Self-mode transition, oscillation and inverse hysteresis in ECR discharges

Microwave (MW) ECR (electron cyclotron resonance) plasma sources have been applied widely in important application fields such as advanced micro-manufacturing,^1–3 powerful ion sources,^4,5 and long-life electric thrusters.^6–10 However, operation of ECR plasma sources is sometimes intractable due to the presence of discontinuous discharge modes, hysteresis loops, and oscillations.^11–22 Existing investigations about theses ECR-discharge instabilities have been concentrated on influencing parameters or factors such as MW power, gas pressure, and gas species.^{11–14,16,18,20,21} In comparison, works on the effects of impedance matching networks are scanty.^15,17,19,22 Minomo et al. suggested that unstable ECR discharges could be stabilized by keeping the reflection coefficient of incident MWs at a nonzero value.¹⁵ Asmussen and Mak also found that stable ECR plasmas could be produced by operating in a slight mismatch condition.¹⁷ Angra et al. reported that unstable ECR plasmas were highly sensitive to the three-stub-tuner’s configuration.¹⁹ As in Refs. 15 and 17, Muguira et al. also confirmed the conclusion that unstable ECR plasmas could be stabilized by manipulating an automatic triple-stub tuner.²² Although an impedance matching network was confirmed to play a stabilizing role in unstable MW ECR discharges, the underlying mechanism has not been explicated. Positive and negative feedback regions were proposed in radio-frequency (RF) inductive and capacitive discharges to explain effects of an impedance matching network on different evolutions of discharge-mode transitions or voltage waveforms.^23,24 However, it is unclear that whether the concept of positive and negative feedback regions suggested in RF discharges is also applicable to MW ECR ones.

Of various ECR ion thrusters, the engine with a cross-magnetic-field is attractive due to its higher ion extraction current.^6,9 In such a magnetic field configuration, the low electron-density discharge is sustained by ordinary (O) wave ionization in the front of the rod antenna, where the calculated MW electric field is parallel with the static magnetic field.⁹ In the high electron-density regime, the ionization region shifts to the upstream ECR layer, where the calculated MW electric field has the component perpendicular to the static magnetic field, In this case, the plasma is produced mainly by X-mode waves. Discharges between O and X wave modes are not continuous, but can transit abruptly.⁹ As in previous unstable ECR-discharges, the O ↔ X wave mode discharge transitions in the cross-magnetic-field are affected by discharge power and gas pressure (or flow rate),⁹ but the influence of other control parameters or components such as an impedance matching network remains veiled.

In this paper, further investigations are addressed to the effects of an impedance matching network on O ↔ X wave mode ECR discharge transitions under different gas-flow-rate (or pressure) regions and wall conditions. Mechanisms underlying the reversed self-mode transition, inverse hysteresis, and oscillation are discussed.

The experimental system for the ECR discharge in the cross-magnetic-field is shown in Fig. 1, details of which were described in Ref. 9. The ECR plasma source was installed in a large vacuum chamber with a diameter of 51.0 cm and a length of 66.0 cm. The chamber was evacuated by a turbo molecular pump (1000 L/S) and a rotary one (14 L/S). The Xe gas flow rate was monitored with a mass flow controller (MFC) and used to control the gas pressure in the small ECR discharge chamber. A MW power generator (MPG) was used to produce the 2.45 GHz MW. The produced MW was injected into the ECR discharge chamber via a MW power meter (MPM, Bird Technologies 7022), a three-stub coaxial tuner (TSCT), a direct current block (DCB) and a molybdenum rod-antenna. The screen grid (SG) and accelerator grid (AG) were not biased to extract ion in discharges of this paper. A K-type thin film thermocouple (not shown in Fig. 1) was stuck on the outside surface of the ECR plasma chamber to measure the wall temperature. The magnetic field in the ECR plasma chamber is the same as that described in Ref. 9. Sizes of the key components of the ECR plasma source are listed in Table I.

To capture dynamic images of oscillating discharges, a high-speed camera (Phantom, V1610) was installed outside the observation window of the large vacuum chamber. The camera was set at a frame rate of 10 000 fps (frames per second) with a pix resolution of 265 × 265 pixels and an exposure time of 99.498 µs. The camera at the above setting could only record 101 033 images over 10.1 s due to the limitation of the camera’s internal storage capacity. The recorded images were converted to 8-bit grayscale (0 to 255 scale) files by the image processing software Image J,²⁵ in order to enable quantitative analysis of investigated discharges.

