Subterahertz Photonic Crystal Klystron Amplifier

Jacob Stephens; G. Rosenzweig; M. A. Shapiro; R. J. Temkin; J. C. Tucek; K. E. Kreischer

doi:10.1103/PhysRevLett.123.244801

Subterahertz Photonic Crystal Klystron Amplifier

Jacob Stephens, G. Rosenzweig, M. A. Shapiro, R. J. Temkin, J. C. Tucek, K. E. Kreischer

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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Abstract

This Letter reports the successful experimental demonstration of amplification of subterahertz radiation in a klystron with photonic crystal cavities. The klystron has six cavities, with each cavity having a series of oversized photonic crystal cells made up of a 5×3 array of square posts. The center post is removed from each cell to form a highly oversized (0.8 mm∼λ/4) beam tunnel, with power coupling from cell to cell through the tunnel. The pulsed electron beam is operated at 23.5 kV, 330 mA in a 0.5 T solenoidal field. At 93.7 GHz, a small-signal gain of 26 dB and a saturated output power of 30 W are obtained. Experimental results are in very good agreement with the predictions of a particle-in-cell code. The successful achievement of high gain operation of a photonic crystal klystron amplifier is promising for the future extension of klystron operation well into the terahertz frequency region.

Original language	English
Article number	244801
Pages (from-to)	244801
Journal	Physical Review Letters
Volume	123
Issue number	24
DOIs	https://doi.org/10.1103/PhysRevLett.123.244801
State	Published - Dec 12 2019

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10.1103/PhysRevLett.123.244801

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@article{4d9710f6f6784eac8d63c8d89eb5b88f,

title = "Subterahertz Photonic Crystal Klystron Amplifier",

abstract = "This Letter reports the successful experimental demonstration of amplification of subterahertz radiation in a klystron with photonic crystal cavities. The klystron has six cavities, with each cavity having a series of oversized photonic crystal cells made up of a 5×3 array of square posts. The center post is removed from each cell to form a highly oversized (0.8 mm∼λ/4) beam tunnel, with power coupling from cell to cell through the tunnel. The pulsed electron beam is operated at 23.5 kV, 330 mA in a 0.5 T solenoidal field. At 93.7 GHz, a small-signal gain of 26 dB and a saturated output power of 30 W are obtained. Experimental results are in very good agreement with the predictions of a particle-in-cell code. The successful achievement of high gain operation of a photonic crystal klystron amplifier is promising for the future extension of klystron operation well into the terahertz frequency region.",

author = "Jacob Stephens and G. Rosenzweig and Shapiro, {M. A.} and Temkin, {R. J.} and Tucek, {J. C.} and Kreischer, {K. E.}",

