Study on a bandwidth enhancing mechanism for high-power high-efficiency klystrons Open Access

Klystron, a typical high-power microwave vacuum electronic device, serves as the final-stage power amplifier in numerous microwave electronic systems. Its applications span critical military and civilian domains, including radar systems, communication networks, television broadcasting, electronic warfare, particle accelerators, and high-energy physics research.^1–5 Modern klystron development aims to achieve RF power generation ranging from MW to tens of MW, operating at frequencies from hundreds of MHz to several GHz. High-beam-perveance designs (0.5–2.5 μP) have emerged as a preferred approach for attaining these power levels,⁶ offering three key advantages: (1) Lower beam voltage requirements, which alleviate constraints related to electron gun insulation and circuit RF breakdown suppression; (2) simplified implementation of high-voltage modulators deployment and x-ray shielding;⁷ and (3) reduced interaction circuit dimensions, enabling a more compact beam optics system.

However, increasing beam perveance typically leads to a degradation in efficiency. To achieve high-efficiency (HE) under high-beam-perveance conditions (0.5–2.5 μP), two general strategies are commonly employed: (1) For very-high-perveance designs (1.5–2.5 μP), where space charge effects are more pronounced, HE is achieved through parameter optimization based on the traditional beam bunching method;^8,9 (2) For mild-high-perveance designs (0.5–1.5 μP), the core oscillation method (COM) has been demonstrated to be effective in achieving HE performance.¹⁰ It is also worth noting that above high-beam-perveance HE klystrons normally do not incorporate high-order harmonic cavities (like core stabilization method^11,12) due to the increased risk of inducing the reflected electrons.

Nevertheless, previous studies on HE klystrons have ignored the issue of bandwidth. Although klystrons are inherently narrowband devices developed for specific applications, their instantaneous bandwidth still remains a critical design consideration for several reasons: (1) The narrow bandwidth imposes stringent manufacturing tolerances, where even minor fabrication or assembly deviations can significantly degrade performance, hindering practical implementation; (2) limited bandwidth increases the device's instantaneous response time; and (3) narrow bandwidth also reduces operational stability, particularly under high-duty-cycle conditions. To address this issue, a variety of bandwidth enhancement techniques have been proposed, including operating cavities in the fundamental TM₀₁₀ mode,¹³ increasing the number of beams,^13,14 adding idler cavities,^13–15 employing multiple-gap cavities,¹⁶ lowering the cavity quality factor via incorporating lossy materials¹⁷ or introducing coupled passive cavities,¹⁸ designing cavities with special structures.^19–21 These methods are often used independently or in combination to achieve the desired bandwidth. Unfortunately, based on our preliminary studies, these methods are inherently complex and often require a complete overhaul of the original HE klystron design.

In this paper, we proposed a simple yet effective approach to broaden the bandwidth without introducing additional manufacturing complexities. The key innovation lies in strategically downshifting the resonant frequencies of selected gain cavities. When applied to HE klystrons with beam perveance above 0.5 μP, this new method enables three to five times increase in instantaneous bandwidth without sacrificing conversion efficiency (or even slightly improving it in some cases) or circuit length.

In addition to bandwidth improvement, this technique also enhances device stability. In high-power HE klystrons, backstreaming electrons from the collector often cause spurious oscillations.²² A common solution is to use oversized collectors to reduce the backstreaming current rate (BCR).^23,24 With the proposed method, it is discovered that the threshold for spurious oscillations in high-power, HE klystrons could also been improved significantly. This improvement enables more compact and rational collector designs without the need for excessively large structures,²⁵ thereby facilitating the miniaturization of high-power, high-beam-perveance, HE klystrons.

To demonstrate the effectiveness of the proposed mechanism, two representative examples are presented: A X-band 2.2-μP HE single-beam klystron (SBK) and a 0.6-μP HE SBK. The article is organized as follows. In Sec. II, the effect of downshifting the frequency of a single gain cavity on bandwidth and efficiency is examined in detail. Section III investigates the impact of downshifting multiple gain cavity frequencies on bandwidth and efficiency. Section IV discusses the applications of the proposed mechanism to the multibeam klystron (MBK) and its effectiveness for low-beam-perveance (<0.5 μP) case. A brief conclusion is provided in Sec. V.

