IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 38, NO. 10, OCTOBER

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1 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 38, NO. 10, OCTOBER Generation of Subgigawatt RF Pulses in Nonlinear Transmission Lines Vladislav V. Rostov, Nikolai M. Bykov, Dmitry N. Bykov, Alexei I. Klimov, Oleg B. Kovalchuk, and Ilya V. Romanchenko Abstract This paper presents the experimental results on the generation of subgigawatt radio frequency (RF) pulses using two types of nonlinear transmission lines (NLTLs). In the high-voltage coaxial lines, we used the following: 1) a periodic gas gap structure and 2) uniformly loaded saturated ferrite with axial bias. The concept of the first line is based on the in-phase composition of RF fields produced by currents in the periodic gas gap structure of the inner conductor. The most stable and efficient narrow-band operation of the system with 12 cylindrical gas gaps (200 kv, 18 ns) was realized at an RF of 1 GHz and an RF power of several hundreds of megawatts. The maximum power conversion reached 10%. The second NLTL lacks spatial dispersion. The selfconsistent dynamics of the traveling wave is observed by coherent magnetic switching in ferrites with axial bias. The pulsed voltage driver produced 9-ns pulses of voltage between 110 and 290 kv. With the optimum external magnetic field, the efficiency of energy conversion was 10%. The peak power of oscillations produced on a resistive load was 700 MW. An increase in central frequency from 600 MHz to 1.1 GHz with incident pulse amplitude was found. Index Terms Nonlinear transmission lines (NLTLs), periodic gas gap switches, saturated ferrites. I. INTRODUCTION THE HIGH-POWER ( W) radio frequency (RF) pulses with a carrier frequency of 1 GHz and a duration of several oscillation periods can be produced through direct energy conversion of a traveling high-voltage pulse with the use of nonlinear elements [1] [4]. The spectrum width of the electromagnetic pulse at 3-dB level estimated as b F =(f max f min )/(f max + f min ) can make up 10% 20%, i.e., can qualify as a wideband spectrum. Nonlinear transmission lines (NLTLs) consist either of lumped nonlinear elements or of elements uniformly distributed on a certain line segment and provide spatial dispersion of excited oscillations. The first type of NLTLs can be referred to as NLTLs with spatial dispersion. The second type of NLTLs is an ensemble of nonlinear oscillators with a characteristic own frequency and temporal dispersion. In the first case, the duration of electromagnetic pulses is determined by the number of lumped nonlinear elements, e.g., gas gap switches. Circuits for producing high-voltage bipolar pulses (b F > 0.25), as a rule, contain two high-voltage gas gap switches. In our experiments, the central conductor of the Manuscript received September 30, 2009; revised February 15, 2010; accepted April 7, Date of publication May 27, 2010; date of current version October 8, The authors are with the Institute of High Current Electronics, Russian Academy of Sciences, Tomsk , Russia ( rostov@lfe.hcei.tsc.ru). Digital Object Identifier /TPS coaxial line had up to 12 gas gap switches [5]. It was shown that an increase in the number of gaps causes an inversely proportional decrease in spectrum width. Because the average delay time of breakdown for a gap displays a nonlinear relation to the amplitude of the applied field, including the RF component, the central frequency in the spectrum of the pulse is a function of the amplitude of the incident TEM wave. Moreover, gas gap switches, nonlinear capacitances, or inductances can be used as the lumped elements. For example, a periodic waveguide structure with ferrite-based nonlinear inductances and capacitive cross couplings was used to produce rather long pulses (about tens of periods) with a peak power of about tens of megawatts [1], [3]. The lower pulse duration takes place in the transmission line uniformly loaded with ferrite saturated by an external longitudinal magnetic field. Because of the azimuthal magnetic field in the incident TEM wave, the high-voltage pulse propagating along the line tends to rotate the magnetization vector in each elementary ferrite volume. Precession of the vector arises with no change of its absolute value. The shape of the excited pulse has a characteristic decay governed by the damped magnetization precession. The