note = "Funding Information: https://orcid.org/0000-0002-2473-0329 Stephens J. C. https://orcid.org/0000-0002-6365-666X Rosenzweig G. https://orcid.org/0000-0003-0579-7891 Shapiro M. A. https://orcid.org/0000-0001-9813-0177 Temkin R. J. Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, USA https://orcid.org/0000-0001-7231-3434 Tucek J. C. Kreischer K. E. Northrop Grumman Corporation , Rolling Meadows, Illinois 60008, USA 12 December 2019 13 December 2019 123 24 244801 5 November 2019 11 July 2019 {\textcopyright} 2019 American Physical Society 2019 American Physical Society This Letter reports the successful experimental demonstration of amplification of subterahertz radiation in a klystron with photonic crystal cavities. The klystron has six cavities, with each cavity having a series of oversized photonic crystal cells made up of a 5 × 3 array of square posts. The center post is removed from each cell to form a highly oversized ( 0.8 mm ∼ λ / 4 ) beam tunnel, with power coupling from cell to cell through the tunnel. The pulsed electron beam is operated at 23.5 kV, 330 mA in a 0.5 T solenoidal field. At 93.7 GHz, a small-signal gain of 26 dB and a saturated output power of 30 W are obtained. Experimental results are in very good agreement with the predictions of a particle-in-cell code. The successful achievement of high gain operation of a photonic crystal klystron amplifier is promising for the future extension of klystron operation well into the terahertz frequency region. Defense Advanced Research Projects Agency 10.13039/100000185 Space and Naval Warfare Systems Center Pacific N66001-16-C-4039 Powerful sources of coherent radiation are needed in the subterahertz and terahertz range of frequencies (0.1–10 THz) for many important scientific, industrial, defense, and medical applications [1–3] . In recent years, gyrotrons [4] , free electron lasers [5] , and synchrotron radiation facilities [6] have been successfully developed in this frequency range. They can provide high average output power levels but are not suitable for many applications because of their relatively large size and cost. In addition, many very innovative concepts are being intensively investigated for generating THz radiation [7–9] , but they may not be compatible with applications requiring higher average power. For applications requiring power levels of several watts to several kilowatts, a more compact device operating at low voltage would be far more desirable. Recently, there have been intensive efforts to extend the operating frequency of the classical vacuum electron devices, traveling wave tubes (TWTs) and klystrons, into the subterahertz and terahertz range. These devices have made remarkable progress, reaching power levels of tens of watts at 220–233 GHz [10–14] and a fraction of a watt at frequencies near 670 [15] and 850 GHz [16] . However, scaling the power of these devices to higher frequency is exacerbated by the very small dimensions of the electron beam tunnel, typically only one-tenth of a wavelength in diameter, which severely limits the device power and creates difficulty in device alignment. Novel concepts are needed to achieve higher operating power from TWTs and klystrons at higher frequency. One important innovative concept is the use of a sheet electron beam, which extends the size of the electron beam by about one order of magnitude in one transverse dimension. Successful sheet beam devices have been built at the kilowatt power level at 94 GHz in W band [17,18] and at the tens to hundreds of watts level near 220 GHz [10,13,14] . These advances are very promising. However, sheet electron beams have limitations. They are extended in one transverse dimension, but remain very small in the other transverse dimension. They are also difficult to align and focus due to space charge forces acting to curl the electron beam at the edges [19] . The novel concept developed here utilizes a symmetric round beam, which propagates in an oversized beam tunnel (0.8 mm in diameter = 1 / 4 wavelength) and passes through an oversized circuit made up of photonic crystal (PC) cells. PC cells have the advantage of confining the design mode while suppressing competing modes. PC-based accelerator cavities, using both metallic and dielectric scattering elements [9,20–22] , have been successfully demonstrated, while all metal PC circuits have been demonstrated in high frequency gyrotron oscillators and amplifiers [23,24] . Although the use of PC structures was anticipated for conventional microwave devices [25] , the application in practice has been very limited (see, e.g., [26–29] ). The design presented here is based on preliminary designs of a PC-based klystron [30,31] . While dielectric scattering elements are an option, here we have elected to employ an all metallic structure owing to the complications associated with dielectrics in vacuum electron devices, such as electron beam induced charging and poor thermal conductivity. The oversized beam tunnel diameter used in this Letter has novel physics and engineering implications. It allows simpler fabrication and a higher electron beam current and power. It also allows the microwave power to couple directly through the beam tunnel, which brings new physics considerations to the device design. The amplifier topology explored here is a version of a klystron called an extended interaction klystron (EIK). In a klystron, the electron beam begins to be bunched at the drive frequency in an input cavity, is further bunched in intermediate cavities, and has power extracted in the final output cavity. An EIK differs from a conventional klystron by using a number of slow-wave structure (SWS) periods or cells in each cavity, as shown in Fig. 1 . As shown, our design has two SWS periods in both the input and output cavities and six in each of the four intermediate cavities. Each period is a 2D photonic crystal structure comprising a square lattice of square posts on the transverse dimension in a 5 × 3 array. Note that the center element of the PC lattice is removed, creating a defect site in the lattice and allowing the electron beam to be transmitted through the structure along the axis. All cavities were designed for a 94 GHz resonant frequency. 