Shown in Fig. 2 is the schematic of the three-stub coaxial tuner, which consists of three identical coaxial branch-lines connected in parallel with each other. The lengths of the inner conducts underneath the sliding piston (see Fig. 2) can be changed by moving the pistons, thus achieving the good impedance matching. The length l_i (i = 1, 2, and 3), as denoted in Fig. 2, cannot be measured directly, but determined indirectly by measuring d_i (i = 1, 2, and 3), namely the length of the inner conductor outside the coaxial branch-line. At the minimal d_i (denoted as d_imin, refer to the illustration for coaxial branch-line 3 in Fig. 2), the sliding piston is moved to the furthest downward position, under which its bottom surface is flushed with that of the external conductor. When d_imin is known, l_i is calculated by d_i-d_imin. For discharges in this paper, only coaxial branch-lines 1 and 2 were tuned, while the sliding piston of coaxial branch-line 3 was fixed at the most downward position, i.e., l₃ = 0.0 mm.

The impedance-matching experiment was first conducted under the conditions that the amplifier gain (A_g) of the MW power generator was kept constant and the Xe gas was not introduced into the ECR plasma chamber, aiming to prevent gas breakdown. The reflected MW power was minimized to a low level by adjusting branch-lines 1 and 2. Simultaneously, the delivered MW power (P_w), calculated as the difference between the incident MW power and the reflected one, achieved its maximum. The minimal reflected MW-power was attained at d₂ = 2.38 cm (refer to Fig. 2 for the denotation). This length was also fixed so that only d₁ could be adjusted to change P_w. The obtained P_w against d₁ is shown in Fig. 3(a), where the curve is asymmetric with respect to the value of d₁ at the maximal P_w. The corresponding value of d₁ is named as d_1m for a concise description. Worth noting is that the asymmetric curve in Fig. 3(a) is not consistent with the symmetric one achieved in the RF regime without discharge (refer to Fig. 4 in Ref. 24). Considering that Fig. 4 in Ref. 24 was plotted against the capacitance of the tuning capacitor in the impedance matching network, Fig. 3(a) is replotted by substituting d₁ with $ph(M)$ Z_in1 calculated from Eq. (1). As expected, the obtained curve of P_w vs X_in1 [see Fig. 3(b)] becomes symmetric with respect to the location of the maximal P_w, indicating that the aforementioned two kinds of impedance matching networks have a common feature, regardless of the differences in both hardware structure and operation frequency.

After the discharge was ignited by introducing 0.15 sccm Xe gas, coaxial branch-line 1 was re-adjusted under the fixed d₂ and A_g. The measurement of P_w and record of image used in Fig. 4 and Figs. 5–11 were conducted at 5 min after the variation of P_w, in order to eliminate the effect of the irregular change in gas temperature. The obtained curves of P_w vs l₁ and X_in1 are shown in Fig. 4. At the presence of plasma, the curve of P_w vs l₁ in Fig. 4(a) is generally similar to what is shown in Fig. 3(a), but the curve of P_w vs X_in1 in Fig. 4(b) still remains asymmetric. Specifically, P_w varies with X_in1 more slowly and rapidly at the left and right sides of the maximal P_w, respectively. This feature is also the same as that defined in terms of positive and negative feedback regions in the RF discharges.^23,24 The equivalent circuit to explain the feedback effect in MW ECR discharges is not as simple as in the unmagnetized RF cases. In magnetized MW discharges under the cross-magnetic field, there exist EPR (electron plasma resonance) and X-wave ECR,^8,9 neither of which can be described by a simple equivalent circuit. Despite of the great discrepancy between MW ECR and RF discharges, the net power against the impedance of the tuning component in the impedance match network displays the similar characteristic. Accordingly, the left and right regions in Fig. 4 can be also regarded as positive and negative feedback regions in our MW ECR discharges.

