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Review

Peniotron: A Promising Microwave Source with Potential That Has Yet to Be Realized

by
Svilen Sabchevski
Institute of Electronics of the Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria
Appl. Sci. 2024, 14(23), 11246; https://doi.org/10.3390/app142311246
Submission received: 29 October 2024 / Revised: 25 November 2024 / Accepted: 28 November 2024 / Published: 2 December 2024
(This article belongs to the Section Applied Physics General)
Browse Figures
Figure 1
<p>Two typical configurations of peniotron interaction circuits: (<b>a</b>) double-ridge waveguide peniotron and (<b>b</b>) <math display="inline"><semantics> <msub> <mi>TE</mi> <mn>11</mn> </msub> </semantics></math>—mode peniotron with a rectangular waveguide. Figures reproduced from [<a href="#B18-applsci-14-11246" class="html-bibr">18</a>] (copyright ©2016 IEICE).</p> "> Figure 2
<p>Circular interaction structures: (<b>a</b>) smooth-wall waveguide (cavity) used in gyropeniotrons with helical electron beams (<math display="inline"><semantics> <msub> <mi>R</mi> <mi>c</mi> </msub> </semantics></math>—cavity radius, <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mi>c</mi> </mrow> </msub> </semantics></math>—guiding center radius of gyrating electrons); (<b>b</b>,<b>c</b>) slotted (vane-loaded) waveguide and rising-sun cavity, respectively, used with uniaxial electron beams. Here, <span class="html-italic">a</span> and <span class="html-italic">b</span> are the inner and outer radius of the slots and <math display="inline"><semantics> <msub> <mi>r</mi> <mi>L</mi> </msub> </semantics></math> is the Larmor radius of the electron orbits.</p> "> Figure 3
<p>Asynchronism in the peniotron due to the fact that the electrons gyrate faster than the cyclotron resonance wave: (<b>a</b>) angular frequencies of the gyrating electrons and the rotating electromagnetic wave; (<b>b</b>) motion of the electron with respect to a coordinate system associated with the wave (in this example, <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>); (<b>c</b>) the field amplitude that the electron “sees” at different moments (indicated by dots) during one cyclotron period.</p> "> Figure 4
<p>On the operating principle of peniotron. The guiding center of the electron orbit drifts in such a way as to bring the electron into a stronger field at the decelerating phase and conversely into a weaker field at the accelerating phase. The orbits of an initially accelerated and an initially decelerated electron are shown in the panes (<b>a</b>,<b>b</b>), respectively. Below them, the distribution of the electric field <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math> in the vertical <span class="html-italic">Y</span> direction along the horizontal axis <span class="html-italic">X</span> is shown.</p> "> Figure 5
<p>Brillouin diagram for the case of electron cyclotron autoresonance.</p> "> Figure 6
<p>Azimuthal electric fields in the vanes of the circuit. Here, the azimuthal angle (0–360°) is linearly stretched.</p> "> Figure 7
<p>Example of concurrent research on LOG and gyro-peniotron development: (<b>a</b>) EOS of LOG with a permanent magnet (shown are a photo of the device, a drawing of the tube, and results from the ray-tracing analysis of the EOS); and (<b>b</b>) a rising-sun cavity of a peniotron (shown is the electric field distribution calculated by the computer program for the evaluation of RF SUPERFISH cavities [<a href="#B80-applsci-14-11246" class="html-bibr">80</a>]).</p> "> Figure 7 Cont.
<p>Example of concurrent research on LOG and gyro-peniotron development: (<b>a</b>) EOS of LOG with a permanent magnet (shown are a photo of the device, a drawing of the tube, and results from the ray-tracing analysis of the EOS); and (<b>b</b>) a rising-sun cavity of a peniotron (shown is the electric field distribution calculated by the computer program for the evaluation of RF SUPERFISH cavities [<a href="#B80-applsci-14-11246" class="html-bibr">80</a>]).</p> ">
Versions Notes

Abstract

:
The peniotron is a fast-wave vacuum tube that can generate coherent microwave radiation in the millimeter-wave range. Although it uses a beam of gyrating electrons like other gyro-devices (gyrotron, gyro-TWT, gyro-BWO, etc.), its operating principle is completely different from that of electron cyclotron masers. The theory predicts a very high efficiency (about 95%) of the peniotron mechanism of interaction and energy transfer from the electron beam to the wave. However, this extremely attractive and advantageous property of peniotrons has not yet been realized in practice. In this paper, we present the current state of research on this class of devices and give an overview of the theory and experimental results of peniotrons and gyro-peniotrons with different configurations. We also discuss the main problems and the reasons for the lower efficiency and finally evaluate the potential for solving the problems and revitalizing the work on this promising device.