1 10.1103/PhysRevLett.123.244801.f1 FIG. 1. Schematic of the PC-EIK amplifier configuration (dimensions in millimeters). The inlaid figure shows a single period of the PC-SWS. See text for more details. A key advantage of the square lattice of square conductors PC topology was that, compared to more widely studied PC topologies such as a triangular lattice of circular scattering elements, the square lattice of square conductors allowed for simplified and improved fabrication of the circuit. Namely, the advantage of this PC topology was that it permitted the circuit to be fabricated using a split block-type methodology, where each plate was fabricated via direct machining. See the Supplemental Material for more information regarding the fabrication [32] . Photonic crystal lattice constants, a = 0.45 and b = 1.32 mm were used for the intermediate cavities, as shown in Fig. 1 . These values were selected to enable a very small amount of external coupling such that the cavity properties (resonant frequency, quality factors, etc.) could be measured experimentally in a cold test, using a vector network analyzer, without affecting device performance. On the other hand, PC lattice constants a = 0.35 and b = 1.25 mm , were used for the input and output cavities, which were selected to minimize the reflected input power at resonance and to optimize cavity loading at device saturation. Additional details regarding the electromagnetic characterization of the PC lattice, including the global frequency band gap map, may be found in the Supplemental Material [32] . The electron gun is designed to produce a 20 kV, 290 mA beam, focused to a 0.6 mm beam diameter. A permanent magnet solenoid with a ∼ 0.5 T on-axis flux density is used to confine the beam on axis. The beam tunnel diameter, D T is fixed at 0.8 mm, which is ∼ λ / 4 , significantly larger than the D T ∼ λ / 10 common to these devices. The SWS acts to reduce the electromagnetic wave phase velocity such that it travels synchronously with the 20 kV electron beam, resulting in efficient energy exchange (i.e., interaction) between the wave and beam. Considering an axially propagating wave in a SWS, from Floquet{\textquoteright}s theorem, the electric field may be decomposed into a Fourier sum of spatial harmonics [33,34] E z ( r → , t ) = ∑ m = - ∞ ∞ E z , m ( x , y ) e i ( ω t - k z , m z ) . (1) Here, k z , m is the m th spatial harmonic of the z component of the propagation vector k → = ( k x , k y , k z ) , where k z , m = ω / v p 0 + 2 π m / p , v p 0 is the phase velocity of the fundamental spatial harmonic, and p is the physical length of the SWS period. Strong interaction occurs with the desired harmonic when k z , m = ω / v z , where v z is the beam electron velocity. Since ω / k z , m is the axial phase velocity of the wave, the synchronism condition is also the condition that the electron beam velocity equals the wave axial phase velocity of the desired harmonic. The PC lattice is optimized to confine the operational electromagnetic mode to the central defect site. Three-dimensional electromagnetic eigenmode calculations were carried out using the commercial software cst microwave studio to obtain both the dispersion characteristics and electric field structure of the lowest order eigenmodes of the PC-SWS (see Fig. 2 ). Figure 2(a) gives the axial dispersion of the lowest order modes of the SWS. The SWS is optimized to utilize the TM 11 -like mode with a 2 π phase advance per period, as indicated by the intersection of the electron beam line ( ω = k z v z ) with this mode at k z p = 2 π . Note that since our defect site is quasirectangular, we use the mode designation of rectangular waveguide apertures, where TM 11 describes the mode structure with a single lobe in both transverse dimensions. For a beam voltage of 20 kV, a frequency of 94 GHz, and a phase advance k z p of 2 π , the synchronism condition requires an axial period, p = 0.87 mm . As shown in Fig. 2(b) , the operational TM 11 -like mode is well confined to the defect region, with a strong electric field on the beam axis, which is necessary to achieve strong interaction with the electron beam. On the other hand, the next higher order eigenmodes given in Figs. 2(c) and 2(d) (i.e., the dipole modes) are not confined to the defect site. Moreover, these modes are also bidirectional, featuring electric fields oriented in opposing directions with a null in the electric field in the region of the electron beam. For these reasons, these modes do not couple well to the electron beam and will not compete with the operational mode. 2 10.1103/PhysRevLett.123.244801.f2 FIG. 2. (a) Axial dispersion relation of the operational, TM 11 -like mode, and the next lowest order modes (dipole modes nos. 1 and 2), calculated for a = 0.35 and b = 1.25 mm . The 20 kV electron beam line ( ω = k z v z ) is also shown. (b) Axial electric field distribution of the TM 11 -like mode. (c) Axial electric field distribution of dipole mode no. 1. (d) Axial electric field distribution of dipole mode no. 2. Low power microwave measurements (cold tests) of the fabricated structure revealed that Ohmic quality factors, external cavity loading factors, and cavity frequencies were in good agreement with the design parameters, suggesting successful fabrication of the amplifier. Amplifier tests were conducted using 2 – 10 μ s high voltage pulses at pulse repetition rates near 1 Hz (see example waveforms in Fig. 3 ). At 20 kV, the electron gun produced 290 mA, with 90% beam transmission through the circuit. The temporal response of the 94 GHz microwave output is also shown in Fig. 3 , demonstrating that the device output directly follows the applied voltage and current. The input drive power was provided by a solid-state amplifier multiplier chain source operated continuously (not shown in Fig. 3 ). 