In practical operation, d₁ is a convenient control-parameter in manipulating the stub tuner. For this reason, we selected d_i in plotting figures other than Figs. 3 and 4. Shown in Fig. 5 is the curve of P_w vs d₁ obtained when A_g is increased above a threshold higher than that in Fig. 4. The curve in the negative feedback region is qualitatively identical to the counterpart in Fig. 4(a), namely the discharge evolves continuously with l₁ or P_w. In the positive feedback region of Fig. 5, however, the discharge becomes discontinuously. This discontinuity was attributed in Ref. 9 to the abrupt discharge-transition from the ordinary (O) wave mode existing in the low P_w region to the extraordinary (X) mode appearing in the moderate P_w region. The investigation in Ref. 9 was primarily focused on the effect of gas flow rate (gas pressure), while the influence of impedance matching was unexplored. For discharges in Fig. 5, other external control-parameters are unchanged except the manipulation of the impedance matching network. Therefore, the effect of the impedance matching network is the cause for the continuous and discontinuous discharge-transitions in the negative and positive feedback regions. The O ↔ X wave-mode transitions are intrinsically driven by P_w, and thus can occur in either the positive or the negative feedback region. However, the O ↔ X wave-mode transitions are governed by not only the discharge but also the impedance matching network that is interacting with the internal discharge. To obtain an easy description, the elucidation of the interaction is started below with the simple result in Fig. 3(b), where the interaction does not exist.

The maximal P_w in Fig. 3(b) requires both X_in = −X_s and R_in = R_s, i.e., the impedance of the load equals the conjugate impedance of the power generator. When d₁ or X_in is increased in the left or right side of d_1m, P_w respectively approaches to and shifts away from its maximum as a result of the deviation from the impedance-matching state for the maximal P_w. The reason for selecting coaxial branch-lines 1 as the tuner is that the reflected power is more sensitive to changing d₁. Compared with the Γ-shaped impedance matching network used widely in radio-frequency (RF) plasma sources, the role of coaxial branch-line 1 in Fig. 2 is analogy to that of the tuning capacitor in series with RF plasmas. In the absence of plasmas including ECR ones, discharge circuits are linear. The adjustment of coaxial branch-line 1 results in a significant variation in the reactance of the linear load. In other words, X_in varies greatly when d₁ is tuned. With the changing X_in, P_w or U_s varies accordingly. R_s and X_s are the electric parameters of the power source and almost constant. From the above, P_w in Eq. (2) is strongly affected by X_in during the tuning of coaxial branch-line 1 in the absence of nonlinear ECR discharges. Consequently, the curve of P_w vs X_in1 in Fig. 3(b) is symmetric with respect to the maximal P_w achieved at X_in = −X_s.

After the discharge is ignited, the understanding about the behaviors of P_w becomes difficult due to the presence of nonlinear ECR plasmas that can be also regarded as a part of the load’s resistance and reactance in Eq. (2). Accordingly, the quantitative analysis about the influence of varying plasma-impedance on P_w is not an easy task.⁶ For this reason, a qualitative discussion is conducted below.

In both negative and positive feedback regions (see Fig. 4), the variation of the load impedance at the presence of a discharge has two contributions: (1) the direct change in the impedance of the adjusted coaxial branch-line; (2) the induced change in the plasma impedance as a result of the varied P_w. In the negative feedback region, the above two contributions counteract each other, leading to the reduced net variation in X_in1 or Z_in1, as evidenced by the lower absolute-slope of the P_w-X_in1 curve. When the variation in P_w is suppressed, the larger change of P_w required by a discontinuous discharge-transition is prohibited, and thus, a continuous discharge-transition is the natural consequence. In the positive feedback region, however, the above situation is inversed: the influence of tuning the coaxial branch-line on P_w is augmented by the simultaneously induced change in the plasma impedance, boosting P_w to vary more steeply with Z_in1, as shown by the curve at the right side of d_1max in Fig. 4. The large variation of P_w due to changes in parameters such as d₁ or Z_in1 can allow the discharge to transit across the wide power-gap between the O ↔ X wave modes in a discontinuous manner. In the low P_w (electron density) region, where only the O-wave mode exists,⁹ discharges also evolve continuously in the positive feedback region [see Fig. 4(b)]. Results in Figs. 4 and 5 indicate that the presence of the discontinuous discharge-transition requires both the eternal matching condition and the internal discharge mode.

Comparing the locations of d_1max in Figs. 4(a) and 5, i.e., separatrixes of the negative and positive feedback regions, one can find that d_1max is not constant but varies with A_g. To quantify the relationship between d_1max and A_g, A_g is substituted by the maximal P_w at the separatrix, i.e., P_wmax. The curve of d_1max vs P_wmax obtained at 0.15 sccm of Xe is shown in Fig. 6.

