1. Introduction
A reflex klystron oscillator as a microwave source has a short beam tunnel, no use of an external magnet, and a voltage control of the starting current by a repeller [
1,
2]. It was proposed originally in 1939 [
3]. However, the conventional reflex klystron oscillator using a thermionic cathode has significant heat loss, bulky dimensions, and long pre-heating times, which would cause difficulties in several important characteristics, including miniaturization, fast turn-on, and submillimeter-wave band working frequency of the device. A field-emission cold cathode exhibits an instantaneous turn-on response, room temperature operation, and size reduction, which has been applied for novel vacuum devices [
4]. Among the field-emission materials, carbon nanotubes (CNTs) have excellent electron-emitting characteristics, such as high current density and electrical conductivity, and high physical stability [
4,
5,
6,
7], and have been used as cold cathodes in the study of novel microwave and terahertz frequency sources [
8,
9,
10,
11,
12,
13,
14]. The klystron based on a cold-cathode has also been followed with interest by researchers, especially in miniaturization and terahertz band devices [
15,
16,
17,
18]. For example, Manohara1 et al. designed a monolithic THz nanoklystron using carbon nanotubes as a cold cathode via photolithography and deep ion etching (DRIE) on a Si substrate and fabricated a CNT cold-cathode [
16]. The analytical simulations of terahertz klystron oscillators have been established [
17,
18,
19]. The influence of the incident electron beam aperture angle has also been studied [
17]. Although some progress has been made in both the design and analytical simulation, device fabrication and performance remain challenging. For the operation of a reflex klystron oscillator as a closed-loop system, the returning electron beam is crucial to provide a precondition for the electron bunch and to form a feedback mechanism to initiate oscillations. A higher extracting grid-electrode voltage for a reflex klystron oscillator based on a cold-cathode electron gun would affect the returning electron beam characteristics.
In this study, a CNTs cold-cathode e-gun was designed and fabricated. An X-band reflex klystron oscillator prototype structure was designed and assembled based on the CNT gun. A study of the returning electron beam in the device structure was presented. To characterize the effect of high voltage for extracting electrons on the returning electron beam, a threshold voltage was defined, and an approach was proposed to decrease the threshold voltage and improve the characteristics of the returning electron beam. From these results are expected to provide regularities and rules for optimization of start-oscillation conditions for cold-cathode reflex klystron oscillators.
2. Design and Fabrication
A coaxial cold-cathode e-gun was designed and fabricated consisting of a CNT cold cathode, an extracting grid electrode, a ring-shaped focus electrode, and an anode [
20], as shown in
Figure 1a,b. A ultralong vertical CNT film emitter of about 1.85 mm in height and 3 mm in diameter was prepared by the chemical vapor deposition method [
21,
22]. The edge morphology of the CNT emitter was shaped as a convex surface with a curvature radius of about 0.5 mm at the edge by a mechanical polishing treatment to eliminate the edge effect [
20], as shown in the inset of
Figure 1b. The focusing electrode with a ring having an inner diameter of 5 mm and height H
f of 1 mm was placed 1 mm above the grid electrode.
Figure 1d shows the electrical scheme of the measurement setup of the electron gun, where the phosphor anode was placed 3 mm above the focus electrode. The cathode voltage was set at 0 V. Direct-current (DC) voltage was applied to the focus electrode and the anode. A pulsed voltage supply was generated using a pulsed power supply combined with a DC power supply. A voltage pulse with a duty cycle of 1.6% at 800 Hz was applied to the grid electrode. A high voltage differential detector (CYBERTEK DP 6150) was connected to the sample resistor R
2 in parallel. The voltage waveform was visualized on the oscilloscope (TEKTRONIX MDO 3024). The CNT cold-cathode emission current I
c and anode current I
a could be obtained from the sample resistors R
1 and R
2 using the relation I = V/R respectively.