3 10.1103/PhysRevLett.123.244801.f3 FIG. 3. High voltage pulse, beam, and collector current and 93.7 GHz output diode signal. Small-signal gain measurements were performed with approximately 1 mW of input power (see Fig. 4 ). Although the PC-SWS was designed for nominal operation at 20 kV, improved amplifier performance was observed for higher operating voltages near 23.5 kV. As shown in Fig. 4 , successful operation of the amplifier was achieved with better than 25 dB of small-signal gain for voltages ranging from 23.2 to 23.5 kV, with a peak gain of 26 dB. Moreover, although the absolute gain was reduced, increased bandwidth was achieved for an operating voltage of 22.9 kV while still producing better than 15 dB of gain. 4 10.1103/PhysRevLett.123.244801.f4 FIG. 4. Experimental small-signal gain-bandwidth measurements at the specified voltages. As detailed in the Supplemental Material [32] , the majority of cavity resonant frequencies were measured near 93.7 GHz; thus the peak in gain near 93.7 GHz is expected. There are a number of possible explanations for why the device was found to exhibit improved performance for higher voltage (i.e., 23.5 versus 20 kV). Most notably, operation of the electron gun diode at different voltage yields a significantly different electron beam with regard to the beam diameter, scalloping, and the location of scalloping minima and maxima, all of which strongly influence wave-beam interaction in the circuit. The process of beam formation is further complicated by possible small misalignment of the device axis with respect to the magnetic field axis. Additional factors, such as machining errors, could also contribute to this effect. The large-signal performance of the device is given in Fig. 5 for a fixed operating voltage of 23.5 kV and a frequency of 93.72 GHz. To test the amplifier to saturation, a commercial extended interaction oscillator was used to provide up to 350 mW of input power. The saturated output power was measured to be 30 W. Also shown are the results of particle-in-cell simulations performed in cst particle studio . The simulations predicted ∼ 25 dB linear gain and a saturated output power of 15 W, slightly lower than the observed values but still in very good agreement. 5 10.1103/PhysRevLett.123.244801.f5 FIG. 5. Experimental output power versus input power for a frequency of 93.72 GHz and an operating voltage of 23.5 kV and comparison with cst particle-in-cell (PIC) simulation. The present version of this klystron is an initial result, which was designed to demonstrate the basic concept of a klystron with an oversized beam tunnel and photonic crystal cavities. The achieved efficiency in this proof-of-principle device is lower than in conventional klystrons at W band. Higher efficiency may be achieved in future designs by better optimization and fabrication techniques and by using a multistage depressed collector. Higher gain and efficiency would also be obtained by using much higher beam current; the higher current is enabled by the oversized beam tunnel. To review, a new klystron amplifier concept employing cavities with a PC-SWS was proposed, built, and tested. The klystron featured an oversized electron beam tunnel ( ∼ λ / 4 ), demonstrating that conventional scaling laws, which dictate that the electron beam is on the order of one-tenth of a wavelength, may be relaxed. One may reasonably anticipate the upper limit for the beam tunnel dimensions to be D T ∼ λ / 1.7 , which corresponds to the point at which the fundamental TE 10 mode is no longer cut off. Moreover, it may be that other limiting factors also arise before this is achieved. Additional studies are necessary to address this point further. Experimental low power microwave (cold test) measurements of the PC-SWS cavity properties showed successful fabrication of the cavities and overall structure. In pulsed operation at 23.5 kV, the klystron demonstrated 26 dB of small-signal gain at 93.7 GHz with a saturated output power of 30 W, in good agreement with simulation. These results demonstrate the viability of using a photonic crystal structure as the unit cell in a klystron. Furthermore, the successful results also show the feasibility of having the electromagnetic wave propagate from cell to cell directly through the beam tunnel, rather than through slots, as in a klystron with a conventional voltage electron beam. Future work could take advantage of the oversized nature and simple fabrication of the present design to achieve high output power levels at much higher frequencies, perhaps 250–500 GHz or even up into the terahertz band. Such extensions would be enabled by the oversized nature of the beam tunnel and the simplified PC-SWS structure that can be directly machined. 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year = "2019",