The most remarkable is that d_1max rises with the increasing P_wmax. As the Xe gas flow rate is varied under a constant A_g, the obtained d_1max (see Fig. 7) increases with the increasing gas flow rate, but the curve deviates from the quasi-linearity as shown in Fig. 6. The above results suggest that, as A_g or the gas flow rate is varied at a fixed d₁, the discharge can shift between the positive and negative feedback regions. Therefore, care must be taken for each discharge to ascertain its characteristic feedback region.

In the negative feedback region where mode transitions tend to be continuous (see Fig. 5), ECR discharges are relatively stable. At the boundary between the negative and positive feedback regions, the reflection coefficient of incident MW achieves its minimum. However, ECR discharges under this condition are less stable than those in the negative feedback region. For this reason, investigators in Refs. 15, 17, and 22 operated their ECR discharges at the mismatch state, which is believed to be lied in the negative feedback region.

Variations in plasma parameters with discharge power, such as electron density and electron temperature, are important to understand characteristics of plasma sources. In this paper, electron density and electron temperature are not measured. As a monitoring signal of ECR discharges, the total gray (G_t) values of images captured from discharges in the positive feedback region are extracted using Image J software.^25,26 At three typical Xe gas flow rates, the obtained G_t-values against the increasing and decreasing P_w are shown in Fig. 8.

In the ramping-up stage of P_w at 0.55 sccm [see Fig. 8(a)], the G_t-value jumps from the lower branch of the curve at a critical P_w to P_w1 of the upper branch. In the ramping-down stage of the upper branch, the G_t-value reverts to the lower branch at P_w2. The fact of P_w2 being lower than P_w1 indicates that the observed hysteresis is normal. At the moderate gas flow rate [see Fig. 8(b)], the hysteresis-loop almost disappears. As the gas flow rate decreases to 0.15 sccm [see Fig. 8(c)], P_w2 exceeds P_w1, indicating that the hysteresis loop becomes inverse or abnormal.

In order to gain more insight, the power difference ΔP_whl (=P_w1 − P_w2) is defined as the width of the hysteresis loop to evaluate the evolution of the hysteresis. The obtained ΔP_whl against gas flow rate is shown in Fig. 9. For the inverse hysteresis appearing in the low gas-flow-rate region, the loop width ΔP_whl is negative. As the gas flow rate increases to around 0.22 sccm, ΔP_whl reduces to zero. The zero loop-width is maintained until the gas flow rate exceeds 0.38 sccm. After ΔP_whl becomes positive, it varies at a smaller rate than that in the low gas-flow-rate region. On the lower branches of curves shown in Fig. 8, the hysteresis loops also exists, and thus the corresponding loop-width can be defined. The dependence of this loop-width on gas flow rate is qualitatively similar to that shown in Fig. 9.

In the moderate gas-flow-rate region of Fig. 9, as denoted by the two green lines, the two loop-widths defined above become sufficiently narrow that discharges are subject to small variations of discharge parameters. The triggered oscillations will be discussed in Subsection III E.

The inverse hysteresis-loop shown in Fig. 8(c) was ever observed in two RF inductively coupled plasma (ICP) sources.²⁷ The appearance of such loops in MW ECR and RF inductive discharges requires a common condition, namely they exist in small-sized plasma sources operated in low pressure region. This suggests that there exists a same mechanism underlying the inverse hysteresis. Lee and Chung ascribed the inverse hysteresis to the evolution of electron energy distribution (EEDF).²⁷ However, the effect of EEDF is not the cause to produce the inverse H → E mode transition because such an evolution even exists in the Faraday-shielded RF ICPs,^28,29 where no discharge mode transition occurs. Zhao and Ding suggested a consistent explanation on the inverse hysteresis:³⁰ electron density is reduced with decreased neutral density due to gas temperature rise resulted from the slow wall gas-heating.³¹ During the ramping-up phase of P_w in the X-wave mode discharge (see Fig. 8), the wall temperature rises to a high level. The subsequent ramping-down of P_w is carried out at a time rate of change that is not sufficiently low. Consequently, the temperature of the wall overheated in the high-P_w X-wave mode discharge cannot immediately follow the decreasing P_w, and thus, are higher compared with that at P_w in the ramping-up phase. At a constant gas flow rate, the neutral density is reduced in the ramping-down phase due to the increased gas temperature. In low gas pressure (gas flow rate) region [see Fig. 8(c)], the reduction in neutral density is relatively large. Accordingly, at 0.15 sccm, the X-wave mode discharge transits to the O-one at P_w2 that is higher than P_w1, forming the inverse hysteresis-loop.