1. Introduction

The peniotron is a vacuum tube that can generate coherent electromagnetic radiation and operate as an oscillator or amplifier, especially in the millimeter-wave range. The basic principle of the peniotron operation is based on the interaction between a helical or uniaxial electron beam of gyrating electrons (as in the gyro-devices such as gyrotron, gyro-backward oscillator (gyro-BWO), gyro-traveling wave tube (gyro-TWT), cyclotron auto-resonance maser (CARM), etc.) and electromagnetic waves within a specially designed waveguide or cavity resonator structure. The special nature of the peniotron interaction enables an efficient energy transfer from the electrons to the electromagnetic field. The design typically includes a series of vanes or resonators that help to shape and guide the electromagnetic waves, improving performance and efficiency.
The similarity between the peniotron and the gyrotron is due to the following common features: (i) both are fast-wave tubes since the electromagnetic wave propagates in the interaction circuit at a phase velocity greater than the speed of light in vacuum, and therefore, no slow-wave structures are used; (ii) the interaction circuit is immersed in a uniform magnetic field. The main difference between these devices is that their operation is based on different mechanisms. The gyrotrons work on a physical principle known as electron cyclotron maser instability, which originates from the relativistic dependence of the mass of gyrating electrons on their energy, leading to their bunching. In peniotrons, as in conventional gyrotrons, helical electron beams can be used, and in this case they are called gyro-peniotrons. More typical, however, is the use of an axis-encircling (also known as uniaxial) electron beam as in the large-orbit gyrotron (LOG). In any case, however, the operation of peniotrons and gyro-peniotrons is not based on relativistic effects but on a specific (systematic) displacement of the guiding center of the rotating electrons during their passage through the interaction structure.
While the physics of mainstream gyro-devices is being studied continuously and is presented in a large number of publications and monographs (see, e.g., [1,2,3,4,5,6,7,8]), the literature on peniotrons is less extensive. The same is true for the applications of these two classes of devices (for the numerous usages of the gyro-devices in physics research and advanced technologies, see, e.g., the recent reviews [9,10,11,12,13,14,15,16]).
One of the main advantages of the peniotron over other types of microwave devices, such as gyrotrons, is the relatively low magnetic field requirement and reduced complexity in operation. In particular, when operating the peniotron at high harmonics, lower magnetic field intensity is needed, and, therefore, more simple magnets can be used. The peniotron can achieve high efficiencies—up to 95% in some configurations—and is therefore suitable for applications that require high output power without excessive energy loss. Additionally, high efficiency also means less energy from the spent electron beam that has to be dissipated at the collector.
In this article, we provide a brief overview of the theoretical work and experimental studies on peniotrons in order to critically evaluate the potential of these devices and their prospects for further development. The rest of the paper is organized as follows. In Section 2, we briefly present the genealogy, the history of discovery, and the different types of peniotrons. The underlying principles and the theory of their operation are described in Section 3. Subsequently, in Section 4, we overview some of the known implementations of this class of devices and their main output parameters obtained experimentally. Before drawing a conclusion, in Section 5, we discuss some of the problems in the development of peniotrons and the possible solutions.

