Experimental studies on radio frequency sources for ionospheric heaters

Existing IM heaters are in fixed locations at high latitudes. At present, the largest ground-based ionospheric heating facility is the High-Frequency Active Auroral Research Program (HAARP) array located in Gakona, Alaska.² This array currently uses triode based Amplitude Modulation (AM) amplifiers to transmit power in the ionosphere. There are, however, opportunities for the exploration of new phenomena due to IM at mid-latitudes. These explorations would be enhanced if the heater were transportable. A mobile heater for ionospheric modification studies requires a new Megawatt (MW) class Radio Frequency (RF) source operating with an antenna array that is 1/20 the area of HAARP.³ To deliver an effective power density comparable to that of HAARP, the total source power must be in the range of 16 MW in order to achieve the same ERP as HAARP, thus demanding highly efficient sources.⁴ The type of tube, currently under development at the University of Maryland for mobile IM research, is a hybrid version of a triode and a klystrode⁵ operating in class D as described previously in Refs. 1, 4, 6, and 7. The existing design uses a 70 kV-30 A beam; thus, a full system design would require 8 tubes/antennas to be mounted onto a mobile platform to match the power of HAARP.

Klystrodes are commonly used in radio and TV broadcast and operate at frequencies above 100 MHz in class-B or class-C, density modulating the beam on and off and generating RF in the output resonant cavity.⁸ By operating in class-D, the pulse width is less than or equal to a quarter of an RF period to improve efficiency such that all electrons arrive at the output interaction space at approximately the same time. For ionospheric modification, the frequency of the RF source should be in the range of 3–10 MHz.^2,3 At these low RF frequencies, conventional cavities would be too large. The UMD tube design uses an external resonant lumped element circuit to extract the beam's kinetic energy. The beam passes through the output interaction space towards the collector that is connected to a tunable resonant pi-circuit. The beams' kinetic energy is then extracted as they are being slowed down by the high voltage on the floating collector, unlike a grounded collector in a klystrode.

Only the pi-circuit efficiency is being studied and reported here, using a low power electron beam produced by a gridded thermionic electron gun. This scaled study allows us to focus on the pi-circuit alone in order to show proof of principle without the experimental complications of a MW beam. The gun produces an electron beam bunched at the driving frequency with narrow phase angle spread that is then retarded and collected by the floating collector with resonant impedance matching to the output RF load.

This paper is organized as follows: in Sec. II, we present the idea of using a pi-circuit to extract the beam power. Section III describes the experimental setup, including the gridded electron gun and the pi-circuit. In Sec. IV, we describe the results of extracted power and the effect of the collector charging up to a high potential relative to the ground, causing some electrons to be deflected away from the collector. In Sec. V, we discuss experimental results and compare them with the theory and Pspice simulations.⁹ Section VI summarizes this work.

A schematic of the experimental configuration is shown in Fig. 1(a). It is a variation of the basic configuration considered in our previous work.¹ A density modulated beam is first accelerated through an anode cathode potential, and then, the electron kinetic energy is extracted using a decelerating gap in the output interaction space, connected to a tunable resonant circuit that presents AC impedance to the beam. The designed value of the impedance is such that the voltage that develops across the decelerating gap in response to the modulated beam current is sufficient to extract nearly all the beam energy. The type of resonant circuit we are considering is a pi-circuit [shown in Fig. 1(b)], the topology of which resembles that of the Greek letter π.¹⁰ Other circuit configurations, such as the resonant transformer scheme, were explored but proved to have poor efficiency and a low reactive path to the ground.⁴ Pi-circuits are conventionally found in 13.56 MHz plasma generators used for deposition and etching. The circuit is used in this application to match external circuits with different real impedances in order to optimize the power transfer between them.