Results from Figs. 4 and 5 are obtained by changing d₁ in discharges operated in the feedback region. The effect of d₁ on the width of hysteresis loop (ΔP_whl) can be investigated by varying P_w under different d₁ values. The obtained curves of ΔP_whl vs d₁ under different gas flow rates are shown in Figs. 10 and 11. For the inverse hysteresis (see Fig. 10), the absolute loop-width rises with the increasing d₁. In the case of the normal hysteresis (see Fig. 11), the curve shape is seemingly opposite to that shown in Fig. 9, but the behavior is essentially the same, i.e., the width of the normal hysteresis-loop also rises with the increasing d₁.

Self-mode-transitions are believed to occur automatically in various discharges. But as far as we know, there have been only two specific investigations on this topic. One is the E → H mode transition in the RF inductively coupled plasma (ICP),³² and the other is the undetermined mode transition in MW ECR plasma.³³ Recently, the slow wall gas-heating was proposed as the cause for the observed long drift toward the self-E → H mode transition point.³⁰ The H → E mode transition is the counterpart of the E → H mode transition and has also been extensively investigated. However, no self-H → E mode transition has been reported. The E and H modes in RF ICPs correspond respectively to the O- and X-wave modes in our ECR plasmas. The arising question is that whether the self-O → X wave mode transition, especially the self-X → O one, can occur in our ECR discharges.

The first experiment is to confirm the self-O → X wave mode transition. According to the requirement for triggering the self-E → H mode transition in the RF ICP,³² the chamber wall of the ECR plasma source was first pre-heated in the “hot” 3.5-W X-mode discharge for 30 min, and then, the discharge was switched from the X-wave mode to the O-wave mode in the vicinity of the O → X wave mode-transition point. Henceforth, the temperature of the chamber’s external surface was monitored by the thermocouple described in Sec. II. Owing to the slow variation of the external wall temperature, the voltage standing wave ratio (VSWR) recorded by the MW power meter could be also monitored synchronously. The obtained time-evolutions of both the wall temperature and VSWR at 0.15 and 0.55 sccm are shown respectively in Figs. 12 and 13.

The time evolution of VSWR in Fig. 12(a) can be divided into three characteristic regions: (1) region I where the overall VSWR drops with time at a small rate of change; (2) region II, in which the VSWR oscillates irregularly with a very small amplitude; (3) region III, the domain immediately after the step fall of the VSWR due to the self-O → X wave mode transition. After entering region III of the X-mode discharge, the VSWR ceases to oscillate immediately, implying that the discharge stability is recovered.

As argued in Ref. 30, the wall temperature in Fig. 12(b) does decrease before the self-O → X wave-mode transition. This outcome is natural because the wall overheated in the “hot” X-mode discharge is cooled slowly down in the “cold” O-wave mode discharge with a low P_w. As a result of the reduced wall gas-heating in regions I and II (see Fig. 12 and refer to Ref. 30), the gas temperature and neutral density drops and rises, respectively. In the low-pressure region where the electron-neutral collision is weak, the rising neutral-density causes the increasing electron density.³⁴ In this way, the O-wave mode discharge automatically shifts slowly toward to the O → X wave mode transition point, as evidenced by the slow drop in the VSWR signifying the discharge state. After the self-O → X wave mode transition, P_w increases steeply and the wall temperature starts to rise. The reason for which is that, as the discharge enters the X-mode region with a relatively high-P_w, the power deposited onto the chamber wall becomes larger than that transmitted from the wall.

At 0.55 sccm, the time evolution of VSWR in Fig. 13(a) is also characterized by the three regions in Fig. 12(a), but there exist the following two differences: (1) the oscillating amplitude of VSWR in region II of Fig. 13(a) is larger than the counterpart in Fig. 12(a); (2) the self-O → X wave mode transition at 0.55 sccm takes place in a shorter time-interval than that at 0.15 sccm. In other words, the former discharge-transition develops faster than the later one. The behind reason is the gas pressure or gas flow rate. During the self-mode-transition, electron density varies spontaneously, the change rate of which is determined by ionization rate that subsequently depends on gas pressure or gas flow rate. In the 0.55-sccm case where the gas pressure is relatively higher, the larger ionization-rate can drive a faster self-mode-transition. The large oscillating amplitude in region II at 0.55-sccm [see Fig. 13(a)] is also related to the gas pressure, details of which will be discussed in Subsection III F.

