Quasisteady state interpulse plasmas

JOURNAL OF APPLIED PHYSICS 101, 113311 共2007兲

Quasisteady state interpulse plasmas Sudeep Bhattacharjeea兲 and Indranuj Dey Department of Physics, Indian Institute of Technology, Kanpur 208016, India

Abhijit Sen Institute for Plasma Research, Bhat, Gandhinagar 382 428, India

Hiroshi Amemiya Graduate School of Chuo University, Bunkyo, Tokyo 112-8551, Japan

共Received 11 January 2007; accepted 16 April 2007; published online 13 June 2007兲 The generation of quasisteady state plasmas in the power off phase, by short pulses 关pulse duration 共␶ p兲 ⬃ 0.5– 1.2 ␮s兴 of intense 共60– 100 kW兲 microwaves in the X band 共9.45 GHz兲 is observed experimentally. The steady state is sustained from a few to tens of microseconds and depends upon the ionization processes in the interpulse phase and the characteristic diffusion length. The results are explained by a model, which considers the electron acceleration effects by the large amplitude of the field, the energy losses, and the characteristic electromagnetic field decay time. The effects of wave frequency, microwave power density, and particle diffusion on the steady state are investigated. A striking difference with conventional afterglows of pulsed discharges is pointed out. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2743825兴 I. INTRODUCTION

Pulsed plasmas have found wide applications both in industry and for basic studies.1–5 The prime advantages include additional control over the plasma properties by being able to vary the pulse duration, duty cycle, and the repetition frequency. The pulsing parameters are known to provide control over the electron energy distribution function6 and gas heating effects can be avoided.7 Pulsed plasmas have therefore found attractive applications that include generation of metastables,8 radicals,9 and negative ions.10 Previously, pulsed discharges that have been widely investigated belong to low to moderate powers 共few 100 W – 2 kW兲 and relatively wide duration 共10 ␮s – 100 ms兲 pulses.11–13 In most of these studies, it has been reported that the plasma attains a steady state within the pulse and after the end of the pulse the plasma decays temporally with the electron temperature attaining close to thermal values. Such a behavior is typical of afterglow plasmas. However, if high power 共60– 100 kW兲 is supplied to the plasma in small duration pulses 共␶ p = 0.5– 1.2 ␮s兲, the parent plasma is quite active and is followed by a comparatively long lived plasma in the power off phase, with electrons still having a high average energy 共3 / 2kTe兲. Such an “interpulse plasma”14 in the power off phase has interesting properties15–17 that are distinctly different from afterglow plasmas. Some of these experimentally determined differences from our earlier work on microwaves of 3 GHz are, as follows: 共a兲 the plasma buildup is extended beyond the pulse duration with the peak density attained a few to tens of microseconds later in the power off phase, 共b兲 a high value of electron temperature 共⬃6 – 10 eV兲 continues for a time comparable to the buildup time, and 共c兲 enhanced interpulse a兲

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plasma densities could be obtained at a pressure 共␻ / ␯c Ⰶ 1兲 where resonant wave absorption such as electron cyclotron resonance 共ECR兲 may be considered as negligible 共here ␻ is the wave frequency and ␯c is the electron neutral collision frequency兲. In this article we report experimental observations on the generation of a quasisteady state in the power off phase of a plasma produced by high frequency 共9.45 GHz兲 pulsed mode microwaves in the X band. For the time between the pulses 共interpulse time兲 where the steady state is obtained, the plasma is basically without an external energy source. The dependence of the steady state on the plasma collisionality is studied over a pressure range from 1 mTorr to 1 Torr. The influences of microwave pulse parameters such as the pulse amplitude and repetition frequency and the characteristic diffusion length on the steady state are investigated. The experimental results are complemented by theoretical model calculations that are based on the coupled rate equations of the plasma density and the electron temperature. Good agreement is found between the experimental observations and the model calculation results. The manuscript has been arranged as follows. In Sec. II, the experiment is described. The results are presented in Sec. III. The model and results from the model are presented in Sec. IV. Some discussions and conclusions are drawn in Sec. V. II. EXPERIMENT