Figure 1c shows the field emission characteristics of I
c versus grid voltage V
g in the e-gun. A field emission current of 28.3 mA was measured at an electric field of 10 V/μm, and the corresponding emission current density was 400 mA/cm
2. The vacuum pressure in the chamber was 5 × 10
−5 Pa. The waveforms of the cathode current I
c, anode current I
a, and grid voltage V
g at a focusing voltage V
f of −50 V were shown in
Figure 1e. The spot size of the electron beam on the anode was measured as about 3.8 mm in diameter, as shown in the top half of
Figure 1f. The lower half of
Figure 1f shows the emission site pattern of the CNT emitter distributed uniformly on an indium tin oxide (ITO) glass anode (captured at a field-emission pulse current of 15 mA) in a diode configuration with a gap of 0.2 mm.
A schematic diagram of the designed re-entrant cavity is shown in
Figure 2a. A coupling loop at the sidewall was designed as the output port. The simulation result of the microwave electric field distribution in eigenmode is shown in the bottom part of
Figure 2a. Image 4 of
Figure 2b shows the photograph of the re-entrant resonant cavity. The lower and upper plate of the cavity are shown in image 1 and 2 of
Figure 2b, and the corresponding grids in image 3 of
Figure 2b. The resonant frequency of the cavity is 8.376 GHz measured by using a vector network analyzer (KEYSIGHT N5247A). A reflex klystron oscillator structure consisting of the cold-cathode electron gun as an electron-beam source, the re-entrant cavity as an anode, and the repeller was designed and assembled, as shown in
Figure 2c,d. The barrel type repeller with an inner-diameter of 6 mm and a height of 7 mm was placed 0.5 mm above the cavity.
Figure 2e illustrates the electrical scheme of measurement setup of a reflex klystron oscillator structure.
3. Results and Discussion
In the cold-cathode reflex klystron oscillator, the electron beam from the e-gun passes through the gap of the resonant cavity, moves forward to enter the repeller space, and then decelerates and returns to the resonant cavity by the repeller. At a certain anode voltage V
a, the anode current I
a originates from the interception of electrons by the grids and walls of the cavity. The negatively biased repeller can repel the electron beam entering the repeller but also can bend the equipotential line and focus the electron beam in the repeller [
23]. With the modulation of the repeller voltage V
r, a fraction of the electrons returning to the cavity is not intercepted by the grids of the cavity and forms a returning electron beam. Under the correct feedback conditions [
1], the returning electron beam can provide preconditions for the electron bunch to generate an induced current for beam–wave interaction and form a feedback mechanism, which is necessary to initiate oscillations. Because the electron beam returning to the cavity and the forward electron beam occur simultaneously, it is difficult to measure the returning electron beam individually. Here, the returning beam was investigated indirectly by measuring variations of the anode current I
a.
Figure 3a–c show the anode current I
a as a function of the repeller voltage V
r at fixed anode voltages V
a. The focusing voltage V
f is fixed at –50 V, and the grid voltage V
g is fixed at 1610 V. I
a increases continuously with V
r ramped up from 0 V to −450 V at V
a of 275 V. I
a first decreases and then increases gradually with V
r from 0 V to −450 V at V
a between 300 V and 700 V. A valley starts to appear in the curve at V
a of 300 V, which is induced by an increase of the returning electron beam, as shown in the black rectangle in
Figure 3a–c. Above V
a of 700 V, I
a shows the trend of increase, decrease, and increase gradually with Vr from 0 V to −450 V. It is inferred that the electrons that pass through the cavity move forward a short distance and return to the cavity at the anode voltage V
a below 275 V. The electric field near the cavity is relatively non-uniform, so most electrons with larger transverse velocity returning to the cavity would be intercepted easily by the cavity with V
r, resulting in an increase in I
a. As V
a increases from 300 to 700 V, the electric field near the cavity becomes gradually uniform and facilitates a decrease in the transverse velocity of the electrons. The number of electrons that is not intercepted is gradually more than that intercepted by the grids and walls with low V
r, resulting in a reduction in I