In contrast, at the lower gas flow rate of 0.15 sccm, the time evolution of wall temperature in region III of Fig. 13(b) is distinctive from that in Fig. 12(b), namely the wall temperature as well as the gas temperature in Fig. 13(b) continues dropping after the self-O → X wave mode transition. This discrepancy is originated from the differences before and after the O → X wave mode transition. As stated above, the P_w-values in the pre-heating discharges for 0.15 or 0.55 sccm Xe are both 3.5 W. This value is relatively higher than those before and after the O → X wave mode transition at 0.55 sccm [see Fig. 8(c)]. Therefore, the relatively smaller rise of P_w during the self-O → X wave mode transition at 0.55 sccm can neither elevate nor maintain the temperature of the overheated wall. Consequently, the wall is cooled down throughout the O → X wave mode transition. For the 0.15-sccm discharge, however, the pre-heating discharge power of 3.5 W is not sufficiently higher compared with those before and after the O → X wave mode transition [see Fig. 8(c)]. As a result, the rise in P_w during the self-O → X wave mode transition can reverse the cooling-down process, leading to the rise in the wall temperature.

In contrast to the overheated wall discussed above, experiments in this subsection were conducted with the initially cold wall: the plasma source was first operated in the “cold” 1.0-W O-wave mode discharge for 5.0 min, and then, the O-wave mode discharge was switched to the X-mode discharge near the X → O wave mode-transition point. The obtained time evolutions of wall temperature and VSWR at 0.15 and 0.55 sccm are shown respectively in Figs. 14 and 15. In the two cases, the corresponding time evolutions have the similar tendency, and the irregular VSWR-oscillation shown in Fig. 12 disappears throughput the transition. The self-X → O wave mode-transitions, as evidenced by the steep rises in VSWR, occur as the wall temperatures increase slowly to their respective thresholds.

The reason for the wall-temperature rise throughout the various time domains in Figs. 14 and 15 is that, P_w in the discharge preset near the X → O wave mode-transition point and that immediately after the X → O wave mode-transition are both higher than the initial discharge-power of 1.0 W. Unlike the cooling down of the overheated wall in subsection (a), electron density during the heating up of the initially cold wall decreases, which induces the required shift to the X → O wave mode transition.

As stated above, only the self-E → H mode transition was observed in the RF ICP,²⁷ and no self-H → E mode transition has been reported. The behind reason is that, in the normal operation, the RF inductive discharge was preset at the H → E mode transition point under the condition of hot wall preheated in the H-mode discharge. In this situation, the shift required for the self-H → E mode transition is prevented during the subsequent cooling down of the hot wall. For ECR discharges in Figs. 14 and 15, the situation is reversed, namely the initially cold wall is heated up, leading to the required shift to trigger the self-X → O wave mode transition.

The observed oscillations occur in the moderate gas-flow-rate region in Fig. 9 and are characterized by irregularity, namely the oscillations are not periodic and the amplitudes are not constant. Generally, the oscillations occurring in the central zone of the moderate gas-flow-rate region are fast and have the small amplitudes. When the gas flow rate is varied toward to either the high or low value, the oscillations become slow, while the amplitudes increase. The oscillation was not investigated in the entire gas-flow-rate region, but at a typical gas flow rate of 0.4 sccm in the positive feedback region. Additionally, in order to trigger the oscillation, P_w was required to increase above a threshold.

The oscillation was monitored by the fast camera described in Sec. II. Thanking to the camera’s capability of long-time recording, images of multiple oscillating-discharges can be recorded. One of the selected scenarios is shown in Fig. 16. The naked-eye comparison between the images finds that the discharge undergoes a complete cycle. Namely the discharge starts from a low intensity [see Figs. 16(a)–16(e)], jumps to a high intensity with a long duration [see Figs. 16(f)–16(s)], and finally recovers to the initial state [see Figs. 16(t)–16(w)]. In order to quantify the above primary judgment, the G_t-value of each image in Fig. 16 is extracted sequentially and shown in Fig. 17. Obviously, the G_t-value exhibits two steep changes: the soaring up is caused by the O → X wave mode transition, while the other by the X → O one.