2. Genealogy, History of Discovery, and Varieties of Peniotrons

Starting from the thirties of the 20th century, the active research on the interaction of electron beams with electromagnetic fields has brought to life what is nowadays called a family of classical microwave tubes, such as magnetrons, clystrons, backward-wave oscillators (BWOs), travelling-wave tube amplifiers (TWTAs), etc. [17]. By the mid-sixties, these devices had reached technical maturity and widespread applications. The accumulated knowledge in this field of study has made possible exploring novel concepts and developing new devices such as peniotrons, gyrotrons, free-electron lasers (FELs), etc., that allow for achieving higher frequencies of the generated high-power radiation.
The beginning of the development of the peniotron is well presented in [18]. According to the historical records of the Department of Electrical Engineering of Tohoku University (Japan), the idea of a new interaction mechanism, which is the basis for the operation of the peniotron, was conceived by Professor Y. Koike in 1957. He coined the name “peniotron” for the new device after the Greek word “penio”, which means spool. This groundbreaking idea was then further developed by Professor S. Ono and successfully implemented at the same university. In the first realization of the peniotron, Professor K. Yamanouchi used a double-rige waveguide (shown in Figure 1a) as an interaction structure in which gyrating electrons interact with an electromagnetic wave [19]. The next advance was made by Professor K. Yokoo, who proposed TE 11 -mode rectangular (see Figure 1b) and circular waveguide interaction circuits [20]. This eventually led to an extremely high efficiency of 94%, which was achieved in 1998 [21].
These pioneering developments in Japan soon aroused great interest worldwide, and many researchers engaged in theoretical and experimental studies on peniotrons and explored various configurations as interaction structures [22,23,24,25,26,27,28,29]. In addition to the aforementioned double-ridge waveguide, these include the gyro-peniotron, which uses the circular waveguide and the magnetron waveguide (cavity), as well as the spatial harmonic gyro-peniotron. Some of the investigated configurations are shown in Figure 2. In the spatial harmonic peniotrons due to the presence of non-uniformity (ridges, grooves, corrugations, etc.) in an azimuthal direction of their interaction structures (unlike waveguides and cavities with smooth walls), the eigenmode is an infinite sum of azimuthal spatial modes in a circular cylinder.
The helical electron beams used in gyro-peniotrons are generated in electron-optical systems (EOSs) with magnetron injection guns (MIGs) analogous to those of gyrotrons. On the other hand, the axis-encircling electron beams used in LOGs and peniotrons are generated in EOSs with cusp-type electron guns. For this reason, these two devices were originally called cusptrons (see e.g., [30]).

3. Principle of Operation and Theory of Peniotron

3.1. Qualitative Description of the Peniotron Interaction

In the interaction structure of the peniotron, the rotational kinetic energy of the beam electrons gyrating at relativistic cyclotron frequency Ω C
Ω C = e B γ m 0 ,
is converted into microwave energy. Here, e and m 0 are the charge and rest mass of an electron, γ is the relativistic Lorentz factor γ = ( 1 − v 2 c 2 ) − 1 / 2 = ( 1 − v z 2 + v ⊥ 2 c 2 ) − 1 / 2 , with v z and v ⊥ being the axial and transverse components of the total velocity v of the electron, respectively.
The peniotron interaction differs significantly from that of the cyclotron resonance masers (gyro-devices) because it is based on a completely different mechanism of energy extraction. This mechanism is due to a drift in the guiding center of the electron orbits in directions that cause each electron to lose energy to the transverse electric field. Such a drift takes place in a strong azimuthal electric field, with an angular mode number m that is related to the beam cyclotron harmonic number s by the relation m = s + 1 [31]. As mentioned above, in the peniotron, the electrons rotate in azimuthal direction with angular frequency Ω C , while the field rotates with a frequency of m − 1 m Ω C , as illustrated in Figure 3, i.e., the electron rotates faster than the wave. This means that (see Figure 3c) in one cyclotron orbit, the electron advances through one cycle of the wave.
In the gyrotron, the synchronization condition between the beam and the wave is given by the following relation
ω = Ω CH + v z k z ,
where ω is the Doppler-shifted cyclotron frequency, k z is the axial wavenumber and Ω C H = s Ω C , 10 m u s = 1 , 2 , 3 , ⋯ is the harmonic number of gyrotron operation.
Similarly, in the gyro-peniotron, the resonance condition is [32]
ω = ( s ± 1 ) Ω C + v z k z ,
Obviously, (3) can be written in a form equivalent to (2) if ( s ± 1 ) = S , where S is also an integer.
In the “traditional” peniotron (term introduced in [31]) with ridges (see Figure 1a),
ω = S Ω CH + v z k z , S = 2 P , P = 1 , 2 , 3 , ⋯ ,
where P is the spatial harmonic number of operation (also called the order of operation).
The working principle and the physical mechanism of the “traditional” peniotron with a double-ridge waveguide interaction structure, which operates in the fundamental mode ( P = 1 ), are illustrated in Figure 4 [31]. Depending on the phase of the electromagnetic wave, an electron near the ridges is either accelerated or decelerated by the strong electric field there. This causes the radius of its orbit to increase or decrease. If the field of the wave changes by one full period (or an integer multiple thereof) during the time it takes the electron to complete half a revolution and reach the opposite pair of ridges, the accelerated electron is accelerated again, but by a smaller force, as it is now further away from the ridges. In contrast, the initially decelerated electron is further decelerated by a greater force than before, as it is now closer to the ridges. In such a way, during each complete revolution, the electrons lose some energy to the wave regardless of the initial phase. Thus, as long as the alternating acceleration and deceleration of the electrons remain synchronized (“in phase”), the electron continuously loses its transverse energy until it is completely converted into microwave energy and the radius of the electron orbit becomes vanishingly small. All this leads (at least theoretically) to a microwave source with a very high efficiency and narrow bandwidth.
Another variant of this class of devices deserves special attention, namely, the autoresonant peniotron (ARPO) [33,34], which makes use of electron cyclotron autoresonance (see e.g., [35]), similar to the cyclotron autoresonance maser (CARM). The operating point, or point at which the beam line crosses the dispersion curve of the waveguide mode during cyclotron autoresonance, is unaffected by the electron energy change that occurs during the beam-wave interaction and thus the frequency remains constant. This is illustrated in Figure 5, where the Brillouin diagram for such an interaction is shown. Moreover, at cyclotron autoresonance, the injected beam electrons can transfer not only their transverse but also their longitudinal energy to an electromagnetic wave, so that a much higher conversion efficiency can be achieved. In the ARPO tube, by combining this mechanism with the peniotron interaction, almost the entire kinetic energy of an injected electron beam is transferred to the wave, so that theoretically an extremely high conversion efficiency can be achieved.