a. However, the repulsive force acting on the electrons increases, and the electric field between the repeller and cavity becomes distorted gradually as the difference between V
r and V
a increases; more electrons returning to the cavity are hit easily on the grids and walls of the cavity, which results in an increase in I
a again. The amount of 300 V is thought of as the starting voltage to develop a valley, called threshold voltage V
aT. As V
a further increases, I
a first increases slightly, as shown in
Figure 3c. It is considered that the kinetic energy of electrons through the gap of the cavity at higher V
a increases, while the ability of the small V
r to repel and focus the beam returning to the cavity is weak. Thus, a little more electrons fall easily on the cavity. In curves, the valley value (indicated by the black arrow in the black rectangle) gradually shifts to the left and gets larger. Owing to the increasing kinetic energy of electrons with increasing V
a, a higher V
r is needed to reflect these electrons along their original path, and the returning electron beam increases. Here, I
a0 is the current at V
r of 0 V, and I
ar is the valley value of Ia. In order to numerically illustrate the returning electron beam, ΔI
a is calculated by the difference between I
a0 sand I
ar to indicate the variation maximum of the returning electron beam amplitude. ΔI
a obtained as a function of V
a and V
r is shown in
Figure 3d. ΔI
a increases at first and tends to saturate with V
a and V
r.
Figure 4a shows I
a as a function of V
a for corresponding to fixed V
g at V
r = 0 V. As V
a increases, I
a increases and then tends to saturate. When V
g increases, the cathode emission current I
c increases, and I
a also increases at the same V
a. At lower V
g, I
a tends to saturate at lower V
a. The voltages of V
a1, V
a2, V
a3, and V
a4 are 225 V, 300 V, 350 V, and 375 V, respectively, which are the threshold voltages at corresponding V
g. It is seen that the threshold voltage V
aT is higher when V
g is larger. It is deduced that the electrons emitted from the cold-cathode have higher initial velocity, and the electron beam focusing becomes difficult at larger V
g. At the same time, it is more difficult to decelerate the electrons and for them to be well focused axially in the repeller space by V
r, so the number of electrons intercepted increases. Consequently, the larger V
g causes a higher V
aT, and a larger threshold voltage is required to improve the electric field near the cavity and the electron beam focusing.
Figure 4b shows ΔI
a as a function of V
a and V
r at fixed V
g. ΔI
a corresponding to the above four threshold voltages are shown in the inset of
Figure 4b. ΔI
a increases and then tends to saturate with V
a at fixed V
g. It can be seen that the larger V
g can generate a greater I
a and then a larger ΔI
a. The larger ΔI
a can generate more electron bunches and a sufficient feedback mechanism.
The large V
g increases the threshold voltage V
aT. Therefore, it is expected that decelerating electron velocity entering the repeller space can facilitate lowering of the threshold voltage.
Figure 5a shows V
aT as a function of V
f. The high negatively biased V
f can decelerate electron velocities from the extracting grid electrode and then decrease V
aT. The focusing electrode height H
f can also decelerate electron velocities by extending the time passing through the focusing electrode.
Figure 5b shows V
aT as a function of V
g at three different conditions, where the condition I is V
f = −50 V and focusing electrode height H
f = 1 mm, the condition II is V
f = −250 V and H
f = 1 mm, and the condition III is V
f = −50 V and H
f = 2 mm. At the same V
g, it has the lowest V
aT under the condition III, followed by the condition II.
Figure 5c shows I
a as a function of V
a, respectively corresponding to the above three conditions at V
g of 1610 V.
Figure 5d shows ΔI
a as a function of V
a and V
r corresponding to above three conditions, respectively, at V
g of 1610 V. I
a and ΔI
a under the condition III emerges and saturates at low V
a, the condition II at moderate V
a, and the condition I at high V
a. ΔI
a under the condition III is also larger than the other at the same V
a. The way to reduce V
aT can provide a possibility to decrease the operating voltage. The low operating voltage can reduce the starting current in favor of starting oscillation and power dissipation for a reflex klystron oscillator [
8].