Wanying ZHU (朱婉莹),Ruilin CUI (崔瑞林),Ruoyu HAN (韩若愚),Feng HE (何锋) and Jiting OUYANG (欧阳吉庭)

School of Physics,Beijing Institute of Technology,Beijing 100081,People’s Republic of China

Abstract We present here a kind of low-frequency oscillation in argon helicon discharge with a half helical antenna.This time-dependent instability shows a global quasi-periodic oscillation of plasma density and electron temperature,with a typical frequency of a few tens of Hz which increases with external magnetic field as well as radiofrequency (RF) power.The relative oscillation amplitude decreases with magnetic field and RF power,but the rising time and pulse width do not change significantly under different discharge conditions.The oscillation can only be observed in some specific conditions of low magnetic fields and low RF power when the gas flows in from one end of the discharge area and out from another end.This global instability is suggested to be attributed to the pressure instability of neutral depletion,which is the result of compound action of gas depletion by heating expansion and gas replenishment from upstream.There are two kinds of oscillations,large and small amplitude oscillations,occurring in different discharge modes.This study could be a good verification of and complement to earlier experiments.This kind of spontaneous pulse phenomenon is also helpful in realizing a pulsing plasma source without a pulsed power supply.

Keywords: helicon plasma,low-frequency oscillation,global instability,neutral depletion

1.Introduction

Due to the advantages of high ionization rate,high plasma density and being electrodeless,helicon plasmas have wide application potential in plasma processing [1-4]and electric space propulsion [5-8].Driven by radiofrequency (RF) power supply,there are probably extremely complex plasma-wave interactions in helicon plasma,resulting in nonlinear phenomena and/or instabilities.Generally,there are two kinds of instabilities in plasmas: configuration-space instabilities (or macro-instabilities) and velocity-space instabilities (or micro-instabilities) [9].The former concerns the effect on spatial distribution or uniformity of plasma,while the latter relates to the time-dependent instability[10,11].We focus on the time-dependent instability of helicon plasma in this work.

Previously,time-dependent instability has been observed in helicon plasmas.In a current-free linear device with a steady-state uniform magnetic field,there are three main drivers of intrinsic instability: potential gradient,pressure gradient and discharge mode transition [12,13].These ionization instabilities were excited in the presence of a double layer (DL) whose potential drop was greater than that of the ionization potential of neutral gas.In helicon plasma,Aaneslandet al[14]and Scimeet al[15,16]found that ion-acoustic-like,electrostatic instabilities appear at large beam current densities coincident with the DL vanishing.

Radial pressure gradient is the second cause of low-frequency instability.In helicon plasma,many researchers including Chen [17],Gilmore [12]and Tynanet al[18,19]observed these instabilities resulting from a hybrid mode of Kelvin-Helmholtz (KH) and resistive drift-wave (DW).The frequency is in the range of 0.2-5 kHz and increases linearly in a magnetic field larger than 198 G.

Discharge mode transition can also lead to self-pulsing phenomena,which have commonly been observed in DC discharge of corona [20,21],hollow cathode discharges [22],and parallel-plate discharges [23],as a mode transition between Townsend and glow discharge.In RF discharge,normal selfpulsing has also been observed as a mode transition between capacitively coupled plasma (CCP) and inductively coupled plasma (ICP) [24-27]due to relaxation discharge.In helicon plasma source,breathing oscillations were first observed in argon discharge by Boswellet al[28],when a gas source was on the same side of the chamber as the vacuum pumps.These relaxation oscillations of the order of several milliseconds have also been identified as discharge transitions between a low-density,inductive discharge and a high-density,helicon-wave discharge [13]which is induced by ion pumping [29-31](or neutral pumping[32-34]).However,these breathing oscillations could not be observed in the flowing helicon plasma studied by Denninget al[35]when the gas source was on the opposite side of the chamber from the vacuum pumps,since the neutral gas is considered to be continuously pulled through the source region.However,oscillation could still happen in the flowing plasma under the proper conditions,as we observed recently for the first time.This study could be a good verification of and complement to earlier experiments.Moreover,the study of the mechanism of instability is helpful in obtaining the required plasma.On the other hand,this kind of spontaneous pulse phenomenon is beneficial for realizing a pulsing plasma source without a pulsed power supply,and is also helpful in the fields of electrostatic electromagnetic signal diagnosis and detection.

