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`Time-dependent gas density and temperature measurements in pulsed helicon discharges in
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`argon
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`GILLETTE 1212
`
`

`

`INSTITUTE OF PHYSICS PUBLISHING
`
`Plasma Sources Sci. Technol. 12 (2003) 345–357
`
`PLASMA SOURCES SCIENCE AND TECHNOLOGY
`
`PII: S0963-0252(03)62646-0
`
`Time-dependent gas density and
`temperature measurements in pulsed
`helicon discharges in argon
`
`B Clarenbach1, B Lorenz1, M Kr¨amer1 and N Sadeghi2
`
`1 Experimentalphysik II, Ruhr-Universit¨at Bochum, D-44780 Bochum, Germany
`2 Laboratoire de Spectrom´etrie Physique, Universit´e Joseph Fourier—Grenoble I and CNRS,
`B.P. 87 38402 Saint Martin d’H`eres Cedex, France
`
`E-mail: mk@ep2.rub.de
`
`Received 5 November 2002, in final form 23 April 2003
`Published 22 May 2003
`Online at stacks.iop.org/PSST/12/345
`
`Abstract
`Time-dependent measurements of the temperature and density of the
`∗(3P0) metastable atoms in two high-density pulsed helicon discharges,
`Ar
`deduced from the absorption profile of the 772.42 nm argon line, are
`presented. A single-mode tuneable diode laser is used for recording these
`profiles, and temperatures up to 1000 K are obtained from their Doppler
`width. As in high-density plasmas the metastable and ground-state atoms
`are strongly coupled by electron impact collisions, the temperature of the
`metastable atoms reflects the gas temperature. From the time variation of
`∗(3P0) density during the discharge pulse we were able to deduce the
`the Ar
`density of the ground-state argon atoms and found for the helicon regime
`that the neutral atoms can be depleted by more than a factor of 10. Over a
`wide range of plasma parameters, we examined the axial asymmetry that is
`characteristic for helicon discharges with helical antenna coupling. In
`particular, we analysed the plasma-induced emission of the Ar (750 nm) and
`Ar+ (461 nm) lines as well as the electron density in the beginning of the
`plasma pulse to better understand the evolution of the plasma and the
`transition to the helicon regime. The measurements of the gas temperature
`and the metastable density reveal the asymmetry to become pronounced
`when the discharge changes from inductively coupled plasma to the helicon
`discharge. In the helicon regime, the argon atom depletion of up to 90% and
`ionization degrees up to 65% were achieved in the antenna zone. In the
`∗(3P0) state, are fed by
`afterglow, all excited states of argon, including the Ar
`electron–Ar+ ion recombination. The measured very high temperature of
`∗(3P0) atoms is partially related to the temperature of the Ar+ ions.
`Ar
`Production of Ar+ in its excited states is also observed during several
`hundreds of microseconds in the afterglow. It is related to the electron–Ar2+
`ion recombination and indicates the presence of a significant amount of
`doubly charged argon ions in the present helicon plasmas.
`
`1. Introduction
`
`Helicon discharges are produced and sustained by helicon
`modes that are whistler waves travelling in a magnetized
`plasma column, i.e. in bounded plasma [1, 2]. These high-
`density sources operate typically at frequencies between the
`
`lower hybrid and the electron cyclotron frequency. To launch
`the rf power into the plasma various antennas have been used.
`The distribution of the rf current flowing in the coupling
`antenna is crucial for the rf power deposition and, thus, the
`spatial distribution of the plasma parameters depends on the
`particular antenna geometry.
`In case of helical antennas, a
`
`0963-0252/03/030345+13$30.00 © 2003 IOP Publishing Ltd Printed in the UK
`
`345
`
`