It is worth noting here that, prior to the O → X wave mode transition, the G_t-value increases slightly (see Fig. 17). This is an indicator for the discharge shift to the O → X wave mode transition point. Immediately after the O → X wave mode transition, the G_t-value undergoes an overshoot, followed by a drop until the minimum. The recovery does not last for a long time, but is interrupted by a drop in the G_t-value. When the G_t-value drops to a threshold, the X → O wave mode transition is triggered. Subsequently, the undershoot in the G_t-value occurs as a transient response of the X → O wave mode transition. Following the undershoot, the G_t-value rises, leading to another O → X wave mode transition, as described above.

Results in Figs. 12(a)–15(a) and 17 confirm that discharges during the self-mode transitions and oscillation are both unstable. However, they differ in the following aspects. Firstly, both occur under different conditions. The self-mode transition can be triggered as long as the preset discharge is sufficiently near the transition mode point under the condition of the cold or hot wall, regardless of the width of the hysteresis loop. The oscillation, however, can only occur in discharges whose hysteresis-loop width is sufficiently narrow. Therefore, in Fig. 9, the moderate gas-flow-rate region with a small width of the hysteresis loop is subject to oscillation. Secondly, the self-mode transitions occur between O- and X-wave-mode discharges [Figs. 12(a)–15(a)], so does the oscillation in Fig. 17. However, it is not true for all observed oscillations. In Fig. 13(a), the discharge in region II is oscillating, despite that the oscillating cannot transiently reach the O-wave mode. Thirdly, the self-mode transitions and oscillations develop in different time scales. The time required for the self-mode transition mainly depends on the gap between the preset discharge and the mode transition point. In Figs. 12–15, the so-called gaps are rather wide, so that the self-mode transitions take several minutes. If the preset discharge is sufficiently close to the mode-transition point, the self-mode transition will occur immediately. In this case, however, the monitor of the time-varying wall temperature or VSWR becomes difficult.

Despite of the above difference, the oscillation in Fig. 17 is essentially the fast self-mode transitions switching reversibly between O- and X-wave mode discharges, in which the widths of the hysteresis-loops on the lower and upper branches of the curves in Fig. 8 are sufficiently small. Therefore, the oscillation is also expected to be driven by the shift in the direct volume gas-heating as well as the indirect wall gas-hating. In view of this, the oscillation shown in Fig. 17 is explained as following. The plateau of the oscillating G_t-value in Fig. 17 is a result of the high P_w after the O-X wave mode transition. The cold wall in the O-wave mode discharge is subsequently heated up. Consequently, the electron density drops slowly with the reduced neural density, as evidenced by the decreasing G_t-value at the right side of the plateau (see Fig. 17). When electron density decreases to the threshold for the X–O wave mode transition, the X–O wave mode transition is thus triggered. In contrast, after the discharge transits into the low-P_w O-wave mode discharge, the processes described above are inversed: the neutral density along with electron density is increased as the hot wall is cooled down. The variation finally leads to the onset of the O-X wave mode transition. The above scenario is repetitive, leading to the oscillation as shown in Figs. 16 and 17. It is worth noting that, the small variation in neutral density due to gas heating can only induce a limited change in electron density, so that the oscillation occurs merely in discharges whose widths of hysteresis loops are sufficiently narrow. This requirement is merely satisfied in the moderate gas-flow-rate (gas pressure) region.

Positive and negative feedback regions are confirmed in MW ECR discharges by adjusting a three-stub coaxial tuner. When mismatched in the negative feedback region, MW ECR discharges are stable, and they become unstable in the positive feedback region. Self-mode transitions from high to low electron-density discharge are achieved for the first time by presetting the discharge under cold-wall condition. The counterpart, namely self-mode transitions from low to high electron-density discharge can be triggered under hot-wall condition. Inverse hysteresis and oscillation occur respectively in the low and moderate gas-flow-rate (gas pressure) regions. Effects of wall gas-heating are suggested to explain the self-mode transition and inverse hysteresis as well as oscillation. The hysteresis is caused by the relatively-stronger wall gas-heating in the low gas-flow-rate (gas pressure) region. The observed oscillation can be regarded as the reversible mode transition between two discharge modes whose widths of hysteresis loops are sufficiently narrow in the moderate gas-flow-rate (gas pressure) region.

This work was partially supported by the National Natural Science Foundation of China under Grants Nos. 11975070 and 11475040 and Open Funds for Science and Technology on Vacuum Technology and Physics Laboratory, Lanzhou Institute of Physics (Grant No. zwk1609).

The authors have no conflicts to disclose.

Z. F. Ding: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Y. R. Yang: Data curation (equal); Investigation (equal). S. H. Fu: Software (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.