In this paper,we present the characteristics of a global oscillation in an argon helicon plasma source when the gas source is on the opposite side of the chamber from the vacuum pumps.The instability is of the order of milliseconds and affected by the magnetic field as well as the RF power.

2.Experimental setup

The experimental apparatus consists of a helicon plasma discharge reactor and a diagnostic system,as shown in figure 1,which has been used previously in [36-38].

The discharge reactor includes a half helical antenna,a discharge chamber,and a pair of magnetic fields.The discharge chamber is a quartz tube ofL= 45 cm in length and viable diameter,connected to a vacuum pump through a stainless-steel diffusion chamber.The base pressure can be pumped to as low as 10-4Pa before filling pure argon.Argon pressure is maintained atp0= 0.3 Pa in experiment.The external magnetic field isB= 0-400 G in the axial center and controlled by the coil current.To describe conveniently,we choose the central position of the antenna asz= 0 cm on the axial axis andr= 0 cm on the radial axis.The upstream is the area ofz＞ 0 cm while the downstream is that ofz＜ 0 cm.

A 13.56 MHz RF power source was applied to the antenna through an RF-matching box.The input power was read out directly from the power supply system.Time-integrated images of plasmas were recorded by a digital camera(Canon EOS 550D) and a high-speed charge-coupled device(CCD) camera (Phantom VEO 410L 650,000 fps).Spectral intensity was measured by an optical fiber outside or localized in the plasma via optical emission spectrometry (OES)(Avaspec-ULS3468).The optical probe can move in both axial and radial directions in the discharge area so that the spatial distribution of light emission can be obtained.

Electron densityneis determined by local optical emission spectrometry(LOES),which has been described in detail in [37]and [38]and corrected by Langmuir probe.The electron density is proportional to the emission intensity of Ar I-750.2 nm when the sampling time was determined,orne=k×IArI750.2(where the constantkis 1.47 × 108cm-3/a.u.in this work forp0= 0.3 Pa).

3.Experimental results

3.1.General characteristic of global instability

3.1.1.Oscillation waveform.In a large discharge tube of Φ= 6 cm,plasma oscillation can be observed in a range of RF powerPRF= 300-500 W and a lower magnetic field ofB＜ 120 G.Figure 2 shows the time-varying electron density and temperature at a power ofPRF= 300 W and pressure ofp0= 0.3 Pa.

Figure 1. Experimental apparatus.

Figure 2.Time-varying electron density and temperature of argon helicon plasma in Φ= 6 cm tube at RF power PRF = 300 W and pressure p0 = 0.3 Pa in different magnetic fields of B = 0 G (a),50 G (b),75 G (c),and 105 G (d).

Figure 3.(a)Electron density ne and temperature Te and(b)relative oscillation amplitude(Δ ne/ne,max,ΔTe/Te,min)changing with magnetic field B at power PRF = 300 W in Φ = 6 cm tube.

Figure 4.Oscillation amplitude of(a)electron density and temperature,and(b)relative amplitude at increasing RF power at B = 50 G and p0 = 0.3 Pa in Φ = 6 cm tube.

It is seen that the plasma parameters vary periodically,with an oscillation frequency off= 23-86 Hz(or a period ofT= 44.2-11.7 ms) at increasing magnetic field.The plasma density ranges fromne= 0.5 × 1011to 8 × 1011cm-3and the electron temperature isTe= 3.9-7.8 eV.

The electron density and temperature behave in an inverse phase in the oscillation.The electron density stays at a higher level constantly,which defines the quasi-stable region interrupted by a gully or valley of minimum,while the temperature has a lower level but is interrupted by a hump.For instance,atB= 75 G,the density isne= 2.8 × 1011cm-3in the period oft= 3.9-14.7 ms,then decreases to a minimum ofne= 2.1 × 1011cm-3and increases again to 2.8 × 1011cm-3int= 14.7-19.4 ms(see figure 2(c)).The electron temperature isTe= 4.1 eV in the period oft= 3.9-14.7 ms,then increases to a maximum ofTe= 4.3 eV and then drops to 4.1 eV int= 14.7-19.4 ms.