`

`B Clarenbach et al
`
`∗
`Ar
`
`pronounced axial asymmetry with respect to the centre of
`the antenna may be observed, which can be attributed to the
`different propagation behaviours of the helicon modes [3–6].
`If the rf power is coupled to the plasma column via a right-
`handed helical Shoji-type antenna [7], helicon modes with the
`azimuthal mode number m = +1 propagate on one side of
`the antenna and m = −1 on the other side, depending on the
`direction of the magnetic field. However, in most cases, the
`m = +1 mode carries the major fraction of the rf power so that
`the rf power is deposited preferably on the corresponding side
`of the antenna. In the following, we denote this side, where the
`electron density is higher, as the m = +1 side of the antenna
`and the other as the m = −1 side.
`In this paper, we have measured the time-dependent
`electron and argon metastable densities on two highly ionized
`pulsed helicon discharges in argon. The emission intensities
`of several atomic and ionic lines have also been analysed. Our
`data enable us to deduce, for the first time, the variation of
`the gas temperature Tg in a wide range of parameters during
`the rf pulse as well as in the afterglow. Tg was obtained
`from the evolution of the Doppler profile of the 772.42 nm
`(2p2 ← 3P0) absorption line. In the present helicon discharges
`−3 and a temperature
`with electron densities ne > 1018 m
`∼= 3 eV, the Ar
`∗
`(3P0) metastable atoms are produced by
`Te
`direct electron impact excitation of the ground-state atoms,
`or through the higher lying excited states after radiative
`cascades. Under these conditions,
`the main destruction
`∗
`(3P0) atoms is by collisions with
`mechanism of the Ar
`electrons. They include transfer to the adjacent resonance state
`∗
`(1P1),
`Ar
`(3P0) + e → Ar
`followed by the emission of 104 nm radiation to the ground-
`state as well as ionization, excitation to the higher 4p states
`∗
`∗
`(3P1) and Ar
`(3P2) states. We should
`and transfers to the Ar
`point out that even in discharges with very low electron
`∗
`(3P2) and
`temperature, the reported relative populations of Ar
`∗
`(3P0) metastable states are often very close to the ratio of
`Ar
`their statistical weights 5
`It is obvious that in helicon
`1 [8].
`discharges, the equilibrium condition by electron collision
`transfer between states is fully satisfied. Therefore, at any time,
`∗
`(3P0) density is representative of the total metastable
`the Ar
`density in the plasma.
`The total electron impact quenching rate coefficient
`(3P2) metastable atoms, kq, was measured as 2 ×
`∗
`of Ar
`−13 m3 s
`−1 for Te > 0.3 eV [9, 10], and we expect a similar
`10
`rate coefficient for reaction (1), even if a coefficient three
`times larger has been proposed in [11]. For electron densities
`ne > 5 × 1017 m
`−3 considered in this paper, the lifetime of
`∗
`(3P0) metastable atoms is therefore short
`the monitored Ar
`enough (<10 μs) to preserve their velocity distribution, i.e.
`that of the ground-state argon atoms, when they are produced.
`Moreover, the cross-section for metastability exchange, σmx,
`through collisions between metastable and ground-state atoms
`is about 1 × 10
`−18 m2 3. These atoms exchange momentum
`
`∗
`
`(1P1) + e,
`
`(1)
`
`3 σmx is deduced from the diffusion coefficient of argon metastable atoms
`
`in argon, D = 1.7 × 1020 molecule m−1 s
`−1 at 300 K [12], given by
`√
`D = (3π /16
`2)(cid:7)w(cid:8)/σ , where (cid:7)w(cid:8) is the mean velocity of argon atoms at
`300 K [13].
`
`346
`
`at a rate frequency of about 1 × 105 s−1. Therefore, the
`
`temperature deduced from our measurements corresponds to
`the temperature Tg of the neutral atoms.
`The results presented in this paper also give information
`on the variation of the neutral gas density ng during the
`plasma pulse. Knowledge of Tg and ng enables us to estimate
`more accurately the different collisional and collisionless
`rf absorption processes in the plasma. Moreover,
`they
`are indispensable quantities for a proper self-consistent
`description of helicon discharges as well as for the evaluation
`of emission spectroscopic measurements with the aid of a
`collisional-radiative model for argon. As helicon discharges
`have high electron density and low gas pressure, the dominant
`processes are electron impact excitation and de-excitation,
`ionization and radiative decay; metastable diffusion to the wall
`and their de-excitation in collisions with argon atoms [12, 14]
`can be neglected.
`This paper is arranged as follows. In section 2, we describe
`the experimental set-up and, in particular, the principles of
`the absorption measurements. The experimental results are
`presented and interpreted in section 3. First, we describe the
`formation of the helicon discharge discussing, in particular,
`the asymmetry of the discharge and the electron heating
`mechanism. In the following sections, we deal with the density
`evolution of the metastable argon atoms, the neutral gas atoms
`and the electrons during the rf pulse; we also describe the
`temporal behaviour of the metastable atoms in the afterglow.
`Finally, section 4 contains conclusions.
`
`2. Experiment
`
`The measurements were carried out on two pulsed helicon
`wave discharges operating in argon, the high-density discharge
`HE-S with small diameter shown in figure 1 (rp = 2.8 cm,
`Lp = 1.4 m) and the large-volume helicon source HE-
`L (rp = 7.8 cm, Lp = 2 m) [5, 6].
`The plasma was
`produced by rf power pulses (Prf (cid:2) 2 kW, τpulse = 2 ms,
`fpulse = 25 Hz) through helical antennas surrounding the
`discharge tube (quartz). The coupling antenna used on HE-S is
`essentially a twisted double-saddle coil consisting of two pairs
`of helical windings with opposite direction of the rf current
`and 180˚ pitch over the antenna length La = 11 cm. Figure 2
`shows a schematic of the antenna where, for simplicity, the
`rf power input connectors have been omitted.
`In practice,
`the two current circuits are in series forming one circuit
`(see [15]). On HE-L, we used a (Shoji-type [7]) helical
`antenna of length La = 22 cm. The particular geometry of
`both antennas provides m = +1 (m = −1) helicon mode
`excitation in positive (negative) magnetic field direction. The
`experimental parameters are typically ne (cid:2) 6 × 1019 m
`−3,
`Te ≈ 3 eV, frf = 25 MHz, p = 0.5–3 Pa and B0 (cid:2) 0.16 T
`for HE-S, while in HE-L the electron density is a factor of
`five smaller, and the remaining parameters are Te ≈ 3 eV,
`frf = 13.56 MHz, p = 0.1–2 Pa and B0 (cid:2) 0.1 T. In this
`paper, we mostly present data from the HE-S discharge, but
`comparable results have also been obtained on the HE-L
`device.
`The temperature and the mean density of the metastable
`(cid:10)
`∗
`[1/2]0
`(3P0) atoms (also identified as 1s3 in Paschen and 4s
`Ar
`in Racah notations, respectively [16]) were deduced from
`
`