month = dec,

day = "12",

doi = "10.1103/PhysRevLett.123.244801",

language = "English",

volume = "123",

pages = "244801",

journal = "Physical Review Letters",

publisher = "American Physical Society",

number = "24",

}

TY - JOUR

T1 - Subterahertz Photonic Crystal Klystron Amplifier

AU - Stephens, Jacob

AU - Rosenzweig, G.

AU - Shapiro, M. A.

AU - Temkin, R. J.

AU - Tucek, J. C.

AU - Kreischer, K. E.

N1 - Funding Information: https://orcid.org/0000-0002-2473-0329 Stephens J. C. https://orcid.org/0000-0002-6365-666X Rosenzweig G. https://orcid.org/0000-0003-0579-7891 Shapiro M. A. https://orcid.org/0000-0001-9813-0177 Temkin R. J. Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, USA https://orcid.org/0000-0001-7231-3434 Tucek J. C. Kreischer K. E. Northrop Grumman Corporation , Rolling Meadows, Illinois 60008, USA 12 December 2019 13 December 2019 123 24 244801 5 November 2019 11 July 2019 © 2019 American Physical Society 2019 American Physical Society This Letter reports the successful experimental demonstration of amplification of subterahertz radiation in a klystron with photonic crystal cavities. The klystron has six cavities, with each cavity having a series of oversized photonic crystal cells made up of a 5 × 3 array of square posts. The center post is removed from each cell to form a highly oversized ( 0.8 mm ∼ λ / 4 ) beam tunnel, with power coupling from cell to cell through the tunnel. The pulsed electron beam is operated at 23.5 kV, 330 mA in a 0.5 T solenoidal field. At 93.7 GHz, a small-signal gain of 26 dB and a saturated output power of 30 W are obtained. Experimental results are in very good agreement with the predictions of a particle-in-cell code. The successful achievement of high gain operation of a photonic crystal klystron amplifier is promising for the future extension of klystron operation well into the terahertz frequency region. Defense Advanced Research Projects Agency 10.13039/100000185 Space and Naval Warfare Systems Center Pacific N66001-16-C-4039 Powerful sources of coherent radiation are needed in the subterahertz and terahertz range of frequencies (0.1–10 THz) for many important scientific, industrial, defense, and medical applications [1–3] . In recent years, gyrotrons [4] , free electron lasers [5] , and synchrotron radiation facilities [6] have been successfully developed in this frequency range. They can provide high average output power levels but are not suitable for many applications because of their relatively large size and cost. In addition, many very innovative concepts are being intensively investigated for generating THz radiation [7–9] , but they may not be compatible with applications requiring higher average power. For applications requiring power levels of several watts to several kilowatts, a more compact device operating at low voltage would be far more desirable. Recently, there have been intensive efforts to extend the operating frequency of the classical vacuum electron devices, traveling wave tubes (TWTs) and klystrons, into the subterahertz and terahertz range. These devices have made remarkable progress, reaching power levels of tens of watts at 220–233 GHz [10–14] and a fraction of a watt at frequencies near 670 [15] and 850 GHz [16] . However, scaling the power of these devices to higher frequency is exacerbated by the very small dimensions of the electron beam tunnel, typically only one-tenth of a wavelength in diameter, which severely limits the device power and creates difficulty in device alignment. Novel concepts are needed to achieve higher operating power from TWTs and klystrons at higher frequency. One important innovative concept is the use of a sheet electron beam, which extends the size of the electron beam by about one order of magnitude in one transverse dimension. Successful sheet beam devices have been built at the kilowatt power level at 94 GHz in W band [17,18] and at the tens to hundreds of watts level near 220 GHz [10,13,14] . These advances are very promising. However, sheet electron beams have limitations. They are extended in one transverse dimension, but remain very small in the other transverse dimension. They are also difficult to align and focus due to space charge forces acting to curl the electron beam at the edges [19] . The novel concept developed here utilizes a symmetric round beam, which propagates in an oversized beam tunnel (0.8 mm in diameter = 1 / 4 wavelength) and passes through an oversized circuit made up of photonic crystal (PC) cells. PC cells have the advantage of confining the design mode while suppressing competing modes. PC-based accelerator cavities, using both metallic and dielectric scattering elements [9,20–22] , have been successfully demonstrated, while all metal PC circuits have been demonstrated in high frequency gyrotron oscillators and amplifiers [23,24] . Although the use of PC structures was anticipated for conventional microwave devices [25] , the application in practice has been very limited (see, e.g., [26–29] ). The design presented here is based on preliminary designs of a PC-based klystron [30,31] . While dielectric scattering elements are an option, here we have elected to employ an all metallic structure owing to the complications associated with dielectrics in vacuum electron devices, such as electron beam induced charging and poor thermal conductivity. The oversized beam tunnel diameter used in this Letter has novel physics and engineering implications. It allows simpler fabrication and a higher electron beam current and power. It also allows the microwave power to couple directly through the beam tunnel, which brings new physics considerations to the device design. The amplifier topology explored here is a version of a klystron called an