When designing HE klystrons using traditional methods, no matter what HE bunching technique is employed, the frequencies of all gain cavities are typically tuned above the operating frequency to provide the required bunching force. However, this approach often results in a compromised instantaneous bandwidth. To address this issue, we drew inspiration from the fundamental principle of staggered tuning technique,¹⁵ in which the frequencies of some gain cavities are intentionally downshifted. Unlike staggered-tuned klystrons,⁵ which sacrifice efficiency significantly in exchange for bandwidth, our approach explores the possibility of strategically downshifting the frequencies of certain gain cavities without effecting their core performance.

Through extensive large-signal simulation studies in KlyC/1.5-D,²⁶ we found that downshifting the frequency of either the first or second gain cavity below the operating frequency (while keeping the other bunching cavities tuned above it) induces an initial debunching effect in the gain cavities, followed by re-bunching in subsequent cavities. This mechanism effectively broadens the bandwidth of high-beam-perveance HE klystrons by a factor of 3–5, while maintaining efficiency or even slightly improving it in specific cases. Additionally, this approach mitigates radial stratification effects, promoting more uniform modulation across both inner and outer beam layers, thereby enhancing overall device stability.

To validate the proposed method, we present two cases of X-band HE SBKs: One with a perveance of 2.2 μP and another with 0.6 μP.

An X-band very-high-perveance (2.2-μP) HE SBK is introduced here for verification purpose, with its key specifications summarized in Table I. Using traditional design methods (where the frequencies of all gain cavities are upshifted above the operating frequency), extensive optimizations were performed in KlyC/1.5-D to develop an RF interaction circuit that meets the required performance criteria. The optimized design achieves a peak conversion efficiency of 50%, with a driven power of 70 W and a gain of approximately 55 dB. The RF interaction circuit has a length of ∼185 mm, a −1 dB instantaneous bandwidth of 40 MHz (0.4% relative bandwidth), and a BCR threshold of 1.3 × 10⁻⁵. (The BCR oscillation threshold is obtained using an improved small-signal theory that incorporates the effect of backstreaming electrons, assuming their energy and radius are identical to those of the incident electrons. Moreover, we consider the worst-case scenario, in which the external magnetic field is sufficiently strong to guide the backstreaming electrons from the collector back to the input cavity without any intermediate loss. For detailed methodology, it could be referred to our previous work.²²) The resonant cavity frequencies are listed in Scheme I of Table II, while Fig. 1(a) depicts the velocity variation, and Fig. 1(c) illustrates the fundamental current modulation depth across different electron beam radii.

It is important to note that in very-high-perveance klystrons, the COM method, due to its extended bunching intervals, induces significant radial stratification effects, severely limiting efficiency improvements and may cause reflected electrons instabilities. As a result, traditional bunching methods with shorter intervals are generally preferred for achieving in very-high-perveance (1.5–2.5 μP) HE klystrons. Conversely, in mild-high-perveance (0.5–1.5 μP) HE klystrons, the COM method has been shown to enhance efficiency more effectively. Therefore, in the subsequent study of the 0.6-μP HE SBK, the COM method is employed to achieve HE.

Building upon the traditional design approach, the novel mechanism proposed in this work was implemented by downshifting the frequency of a single gain cavity below the operating frequency, while slightly optimizing the frequencies and positions of the other cavities. To evaluate the impact of downshifting only the first gain cavity frequency, extensive optimizations were performed in KlyC/1.5-D, with the results summarized in Table II. The frequency detuning of the first gain cavity was varied from −20 to −140 MHz in a step size of 20 MHz, for each case RF circuits are presented as Schemes II–VIII. All schemes maintained a driven power of 70 W, with gains exceeding 54.8 dB.

As illustrated in Fig. 2, the −1 dB instantaneous bandwidth increases as the first gain cavity frequency is reduced, reaching a maximum of 200 MHz (2% relative bandwidth) at a frequency detuning of −100 MHz, while efficiency remains nearly unchanged (<1% variation). However, further downshifting beyond −100 MHz leads to a reduction in bandwidth and a gradual decline in efficiency. Ultimately, Scheme VI^* in Table II was selected as the optimal design, as it achieves a fivefold increase in −1 dB instantaneous bandwidth with no significant efficiency loss compared to the traditional design (Scheme I in Table II). Moreover, the RF interaction circuit length increases by only 4%. The velocity variation for Scheme VI^* is presented in Fig. 1(b), while the fundamental current modulation depth at different electron beam radii is shown in Fig. 1(d). Compared to Fig. 1(c), Fig. 1(d) reveals that the modulation depth initially decreases at the first gain cavity and then rebounds, resulting in a more uniform distribution across electron beam radii. This mitigates the radial stratification effect, thereby enhancing the klystron's stability against reflected electrons. Additionally, the stability of backstreaming electrons is significantly improved, as the BCR threshold for Scheme VI^* increases to 3.9 × 10⁻⁵, a threefold enhancement compared to the traditional Scheme I.