`

`Time-dependent gas density and temperature in Ar
`
`is about 1 μs while a sample rate of 10 μs was chosen in our
`absorption measurements.
`The polarization of the laser light was chosen parallel
`to the external magnetic field to provide absorption on only
`one π (m = 0 − m = 0) Zeeman component of the
`line (J values of the lower and upper states are 0 and 1,
`respectively). The laser frequency was varied in steps of
`0.06 GHz and at each frequency the PMT signal was averaged
`over 128 plasma pulses and then recorded in a file. Similarly,
`we measured and processed the time-dependent emission
`signal when the laser beam is blocked, and subtracted the
`corresponding file from the absorption files. In this way, we
`obtain the waveforms of the transmitted laser signal for about
`40 laser frequency components forming the absorption line
`profile. For each frequency, the signal in the corresponding file
`is converted to the line-averaged time-dependent metastable
`density, (cid:7)N (ν, t )(cid:8), using the relation [18]
`(cid:2)
`(cid:3)
`lf(cid:7)N (ν, t )(cid:8)g(ν, t ),
`= 1
`π e2
`4π ε0
`mec
`
`ln
`
`I0
`Iν (ν, t )
`
`(2)
`
`where I0 is the signal without absorption (i.e. before the plasma
`pulse), l = 2 × 2rp is the absorption path length, f = 0.341
`(cid:4)
`is the oscillator strength of the transition [16] and g(ν, t ) is
`+∞
`−∞ g(ν, t ) dν = 1, related to
`the normalized line profile,
`the distribution function of the velocity of atoms along the
`laser beam. Figure 4 shows an example of the contour plot of
`(cid:7)N (ν, t )(cid:8) obtained from data recorded at different frequencies.
`Assuming the velocity distribution function to be a Gaussian,
`(cid:7)
`(cid:6)
`(cid:5)
`(cid:2)
`(cid:3)2
`the profile can be written as
`
`gas inlet
`
`rf-shielding
`
`quartz tube
`
`helicon antenna
`
`magnetic field coils
`
`quartz window
`
`ionization vacuum gauge
`
`turbo pump
`
`Figure 1. Experimental set-up of the HE-S helicon discharge.
`
`m = -1, kz < 0
`
`B0
`
`m = +1, kz > 0
`
`Figure 2. Helicon antenna on the HE-S helicon discharge.
`
`absorption spectroscopy measurements by means of a single-
`mode diode laser scanning the 772.42 nm (2p2 ← 3P0) line.
`Figure 3 shows a schematic of the experimental set-up.
`After being sufficiently attenuated to avoid saturation and
`optical pumping [17], the laser beam crosses the plasma tube
`transversely, 5 and 43 cm apart from the ends of the helical
`antennas on the HE-S and HE-L discharges, respectively.
`To double the absorption length and increase the sensitivity,
`the beam is reflected by a mirror and then detected with a
`photomultiplier (PMT). A 2 mm diameter iris and a high-pass
`IR filter are placed in front of the PMT to minimize the plasma
`emission signal. The signal of the PMT is acquired by a digital
`oscilloscope, triggered synchronously with the rf pulse that
`produces the plasma; the time resolution of the system (given
`by the input resistance of the amplifier following the PMT)
`
`g(ν, t ) = 2
`γD(t )
`√
`
`ln 2
`π
`
`exp
`√
`where γD(t ) = (2
`kBT (t )/M is the Doppler width
`ln 2/λ0)
`(FWHM) related to the time-dependent temperature T (t ) of the
`metastable atoms and ν is the frequency shift from the line
`centre. Therefore, the line-averaged translational temperature,
`T (t ) can be deduced from the profile of the section at any time t
`of the three-dimensional-plot in figure 4 and the metastable
`density, (cid:7)N (t )(cid:8) from the integral over the laser frequency of
`this profile. Figure 5 shows two examples of the metastable
`density profiles taken 0.1 and 1.88 ms after the breakdown of
`the plasma. We obtained T (t ) by fitting the line profile to a