extended interaction klystron (EIK). In a klystron, the electron beam begins to be bunched at the drive frequency in an input cavity, is further bunched in intermediate cavities, and has power extracted in the final output cavity. An EIK differs from a conventional klystron by using a number of slow-wave structure (SWS) periods or cells in each cavity, as shown in Fig. 1 . As shown, our design has two SWS periods in both the input and output cavities and six in each of the four intermediate cavities. Each period is a 2D photonic crystal structure comprising a square lattice of square posts on the transverse dimension in a 5 × 3 array. Note that the center element of the PC lattice is removed, creating a defect site in the lattice and allowing the electron beam to be transmitted through the structure along the axis. All cavities were designed for a 94 GHz resonant frequency. 1 10.1103/PhysRevLett.123.244801.f1 FIG. 1. Schematic of the PC-EIK amplifier configuration (dimensions in millimeters). The inlaid figure shows a single period of the PC-SWS. See text for more details. A key advantage of the square lattice of square conductors PC topology was that, compared to more widely studied PC topologies such as a triangular lattice of circular scattering elements, the square lattice of square conductors allowed for simplified and improved fabrication of the circuit. Namely, the advantage of this PC topology was that it permitted the circuit to be fabricated using a split block-type methodology, where each plate was fabricated via direct machining. See the Supplemental Material for more information regarding the fabrication [32] . Photonic crystal lattice constants, a = 0.45 and b = 1.32 mm were used for the intermediate cavities, as shown in Fig. 1 . These values were selected to enable a very small amount of external coupling such that the cavity properties (resonant frequency, quality factors, etc.) could be measured experimentally in a cold test, using a vector network analyzer, without affecting device performance. On the other hand, PC lattice constants a = 0.35 and b = 1.25 mm , were used for the input and output cavities, which were selected to minimize the reflected input power at resonance and to optimize cavity loading at device saturation. Additional details regarding the electromagnetic characterization of the PC lattice, including the global frequency band gap map, may be found in the Supplemental Material [32] . The electron gun is designed to produce a 20 kV, 290 mA beam, focused to a 0.6 mm beam diameter. A permanent magnet solenoid with a ∼ 0.5 T on-axis flux density is used to confine the beam on axis. The beam tunnel diameter, D T is fixed at 0.8 mm, which is ∼ λ / 4 , significantly larger than the D T ∼ λ / 10 common to these devices. The SWS acts to reduce the electromagnetic wave phase velocity such that it travels synchronously with the 20 kV electron beam, resulting in efficient energy exchange (i.e., interaction) between the wave and beam. Considering an axially propagating wave in a SWS, from Floquet’s theorem, the electric field may be decomposed into a Fourier sum of spatial harmonics [33,34] E z ( r → , t ) = ∑ m = - ∞ ∞ E z , m ( x , y ) e i ( ω t - k z , m z ) . (1) Here, k z , m is the m th spatial harmonic of the z component of the propagation vector k → = ( k x , k y , k z ) , where k z , m = ω / v p 0 + 2 π m / p , v p 0 is the phase velocity of the fundamental spatial harmonic, and p is the physical length of the SWS period. Strong interaction occurs with the desired harmonic when k z , m = ω / v z , where v z is the beam electron velocity. Since ω / k z , m is the axial phase velocity of the wave, the synchronism condition is also the condition that the electron beam velocity equals the wave axial phase velocity of the desired harmonic. The PC lattice is optimized to confine the operational electromagnetic mode to the central defect site. Three-dimensional electromagnetic eigenmode calculations were carried out using the commercial software cst microwave studio to obtain both the dispersion characteristics and electric field structure of the lowest order eigenmodes of the PC-SWS (see Fig. 2 ). Figure 2(a) gives the axial dispersion of the lowest order modes of the SWS. The SWS is optimized to utilize the TM 11 -like mode with a 2 π phase advance per period, as indicated by the intersection of the electron beam line ( ω = k z v z ) with this mode at k z p = 2 π . Note that since our defect site is quasirectangular, we use the mode designation of rectangular waveguide apertures, where TM 11 describes the mode structure with a single lobe in both transverse dimensions. For a beam voltage of 20 kV, a frequency of 94 GHz, and a phase advance k z p of 2 π , the synchronism condition requires an axial period, p = 0.87 mm . As shown in Fig. 2(b) , the operational TM 11 -like mode is well confined to the defect region, with a strong electric field on the beam axis, which is necessary to achieve strong interaction with the electron beam. On the other hand, the next higher order eigenmodes given in Figs. 2(c) and 2(d) (i.e., the dipole modes) are not confined to the defect site. Moreover, these modes are also bidirectional, featuring electric fields oriented in opposing directions with a null in the electric field in the region of the electron beam. For these reasons, these modes do not couple well to the electron beam and will not compete with the operational mode. 2 10.1103/PhysRevLett.123.244801.f2 FIG. 2. (a) Axial dispersion relation of the operational, TM 11 -like mode, and the next lowest order modes (dipole modes nos. 1 and 2), calculated for a = 0.35 and b = 1.25 mm . The 20 kV electron beam line ( ω = k z v z ) is also shown. (b) Axial electric field distribution