The main components of the pi-circuit are the input capacitor C₁, the output capacitor C₂, and the inductor L₁₂ connecting the two capacitors. The quantity I_Beam is the time dependent beam current driving the circuit, and R_o is the output impedance. The circuit parameters are selected so that the circuit presents a real impedance to the AC portion of the current source I_Beam at the operating frequency. The characteristics of the circuit are primarily determined by L₁₂, C₁, and C₂. We also include dominant parasitic elements C₁₂ and R₁₂ for L₁₂ in the circuit [shown in Fig. 1(c)]. The gap impedance presented to the beam is

where Y₁₁= Y₁+ Y₁₂, Y₁= jωC₁, Y₂₂= Y₂+ Y₁₂, Y₂= jωC₂, and Y₁₂= jωC₁₂+ 1/R₁₂+ jωL₁₂. To sufficiently decelerate the beam before it hits the collector, the pi-circuit must present a high impedance to the beam. For a peak beam current, I_Beam = 1 A with a duty factor of 25%, the sum of the peak AC current components is I₁ = 450 mA at the fundamental, and the circuit when connected to the decelerating gap must offer a gap impedance of $Zgap≅44.43kΩ$ in order to generate a 20 kV peak voltage to completely stop the beam. This deceleration converts the kinetic energy of the beam into the electromagnetic energy stored in the pi-circuit which is eventually delivered into the load R_o.

The above-mentioned pi-circuit should be tunable, efficient, and still offer a constant gap impedance and prevent any damage to the collector. The tunability of the circuit (resonant frequency) is controlled by the L₁₂ and C₁, and the impedance is adjusted by modifying C₂. We solve the circuit equations for the above circuit, keep the inductance of the coil L₁₂ constant, and adjust C₁ and C₂ to control the resonant frequency and the gap impedance. The gap impedance remains constant at all the resonant peaks [Fig. 2(a)], while C₁ [Fig. 2(b)], C₂ [Fig. 2(c)], and Q-factor [Fig. 2(d)] change with frequency in order to achieve specific resonant frequency and maintain the same impedance.

In Figs. 2(a)–2(d), we calculated the circuit parameters over a range of frequencies (3–5 MHz) using a 20 kV, 1 A modulated electron beam. For a highly efficient power conversion, we find that the parasitic resistance R₁₂ of the inductor L₁₂ is required to be very low to maintain a high efficiency.

A pi-circuit was built at the University of Maryland with circuit elements and properties that are suitable for the Naval Research Laboratory (NRL) electron gun (shown in Fig. 3). The NRL gun has a gated and gridded thermionic cathode and was originally designed to operate in the frequency range from 500 MHz to 2.5 GHz by direct coaxial coupling to the grid. The grid is composed of concentric wires with a radius of 30 μm and placed 1 mm in front of the tungsten dispenser cathode that has a Pierce configuration for a focused beam.¹¹ The cathode-anode voltage is designed to operate from 20 to 35 kV with a cathode-grid voltage in the range of 10–200 V, allowing for flexible operation. We were able to drive the grid directly through its biasing electrode (about −30 V relative to the cathode) with square pulses of small duty factor (25%) and a peak voltage of 80 V, in the 3–10 MHz RF frequency range.

This experiment is a scaled-down, proof-of-principle testing of the pi-circuit to be used as a tunable power extraction device for the bunched electron beam. One of the drawbacks of using the NRL electron gun is that its Pierce gun configuration of the cathode leads to a converging electron beam that comes to a focus shortly after going through the exit hole in the anode. From there, the beam diverges and requires a focusing magnetic field to propagate. This is not to be confused with the better design of a magnetically immersed gun guided by a long solenoidal magnetic field.

The electron beam in our experiment propagated through a 24 cm drift section embedded in a short (10 cm) solenoidal magnetic field for beam focusing. The focusing solenoid had 500 turns and could provide 141 G of field at a current of 1 A. The diverging beam was mildly focused by the solenoid to be approximately collimated, and it then hit a collector plate isolated from the ground using a high voltage feed through.