To further verify the reliability of KlyC/1.5-D calculations for 2.2-μP HE klystrons and to validate the effectiveness of the proposed bandwidth enhancement mechanism, CST PIC²⁷ simulations were conducted for both Scheme I and Scheme VI^* in Table II. As shown in Fig. 3, no reflected electrons were observed in either case, with the CST PIC simulations employing an ideal longitudinal magnetic field strength of 1.8 T (approximately ten times the Brillouin magnetic field). The time-domain evolution of instantaneous output power and the corresponding frequency spectra for both schemes are presented in Fig. 4, demonstrating that both designs achieve peak powers exceeding 21.9 MW, with electronic efficiencies of 49.8% and 49.3%, respectively closely matching the KlyC/1.5-D results of 50% and 49.3%. The efficiency-frequency and power-frequency characteristics, shown in Fig. 5, further confirm the excellent agreement between KlyC/1.5-D and CST PIC simulations.

The preceding analysis focused solely on downshifting the first gain cavity frequency. To further explore the proposed mechanism, we investigated the impact of downshifting the second gain cavity frequency. The second gain cavity frequency was detuned from −20 to −120 MHz in a step size of 20 MHz, with optimizations in KlyC/1.5-D yielding the most efficient designs, summarized as Schemes I–VI in Table III. The detuning frequencies of each cavity, conversion efficiency, −1 dB bandwidth, RF interaction circuit length, and BCR threshold for each scheme are detailed in Table III. The effects of downshifting the second gain cavity frequency on the −1 dB instantaneous bandwidth and efficiency are illustrated in Fig. 2(b). As shown in Fig. 2(b), downshifting the second gain cavity frequency to −100 MHz results in the maximum increase in instantaneous bandwidth. While maintaining efficiency and tube length, the instantaneous bandwidth is improved fourfold, and the BCR oscillation threshold is enhanced by a factor of three. However, compared to Fig. 2(a), the bandwidth improvement is less pronounced by downshifting the frequency of the second gain cavity rather than that of the first one.

To further validate the effectiveness of the proposed method, we optimize an X-band 0.6-μP HE SBK in KlyC/1.5-D as a second example by reducing the beam current of the X-band 2.2-μP HE SBK from 213 to 58 A. Similar to the analysis in Subsection II A, we first optimize the design using the COM method to establish a conventional reference scheme, designated as Scheme I in Table IV. This design achieves a higher electronic efficiency of 67% and a −1 dB instantaneous bandwidth of 30 MHz, corresponding to a relative bandwidth of 0.3%.

We then systematically downshift the frequency of the first gain cavity to −20, −40, −60, −80, and −100 MHz, optimizing efficiency to obtain Schemes II–VI in Table IV. Table IV summarizes the detuning frequencies of each cavity, efficiencies, −1 dB instantaneous bandwidths, RF circuit lengths, and BCR thresholds for each scheme. Additionally, we investigate the impact of downshifting the second gain cavity frequency to −20, −40, −60, −80, and −100 MHz. Efficiency optimization yields Schemes I–V in Table V, with their key specifications summarized accordingly. The effects of downshifting the first or second gain cavity frequency on the −1 dB instantaneous bandwidth and conversion efficiency are illustrated in Figs. 6(a) and 6(b), respectively. As shown in Fig. 6, consistent with the findings in Subsection II A, the bandwidth increases with larger gain-cavity-frequency downshifting until it reaches maximum. Meanwhile, the efficiency exhibits a gradual decrease with further frequency downshifting operation, but the reduction remains relatively minor compared to the conventional design. Furthermore, downshifting the frequency of any gain cavity leads to a several-fold or even order-of-magnitude increase in the BCR oscillation threshold. For this case, downshifting the first gain cavity frequency achieves the maximum bandwidth improvement in Scheme IV^* of Table IV. With efficiency remaining nearly unchanged, the instantaneous bandwidth increases threefold, while the BCR oscillation threshold improves by 11 times.