The compact plasma source employs microwaves in the X band 共9.45 GHz兲 which are launched into a circular plasma chamber about 30 cm long. The plasma chamber is kept inside a larger vacuum chamber of about 60 cm diameter and 250 cm length. The plasma is confined by a minimum-B field generated by permanent magnets 关Nd– Fe–B, surface magnetic field 共Bmax兲 ⬃ 1 T兴 surrounding the

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J. Appl. Phys. 101, 113311 共2007兲

FIG. 1. Schematic of the experimental apparatus; OSC, magnetron oscillator; ISO, isolator; SC, straight section; ATT, attenuator; DC, directional coupler; H, rectangular bend; EHT, E-H tuner; W, quartz window; C, chamber; MC, multicusp; OF, optical fiber; WG, waveguide; P, Langmuir probe; PMT, photomultiplier tube; V p, probe voltage; PC, computer; DOS, digital oscilloscope; R, resistor, XY, X-Y chart recorder; TRIG, trigger signal; BX, boxcar integrator.

chamber. The resulting field structure with a null at the center of the chamber provides plasma confinement. A schematic diagram of the experimental setup is shown in Fig. 1 and the radial magnetic field profile for the hexapole is shown in Fig. 2共a兲, including a Poisson simulation field plot in Fig. 2共b兲. The wave launch mode belongs to k ⬜ B, where k is the wave vector and B is the static magnetic field. Argon is used as the test gas. The experiments were carried out on a few different plasma chambers that were designed with the radius chosen as integer multiples of the quarter wavelength of the wave n␭ / 4 共n 艋 4 has been used兲. The small chamber cross section enhances the microwave power density 共⬃10 kW/ cm2兲, which is considerably larger than conventional moderate power, large diameter plasma sources 共e.g., for power ⬃500 W and plasma chamber radius 共a兲 ⬃ 3 cm, the power density ⬃0.01 kW/ cm2兲. Plasma current measurements have been made at the center of the plasma chamber where the magnetic field is almost zero. A circular planar Langmuir probe with a diameter of 4 mm, made of stainless steel with a thickness of 0.1 mm, is used in the fixed voltage 共20 V for electron current and −70 V for ion current兲 mode to study the temporal profiles of the particle 共electron and ion兲 saturation currents and in a sweep voltage mode 共−100 to 100 V兲 to obtain the probe 共I-V兲 characteristics. Both sides of the planar probe were used for charge particle collection and the probe surface was kept parallel to the wave vector. The time varying particle currents 共electron and ion兲 were measured using a fast digital oscilloscope 共Tektronix model TDS2014兲. A boxcar integrator 共Stanford Research Systems, model SR200兲 was used to make time resolved measurements of probe characteristics and the optical data. For the optical studies, the light emitted by the pulsed argon plasma was obtained by an optical probe, which consists of an optical fiber and a lens attached at the tip. The probe is inserted through a radial port onto a tiny gap in the multicusp and the plasma chamber. The obtained light is passed onto a monochromator 共CVI model

FIG. 2. 共a兲 Radial variation of the static B field of the magnetic multicusp in the normalized scale. 共b兲 Two dimensional Poisson field plot. 共c兲 Longitudinal magnetic arrangement, demonstrating axial end plugging.

CM110兲 and the signal is amplified by a photomultiplier tube 共CVI model AD110兲. We have studied the transition 3s23p4 共 1D兲 4s → 3s23p4 共 1D兲 4p, which is the most intense in the visible region of the spectrum of the pulsed argon plasma. III. EXPERIMENTAL RESULTS

Figure 3 shows the buildup of the plasma electron current density. It is seen that the buildup is extended beyond the end of the pulse 共which ends at ⬃1.2 ␮s兲, with the peak

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FIG. 3. Temporal variation of the electron current density Je with pressure p as a parameter.