3.2. Some Basics of the Linear and Nonlinear Theory of the Peniotron and a Brief Overview of the Literature on This Subject

It is instructive to first consider the small signal theory of a four-ridged waveguide. By decomposing the T E 10 mode of such an interaction structure into a Fourier series and solving for the small signal displacements, a dispersion equation has been obtained in [36]. In a transverse cross section, the dependence of the transverse electric field component along the circumference of the electron orbit is an expansion of terms of the form exp ( − j s φ ) , so that the field as seen by the moving electron is given by
exp j ( ω t − k z z − s φ ) = exp ( − j ω s t ) ,
where
− ω s = ω − k z v z − s Ω C .
Here, z and φ are the electron’s axial and angular coordinates, respectively. The peniotron resonance occurs when
ω s = + Ω C leads to ω = ( s − 1 ) Ω C .
The condition ( ω s = + Ω C ) leads to a net absorption of the microwave power, which takes place when the electrons are alternately accelerated and decelerated at a rate equal to the cyclotron frequency. The peniotron is therefore called (see [31]) a “resonant” device, in contrast to “synchronous” devices such as gyrotrons, for which (neglecting the term of the Doppler shift k z v z , which is small and therefore insignificant for gyrotrons)
ω s = 0 leads to ω = s Ω C ,
and the electrons remain in a relatively constant phase of the wave. Since in the traditional peniotron, only odd values of s yield nonzero coefficients [23], taking into account Equation (4) and considering P = 1 , 2 , 3 ( S = 2 , 4 , 6 ) reveals that the corresponding values of n are, respectively, s = 3 , 5 , 7 .
There are several conventions for the designation of the peniotron modes. In a magnetron-type interaction structure, for instance, the modes are denoted by the numbers 0 , 1 , 2 , ⋯ N / 2 when N is an even number of vanes and 0 , 1 , 2 ⋯ ( N − 1 ) / 2 when N is odd. More specifically, the N / 2 mode is called the π mode while the “0” mode is called the 2 π mode because there are N π or 2 N π phase variations, respectively, around the circumference of the circuit. [37].
Figure 6 provides a further illustration of the designation of modes. It applies to a six-vane circuit and makes use of the following convention [38]. In a structure with N vanes, the primary and second azimuthal numbers are i = 0 , 1 , 2 , ⋯ N / 2 and j = N − 1 ( i + j = N ) , respectively. Consequently, in an N-vane circuit, the N / 2 + 1 modes exist, which can interact at i-th (if i ≠ 0 ) and j-th harmonic frequency. According to this convention, the index i determines the phase difference between the adjacent vanes. The field disappears at the conducting walls, except in the openings between ridges, where the fields are assumed constant and their phases are characterized by the primary azimuthal mode numbers. The solid line in the square-wave patterns in this illustration represents the eigenmodes. The Fourier components of these square waves determine the amplitudes of the partial azimuthal modes. A comprehensive analysis of modes and analytical expressions for the fields in slotted waveguides can be found in [39].
In [36], dispersion relations derived from the small signal theory of cyclotron masers and peniotrons are presented, accounting for the possible coexistence of transverse electric (TE) and transverse magnetic (TM) modes as well as TE-TM coupling. This theory considers the displacement (shift) of the electron orbits and predicts a peniotron interaction also in other gyro-devices. Many researchers have since confirmed the latter point, demonstrating the coexistence and competition of the peniotron and gyrotron interactions even in a typical cylindrical gyrotron cavity with an helical electron beam generated by an MIG [40,41,42,43].