`Gaussian and (cid:7)N (t )(cid:8) by integrating over the profile.
`To analyse the influence of the electron density ne on
`(cid:7)N (t )(cid:8) and T (t ), we used a Langmuir probe measuring the
`time-dependent ion saturation current that is proportional to ne.
`The absolute density was then obtained by calibration with a
`microwave interferometer (λ = 4 mm on HE-S, λ = 8 mm
`on HE-L).
`On the HE-S discharge, we also recorded the time-
`dependent emission intensity of several argon lines during
`the rf pulse and in the afterglow by means of a 25 cm
`monochromator (Jarrel-Ash Ebert optical mount) backed by
`a PMT. A quartz lens and a mirror provide the image of
`the plasma zone on the entrance slit of the monochromator
`monitored by laser absorption. The emission signal is averaged
`and acquired by a digital oscilloscope with a time resolution of
`10 μs. The observed lines correspond to the infrared 4p → 4s
`transitions of the argon atom and the 461 nm line of the Ar+ ion.
`
`−4 ln 2
`
` ν
`
`γD(t )
`
`,
`
`(3)
`
`347
`
`

`

`B Clarenbach et al
`
`computer
`
`Figure 3. Schematic diagram for the absorption measurements.
`
`3. Experimental results
`
`∗
`
`(3P0) metastable
`The density and the temperature of the Ar
`atoms were measured for different plasma parameters, namely,
`the gas pressure, the rf power and the magnetic field strength.
`By changing the direction of the external magnetic field, we
`were able to monitor both sides of the antenna and, thus, to
`study the axial asymmetry of the helicon discharge which is
`intimately related to the different propagation behaviours of
`the m = +1 and m = −1 helicon modes.
`As an example, figure 6 shows the time-dependence of the
`gas temperature and the metastable density for both magnetic
`field directions measured on the HE-S discharge at p = 1 Pa,
`B0 = 0.1 T and Prf = 1.4 kW; in figure 6(b) we also plotted
`the electron density ne. Note that the Tg values of figure 6(a)
`∗
`(3P0)
`are deduced from the velocity distribution function of Ar
`atoms averaged along the plasma diameter. A question to be
`answered is whether this velocity distribution is not affected
`by a possible drift velocity of metastable atoms toward the
`wall. However, these neutral atoms cannot be accelerated by
`a radial electric field to gain directed velocity. On the other
`hand, as the quenching rate coefficient of metastable atoms, kq,
`
`is very large, due to the high electron densities (in the order of
`∗
`
`1019 m−3), the mean free path of Ar
`(3P0) atoms is about 1 mm
`and, thus, much shorter than the plasma diameter. Therefore,
`the metastable and ground-state atoms are in thermodynamic
`equilibrium and, assuming no radial drift of the ground-
`state atoms, we conclude that the temperature shown in
`figure 6(a) corresponds to that of the neutral atoms in the
`plasma.
`In figure 6(b), immediately after beginning the plasma
`pulse, the metastable density increases up to its maximum
`value after about 0.1 ms. After that, it decreases rapidly
`by almost one order of magnitude at about 0.5 ms and then
`remains practically constant until the end of the pulse.
`In
`the following section we will explain that this drop is closely
`related to the gas depletion due to the simultaneous action
`of the rise of the gas temperature at constant pressure, the
`ionization of the argon neutrals, and the ion drag. At the
`end of the discharge pulse,
`the metastable density drops
`very rapidly, while the electron density decreases much more
`slowly. The very fast loss of energetic electrons stopping
`∗
`(3P0) atoms, and the continuation of
`the production of Ar
`their efficient quenching by bulk electrons, is responsible
`
`348
`
`