density attained about 20– 30 ␮s later in the power off phase. In general, the plasma buildup time ␶b, defined as the time to obtain the peak density from the end of the pulse, increases with increase in pressure. The trend agrees reasonably well with what was seen earlier in the case of a 3 GHz discharge.15 It may be noted in Fig. 3 that at 40 mTorr the build up and the decay profiles tend to become flatter. Figure 4 shows a typical plasma quasisteady state in the electron current density that is maintained for more than 30 ␮s in the interpulse phase. The result is remarkable in that the steady state is maintained even in the absence of any microwave input power. The end of the microwave pulse is clearly indicated in the figure. The temporal variation of the electron current density Je is shown at a discharge pressure p of 36 mTorr and a pulse repetition frequency f r of 100 Hz. Figure 5 shows the variation of the peak electron current density Jme with pressure p and pulse repetition frequency f r as a parameter. Jme corresponds to the maximum value of the current profiles shown in Fig. 3. The pulse repetition frequency has only a weak influence on Jme. The plasma density

FIG. 4. Temporal variation of the electron current density Je, showing the development of a plasma steady state 共density flattop兲 in the interpulse regime.

J. Appl. Phys. 101, 113311 共2007兲

FIG. 5. Variation of the peak electron current density Jme with pressure p and pulse repetition frequency f r as a parameter.

decreases below 4 mTorr and above 100 mTorr, and the pressure where the steady state is observed 共36– 40 mTorr兲 approximately lies in between these limits. The plasma can be sustained over a wide pressure range of 10−3 – 1 Torr, and for this condition a maximum current density of ⬃100 mA/ cm2 is obtained. Figure 6 shows the variation of the electron confinement time ␶c with pressure p, and the pulse repetition frequency f r as a parameter. The electron confinement time in the discharge may be obtained as the sum of the buildup time ␶b, the quasisteady state time ␶flat, and the decay time ␶d, where ␶d is defined as the e-folding decay time required for the electron current to decay from its peak value to ⬃1 / 10e when measured with a highest sensitivity ⬃0.1 ␮A. The electron confinement time may be considered as a qualitative measure of the amount of time the plasma is sustained. At 100 Hz, ␶c is found to increase steadily from ⬃0.1 ms at 3 mTorr to approximately 10 ms at ⬃40 mTorr, which is the maximum value and corresponds to the pressure at which the plasma steady state is observed in Fig. 4. As we will soon see, from these data we may infer that the flattop duration follows the simulation trend.

FIG. 6. Variation of the electron confinement time ␶c with pressure p and pulse repetition frequency f r as a parameter.

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FIG. 7. Variation of the 404 nm optical intensity with time at a fixed microwave power for a = 2.2 cm.

Figure 7 shows the variation of the optical intensity at 404 nm at 60 mTorr in comparison with the microwave pulse. It may be noted that the intensity of the 404 nm optical line has a delayed buildup and remains constant for ⬃400 ns before undergoing decay. The 404 nm line corresponds to the transition between the states of Ar II 共ion兲 with energy levels, 3s23p4共 1D兲4p 共21.4980485 eV兲 and 3s23p4共 1D兲4s 共18.4265479 eV兲. Thus we can see that although the energy difference between the levels is around 3.07 eV, the excitation energy needed to cause this transition is about 21.5 eV. In order to have this level populated sufficiently for an easily detectable output, a high value of average electron energy is required 共艌21.5 eV兲. This is provided primarily during the pulse on time as can be seen in Fig. 8 for the 0.98 cm radius.

pulse obtained experimentally. The pulsing scheme is implemented in the numerical calculations using the following conditions 共for a pulse on time of ⬃1.2 ␮s兲:

IV. MODEL CALCULATION A. Temporal evolution of the electron energy

The plasma steady state is considered to be a result of a balance between the production and loss mechanisms occurring in the power off phase of the discharge. During the pulse, strong electric fields of short duration accelerate electrons to high energies. The temporal evolution of the electron thermal energy 共␧兲 is determined by a balance between the heating and the loss rates given by,15

⳵␧ ␯c关eE P共t兲sin ␻t兴2 − Lc共␧兲, = ⳵t 2me共␻2 + ␯2c 兲

FIG. 8. Temporal variation of electron energy for different tube radii at a pressure of 40 mTorr, power of 100 kW, and input frequency of 9.45 GHz.