Other notable implementations of the small signal theory are developed in [44,45,46]. Based on the kinetic theory of the traveling-wave gyro-peniotron, a dispersion equation is obtained in [44], which can be used to describe the operation of both the gyrotron and the gyro-peniotron. In [45], Vitello and Menyuk presented a theory for high-harmonic gyrotron oscillators with a slotted cross-section. It is applied to both slotted rectangular oscillators and slotted cylindrical oscillators and allows for obtaining a unified expression for the start-oscillation condition. The authors have shown that slots can lower the starting current in both cylindrical and rectangular geometries and can lead to a decrease in this condition as the harmonic number is increased in the rectangular geometry. A unified theory of gyrotron and peniotron interactions was developed by Lashmore-Davies [46]. It takes into account the space charge effects and provides a general dispersion relation for an electron beam with arbitrary energy and pitch angle (the ratio between the transverse and axial velocity of an electron).
For computer-aided design (CAD) based on numerical experiments, however, the physical models based on the nonlinear (large-signa) theory developed in [47,48,49,50] are more adequate. A comprehensive theory, which describes the beam-wave interaction in a gyro-peniotron and is valid for arbitrary TE modes and arbitrary harmonics of the cyclotron frequency, is presented in [47]. The numerical simulations based on this theory show that under appropriate conditions, an electronic efficiency of about 45% for the third cyclotron harmonic at an operation frequency of 35 GHz could be obtained using a magnetic field as low as 0.42 T. The three-dimensional nonlinear theory of the gyropeniotron amplifier developed by Ganguly et al. [48] is used to study the saturation regime of interaction in a cylindrical waveguide with slotted wall (magnetron type). An extremely high efficiency of about 75% is predicted for interaction between the n-mode and the second cyclotron harmonic of an electron beam with an energy of 70 keV and current of 3.5 A under ideal conditions of zero velocity spread. An efficiency of about 38% is obtained for a beam with 5% velocity spread and 10% guiding centre spread. The performance characteristics of the amplifier are studied for cyclotron harmonics up to order s = 8. Linear and nonlinear analyses on gyropeniotron in a rectangular waveguide using TEn0 mode and an axis-rotating electron beam are presented in [49]. For the TE 201 cavity mode, efficiencies of 51% and 11% are estimated for the fundamental and third-harmonic operations, respectively. The oscillation build-up process from initial excitation until reaching steady-state in the backward wave peniotron oscillator (BWPO) is analyzed in [50] within the framework of the non-stationary nonlinear theory. It leads to the conclusion that single- and multi-frequency oscillations, including chaotic ones, can be generated by BWOP with high efficiency. A self-consistent, large-signal computer simulation code, which is used to study the interaction of an axis-encircling electron beam with the wave in a magnetron-type eight-vane open cavity, is described in [51]. The simulations show that the extremely effective interaction mechanism of an ideal electron beam breaks down when a guiding center spread is taken into account. The observed drastic decrease in efficiency is due to the fact that the ideal peniotron gain mechanism is no longer constantly fulfilled by all electrons when the beam is off-axis and its envelope is rippled.
Powerful tools for numerical studies and CAD of various gyro-devices, including peniotrons, are the particle-in-cell self-consistent physical models based on first principles (Maxwell’s equations and relativistic equation of electron motion) implemented in problem-oriented computer codes [52,53,54,55,56,57,58]. A self-consistent PIC code based on the nonlinear large-signal theory for numerical simulations of peniotrons was developed in [58]. It can be used to analyze the output parameters of peniotrons, taking into account effects such as electron velocity spread and guiding center deviation.