Note that the low-frequency oscillations can also occur even if the magnetic field is absent(orB= 0).This indicates that the appearance of instability in a helicon plasma source is surely not related to the wave-coupled mode but to the CCP or ICP mode.

3.1.2.Oscillation characteristics.The oscillation amplitudes of the electron density and temperature at increasing magnetic field are shown in figure 3.

From figure 3(a),the maximum electron densityne,max(which defines the base of density oscillation) decreases with the magnetic fieldBwhenB＜ 50 G,with a value ofne,max= (7.5-4.3) × 1011cm-3.The variation ofne,maxremains nearly constant whenB＞ 60 G,with a value around 2.4 × 1011cm-3.The minimum electron density is roughly constant whenB＜ 50 G and ＞ 60 G,with values ofne,min～ 0.3 × 1011cm-3and 1.6 × 1011cm-3,respectively.

The minimum electron temperature (which is the base of temperature oscillation)has no significant variation in the whole magnetic field region,with a value ofTe,min～ 4.0 eV,while the maximum electron temperatureTe,maxis roughly constant at different magnetic regions,respectively,i.e.,Te,max～ 7.8 eV inB= 0-50 G andTe,max～ 4.1 eV inB= 60-110 G.

Both oscillation amplitudes show a reduction with magnetic field.From figure 3(b),the relative oscillation amplitude of the density (defined as Δne/ne,max) decreases from 93% to 21%with increasingB.A peak (Δne/ne,max～ 37%) is achieved aroundB= 80 G,which is similar to the low field peak[39-44].The relative oscillation amplitude of temperature(defined as ΔTe/Te,min) decreases with the magnetic field,ranging from 98%to 6%inB= 0-50 G,and stays constant of ΔTe/Te,min= 6% atB＞ 60 G.Both relative amplitudes show two stages at increasing magnetic field,large amplitude oscillation with relative amplitude more than 90% inB= 0-50 G and small amplitude oscillation with relative amplitude less than 40% inB= 60-110 G.Considering the difference in typical density of the CCP and ICP modes,the density at the turning point (aroundB= 60 G) is about 1 × 1011cm-3,which is the critical value for achieving ICP or transition from CCP to ICP.

Figure 4 shows the oscillation amplitude of electron density and temperature at increasing RF power forB= 50 G andp0= 0.3 Pa in Φ = 6 cm tube.

Figure 5.Normalized waveforms of oscillation at different magnetic fields B (conditions are of Φ = 6 cm, p0 = 0.3 Pa, PRF = 300 W).

From figure 4(a),both the maximum electron densityne,maxand minimum densityne,minincrease with the RF power.The jump of density in thene-PRFcurve suggests a mode transition of helicon discharge from CCP to ICP aroundPRF= 400 W [40].Both the maximum electron temperatureTe,maxand minimum temperatureTe,mindecrease slightly along with the decrease in RF power.

Both oscillation amplitudes show a reduction with RF power.From figure 4(b),the relative oscillation amplitude of electron density and temperature shows two stages,i.e.,a large amplitude oscillation with a value more than 80% in 300-400 W and a small one with a value less than 40% in 400-500 W,respectively.

The oscillation has nearly the same waveform of electron density at different conditions,as shown in figure 5.For all the density pulses,the rising time is almost the same,tr= 1.6 ms.The falling edge and the full width at half maximum(FWHM) change subtly and the FWHM is in the range of 2.3-2.5 ms.

The oscillation frequency increases with magnetic field and RF power,as shown in figure 6.

The frequency varies between 22 Hz and 86 Hz,when magnetic fieldBincreases from 0 to 110 G at powerPRF= 300 W.It is noticed that there is a peak of frequency aroundB= 80 G,which is similar to that in electron density(see figure 3),corresponding to the low density peak[39-44].

The frequency also increases with the RF power from 41 to 112 Hz when RF power increases from 300 to 500 W atB= 50 G.The increase in speed of oscillation frequency with RF power inPRF= 300-400 W,f= 41-47 Hz (or 0.06 Hz W-1),is smaller than that in 400-500 W,f= 47-112 Hz(or～0.65 Hz W-1).