Downshifting the second gain cavity frequency yields the maximum bandwidth improvement, shown in Scheme III^* of Table V. In this case, the instantaneous bandwidth is enhanced threefold, with a 1.2% increase in efficiency, while the BCR oscillation threshold improves by eight times. Further details of the beam-wave interaction for Scheme III^* in Table V are presented in Figs. 7(a) and 7(c). Similarly, the beam-wave interaction characteristics of the conventional scheme (Scheme I in Table IV) are shown in Figs. 7(b) and 7(d). As observed in Figs. 7(c) and 7(d), the proposed technique effectively mitigates the radial stratification effect in the klystron.

Notably, further downshifting the frequency of the third or subsequent gain cavities yields only marginal bandwidth improvements while significantly reducing efficiency for all above scenarios. Based on the above studies on bandwidth enhancement for the 2.2 and 0.6-μP HE SBKs, the following conclusions are drawn: (1) for very-high-perveance (1.5–2.5 μP) HE klystrons, downshifting the frequency of the first gain cavity is more effective; (2) for mild-high-perveance (0.5–1.5 μP) HE klystrons, downshifting the frequency of the second gain cavity provides greater benefits; (3) the bandwidth enhancement effect is observed to diminish gradually as perveance decreases.

Section II provides a detailed analysis of the effects of individually downshifting the frequency of either the first or second gain cavity on bandwidth and efficiency. It is intriguing to further investigate the impact of simultaneously downshifting the frequencies of multiple gain cavities. The preliminary studies reveal that simultaneously downshifting the frequencies of three or more gain cavities significantly degrades efficiency performance, contradicting our objective of enhancing bandwidth while maintaining HE. Therefore, this section focuses on analyzing the effects of simultaneously downshifting the frequencies of the first and second gain cavities in high-beam-perveance HE klystrons. The following discussion is conducted based on two previous examples.

Using the X-band 2.2-μP HE SBK from Sec. II as a reference, we simultaneously downshifted the frequencies of the first and second gain cavities within the range of −100 to −20 MHz, selecting several representative frequency combinations. As shown in Table VI, parametric optimizations using KlyC/1.5-D yield the following combinations for the first and second gain cavities: −100 and −20 MHz, −80 and −20 MHz, −60 and −20 MHz, −40 and −20 MHz, −100 and −40 MHz, −80 and −40 MHz, and −60 and −40 MHz (Schemes I–VII). Among these, Scheme II^* in Table VI exhibits the best performance, achieving a 2.1% increase in efficiency, a fourfold enhancement in bandwidth, and an almost threefold improvement in the BCR oscillation threshold, all while maintaining the same RF circuit length. Further details of the beam-wave interaction for this scheme in KlyC/1.5-D are shown in Fig. 8(a). These findings indicate that for very-high-perveance HE klystrons, simultaneously downshifting the frequencies of both the first and second gain cavities can be beneficial.

Similarly, for the X-band 0.6-μP HE SBK example, optimizations in KlyC/1.5-D were conducted to explore a series of frequency combinations for the first and second gain cavities: −100 and −20 MHz, −80 and −20 MHz, −60 and −20 MHz, −40 and −20 MHz, −100 and −40 MHz, −80 and −40 MHz, and −60 and −40 MHz (Schemes I–VII in Table VII). Among these, Scheme IV^* is identified as the optimal design, demonstrating a twofold increase in bandwidth, a 1.5% improvement in efficiency, and a twofold enhancement in the BCR threshold, while maintaining nearly the same circuit length as the conventional design. Further details of the beam-wave interaction for this scheme in KlyC/1.5-D are shown in Fig. 8(b).

In summary of Subsections III A and III B, although simultaneously downshifting the frequencies of both the first and second gain cavities in high-beam-perveance HE klystrons can improve both bandwidth and efficiency, the enhancements are generally less pronounced compared to downshifting only one gain cavity frequency. Given the simpler implementation of the single-cavity frequency downshifting approach, it is recommended that future designs of high-power, high-beam-perveance (0.5–2.5 μP) HE klystrons prioritize downshifting the frequency of a single gain cavity to achieve optimal performance.