reciprocal value (f max f min ) characterizing the pulse duration is specified mainly by the relaxation time of nonlinear oscillators. Experiments are made with NiZn ferrite for which the damping factor is found to be relatively small [6], [7]. II. NLTL WITH TANDEM SWITCHING OF GAS GAPS The experimental facility included a pulse generator based on a Tesla transformer built in a coaxial forming line (FL) charged to 500 kv [5]. In the self-breakdown mode, the main gas gap switch ensured generation of TEM pulses of amplitude U 0 from 50 to 250 kv in a coaxial transmission line (Fig. 1). The generator allowed repetitive pulse operation with a pulse repetition frequency up to 100 Hz, and this was important for preconditioning the electrodes within pulses and for increasing the breakdown voltage stability. The number of successive discharge gaps in the line was between 2 and 12 (Fig. 2). The working chamber with the line was filled with pure nitrogen to a pressure that is controllable between 1 and 20 atm. The radius of the central stainless steel conductor of the line was r =59mm, and the radius of the outer conductor was R = 100 mm. The dielectrical structure was fabricated from polyethylene. The impedance of the line was ρ =32Ω. In most of the experiments, the spacing of annular gaps Δd was 4 mm /$ IEEE

2 2682 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 38, NO. 10, OCTOBER 2010 Fig. 1. Typical waveform of the voltage pulse at the inlet of the line with shorted gas gap switches. Timescale: 10 ns/div. Horizontal cursor shoes the level U 0. Fig. 3. Waveforms: Ch1 (upper, 45 kv/div) capacitive divider voltage, Ch2 (45 kv/div) voltage from the magnetic probe, Ch3 (2.2 ka/div) current at the input of the working chamber with two switches; 5 ns/div. Fig. 2. Geometry of the periodic gas gap structure. (1) Electrodes. (2) Dielectric. Experiments were carried out both with a matched resistive load and with RF irradiation into the free space by a horn antenna. In the latter case, a coaxial-waveguide converter of the TEM mode of the coaxial line to the TM 01 mode of the circular waveguide was used [5]. The mode converter and the antenna ensured matching in the frequency band from 0.5 to 2 GHz corresponding to a calculated value of a power reflection coefficient less than 10%. The RF oscillations were measured using the magnetic probes and a special broadband capacitive voltage divider with a working band higher than 3 GHz. At the flat top of the driving pulse, each switch produces short high-voltage pulses propagating in the same direction as the driving pulse (during the charging of the interelectrode capacitance C g ), as well as in opposite directions (during the switching and rise of the current). Fig. 3 shows an example of two pulses running toward the driving pulse in the geometry with two discharge gaps. In this case (Δd =4 mm, U 0 = 175 kv, and excess pressure 3.5 atm), two gaps are 77 cm apart to minimize the mutual effects of the sources. Increasing the number of discharge gaps caused the corresponding increase in the number of RF oscillation periods. The experiments show Fig. 4. Signal from the wideband receiving antenna (5 ns/div) and the spectrum (500 MHz/div). U 0 = 175 kv; P =4.7atm; Δd =4mm. that, in a certain range of gas pressure, the central frequency of RF oscillations is tuned and that there is a range of optimum pressures in which the efficiency of energy conversion reaches 10%. The increase in efficiency involves narrowing of the spectral band. Fig. 4 shows a typical waveform of the RF pulse taken by the receiving dipole antenna 3 m away from the horn antenna for 12 discharge gaps with a period d = 110 mm. With a gas pressure in the working chamber of 5 atm, the increase in driving pulse amplitude by 10% led to an increase in oscillation frequency by, on average, 20%. For 3-dB level from the maximum tuning band of the output RF pulse power, the tuning bandwidth of the carrier frequency was GHz. With a fixed amplitude of the pulse U 0 = 175 kv, about the same gradual and continuous increase in carrier frequency takes place with decreasing the gas pressure from 5.5 to 3 atm. At the boundaries of the frequency band, the pulse-topulse reproducibility of the amplitude and frequency decreased. Simultaneously, with excitation of the aforementioned oscillations, oscillations below the frequency band of the concurrent wave were found in the spectrum of reflected signals.