3.2.CCD images and OES

The above instability is a universal rather than a local instability such as moving striations in the discharge area,that is,the electron density at different positions along the discharge tube has same behavior of oscillation.To confirm this point,we evidenced by time-dependent discharge images recorded by high speed CCD camera.

Figure 7 shows the time-resolved discharge images recorded atPRF= 500 W andB= 50 G.The white area indicates the shielded part by the helical antenna.

Figure 6.Oscillation frequency changing with(a)magnetic field B at power PRF = 300 W and with(b)RF power at B = 50 G(conditions are of p0 = 0.3 Pa and Φ = 6 cm).

Figure 7.Spatial-temporal discharge images on the central axis of Φ = 6 cm tube at PRF = 500 W, B = 50 G and p0 = 0.3 Pa.

Figure 8.Time-varying normalized light intensity of (a) high-speed camera and (b) LOES of helicon plasma in Φ = 6 cm tube at PRF = 500 W, B = 50 G and p0 = 0.3 Pa.

Figure 9.Time-dependent electron density and temperature of argon helicon plasma in Φ= 0.8 cm tube at PRF = 900 W and p0 = 0.3 Pa in magnetic fields of (a) B = 0 G,(b) 25 G,(c) 50 G and (d) 100 G.

Figure 10.Electron density and temperature (a)and relative oscillation amplitude (b)as a function of magnetic field in Φ= 0.8 cm tube at PRF = 900 W and p0 = 0.3 Pa.

It is seen that there is no significant difference in the local nonuniformity of light emission.The distribution of light emission along the whole axis remains unchanged with time.No movement of light emission along the axial direction can be observed.

The time-dependent electron density measured by local OES and light emission from an ICCD camera (captured atz= -2 cm andr= 0 cm)showed very good consistency,as shown in figure 8.Again,we confirmed that the low-frequency oscillation is indeed a global phenomenon,rather than a local one or a moving striation along the discharge channel.

3.3.Effect of tube size

In a small tube of Φ = 0.8 cm,electron density and temperature can also show periodical oscillations under specific conditions.However,the conditions are much stricter than those in the 6 cm tube.The oscillation appears only at an RF power of around 900 W and a magnetic field below 100 G.Typical oscillation waveforms of electron density and electron temperature atp0= 0.3 Pa and different magnetic fields are shown in figure 9.

Similar to in the 6 cm tube,the oscillation frequency is generally low;f= 51-65 Hz (or a period ofT= 19.6-15.5 ms) at the magnetic field less than 100 G.

The averaged plasma density ranges fromne=2.5 × 1011to 6 × 1011cm-3,and the electron temperature is roughlyTe= 4.5-5.5 eV in all cases.

The electron density and temperature also have a revised phase.The plasma density is generally at a high level;e.g.,atB= 25 G in figure 9(b),the density over a long period isne,max= 5.6 × 1011cm-3,but overlapped by a gully ofne,min= 4.5 × 1011cm-3in a period of 21.1-26.7 ms.In contrast,the temperature has a low level over a long period(corresponding to the period of a high level ofne),Te,min= 4.5 eV,but overlapped by a hump of peakTe,max= 5.2 eV and a FWHM Δt～ 2.6 ms (corresponding to the gully ofne).The rising time for all the density pulses istr= 1.6 ms,and the FWHM increases slightly with the magnetic fields from 2.4 to 4.4 ms.

The changes in the oscillation amplitudes of density and temperature have a similar trend to those in the 6 cm tube.Figure 10 shows the maximum and minimum of the electron densities and temperatures,and their relative oscillation amplitudes with increasing magnetic field.

Figure 11.Oscillation frequency changing with magnetic field at PRF = 900 W and p0 = 0.3 Pa in Φ = 0.8 cm tube.

Figure 12.Schematic of neutral depletion resulting from gas heating.

From figure 10(a),the maximum electron density does not change significantly,with a value ofne,max～ 5.6 × 1011cm-3,while the minimum increases slightly with magnetic field,fromne,max= 4.0 × 1011to 5.0 × 1011cm-3.The maximum electron temperature decreases slightly,fromTe,max= 5.4 to 4.8 eV,while the minimum electron temperature keeps nearly constant,with value ofTe,min～ 4.5 eV.