共1兲

where ␯c is the elastic collision frequency, ␻ is the angular wave frequency, e and me are the electron charge and mass, respectively, and E P共t兲 is the time dependent amplitude of the electric field in the plasma chamber, which depends upon the nature of the microwave pulse. Several improvements have been made to the model described in Ref. 15. First, a time dependent electric field has been incorporated based upon the shape of the microwave

E P共t兲 = E Po exp关共t − t1兲/t1兴 =E Po

共for t ⬍ t1兲,

共for t1 艋 t 艋 t2兲,

=E Po exp关− 共t − t2兲/␶兴

共for t ⬎ t2兲,

共2兲 共3兲 共4兲

where E Po is the amplitude of the electric field, t1 is the rise time of the pulse 共⬃150 ns兲, and ␶ is the fall time of the electromagnetic field at the end of the pulse 共⬃175 ns兲. The flat region of the pulse extends from t = t1 to t = t2 共⬃1.05 ␮s兲. Second, when the microwave pulse switches off, the electromagnetic field energy does not become zero at once, but it decays slowly with a characteristic time ␶d. This can be attributed to the decay of the wave in the plasma, which is proportional to the electron collision time and possible multiple reflections inside the chamber, which results in the elongation of the time taken by the electromagnetic energy to die out completely. We obtain the total decay time ␶d to be

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⬃3 ␮s. Therefore we replace the ␶ of Eq. 共4兲 by ␶ f = ␶ + ␶d as the total decay time of the electromagnetic energy in the plasma. For an input frequency of f = 9.45 GHz and a pressure range of p = 共10– 100兲 mTorr with peak microwave power Po = 25– 100 kW, we have performed numerical simulations to obtain the plots of ␧ vs time t. For a chamber radius a = 0.98 cm, the electron energy was found to saturate within the pulse 共1.2 ␮s兲 with the maximum energy ␧max ⬃ 24– 32 eV after which it dropped to about 8 eV just after the end of the pulse. It may be noted that this drop was not exponential. It then decayed with a weak exponential and around 100 ␮s was found to be ⬃5 eV. The weak exponential decay after about 2 – 3 ␮s agrees well with our earlier electron temperature measurements in a pulsed 3 GHz microwave discharge.17 Thus, it can be seen that electron energies much above the thermal values can be maintained in the interpulse plasma. At larger radii 共1.4 cm, 2.2 cm兲 the power density decreases and as a result the maximum electron energy decreases, as shown in Fig. 8共a兲, which is an expanded view. It is seen from Fig. 8共b兲 that a steady value of the electron energy stays on for a longer time in the case of a larger radius, which indicates that the energy diffusion time is longer in the case of a larger radius.

冉 冊 冉冊

The plasma evolution may be modeled by jointly considering the rate equations for the plasma 共electron兲 density and the electron energy 关Eq. 共1兲兴, 共5兲

where ne is the electron density, Ng具␴␯典 is the ionization rate of the background gas given by Ng具␴␯典 = Ng兰E⬁ 冑2E / me ␴共E兲F共E兲dE, ␴共E兲 being the collision cross i section, Ng is the neutral density, the electron energy distribution function F共E兲 is assumed to be Maxwellian,15 D is the diffusion rate of the generated plasma, and ␦ is the secondary electron coefficient for the electrons that are either reflected back or generated due to the primary plasma electrons impacting the chamber wall. The effect of the secondaries from the metal boundary is an addition to the previous model. We can write Eq. 共5兲 as

⳵ne D = Ng具␴v典ne − 2 共1 − ␦兲ne , ⳵t ⌳

共6兲

where we have approximated ⵜ2 by 1 / ⌳2, ⌳ being the characteristic diffusion length which we consider as the scale length in our problem. We may write D / ⌳2 = ␳ as the decay rate due to radial diffusion. In addition, when we include the effects of the static radial magnetic field the diffusion coefficient D is given by the modified diffusion coefficient D⬜ given by the equation D⬜ =

D , 共1 + ␻2c /␯2c 兲

␻c = eB / me, is the electron cyclotron frequency. D may be taken as the free electron diffusion given by D = ␬Te / me␷e. We take an average value of B ⬃ 0.6 T for our calculations. The characteristic diffusion length ⌳ can be estimated by including the effect of the radial magnetic field as 1 2.4 2 = ⌳ R

B. Temporal evolution of the plasma

⳵ne = Ng具␴v典ne − D共1 − ␦兲ⵜ2ne , ⳵t

FIG. 9. Temporal variation of the plasma 共electron兲 current density for different gas pressures at a peak power of 50 kW, radius of 2.2 cm, and frequency of 9.45 GHz.