of the TM 11 -like mode. (c) Axial electric field distribution of dipole mode no. 1. (d) Axial electric field distribution of dipole mode no. 2. Low power microwave measurements (cold tests) of the fabricated structure revealed that Ohmic quality factors, external cavity loading factors, and cavity frequencies were in good agreement with the design parameters, suggesting successful fabrication of the amplifier. Amplifier tests were conducted using 2 – 10 μ s high voltage pulses at pulse repetition rates near 1 Hz (see example waveforms in Fig. 3 ). At 20 kV, the electron gun produced 290 mA, with 90% beam transmission through the circuit. The temporal response of the 94 GHz microwave output is also shown in Fig. 3 , demonstrating that the device output directly follows the applied voltage and current. The input drive power was provided by a solid-state amplifier multiplier chain source operated continuously (not shown in Fig. 3 ). 3 10.1103/PhysRevLett.123.244801.f3 FIG. 3. High voltage pulse, beam, and collector current and 93.7 GHz output diode signal. Small-signal gain measurements were performed with approximately 1 mW of input power (see Fig. 4 ). Although the PC-SWS was designed for nominal operation at 20 kV, improved amplifier performance was observed for higher operating voltages near 23.5 kV. As shown in Fig. 4 , successful operation of the amplifier was achieved with better than 25 dB of small-signal gain for voltages ranging from 23.2 to 23.5 kV, with a peak gain of 26 dB. Moreover, although the absolute gain was reduced, increased bandwidth was achieved for an operating voltage of 22.9 kV while still producing better than 15 dB of gain. 4 10.1103/PhysRevLett.123.244801.f4 FIG. 4. Experimental small-signal gain-bandwidth measurements at the specified voltages. As detailed in the Supplemental Material [32] , the majority of cavity resonant frequencies were measured near 93.7 GHz; thus the peak in gain near 93.7 GHz is expected. There are a number of possible explanations for why the device was found to exhibit improved performance for higher voltage (i.e., 23.5 versus 20 kV). Most notably, operation of the electron gun diode at different voltage yields a significantly different electron beam with regard to the beam diameter, scalloping, and the location of scalloping minima and maxima, all of which strongly influence wave-beam interaction in the circuit. The process of beam formation is further complicated by possible small misalignment of the device axis with respect to the magnetic field axis. Additional factors, such as machining errors, could also contribute to this effect. The large-signal performance of the device is given in Fig. 5 for a fixed operating voltage of 23.5 kV and a frequency of 93.72 GHz. To test the amplifier to saturation, a commercial extended interaction oscillator was used to provide up to 350 mW of input power. The saturated output power was measured to be 30 W. Also shown are the results of particle-in-cell simulations performed in cst particle studio . The simulations predicted ∼ 25 dB linear gain and a saturated output power of 15 W, slightly lower than the observed values but still in very good agreement. 5 10.1103/PhysRevLett.123.244801.f5 FIG. 5. Experimental output power versus input power for a frequency of 93.72 GHz and an operating voltage of 23.5 kV and comparison with cst particle-in-cell (PIC) simulation. The present version of this klystron is an initial result, which was designed to demonstrate the basic concept of a klystron with an oversized beam tunnel and photonic crystal cavities. The achieved efficiency in this proof-of-principle device is lower than in conventional klystrons at W band. Higher efficiency may be achieved in future designs by better optimization and fabrication techniques and by using a multistage depressed collector. Higher gain and efficiency would also be obtained by using much higher beam current; the higher current is enabled by the oversized beam tunnel. To review, a new klystron amplifier concept employing cavities with a PC-SWS was proposed, built, and tested. The klystron featured an oversized electron beam tunnel ( ∼ λ / 4 ), demonstrating that conventional scaling laws, which dictate that the electron beam is on the order of one-tenth of a wavelength, may be relaxed. One may reasonably anticipate the upper limit for the beam tunnel dimensions to be D T ∼ λ / 1.7 , which corresponds to the point at which the fundamental TE 10 mode is no longer cut off. Moreover, it may be that other limiting factors also arise before this is achieved. Additional studies are necessary to address this point further. Experimental low power microwave (cold test) measurements of the PC-SWS cavity properties showed successful fabrication of the cavities and overall structure. In pulsed operation at 23.5 kV, the klystron demonstrated 26 dB of small-signal gain at 93.7 GHz with a saturated output power of 30 W, in good agreement with simulation. These results demonstrate the viability of using a photonic crystal structure as the unit cell in a klystron. Furthermore, the successful results also show the feasibility of having the electromagnetic wave propagate from cell to cell directly through the beam tunnel, rather than through slots, as in a klystron with a conventional voltage electron beam. Future work could take advantage of the oversized nature and simple fabrication of the present design to achieve high output power levels at much higher frequencies, perhaps 250–500 GHz or even up into the terahertz band. Such extensions would be enabled by the oversized nature of the beam tunnel and the simplified PC-SWS structure that can be directly machined. 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PY - 2019/12/12