From figure 10(b),both the relative oscillation amplitudes of density and temperature decrease with increasing magnetic strength in magnetic field ofB= 0-100 G,from Δne/ne,max= 31% to 13%,and ΔTe/Te,min= 21% to 8%,respectively.This amplitude of oscillation is small with value less than 30%.

The oscillation frequency increases with the magnetic field,fromf= 52 to 65 Hz inB= 0-100 G,as shown in figure 11.

This indicates that global oscillation is a common phenomenon in a helicon discharge system.A larger tube is helpful for easy observation of the oscillation.

4.Discussion

From the above results,there exists a global instability of low-frequency oscillation in helicon discharge with gas flow passing through the discharge area,i.e.,the inlet (filling the gas) and outlet (vacuum pump) of the filling gas are at opposite ends of the discharge tube.The RF power and magnetic field should be in a suitable low-level range.The oscillation frequency increases,while the relative amplitude decreases with magnetic field and PF power.

As is known,there are two mechanisms inducing lowfrequency intrinsic instability,i.e.,potential gradient (like DL) and pressure gradient [12].Generally,the oscillation frequency induced by DL instability (potential gradient) is roughly 1 kHz or abovef= 5-195 kHz [14-16],which is much larger than in the present work (of the order of several tens of Hz).This oscillation is generally related to the ionacoustic velocity [15],which is of the order of= 2.5 - 3 km s-1,much higher than the thermal acoustic velocity of the gas flow.In fact,we did not measure the DL under low RF power and magnetic field.Energetic electrons are not abundant enough for DL formation and hence the instability.Thus,this global instability should not be related to DL instability or potential gradient.

We suggested that the oscillation observed in this work should be induced by pressure instability,including neutral depletion,neutral pumping [32]and/or neutral heating [34],etc.

4.1.Pressure balance along discharge channel

In a magnetized plasma,the total pressure comes from several aspects including particles (neutrals,ions,and electrons) and magnetic fields,expressed as:

The particle pressure ispa=n akBTa(a= e,i,n represents electrons,ions and neutrals,naandTaare their number density and temperature,kBis Boltzmann constant),and the magnetic pressure ispB=B2μ0.

We focus on the pressure balance along the discharge tube.Since the magnetic field is weak and axial(or along the discharge tube),only electrons but no ions can be magnetized in the azimuthal direction,and coupling between electrons and magnetic field is then very weak in the axial direction.The pressure consists of only the particles and the magnetic pressure does not contribute to the total pressure,orptotal=pe+pi+pn.

For typical helicon plasmas in low magnetic fields and RF powers,ni,eis about 1011-1012cm-3,Te～ 3.0 ± 1.0 eV,Ti～Tn～ 400-1000 K.Then,the magnitude of charged particles is roughlype= 0.04-0.4 Pa,andpi= (0.5-1.4) ×10-3Pa.That is,electron pressure is of the same order as the neutral pressure (which is of the order of the pressure in the diffusion chamberp0),but ion pressure is very low compared with electron pressure and neutral pressure.In this case,only electron and neutral pressures are the domain terms that must be included when considering the axial direction,or the axial pressure balance is controlled mainly by electrons and neutrals,ptotal=pe+pn=nekBTe+n nkBTn.

4.2.Oscillation induced by pressure instability

In a stable discharge state,the local pressure should be balanced inside the plasma.In the axial direction,the upper pressure is that of the inlet(controlled by the feeding gas)and the downward pressure is that of the outlet (opening to the diffusion chamber).For simplicity,we take the discharge area as a whole system.In a stable gas feeding system,both are constant,sayp1andp0.

In the discharge area,the pressure should be stable to maintain a stable discharge.The pressure difference between the up-and downstream should be constant to sustain the gas flow.That is,the local neutral and electron pressures remain unchanged.Since the pressures are functions of the density and temperature ofnn,ne,TnandTe,any factor influencing these parameters affects the pressure balance.

The local electrons are produced by ionization,with a production rate ofZioni=nenn〈σioniυe〉 (where the ionization coefficient 〈σioniυe〉is related to the electron temperature and the ionization cross section).The ionization time can be neglected compared with the gas flow.