`

`Time-dependent gas density and temperature in Ar
`
`γ
`
`D= 0.82558 GHz => Tg= 362 K
`
`2.0
`
`1.5
`
`1.0
`
`0.5
`
`0.0
`
`Ln (I0/Iν(r))
`
`ln ( I0 / I )
`
`2.4
`
`2.0
`
`1.5
`
`0.8
`
`0.5
`
`0.3
`
`0.2
`
`0.1
`
`0.1
`
`0.0
`
`0.5
`
`1.5
`1.0
`frequency (GHz)
`
`2.0
`
`0.0
`
`0.5
`
`2.0
`1.5
`1.0
`frequency (GHz)
`
`2.5
`
`3.0
`
`4
`
`3
`
`2
`
`1
`
`time (ms)
`
`0
`0.0
`
`0.14
`
`γ
`
`D= 1.28156 GHz => Tg= 847 K
`
`0.12
`
`0.10
`
`Ln (I0/Iν(r))
`
`0.08
`
`0.06
`
`0.04
`
`0.02
`
`0.00
`
`0.0
`
`0.5
`
`1.5
`1.0
`frequency (GHz)
`
`2.0
`
`2.5
`
`3.0
`
`0.0
`
`ln ( I0 / I )
`
`1.5
`
`1.0
`
`0.5
`
`0.0
`
`0
`
`1
`
`2
`time (ms)
`
`3
`
`2.0
`
`4
`
`1.5
`
`0.5
`
`1.0
`
` frequency (G Hz)
`
`Figure 4. Contour and three-dimensional plots of the transmitted
`laser signal (B0 = 100 mT, Prf = 1.4 kW, pAr = 1.5 Pa).
`
`Figure 5. Measured absorption line profiles and Gaussian fit at
`0.1 ms (top) and 1.88 ms (bottom) in the plasma pulse.
`
`for the density drop. The augmentation of the metastable
`atoms after 0.3–0.5 ms in the afterglow results from electron–
`ion recombination producing atoms in excited states.
`In
`the following, we will discuss this behaviour separately,
`during the discharge pulse and in the afterglow. We finally
`note that very similar observations were made on the HE-L
`discharge.
`
`3.1. Plasma formation
`
`To get a better insight in the evolution of the plasma and the
`transition to the helicon regime, we analyse the electron density
`and the plasma-induced emission of the Ar (750 nm) and Ar+
`(461 nm) lines in the beginning of the plasma pulse. The upper
`level of the 750 nm line, 4p[1/2]0 has a radiative lifetime of
`24 ns [19] and is located 13.5 eV above the ground-state. This
`level is very efficiently populated by electron impact excitation
`from the ground-state [20, 21], whereas its population from
`metastable states is very inefficient [22]. The intensity of this
`line is therefore directly related to the excitation rate (from
`the ground-state into the 2p1 state) and, to some extent, to the
`ionization rate from this state. The upper level of the 461 nm
`(cid:10) 2F7/2) has a radiative lifetime of 8.4 ns [23]. Electron
`line (4p
`impact excitation of this level from the ground-state atom (ion)
`
`has a threshold at 36 eV (21 eV), and the emission intensity of
`this line can give information of high-energy electrons.
`We will discuss the plasma formation from figure 7
`showing the temporal behaviour of the line intensities as well as
`the electron density in the first 300 μs of the rf pulse. The light
`intensities have not been corrected for the wavelength response
`of the detection system and their noise level is about 0.5. To
`some extent, we also refer to figure 6 (small diagrams) for the
`evolution of metastable atoms density in the same period. In
`particular, the double peak of the metastable density observed
`on the m = +1 side in the early discharge (at the beginning
`of the pulse) can be attributed to the evolution of the electron
`temperature as discussed below.
`We can distinctly observe four discharge regimes.
`(i) From breakdown until t = 30 μs, the 750 nm intensity
`increases continuously, with almost the same intensity on both
`sides of the antenna. Simultaneously, but with a somewhat
`longer rise time, the electron density increases. In this regime,
`the breakdown and the rf power deposition in the plasma is
`expected to be due to electrostatic coupling from the antenna,
`and the electron temperature is known to be higher than 5 eV
`[24, 25].
`(ii) Between 30 and 70 μs, the electron density continues
`to increase, whereas the intensity of the 750 nm line stays
`almost constant. The slight intensity difference between the
`
`349
`
`