共7兲

where D is the diffusion coefficient for the case when B = 0,

2

+

␲ L

2

␹,

共8兲

where ␹ = ␯2c / 共␯2c + ␻2c 兲, R is the effective plasma radius, and L is the length of the plasma chamber 共⬃30 cm兲. The secondary electron coefficient ␦ can be estimated using the form18

␦ = ␦s共␧/␧m兲exp关2共1 − 冑␧/␧m兲兴.

共9兲

We use ␦s = 1.4 and ␧m = 400 V, for the stainless steel surface of the multicusp that bounds the plasma. Taking ␰ = ␧ / Ei, the rate of change of the electron density can finally be written as

冉 冊 冉 冊

1 1 ⳵ne D = C冑␲ 2 + exp − ne − 2 共1 − ␦兲ne , ⳵t ␰ ␰ ⌳

共10兲

where the terms on the right hand side are a function of the electron thermal energy 共␧兲. Therefore, ␧共t兲 evaluated from Eq. 共1兲 by the numerical simulation can be fed to Eq. 共10兲 to obtain ne as a function of time t. To compare our results with the experimental data, where the evolution of the plasma 共electron兲 current density 共Je兲 with time is obtained, we evaluate Je using Je =

冑

冉 冊

1 e3 exp − ne冑␧. 2 M

共11兲

The simulation results have been plotted in Figs. 9–12. In Fig. 9, we see the variation of Je with pressure for a fixed power and radius. In conformity with the experimental result 共Fig. 3兲, the plasma tends to a quasisteady state at a lower pressure 共⬃36 mTorr兲. Figure 10 shows the variation of Je with the radius of the multicusp at a fixed power and pressure. We see that Je is

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FIG. 10. Temporal variation of the plasma 共electron兲 current density for different tube radii at a pressure of 40 mTorr, peak power of 100 kW, and frequency of 9.45 GHz.

higher and there is a better flattop at a larger radius. This can be understood from the decay rate due to radial diffusion ␳ 关Eqs. 共6兲–共8兲兴. Since ␳ = D / ⌳2, therefore for a larger radius 共hence larger ⌳兲 ␳ will be smaller and hence the plasma will diffuse out more slowly thereby giving a higher current density and better flattop. Also the field decay time ␶ will be longer for the larger radius, which will result in a slower decay of microwave energy from the plasma, thereby enhancing the plasma production. Figure 11 shows the dependence of Je on the frequency of the incident microwave radiation at fixed radius, power, and pressure. This was not possible to do experimentally because of a fixed frequency source. As the frequency is increased from 4 to 30 GHz, we see that Je decreases, which is evident from Eq. 共1兲, as the energy gain dependence on the wave frequency goes as 1 / ␻2. Although at 4 GHz the wave frequency nearly equals the cutoff frequency of the waveguide, however, from our earlier experiments,19 we have found that microwaves can be made to propagate and sustain

FIG. 11. Temporal variation of the plasma 共electron兲 current density for different input frequencies at a pressure of 40 mTorr, peak power of 100 kW, and radius of 2.2 cm.