4. Remarkable Successful Realizations of Peniotrons

A detailed report on state-of-the-art high-power gyro-devices and free-electron masers (including peniotrons) is published every year by Professor M. Thumm [59]. Table 1 contains some of the most representative data pertaining to experimental research on peniotrons, which are taken from that report. Most of these experiments were conducted during the apogee of the research and development of peniotrons, which is evident from the literature in the 1990s.
The highest output power of 25.7 kW at a frequency of 34.1 GHz and an efficiency of 36% was demonstrated by the peniotron developed by the team at the University of California at Davies and the Northrop Grumman Corporation, which operates with the TE 11 mode in a circular cavity at the second harmonic of the cyclotron frequency [60]. This device incorporates a fundamental-mode four-vane slotted (magnetron-type) interaction circuit and a cusp electron gun that provides the high-quality axis-encircling electron beam required for efficient interaction.
Another example is the experimental investigation of the modified peniotron oscillator using a TE 11 rectangular waveguide cavity [20,62]. The results presented in [69] show an electronic efficiency of 50% (although the calculations had predicted 80%), which has been increased to 62% by using a potential-depressed collector. The tube was operated with an output power of 10 kW at a frequency of 10 GHz using an electron beam with a voltage and current of 30 kV and 0.42 A, respectively. The authors emphasize the importance of aligning the axes of the tube and the magnetic circuits in order to form an axially symmetric, hollow, rotating electron beam with a small dispersion of the velocity ratio and an increase in the electronic efficiency.
A 3 mm waveband peniotron generator operating at the 10th harmonic of the cyclotron frequency with 2 π -mode of an 11-slot magnetron waveguide was designed and tested in [70]. A mono-helical electron beam was formed and focused by a Sm-Co permanent magnet system. In the experiments, an output power of 80 W and a maximum interaction efficiency of 7.5% were obtained using an electron beam with a voltage and current of 20 kV and 0.65 A, respectively. It was observed that as the output power increased further to 100 W, the efficiency dropped to 6.8%. The maximum efficiency of 8% was attained with a higher accelerating voltage of 22.5 kV and a cathode current of 0.5 A. The output signal frequency under magnetic field tuning varied in the range from 91.0 to 91.3 GHz.
For further details on the construction of the experimentally studied devices presented above and the experimental setups used, the reader is referred to the papers cited in this section.
It can be stated that the number of theoretical works and numerical simulations far exceeds the number of experimental studies and practical realizations of peniotron tubes. In the past, the latter were mainly carried out by two teams—one from Tohoku University and the other from the University of California at Davis.
Regrettably, the efficiency achieved in all of the above-mentioned experiments is far below what the theory predicts. The probable causes are discussed in the next section, where some conclusions are drawn on this basis.

5. Discussion and Conclusions

The most promising and attractive feature of peniotrons is the high-energy conversion efficiency predicted by theory. However, such a remarkable efficiency applies only to a tube with an ideal electron beam, the formation of which requires a precisely fabricated, assembled and aligned electron-optical and magnetic system and an interaction circuit to generate it. Any deviation from the ideal conditions leads to a deterioration in the quality of the electron beam and ultimately to a drastic decrease in interaction efficiency.
While the generation of an ideal electron beam is practically impossible (due to the scattering of initial velocities, roughness of the cathode, non-uniformity of emission, misalignment of the components of the electron-optical system, etc.), the main task is to generate at least an appropriate electron beam with a minimized spread of electron velocities, velocity ratio (pitch factor) and a guiding center radius of electron orbits (resulting in a ripple of the electron beam envelope).
The lack of electron guns producing high-quality axis-encircling electron beams is the main reason for the low efficiency obtained in the peniotron experiments. However, in the wake of recent interest in LOGs, efficient EOSs have been developed that generate high-quality uniaxial beams (see, e.g., [71,72,73,74,75,76]). It is believed that they could be used in future peniotron projects that could benefit from a cross-fertilization of these two research topics. An attempt in this direction has been made in [77]. Figure 7a shows the EOSs of the LOG with a permanent magnet and a gradual magnetic field reversal near the emitter. It produces a high-quality axis-encircling beam with a small ripple and velocity dispersion. It was developed using the self-consistent ray-tracing code GUN-MIG/CUSP from the problem-oriented package GYROSIM [78] for a LOG [79]. The rising-sun cavity of the peniotron is shown in Figure Figure 7b.
Another problem is the proper selection of the operating mode. Mode competition is a serious problem for all gyro-devices and peniotrons are no exception. However, while the interaction of modes in gyrotrons is well studied [76,81], there are far fewer studies on this phenomenon in peniotrons. As shown in [82], starting oscillation currents in the cyclotron-maser are generally much smaller than those of the peniotron interaction, and this often leads to strong competition between the peniotron and gyrotron modes. The results presented in [82], however, indicate that the mode competition for the gyro-peniotron can be easily avoided for the TE 211 mode and other low-order azimuthal modes if a large-orbit axis-encircling beam is used. At the same time, serious-mode competition and gyro-peniotron suppression are found for small-orbit off-axis beams.
There are also formidable problems related to the manufacturing of interaction circuits with tiny corrugations (e.g., vanes) in waveguides that are situated very close to the electron beam envelope and must be precisely aligned with the tube axis. In the pioneering experiments with peniotrons, solving these problems was a challenging task. Nowadays, however, with the advances in modern processing technologies, most of these problems could be solved effectively. In addition to the state-of-the-art and quite expensive CNC machines [83], various other advanced technologies can be used as in other microwave components and devices [84]. Among them are photolithography, LIGA (German acronym for Lithographie, Galvanoformung, Abformung (Lithography, Electroplating, and Molding)) [85,86], and 3D metal printing [87,88]. For example, nowadays, the micromachining for terahertz waveguide devices is characterized by (i) high-dimensional accuracy through precise photolithography; (ii) high flexibility, which allows for us to form any shape of structural elements; (iii) and low cost, as the underlying technologies are based on mature and widely used techniques and equipment.
Solving each of the problems mentioned above is a challenging task in itself. It is even more difficult, however, to solve them simultaneously. This is only possible with a systematic approach based on computer-aided design (CAD).
And last but not least, there are “generational” problems. As a matter of fact, the pioneers that discovered, studied, and promoted the peniotrons have already retired, and their successors have been engaged in the development of the mainstream gyro-devices (mainly gyrotrons, which already provide megawatt-level output power and advanced to the THz frequencies). Nevertheless, there is hope that the new generation of researchers will rediscover the potential of peniotrons and will be motivated to realize it. The main goal of this paper was to inspire them to continue research on this promising microwave source.
All this allows us to conclude that we could expect a renewed interest in the theory and development of the next generation of peniotrons. The philosophy behind this belief is that throughout history, many breakthroughs have emerged from revisiting old ideas or technologies that were once considered obsolete or difficult to realize.