`

`m = +1
`m = - 1
`
`1400
`
`1200
`
`1000
`
`800
`
`600
`
`400
`
`200
`
`(a)
`
`Tg (K)
`
`B Clarenbach et al
`
`0
`
`0.0
`
`0.5
`
`1.0
`
`1.5
`
`2.5
`
`3.0
`
`3.5
`
`4.0
`
`2.0
`time (ms)
`
`2.0
`
`1.6
`
`1.2
`
`0.8
`
`0.4
`
`2.0
`
`1.6
`
`1.2
`
`0.8
`
`0.4
`
`0.0
`0.00
`
`0.05
`
`0.15
`0.10
`time (ms)
`
`0.20
`
`0.0
`0.25
`
`ne (1019m-3)
`
`ne (1019m-3)
`
`3012345
`
`0.8
`
`0.6
`
`0.4
`
`2
`
`0.2
`
`1
`
`0.0
`0.25
`
`0
`4.0
`
`1.6
`
`1.2
`
`0.8
`
`0.4
`
`0.0
`0.00
`
`0.05
`
`0.15
`0.10
`time (ms)
`
`0.20
`
`2.0
`time (ms)
`
`2.5
`
`3.0
`
`3.5
`
`m = +1
`
`m = -1
`
`1.6
`
`1.2
`
`0.8
`
`0.4
`
`0.0
`1.5
`
`1.2
`
`0.9
`
`0.6
`
`0.3
`
`(b)
`
`[3P0] (1016m-3)
`
`[3P0] (1016m-3)
`
`0.0
`0.0
`
`0.5
`
`1.0
`
`1.5
`
`Figure 6. Time-dependence (a) of the gas temperature and (b) metastable (•,
`(HE-S: B0 = 100 mT, Prf = 1.4 kW, pAr = 1.0 Pa).
`m = +1 and −1 sides reflects nearly the difference in ne.
`During this period,
`the metastable density also levels off
`(figure 6), and the intensity of the 461 nm line is below the
`detection limit of our optical system. A constant excitation rate
`of atomic levels along with an increase of the electron density
`can only be understood if the electron temperature decreases
`simultaneously. The logarithmic slope of ne corresponds to
`the ionization frequency νI, that is strongly dependent on
`the high energetic part of the electron energy distribution
`function (EEDF), provided that the charged particle losses
`(by ambipolar diffusion and electron–ion recombination) are
`slow processes compared to ionization. Thus, the continuous
`
`) and electron densities (——) on the m = +1 and −1 side
`
`diminution of the slope of ne indicates a drop of the ionization
`rate. This is also supported by the slight decrease of the
`metastable density (see inset in figure 6(b))—reflecting the
`diminution of the excitation rate of argon atoms. As was
`already reported [26, 27], the transition from the electrostatic
`rf power coupling to the inductive coupling (ICP) regime is
`always associated with a lowering of Te. We thus conclude
`that, after about 30 μs, the discharge enters the ICP regime in
`which the plasma is mainly located under the antenna.
`(iii) Between 70 and 130 μs, several phenomena are
`observed. The electron density increases almost exponentially
`on the m = −1 side, whereas the growth is stronger than
`
`350
`
`