The pi-circuit used in the experiment was composed of a large core 7-turn inductor, L₁₂ of radius 12.2 cm, made from 0.95 cm outer diameter copper tubing, a vacuum variable capacitor (VVC) for C₁, and two VVCs in parallel for C₂. The values for each component are shown in Tables I and II in Sec. V. The output load was 50 Ω, and the input RF voltage induced in the pi-circuit on C₁ is measured with a 1000:1 voltage divider (ROSS Model VD90-4.1-A-LB-A) into the oscilloscope. The divider is composed of a capacitive/resistive divider, where the input R is 360 MΩ and input C is 3.3 pF and the output R is 564 kΩ and output C is 2980 pF. The ROSS divider's normal frequency range is from DC to 5 MHz. The output voltage is measured directly on the same oscilloscope after attenuation with high power RF attenuators.

The time dependent electron beam current could only be measured directly on the collector before the pi-circuit was connected to it. It is measured using a 50 Ω terminator, and the current waveform is recorded on the same oscilloscope. With the pi-circuit connected, the current on the collector runs through L₁₂ in the pi-circuit and returns to the ground through the output load resistor of 50 Ω. The DC offset of the output RF voltage is the voltage drop generated by the average beam current on the load resistor. This DC offset voltage therefore can be used to monitor the average current received by the collector. With the assumption that the current temporal profile does not change with the connection of the pi-circuit to the collector, the actual current driving the pi-circuit during the experiment can be scaled with this DC offset voltage at the load resistor.

The driving RF signal was optically relayed to a high voltage pulser floating at the cathode voltage. The output of the HV pulser was connected in series with the biasing DC voltage source and then directly to the bias electrode for the grid. The overall timing of the experiment was provided by a Stanford Delay Generator (Model 535) which also externally triggered the oscilloscope. The voltage and current profiles on the oscilloscope were therefore synchronized in time, and their relative phase was determined. The input power to the pi-circuit was calculated as the product of the measured induced input RF voltage and the inferred driving current, with the relative phase included. The output power is simply the average of the output RF voltage squared divided by the load resistance.

A sweep of frequencies on the grid in optimizing the output power was performed to establish the resonant frequency of the pi-circuit. At this resonant frequency, power transfer efficiencies of the pi-circuit were calculated from the input and output powers at various C₂ values for different impedance matching of the pi-circuit to the electron beam. The intrinsic values of the capacitance for C₁ and C₂, the inductance for L₁₂, and the internal resistance of R₁₂ were measured using an LCR meter at a frequency of 10 kHz. High frequency properties such as the internal capacitance C₁₂ and R₁₂ were established by studying the behaviors of the inductor near its self-resonance using a signal generator.

In order to maximize the beam current collected onto the collector, the solenoid field was swept to determine an operating point for the solenoid. The optimal operating point for the solenoid was 1.8 A, collecting a beam current of 0.98 A. After this, the resistor that connects the collector to the ground (used to measure current) was removed and the pi-circuit was connected. The power entering the pi-circuit, P_in, was estimated from the phased product of the alternating Voltage V_in and the alternating beam current inferred I_Beam. The voltage was measured directly, but the alternating beam current was measured separately as described in Sec. III. We did measure the DC component of the beam current with the pi-circuit connected using the DC offset observed on the load resistor. The DC current with the pi-circuit connected was reduced from that measured with the resistor connected. We attribute the reduction in the total current entering the pi-circuit due to the collector charging up to a sufficiently high potential relative to the grounded pipe walls, and this causes some of the electrons to be deflected away from the collector, thus reducing the actual total current entering the pi-circuit, as opposed to the measured current when the 50 Ω resistor is connected to the collector and the pi-circuit is disconnected.

The measured RF voltage V_in induced on the input capacitor C₁ of the pi-circuit is shown as the blue curves in Fig. 4(a) for C₂ of 2.7 nF (near maximum output power).