Y1 - 2019/12/12

N2 - This Letter reports the successful experimental demonstration of amplification of subterahertz radiation in a klystron with photonic crystal cavities. The klystron has six cavities, with each cavity having a series of oversized photonic crystal cells made up of a 5×3 array of square posts. The center post is removed from each cell to form a highly oversized (0.8 mm∼λ/4) beam tunnel, with power coupling from cell to cell through the tunnel. The pulsed electron beam is operated at 23.5 kV, 330 mA in a 0.5 T solenoidal field. At 93.7 GHz, a small-signal gain of 26 dB and a saturated output power of 30 W are obtained. Experimental results are in very good agreement with the predictions of a particle-in-cell code. The successful achievement of high gain operation of a photonic crystal klystron amplifier is promising for the future extension of klystron operation well into the terahertz frequency region.

AB - This Letter reports the successful experimental demonstration of amplification of subterahertz radiation in a klystron with photonic crystal cavities. The klystron has six cavities, with each cavity having a series of oversized photonic crystal cells made up of a 5×3 array of square posts. The center post is removed from each cell to form a highly oversized (0.8 mm∼λ/4) beam tunnel, with power coupling from cell to cell through the tunnel. The pulsed electron beam is operated at 23.5 kV, 330 mA in a 0.5 T solenoidal field. At 93.7 GHz, a small-signal gain of 26 dB and a saturated output power of 30 W are obtained. Experimental results are in very good agreement with the predictions of a particle-in-cell code. The successful achievement of high gain operation of a photonic crystal klystron amplifier is promising for the future extension of klystron operation well into the terahertz frequency region.

UR - http://www.scopus.com/inward/record.url?scp=85076551803&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.123.244801

DO - 10.1103/PhysRevLett.123.244801

M3 - Article

C2 - 31922865

VL - 123

SP - 244801

JO - Physical Review Letters

JF - Physical Review Letters

IS - 24

M1 - 244801

ER -

Subterahertz Photonic Crystal Klystron Amplifier

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