`

`Time-dependent gas density and temperature in Ar
`
`the electron density continues to
`(iv) After 130 μs,
`increase on both sides, however, the slope of the density
`curve decreases continuously, until ne becomes nearly constant
`(on the m = +1 side after t = 250 μs). Obviously,
`the ionization is then increasingly compensated and finally
`balanced by diffusion losses that are mainly caused by cross-
`field diffusion due to the high electron–ion collision frequency
`scaling linearly with ne and the large aspect ratio of HE-S.
`Indeed, taking the density at 300 μs, we estimate a diffusion
`time of about 40 μs; this value is several times shorter than the
`axial ambipolar diffusion time (for a total plasma length ∼=1 m)
`that is primarily determined by the ions (see also section 3.3).
`Let us now compare the growth of the intensities of the atomic
`and ionic lines on the two sides with each other. As mentioned
`above, this growth is much more pronounced for the ionic line
`than for the atomic line. Moreover, at 300 μs, we see that
`the intensity of the ionic line differs on the two sides by a
`factor 40, while the atomic line intensity (as well as ne) differs
`only by a factor 2. In particular, from the evolution of the ionic
`line intensity in this period, we can draw the conclusion that
`the electron heating mechanism in the helicon regime starts
`primarily on the m = +1 side and affects predominantly the
`energetic part of the EEDF. On the m = −1 side, the much
`faster enhancement of the 750 nm line intensity compared to
`that of ne as well as starting of the build up of 461 nm emission
`evidence the emergence of high-energetic electrons on this
`side. We also note the decrease of the 750 nm intensity on
`the m = +1 side after t = 150 μs that is expected to be
`due to the gas depletion starting then (see next section). The
`fact that the 461 nm intensity continues to increase on this
`side up to 200 μs whereas the Ar density decreases, proves a
`significant contribution from reaction (5). On the other hand,
`this intensity staying nearly constant after 200 μs although
`ne increases further, indicates that there is also a significant
`contribution from reaction (4) for excitation of the upper state
`of this line from the ground-state or the metastable states of
`argon. After 300 μs, the discharge regime is well established,
`and the different parameters change only very slowly.
`
`From the observations described above, we infer the
`following physical picture of the formation of the helicon
`discharge: after passing the capacitive and ICP regimes, the
`discharge enters the helicon regime that is characterized by the
`onset of helicon mode propagation and rf power absorption
`(concerning the various discharge regimes see [28]). As
`the helical antenna excites predominantly the m = +1
`helicon mode travelling in positive magnetic field direction,
`the rf energy is mainly deposited on the m = +1 side of
`the antenna. High-energy electrons are thus expected to
`be produced predominantly on this side and the discharge
`becomes axially asymmetric [5]. Hence, the line intensities
`of the Ar atomic and ionic lines increase on the m = +1 side
`first when the m = +1 helicon mode starts propagating. In
`particular, the intensity of the argon ion line (461 nm) increases
`much faster than expected from the n2
`e dependence. Moreover,
`the very large ratio of the argon ion line intensities on the
`two sides of the antenna after 300 μs, whereas the ratio of
`the densities is only 2, cannot be understood in terms of this
`dependence. From these findings we conclude that the electron
`heating affects mainly the tail of the EEDF which cannot be
`described by the temperature of the bulk electrons. To be more
`
`351
`
`750; m=+1
`461; m=+1
`750; m=-1
`461; m=-1
`ne; m=+1
`ne; m=-1
`
`0
`
`50
`
`150
`100
`Time (μs)
`
`200
`
`25
`
`0
`
`3
`
`00
`
`1000
`
`100
`
`10
`
`1
`
`0.1
`
`Line intensity (arb. u.) and ne (1017m-3)
`
`Figure 7. Electron density and intensities of Ar I 750 nm and Ar II
`461 nm lines on the m = +1 and −1 sides in the beginning of the rf
`pulse (HE-S; B0 = 100 mT, Prf = 1.4 kW, pAr = 1.0 Pa).
`exponential on the m = +1 side, indicating a more efficient
`ionization there. In the same period, the intensity of the 750 nm
`line starts to increase on this side, but decreases on the m = −1
`side. (Note that this behaviour is in reasonable agreement with
`∗
`(3P0) density on the two sides of the
`the evolution of the Ar
`antenna, shown in figure 6(b).) At t = 130 μs, the intensity of
`the line differs by almost one order of magnitude, whereas the
`difference in ne is only a factor of two. This diminution of the
`excitation rate on the m = −1 side cannot be associated with
`gas depletion (see later), because the gas temperature stays
`nearly constant during this period (figure 6(a)), and the degree
`of ionization does not exceed a few per cent. In contrast to this
`behaviour, the evolution of the ionic line at 461 nm is much
`more pronounced: the line intensity builds up on the m = +1
`side with a short rise time, while it still stays at noise level on
`the m = −1 side. If the upper state of this line was excited
`from the ground-state of Ar,
`Ar + e → (Ar+)
`
`(4)
`
`∗
`
`+ 2e (−36 eV),
`
`the intensity should increase proportionally to ne provided that
`Te is constant. On the other hand, it should scale as n2
`e, if the
`state was excited from the ground-state of the ions,
`Ar+ + e → (Ar+)
`+ e (−21 eV).
`∗
`
`(5)
`
`However, we observe a much faster rise of the intensity than
`for n2
`e, indicating that the fraction of electrons whose energy
`exceeds 21 eV (or 36 eV for reaction (4)) increases significantly
`on the m = +1 side.
`
`

