspired klystrons and conventional klystrons.

5 Conclusion

This paper reviews the recent advances of metamaterial-inspired klystrons, which offer significant advantages such as miniaturization and high efficiency. These novel metamaterial-inspired klystrons have promising applications in large scientific facilities, radar, communications, medical imaging, microwave heating, and other fields. We will continue to strengthen the research on metamaterial-inspired klystrons and advance their engineering applications. For instance, metamaterial-inspired multibeam klystrons are being investigated, aiming to reduce operating voltage while achieving miniaturization.

Acknowledgments

We sincerely appreciate the kind invitation from Professor Runhua Fan of Shanghai Maritime University.

Funding

This research was funded in part by the National Natural Science Foundation of China (Grant Nos. 62371108 and 62131006), by the Natural Science Foundation of Sichuan Province (Grant No. 2025ZNSFSC0042), and by the National Key Laboratory of Science and Technology on Vacuum Electronics (NKLV-KG-2025-03).

Conflicts of interest

The authors of this article have no conflict of interest.

Data availability statement

All data and evidence supporting the conclusion of this study are provided within the article and cited references.

Author contribution statement

Conceptualization, Z.D.; Methodology, Z.D.; Validation, C.W. and D.L.; Formal Analysis, C.W. and D.L.; Investigation, C.W. and D.L.; Resources, Z.D.; Data Curation, C.W. and D.L.; Writing – Original Draft Preparation, Z.D., C.W. and D.L.; Writing – Review & Editing, Z.D., C.W. and D.L.; Visualization, C.W. and D.L.; Supervision, Z.D.; Project Administration, Z.D.; Funding Acquisition, Z.D.

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Cite this article as: Chuanchao Wang, Deyong Li, Zhaoyun Duan, Research progress in metamaterial-inspired klystrons, EPJ Appl. Metamat. 13, 1 (2026), https://doi.org/10.1051/epjam/2025008

All Tables

Table 1

Comparison of parameters of the metamaterial-inspired klystrons and conventional klystrons.

In the text

All Figures

thumbnail Fig. 1

Schematic diagram of natural material and metamaterial [3].
In the text
thumbnail Fig. 2

Design model of a 37-beam S-band metamaterial-inspired cavity and the gap of a partial channel with a sleeve and a helix [23].
In the text
thumbnail Fig. 3

Schematic diagram of (a) narrowly-defined transition radiation and (b) broadly-defined transition radiation in a klystron [3]. (c) Metamaterial unit cell, metamaterial-inspired resonant cavity, and electric field and surface currents distribution of CeSRR [29].
In the text
thumbnail Fig. 4

(a) Design model of 3-gap MEIRC. (b) Design model of the 2-gap MEIRC (left) and 3-gap MEIRC (right) with rod couplers. (c) Prototype of MEIRCs. (d) Schematic diagram of the 3-cavity metamaterial-inspired EIK [32].
In the text
thumbnail Fig. 5

(a) Design model of CeSRR and metamaterial-inspired resonant cavity (idler cavity). (b) Schematic diagram of metamaterial-inspired interaction structure. (c) Prototype of S-band metamaterial-inspired klystron [34].
In the text
thumbnail Fig. 6

Design model of (a) single-bridge CeSRR and (b) metamaterial-inspired resonant cavity. (c) Prototype of the metamaterial-inspired input cavity and test platform. (d) Schematic diagram of 714 MHz metamaterial-inspired klystron [37].
In the text
thumbnail Fig. 7

Schematic diagram of 324 MHz metamaterial-inspired high-frequency structure [40].
In the text
thumbnail Fig. 8

Design model of (a) FGCeSRR and (b) metamaterial-inspired resonant cavity with FGCeSRR. (c) Schematic diagram of X-band metamaterial-inspired klystron [43].
In the text

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