Sections II and III focused on the application of the proposed technique to X-band high-beam-perveance HE SBKs. To further validate its general applicability to MBKs, we now examine its implementation in a 4-beam S-band 4-MW HE MBK with a beam perveance of 1.7 μP. The key specifications of this MBK are summarized in Table VIII. Similar to the analysis conducted for SBKs, the conventional design (Scheme I in Table IX), optimized using KlyC/1.5-D, achieves a maximum efficiency of 50.3% (with an input power of 45 W), an RF interaction length of approximately 352 mm, a −1 dB instantaneous bandwidth of 13 MHz (relative bandwidth of 0.4%), and a BCR oscillation threshold of 1.9 × 10⁻⁵. By downshifting the frequency of the first gain cavity, the optimized design achieves an efficiency of 50.4% (with an increased input power of 75 W), while maintaining an RF interaction length of 352 mm. Notably, the −1 dB instantaneous bandwidth is significantly improved by 3.5 times to 45 MHz (relative bandwidth of 1.5%), and the BCR oscillation threshold increases by 6.8 times to 1.3 × 10⁻⁴. These results demonstrate that the proposed mechanism effectively enhances the bandwidth of MBKs as well. The cavity frequencies, RF interaction circuit length, and BCR threshold for the optimized design are summarized in Table IX as Scheme II^*.

To further verify these findings, CST PIC simulations were conducted for both Scheme I and Scheme II^* in Table IX. As shown in Fig. 9, no reflected electrons were observed in either case. The output signals and spectra for each port are presented in Fig. 10, while the efficiency-frequency and power-frequency characteristics are depicted in Fig. 11. As clearly demonstrated in Fig. 11, the CST PIC simulation results exhibit excellent agreement with the KlyC/1.5-D calculations, confirming that the proposed mechanism is also effective in enhancing the bandwidth of high-power, high-beam-perveance, HE MBKs.

Additionally, we also investigated the applicability of this technique to low-perveance HE klystrons. The results indicate that for low-perveance (0.1–0.3 μP) HE devices, the bandwidth enhancement effect is relatively modest (by tens of percent).

This paper presents a simple yet effective mechanism for enhancing the bandwidth of high-beam-perveance (0.5–2.5 μP) HE klystrons by a factor of 3–5 through the strategic downshifting of selected gain cavity frequencies. This improvement is achieved without compromising original high-efficiency performance while maintaining the original tube length. Notably, the proposed technique does not introduce additional manufacturing complexities. Instead, by expanding the bandwidth, it relaxes fabrication precision requirements, thereby simplifying the manufacturing process. Furthermore, the proposed mechanism significantly mitigates radial stratification effects, leading to improved stability regarding direct reflected electrons in HE klystrons. In particular, it increases the threshold for spurious oscillations induced by collector-originating backstreaming electrons by several times, further enhancing overall device stability. Given these advantages, it is strongly recommended to incorporate this mechanism into the design of future high-beam-perveance HE klystrons.

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 62371114 and 61988102) and in part by CETC's extended support funding project under Grant K2301290.

The authors have no conflicts to disclose.

Zixuan Su: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Resources (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Jinchi Cai: Conceptualization (lead); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (lead); Software (lead); Supervision (lead); Writing – review & editing (lead). Jian Zhang: Data curation (equal); Formal analysis (equal); Methodology (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Xiancai Lin: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal). Xinke Zhang: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal). Muhammad Asad: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Zhen Zhang: Conceptualization (equal); Methodology (equal); Validation (equal). Lin Zeng: Formal analysis (equal); Methodology (equal); Visualization (equal). Cheng Zhang: Data curation (equal); Investigation (equal); Validation (equal). Guanyu Pan: Investigation (equal); Validation (equal). Zhixin Liang: Formal analysis (equal); Visualization (equal). Pengcheng Yin: Data curation (equal); Investigation (equal); Validation (equal). Jin Xu: Conceptualization (equal); Data curation (equal). Lingna Yue: Investigation (equal); Visualization (equal). Hairong Yin: Conceptualization (equal); Resources (equal). Yong Xu: Data curation (equal); Resources (equal). Guoqing Zhao: Project administration (equal); Resources (equal). Wenxiang Wang: Conceptualization (equal); Supervision (equal). Yanyu Wei: Project administration (equal); Resources (equal); Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.