`

`B Clarenbach et al
`
`specific, a significant number of electrons with directed energy
`in positive magnetic field direction are likely to be generated;
`otherwise, due to the low collisionality of these energetic
`electrons, we would expect that the argon ion line intensity
`increases almost simultaneously on both sides of the antenna
`whereas the argon ion line intensity on the m = −1 side is
`observed to be practically zero in the first 150 μs of the rf pulse.
`A candidate for such an anomalous heating process,
`starting at about 70 μs, could be electron acceleration by the
`m = +1 helicon wave. The evolution of the 750 nm line
`intensity on both sides seems to indicate that after beginning of
`the helicon propagation at t ∼= 70 μs, the energetic electrons
`are generated on the m = +1 side whereas the number
`of the electrons in the high-energy tail of the distribution
`function is reduced on the m = −1 side. This behaviour
`is in accordance with previous investigations reporting that
`high-energy electrons of the antenna region are trapped and
`accelerated, during half a period, in the axial electric field
`of the m = +1 helicon mode travelling along the plasma
`column [29].
`In that paper, it was emphasized that only
`suprathermal electrons having initial velocities close to the
`wave phase velocity in the m = +1 direction can be trapped
`and accelerated by the helicon wave thus providing them
`higher kinetic energy. One is therefore tempted to conclude
`that the m = +1 helicon wave produces electrons with high
`directed energy that are able to enhance the ionization rate
`and populate the highly excited states of Ar and Ar+. The
`threshold energy for these processes ranges approximately
`between 14 and 36 eV, and cross-sections for excitation to the
`upper Ar levels or for ionization become significant for electron
`energies in the range of 20–30 eV [30]. To get efficient energy
`gain, mainly electrons with energies in the range 10–15 eV
`must be accelerated to above 20 eV. In case of our helicon
`source HE-S produced at the rf frequency frf = 25 MHz
`and a measured axial helicon wavelength λz = 15 cm [15],
`the trapping energy corresponding to the phase velocity of
`the wave along the magnetic field, vz = ω/ kz, is about
`40 eV that holds for the (quasi-stationary) discharge, i.e. after
`200–300 μs. For the lower electron density in the time interval
`70 μs < t < 200 μs, we expect even larger phase velocity
`and, thus, higher energy. We estimated the fraction of the
`electrons being in resonance with the wave from the parallel
`phase velocity, the rf power carried by the helicon wave and
`the axial rf electric field Ez. The relation between the energy
`flux and the electromagnetic field was obtained from helicon
`wave theory presented in [31], and Ez was estimated for
`collisional plasma with predominant electron–ion collisions
`yielding wave potential oscillation amplitudes, Ez/ kz, less
`than 1 V. It turns out that the number of resonant electrons is
`−7 for Maxwellian EEDF);
`then extremely small (fraction <10
`moreover, the rise of ionic line intensity due to the change
`(flattening) of the EEDF at resonance energy is expected to be
`weak because the excitation cross-sections vary only weakly
`at high energies.
`During the last decade, resonant electron heating leading
`to enhanced ionization has been treated in numerous papers
`[28, 32]. Thorough investigations have been reported on
`time-resolved energy analyser measurements of the EEDF
`performed in the energy range up to 25 eV [33, 34]. However,
`the results were contradictory in that Molvik et al [33] observed
`
`352
`
`electrons energy modulated by the helicon wave whereas
`Blackwell and Chen [34] showed the absence of high-energy
`resonant electrons. This