If there is a disturbance in any of the parameters ofnn,ne,Tn,orTe,the pressure balance is broken.When the ionization becomes strong occasionally,more electrons are produced,leading to an increase inneand hencepesinceTeis much higher thanTn.Another effect is the gas heating by discharge;hence,the neutral temperatureTnand ion temperatureTiincrease.Then the local total pressure rises up.As a result,the gas flow of neutrals from upstream is prevented.Parts of neutrals and charged particles expand or diffuse out of the discharge (source) region due to higher pressure.A serious neutral depletion appears in the source region.Consequently,the ionization rate is limited by the reduction of neutrals,causing a drop in the electron density and pressure,and hence the local total pressure.This reduced pressure allows neutrals from the inlet to replenish the gas in the source region again,to improve the ionization rate and hence the electron density and pressure.This process continues and recycles,leading to an oscillation in electron density and temperature.This oscillation instability is caused by the pressure instability of neutral depletion and/or heating expansion,or a kind of acoustic instability.In fact,the heating effect indeed exacerbates the neutral depletion effect [34].The process is schematized in figure 12.

Gas heating by the discharge is generally due to ionneutral collisions,during which the kinetic energy of hot ions is transferred to the cold neutrals (argon atoms).Assuming that every ion-neutral collision is considered to heat the neutral,the average neutral temperature is estimated as 350-430 K [45].If the gas expansion is adiabatic,the work done by gas expansion isThen the velocity of gas expansion is roughly estimated to be υ = 180-280 m s-1,withM= 0.04 kg mol-1,Cv,m= 12.48 J/(mol·K),T2= 300 K,T1= 350-430 K.Considering that the discharge area isL= 45 cm in length,a time interval oftex=L/υ = 1.6-2.5 ms is needed for the heated gas to rush out.This is very close to the rising time of the oscillation in the experiment,ortr= 1.6 ms.This time is not sensitive to discharge conditions like RF power,magnetic field,etc,which is consistent with the experiment.

Under this mechanism,the oscillation frequency is related to the heating efficiency of the gas by RF power supply in the discharge area.When the RF power and/or magnetic field is higher,helicon discharge is stronger.The heating speed of electrons and neutrals is then faster,and shorter time is needed to heat the whole gas (neutrals,ions and electrons).Gas expansion of the discharge area should be more frequent,or the oscillation has a higher frequency.This is consistent with the experimental observation.If the electron density has a peak at specific magnetic field (i.e.,low field peak),the oscillation also shows a change in frequency.This was observed in figure 6.

If the heating speed is too fast,or the electron pressure is dominant at very high RF power and/or magnetic field,the pressure due to overheating is not large enough to disturb the pressure balance sufficiently.Hence,the oscillation should disappear.This situation occurs when helicon discharge enters strong wave coupled mode.

For a small tube,the upstream pressure increases due to the larger pressure loss in the tube.Then the electron pressure threshold for oscillation is higher than that in the larger tube.In this case,the RF powers for oscillation should be higher.On the other hand,the electron density and pressure should not be so high as to dominate the total pressure.Therefore,the operating ranges for oscillation in a small tube are limited.This is why it is more difficult to observe the oscillation in a 0.8 cm tube than in a 6 cm tube.

5.Conclusion

In summary,a kind of quasi-periodic oscillation of electron density and temperature has been observed in argon helicon plasma.The typical frequency is in the range of 20-120 Hz,increasing with RF power and external magnetic field,while the relative amplitude decreases with RF power and external magnetic field.This oscillation can only be observed in low magnetic fields (less than 110 G in this work) and low RF power (below 500 W in a 6 cm tube and 900 W in a 0.8 cm tube).This global instability occurring in the whole discharge area is suggested to be induced by the pressure instability of the neutral depletion.The gas expansion by overheating,with a velocity of 180-280 m s-1,determines the width of the oscillation,about 1.6-2.5 ms,which does not change significantly with the discharge conditions.The heating efficiency of gas in the discharge area by RF power determines the time interval to reach an equilibrium or overheated state,and hence determines the oscillation frequency.The operating conditions for oscillation in a small tube are much stricter than those in a large tube.

Acknowledgments

This work was supported in part by National Natural Science Foundation of China (No.11975047).

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