Funding

This research received no external funding.

Data Availability Statement

Not applicable.

Acknowledgments

I pay tribute and express my gratitude to my brilliant teachers who inspired me to work on various gyro-devices. Among them are S.I. Molokovsky, G.S. Nusinowich, V.L. Bratman, and T. Idehara, just to mention a few. I also appreciate the longstanding and fruitful collaboration with my colleagues and friends M.Yu. Glyavin, M. Thumm, J. Dattoli, E. DiPalma, and I.P. Spassovski, and to my students and coworkers at the Research Center for Development of Far-Infrared Region at the University of Fukui (FIR UF), Japan.

Conflicts of Interest

The author declares no conflicts of interest.

References

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Figure 1. Two typical configurations of peniotron interaction circuits: (a) double-ridge waveguide peniotron and (b) TE 11 —mode peniotron with a rectangular waveguide. Figures reproduced from [18] (copyright ©2016 IEICE).
Figure 1. Two typical configurations of peniotron interaction circuits: (a) double-ridge waveguide peniotron and (b) TE 11 —mode peniotron with a rectangular waveguide. Figures reproduced from [18] (copyright ©2016 IEICE).
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Figure 2. Circular interaction structures: (a) smooth-wall waveguide (cavity) used in gyropeniotrons with helical electron beams ( R c —cavity radius, R g c —guiding center radius of gyrating electrons); (b,c) slotted (vane-loaded) waveguide and rising-sun cavity, respectively, used with uniaxial electron beams. Here, a and b are the inner and outer radius of the slots and r L is the Larmor radius of the electron orbits.
Figure 2. Circular interaction structures: (a) smooth-wall waveguide (cavity) used in gyropeniotrons with helical electron beams ( R c —cavity radius, R g c —guiding center radius of gyrating electrons); (b,c) slotted (vane-loaded) waveguide and rising-sun cavity, respectively, used with uniaxial electron beams. Here, a and b are the inner and outer radius of the slots and r L is the Larmor radius of the electron orbits.
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Figure 3. Asynchronism in the peniotron due to the fact that the electrons gyrate faster than the cyclotron resonance wave: (a) angular frequencies of the gyrating electrons and the rotating electromagnetic wave; (b) motion of the electron with respect to a coordinate system associated with the wave (in this example, m = 2 ); (c) the field amplitude that the electron “sees” at different moments (indicated by dots) during one cyclotron period.
Figure 3. Asynchronism in the peniotron due to the fact that the electrons gyrate faster than the cyclotron resonance wave: (a) angular frequencies of the gyrating electrons and the rotating electromagnetic wave; (b) motion of the electron with respect to a coordinate system associated with the wave (in this example, m = 2 ); (c) the field amplitude that the electron “sees” at different moments (indicated by dots) during one cyclotron period.
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Figure 4. On the operating principle of peniotron. The guiding center of the electron orbit drifts in such a way as to bring the electron into a stronger field at the decelerating phase and conversely into a weaker field at the accelerating phase. The orbits of an initially accelerated and an initially decelerated electron are shown in the panes (a,b), respectively. Below them, the distribution of the electric field E y in the vertical Y direction along the horizontal axis X is shown.