The red curve is the simulation result that will be discussed in Sec. V. The V_in waveform has an envelope that increases over several microseconds and decays similarly when the drive RF pulses have ended. The rise and fall times of the envelope are related to the Q-factor of the pi-circuit where the power loss is from both the power in the output resistor and the internal resistance of the inductor. Similarly, the measured output RF voltage V_out is shown as the blue curve in Fig. 4(b). A magnified view of the input RF voltage V_in and the input current I_Beam profile is shown in Fig. 5, indicating that there is a phase lag between the voltage waveform and the current waveform. This phase lag affects the calculation of input power from the multiplicative product of the voltage and current waveforms at the input capacitor.

The output power P_out is inferred from the measurement of the voltage across the output 50 Ω resistor. The power was optimized by sweeping the frequency of the drive RF in the experiment and observing the maximum V_in and V_out, obtaining the 4.09 MHz resonant frequency, as was similarly done.¹² The solenoid current was fixed, and we varied the capacitance of C₂. This would test the influence of circuit impedance as changed by varying C₂ on the circuit performance. Also, by varying C₂, we are varying the induced V_in and consequentially extracting as much kinetic energy from the beam as possible. Figure 6(a) shows the input and output powers, and Fig. 6(b) shows the efficiency inferred at various capacitances for C₂, at an RF drive frequency of 4.09 MHz.

When the capacitor C₂ was varied from 1.5 to 2.7 nF, the input and output power changed, where the output power peaked between 2.3 and 2.5 nF, corresponding to a circuit efficiency [Fig. 6(b)] of 70%–63%.

This observation of power transfer and transfer efficiency was tested at another frequency of operation to observe any frequency dependence. The resonant frequency of the circuit was lowered to 3.1 MHz by increasing the inductance of the L₁₂ inductor. In Fig. 7(a), the input RF voltage V_in is shown as the blue curve, while the output RF voltage V_out is similarly shown as the blue curve in Fig. 7(b), for both C₂ of 2.7 nF (near maximum output power).

The red curve is the simulation result that will be discussed in Sec. V. A magnified view of the input RF voltage V_in and the input current I_Beam profile is shown in Fig. 8 at this frequency, illustrating the phase lag between the voltage waveform and the current waveform.

Figure 9(a) illustrates the input and output power and Fig. 9(b) illustrates the efficiency measured at various capacitances for C₂ at an RF drive frequency of 3.1 MHz.

At 3.1 MHz, the output power peaked between 3.1 and 3.3 nF, corresponding to a circuit efficiency of 60%–56%. When the circuit was operated at 4.09 MHz, its efficiency [Fig. 6(b)] was between 70% and 63%. One should note that the overall input power in the 3.1 MHz case is higher than the corresponding input power in the 4.09 MHz. Since the input currents for both cases are about the same, the phase lags between the current and voltage in the two cases are different as is the duty-factor as shown in Figs. 5 and 8.

The resonant pi-circuit was simulated using Pspice where the current source in the simulations used the inferred beam current from the experiment when the pi-circuit was disconnected and scaled with this DC offset current measured at the load resistor when the pi-circuit was connected.¹⁰ The measured circuit parameters (C₁, L₁₂, R₁₂, C₁₂, and C₂) for the pi-circuit used in both the experiment and simulations are shown for 4.09 MHz in Table I. The measurements were performed using a combination of an LCR meter and a network analyzer.

The inductor was designed keeping the estimated AC resistance in mind. However, the measured resistance values differed from the estimated values. This is a result of operating the pi-circuit at a frequency close to the self-resonant frequency (SRF) of the inductor.¹³ The frequency dependent parasitic resistance of a real inductor is due to the skin effect (increased resistance due to reduced cross sectional area for current flow) and the capacity effect (increased resistance due to operating close to the SRF) at higher frequencies. A more accurate formula to calculate the intrinsic resistance of the inductor, which accounts for the effects near the SRF, is given by¹³ 

where ω is the operating frequency of the circuit, ω_o is the SRF of the inductor, and r_AC is the AC resistance associated with the skin-depth. When the operating frequency of the pi-circuit is far away from the SRF (⁠$ω2≪ωo2/3$⁠) of the inductor, the resistance of the coil R_AC approaches the AC resistance r_AC due to the skin depth. As we approach the SRF, the quantity ω²/ω_o² approaches 1 and consequently, the additional terms involving this ratio dominate the final value. Hence, designing an inductor with its SRF far from the frequency of operation and accounting for the capacity effect becomes a central aspect of the pi-circuit construction.