3 ROSTOV et al.: GENERATION OF SUBGIGAWATT RF PULSES IN NLTLs 2683 Interpretation of the results for a large number of gaps requires a model describing the wave process in the periodic system with wavenumber dispersion h = h(f) in a certain band and synchronism between the wave (or spatial harmonic) phase velocity and average velocity of the front d d/c +Δt 2πf = V ph = ±h + n2π/d. (1) Here, Δt is the average time interval between the instant the pulse front arrives in a gap and the onset of switching with some voltage drop across the gap, the sign + corresponds to the traveling wave propagating with the driving pulse, the sign corresponds to the backward wave, n =0, ±1,..., and c is the velocity of light. The dependence of Δt on the voltage drop is responsible for nonlinearity of the structure. For excitation of the traveling wave, we can consider dispersion of a cold periodic structure that is easy to obtain analytically [5]. The boundaries of the first transparency band can be written as f low = c d πd 4cρC g f high = c πd 1+ d 4cρC g. (2) The experimental frequency band is agreed with estimation by (2) at C g 4 pf. The measurement showed the capacitance of 5 ± 2 pf. However, in this case, the slowing of the fundamental TEM wave in the cold periodic structure is not very high (h 2πf/c). Therefore, the most probable phase relation between the forward traveling wave and the effective velocity of breakdown replacement could be explained by the existence of the (+1)st spatial harmonic Fig. 5. Pulse shape at the NLTL inlet. 2πf(d/c +Δt) hd = 2π. (3) Therefore, we can assume that typical means of Δt are ranging as 1/f. The measured low-frequency spectral components, probably, correspond to the condition 2πf b (d/c +Δt)+h b d = 2π (4) where f b and h b are the frequency and the wavenumber of the backward wave in a hot line with discharge gaps and multichannel switching. III. NLTL WITH SATURATED FERRITE In experiments, a similar Tesla transformer inside a single FL (30 Ω, 9 ns) with a charge voltage up to 600 kv was used [6]. The experimental setup consists of two uniform sections filled with transformer oil and the NLTL between them. The electric length of the uniform sections was equal to half the pulse duration, exclusive of the reflection effect on measurements. The energy of the high-voltage pulse and excited RF oscillations was absorbed in a matched resistance loading the output of the transmission line. The NLTL was filled with transformer oil for increasing the electric strength. The NLTL length was made up by ferrite rings and was varied up to 77 cm with a step of Fig. 6. Waveforms of the power P (t) =U 2 /ρ for two lines with (solid line) 41 and (dashed line) 77 cm. (a) With no magnetic field. (b) H 0 =40kA/m. 9 cm. The power consumed by the dc solenoid was no greater than 1 kw for a maximum magnetic field (H 0 80 ka/m), and therefore, no special cooling was required. Signals were measured with broadband capacitive dividers. The maximum amplitude of the driving voltage pulse at the NLTL inlet was 295 kv (Fig. 5). With no magnetic field, a stationary shock front of duration 0.5 ns at a level of is formed in the NLTL even over a few lengths of the inner diameter of the line [6]. Further increasing the ferrite section length decreases the pulse duration due to irreversible energy losses with a dissipation rate of 0.1 J/cm [Fig. 6(a)]. The magnetic field μ 0 H 0 B s changes the situation [Fig. 6(b)], and oscillations of amplitude, which is also dependent on the pulse current, with the maximum at certain magnetic fields are observed [7]. It is remarkable that, within the pulse, the power integral remains nearly constant with increasing the system length [Fig. 6(b)]. The energy conserved in the pulse propagating in the NLTL with saturated ferrite is indicative of a minor role of dissipative processes in the video to radio pulse energy conversion. The cooperative mode of oscillations is affected by the synchronism of the shock front velocity and the phase velocity of the electromagnetic wave [1], which

4 2684 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 38, NO. 10, OCTOBER 2010 [5] D. N. Bykov, N. M. Bykov, and V. V. Rostov, Energy conversion of a high-voltage pulse to electromagnetic oscillations in a coaxial line with a periodic structure of gas switches, in Proc. 15th Int. Symp. High Current Electron., Tomsk, Russia, 2008, pp [6] K. V. Afanasyev, O. B. Kovalchuk, V. O. Kutenkov, I. V. Romanchenko, and V. V. Rostov, Formation of subnanosecond rise times of high-voltage pulses in an unsaturated-ferrite-loaded coaxial line, Instrum. Exp. Tech., vol. 51, no. 3, pp , May [7] V. P. Gubanov, A. V. Gunin, O. B. Kovalchuk, V. O. Kutenkov, I. V. Romanchenko, and V. V. Rostov, Effective transformation of the energy of high-voltage pulses into high-frequency oscillations using a saturated-ferrite-laded transmission line, Tech. Phys. Lett., vol. 35, no. 7, pp , Jul Fig. 7. Spectrum of the signal at the NLTL outlet. is