Figure 4. On the operating principle of peniotron. The guiding center of the electron orbit drifts in such a way as to bring the electron into a stronger field at the decelerating phase and conversely into a weaker field at the accelerating phase. The orbits of an initially accelerated and an initially decelerated electron are shown in the panes (a,b), respectively. Below them, the distribution of the electric field E y in the vertical Y direction along the horizontal axis X is shown.
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Figure 5. Brillouin diagram for the case of electron cyclotron autoresonance.
Figure 5. Brillouin diagram for the case of electron cyclotron autoresonance.
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Figure 6. Azimuthal electric fields in the vanes of the circuit. Here, the azimuthal angle (0–360°) is linearly stretched.
Figure 6. Azimuthal electric fields in the vanes of the circuit. Here, the azimuthal angle (0–360°) is linearly stretched.
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Applsci 14 11246 g007aApplsci 14 11246 g007b
Figure 7. Example of concurrent research on LOG and gyro-peniotron development: (a) EOS of LOG with a permanent magnet (shown are a photo of the device, a drawing of the tube, and results from the ray-tracing analysis of the EOS); and (b) a rising-sun cavity of a peniotron (shown is the electric field distribution calculated by the computer program for the evaluation of RF SUPERFISH cavities [80]).
Figure 7. Example of concurrent research on LOG and gyro-peniotron development: (a) EOS of LOG with a permanent magnet (shown are a photo of the device, a drawing of the tube, and results from the ray-tracing analysis of the EOS); and (b) a rising-sun cavity of a peniotron (shown is the electric field distribution calculated by the computer program for the evaluation of RF SUPERFISH cavities [80]).
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Table 1. Experimental results of peniotrons (data from [59]). Notations: c—circular cavity; r—rectangular cavity; EE—electron efficiency; DC—single-stage depressed collector; A—autoresonance operation; n Ω C —operation at n-th harmonic of the cyclotron frequency.
Table 1. Experimental results of peniotrons (data from [59]). Notations: c—circular cavity; r—rectangular cavity; EE—electron efficiency; DC—single-stage depressed collector; A—autoresonance operation; n Ω C —operation at n-th harmonic of the cyclotron frequency.
InstitutionTypeFrequency [GHz]ModePower [kW]Efficiency [%]Pulse Length [ms]
UC Davis [60]Peniotron (cusp gun)34.0
( 2 Ω C )		 TE 11 c 25.7360.02
Univ. Tohoku [21,40,61,62,63,64,65,66,67]Peniotron (magnetron-type cavity)10.0
10.5 2 Ω C
10.5 2 Ω C
30.3 3 Ω C
30.3 3 Ω C
100 10 Ω C
10		 TE 11 r
TE 31 c
TE 31 c
TE 41 c
TE 41 c
TE 11 , 1 c ( A )
TE 21 c 		10.0
0.7
1.3
6.9
6.9
0.32
1.5		36
36
10
7
35 ( 75 E E )
44 D C ( 92 E E )
1.7 ( 5 E E ) 25		0.02
Univ. Tohoku and ToshibaGyro-peniotron69.85
( 3 Ω C )		 TE 02 86.750.2
Univ. Fukui [68]Gyro-peniotron140 ( 3 Ω C ) TE 03 811
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Sabchevski, S. Peniotron: A Promising Microwave Source with Potential That Has Yet to Be Realized. Appl. Sci. 2024, 14, 11246. https://doi.org/10.3390/app142311246

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Sabchevski, Svilen. 2024. "Peniotron: A Promising Microwave Source with Potential That Has Yet to Be Realized" Applied Sciences 14, no. 23: 11246. https://doi.org/10.3390/app142311246

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Sabchevski, S. (2024). Peniotron: A Promising Microwave Source with Potential That Has Yet to Be Realized. Applied Sciences, 14(23), 11246. https://doi.org/10.3390/app142311246

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