J. Appl. Phys. 101, 113311 共2007兲

FIG. 12. Temporal variation of plasma 共electron兲 current density for different peak microwave powers at a pressure of 250 mTorr, radius of 2.2 cm, and input frequency of 9.45 GHz.

a plasma even in a waveguide with a dimension slightly below cutoff with minimum reflection 共⬃5 % 兲. We note that there is a better quasisteady state for f = 9.45 GHz, which can be attributed to the fact that the radius a of the multicusp becomes comparable to ␭ 共n␭ / 4, where n = 4兲, which results in better power coupling between the field and the plasma. Figure 12 shows the plot of Je vs t for different peak powers of the incident microwave radiation at a fixed pressure and radius. We can see that the value of Je increases with the increase in microwave power. This is evident from Eq. 共1兲, that the electron energy is directly dependent on the peak microwave power of the pulse. Figure 13 shows the variation of the flattop duration with pressure. It is seen that for a fixed power there is an optimum pressure at which the flattop duration is maximum. The simulation results are in good agreement with the experimental ones particularly in the higher pressure regime. Figure 14 shows the variation of the flattop time ␶flat with microwave power at pressures of 10 and 60 mTorr. A

FIG. 13. Variation of the flattop duration ␶flat with pressure. Dotted line and open squares, simulation; solid line and circles, experiment. The results are for a peak power of 100 kW.

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FIG. 14. Variation of the flattop duration ␶flat with microwave powers at 10 and 60 mTorr. E, experimental values; S, simulation results.

good agreement is obtained with the experimental results. ␶flat shows a gradual increase with increase in microwave power and has a saturation tendency at a higher power ⬃100 kW. V. DISCUSSION AND CONCLUSION

The simulation results are in good agreement with the experimental observations. The delayed plasma buildup tends to a steady state at lower pressures 共⬃40 mTorr兲. The generation of the quasisteady state after the end of the microwave pulse depends upon the ionization processes in the interpulse phase, brought about by the energetic primary electrons generated during the pulse on time by the waves of large amplitude. The steady state duration depends primarily upon the discharge pressure and the decay rate ␳共=D / ⌳2兲 which is related to the chamber size 关Eq. 共6兲兴. The simulation results have predicted the existence of an optimum frequency, which couples to the plasma chamber more efficiently. In Fig. 12 we see that the wave amplitude has an influence on the peak value of the current although the peak current density appears after the microwave pulse is long gone. This is because the plasma current density depends jointly on the plasma electron density and the electron thermal energy. Higher wave amplitudes will therefore give rise to higher electron thermal energies 关as seen from Eq. 共1兲兴. This effect will evidently be reflected in the peak value of the plasma current density. It was not possible to individually delineate the role played by the radiation decay time ␶d, because a change in ␶d is intrinsically related to a change in the chamber radius, which in turn changes ␳ and the peak electric field E Po. However, we have found that its inclusion is significant as seen in Fig. 15. Its effect is currently under further investigation. The secondary electron coefficient ␦ was found to extend the duration of the steady state to some extent in the case of chambers with smaller radius 共⬃1 cm兲, but its effect at larger radii was found to be small. The possibility of achieving a quasisteady state is interesting from the point of view of applications. From the ex-

FIG. 15. Comparison of the plasma 共electron兲 current density evolution in the presence and in the absence of field diffusion time ␶d for a = 2.2 cm, peak power of 50 kW, at a pressure of 60 mTorr.

periments, we have seen that the duration of the steady state is controllable by a proper choice of background pressure, chamber size, and frequency. The pulse repetition frequency is another important factor that can provide control. Thus one can produce a quasicontinuous plasma with high frequency pulsed sources of large amplitude by adjusting the pulse repetition parameters in such a fashion that before the plasma due to the first pulse decays to 90% of its maximum density, a second pulse arrives and reinforces the plasma. This may be quite economical as one saves not only the expenses of acquiring high frequency cw sources but on the power budget as well. Furthermore, this scheme may offer a different method of auxiliary plasma heating in fusion plasmas or ion sources. ACKNOWLEDGMENTS

This work was partially supported by Council of Scientific and Industrial Research 共CSIR兲, India, Grant No. 03共1035兲/05/EMR-II and the United States Asian Office of Aerospace Research and Development 共AOARD兲 Contract No. FA5209-06-P-0242 共Case No. AOARD-064020兲. One of the authors 共S.B.兲 acknowledges a distinguished postdoctoral fellowship from The Institute of Physical and Chemical Research 共RIKEN兲, Japan where part of the work was carried out. 1

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