In order to better understand the model of the pi-circuit and its parasitic elements, we compared the simulated V_in and V_out with experimental V_in and V_out shown in Sec. IV for V_in in Fig. 4(a) and for V_out in Fig. 4(b). When the capacitance of C₂ was decreased, the voltage induced on the V_in and V_out decreased as well and correspondingly the overall power in the circuit, but the transfer efficiency of the circuit increased. This is due to the fact that there is less power stored in the resonator and correspondingly less power being lost in the resistive component of the inductor. When the capacitance C₂ decreases, the circuit has a smaller Q-factor. Figure 10 illustrates the measured Q at various capacitances for C₂ at an RF drive frequency of 4.09 MHz.

The measured Q of the circuit spans a range from 23 to 48. Simulations indicate that there is 8.3–15.1 A of current through the resistor R₁₂ as C₂ is swept over the range, the larger corresponding to the larger C₂. Sweeping C₂ we vary the induced V_in and consequentially extract more kinetic energy from the beam at larger C₂'s. Pspice simulations also illustrate that there is a phase shift increase between the current I_Beam and the induced voltage V_in across C₁ with increasing capacitance C₂.

The measured circuit parameters (C₁, L₁₂, R₁₂, C₁₂, and C₂) for the pi-circuit used in both the experiment and simulations are shown in Table II for the lower frequency of 3.1 MHz.

Once again, to better understand the model of the pi-circuit and its parasitic elements, we compared the simulated V_in and V_out versus experimental V_in and V_out shown in Sec. IV in Figs. 7(a) and 7(b), respectively, at this lower frequency as well. Similarly with the previous operating frequency, when the capacitance C₂ was decreased, the voltage induced on the V_in and V_out also decreased and correspondingly the overall power in the circuit decreased, but the transfer efficiency of the circuit increased as it did in the previous case. Similarly, this is due to the fact that there is less power stored in the resonator and correspondingly less power being lost in the resistive component of the inductor. The circuit has a smaller Q-factor when the capacitance C₂ decreases. Figure 11 illustrates the measured Q at various capacitances for C₂ at an RF drive frequency of 3.1 MHz.

The measured Q of the circuit spans a range from 16 to 76. Simulations indicate that there is 6.5–21.3 A of current through the resistor R₁₂ as C₂ is swept over the range, the larger corresponding to the larger C₂. Similarly to the previous case, by sweeping C₂ we varied the induced V_in and consequentially extracted more kinetic energy from the beam at larger C₂s.

An experiment for a pi-circuit design was described in this manuscript. Using a 20 kV–1 A electron beam produced by a gridded thermionic electron gun operating in class D mode, we drove an external lumped element circuit. Detailed analyses of efficiency has showed that we were able to extract at most 84% of the power when the circuit was tuned to have a low Q and as a result low currents in the inductor branch of the circuit, thus dissipating less power in the effective resistance of the inductor. When we tune the pi-circuit to maximize output power, the efficiency drops to 60%, and as a result, more power is dissipated in the inductor branch of the circuit due to the fact that the Q has increased, whereas higher energies were extracted out of the beam.

In terms of a MW class RF source required for IM research, the required gap impedance $Zgap$ will be significantly lower as compared to the gap impedance needed for the NRL experiment. Calculations and cold test measurements have shown the pi-circuit needed for 70 kV-30 A device is significantly less sensitive to the parasitic losses in the inductor as the beam impedance is substantially smaller.¹ 

This work was supported by the Air Force Office of Scientific Research under Grant No. FA95501410019. The authors would like to thank Dr. John C. Rodgers for encouraging and supporting this project throughout the years. We would also like to thank Dr. Thomas Melhorn of NRL for use of the IOT gun.