strongly coupled with the magnetization wave. The peak power of oscillations was 700 MW with the amplitude of 140 kv. The highest efficiency of power conversion for the maximum line length is estimated as 10%. The efficiency for radiated power can be less due to filtration of the low-frequency component. The spectrum of the pulse at the NLTL outlet is shown in Fig. 7. The spectral RF components of magnetization are associated with the RF currents induced in the line and are proportional within the stationary wave. With the maximum voltage amplitude at the NLTL inlet, the central frequency in the high-frequency spectral range was 1.1 GHz and was decreased up to 0.6 GHz with a decrease of voltage to 110 kv. For the optimal conditions, the value Δ (see Fig. 7) was about 14 db. The central frequency tuning with bias magnetic field was about 10% at 3-dB level at fixed high voltage amplitude. The spectrum of the excited oscillations is wideband: b F IV. CONCLUSION The described devices for RF pulse production based on nonlinear elements require further experimental studies. However, even at this stage, they can be interested for some applications due to their features. First of all, there are no transient processes. Both of the subgigawatt RF sources are characterized to the tunable frequency. For an NLTL with periodic gas gap structure, it has been demonstrated that a high tuning of central frequency is achieved by a relatively low change of voltage in the incident TEM wave. Experiments have shown that NLTL with saturated ferrite can operate in the efficient mode. These researches have to be continued in the theory and experiments to find the optimal conditions and corresponding configurations for different ferrites. Vladislav V. Rostov was born in He received the M.Sc. degree in plasma physics from Novosibirsk State University, Novosibirsk, Russia, in 1978 and the C.Sc. and Dr.Sci. degrees from the Institute of High Current Electronics, Russian Academy of Sciences, Tomsk, Russia, in 1985 and 2001, respectively. He is currently the Head of the Physical Electronics Department, Institute of High Current Electronics, Russian Academy of Sciences. Dr. Rostov was the recipient of the Komsomol Award in science in 1987 and the State Award of Russian Federation in science in Nikolai M. Bykov was born in He received the M.Sc. degree in electrodynamics and quantum physics from Tomsk State University, Tomsk, Russia. Since 1984, he has been with the Institute of Tomsk. His research interests include pulsedpower techniques, gas breakdown, and high-power microwaves. Dmitry N. Bykov was born in He received the M.Sc. degree in plasma physics from Tomsk State University, Tomsk, Russia. Since 2005, he has been with the Institute of Tomsk. His research interests include highpower microwaves, subnanosecond gas breakdown, and electrophysics. REFERENCES [1] A. M. Belyantsev, A. I. Dubnev, I. Klimin, Y. A. Kobelev, and L. A. Ostrovskii, Generation of radio pulses by an electromagnetic shock wave in a ferrite-loaded transmission line, Tech. Phys., vol. 40, no. 8, pp , Aug [2] M. P. Brown and P. W. Smith, High power pulsed soliton generation at radio and microwave frequencies, in Proc. 11th IEEE Pulsed Power Conf., Baltimore, MD, 1997, pp [3] N. Seddon, C. R. Spikings, and J. E. Dolan, RF pulse formation in nonlinear transmission lines, in Proc. IEEE Pulsed Power Plasma Sci. Conf., Albuquerque, NM, 2007, pp [4] J. A. Gaudet, E. Schamiloglu, J. O. Rossi, C. J. Buchenauer, and C. Frost, Nonlinear transmission lines for high power applications, in Proc. 28th IEEE Int. Power Modulator Conf., Las Vegas, NV, 2008, p. 82. Alexei I. Klimov was born in He received the M.Sc. degree in plasma physics from Novosibirsk State University, Novosibirsk, Russia, in 1977 and the C.Sc. degree in physical electronics from the Institute of High Current Electronics, Russian Academy of Sciences, Tomsk, Russia, in He is currently with the Institute of High Current Electronics, Russian Academy of Sciences. His research interests include microwaves, high-current electron beams, nanosecond radars, and measurements in the radio frequency band.

5 ROSTOV et al.: GENERATION OF SUBGIGAWATT RF PULSES IN NLTLs 2685 Oleg B. Kovalchuk was born in He received the M.Sc. degree in electrophysics from Tomsk Polytechnic University, Tomsk, Russia, in From 1987 to 2005, he was with the Research Institute of High Voltages, Tomsk Polytechnic University. Since 2005, he has been with the Institute of Tomsk. His research interests include pulsedpower techniques and electrophysics. Ilya V. Romanchenko was born in He received the M.S. degree in physics from Tomsk State University, Tomsk, Russia, in Since 2005, he has been with the Institute of High Current Electronics, Russian Academy of Sciences, Tomsk, where he is currently a Junior Research Fellow with the Physical Electronics Department. His research interests include magnetic nonlinear transmission lines and gas breakdown at high overvoltage.