Magnetic dipole discharges. III. Instabilities
R. L. Stenzel, J. M. Urrutia, C. Ionita, and R. Schrittwieser
Citation: Physics of Plasmas (1994-present) 20, 083505 (2013); doi: 10.1063/1.4817016
View online: http://dx.doi.org/10.1063/1.4817016
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PHYSICS OF PLASMAS 20, 083505 (2013)
Magnetic dipole discharges. III. Instabilities
R. L. Stenzel,1 J. M. Urrutia,1 C. Ionita,2 and R. Schrittwieser2
1
2
Department of Physics and Astronomy, University of California Los Angeles, California 90095-1547, USA
Institute for Ion Physics and Applied Physics, University of Innsbruck A-6020 Innsbruck, Austria
(Received 19 February 2013; accepted 17 July 2013; published online 6 August 2013)
Instabilities in a cross-field discharge around a permanent magnet have been investigated. The
permanent magnet serves as a cold cathode and the chamber wall as an anode. The magnet is biased
strongly negative and emits secondary electrons due to impact of energetic ions. The electrons
outside the sheath are confined by the strong dipolar magnetic field and by the ion-rich sheath
surrounding the magnet. The electron energy peaks in the equatorial plane where most ionization
occurs and the ions are trapped in a negative potential well. The discharge mechanism is the same as
that of cylindrical and planar magnetrons, but here extended to a 3-D cathode geometry using a
single dipole magnet. While the basic properties of the discharge are presented in a companion
paper, the present focus is on various observed instabilities. The first is an ion sheath instability
which oscillates the plasma potential outside the sheath below the ion plasma frequency. It arises in
ion-rich sheaths with low electron supply, which is the case for low secondary emission yields.
Sheath oscillations modulate the discharge current creating oscillating magnetic fields. The second
instability is current-driven ion sound turbulence due to counter-streaming electrons and ions. The
fluctuations have a broad spectrum and short correlation lengths in all directions. The third type
of fluctuations is spiky potential and current oscillations in high density discharges. These appear to
C 2013 AIP Publishing LLC.
be due to unstable emission properties of the magnetron cathode. V
[http://dx.doi.org/10.1063/1.4817016]
I. INTRODUCTION
Cross-field discharges such as Hall discharges,1,2 magnetron discharges,3–6 and surface magnetic field devices7
have attracted much attention since they produce plasmas
more efficiently than field-free discharges. The magnetic
field partially confines the ionizing electrons which enhances
the ionization rate. Magnetrons have the added advantage
that no heated cathodes are required since ion impact provides for secondary electron emission.
In most cross-field devices, the electron transport across
the field is not classical. Since these plasmas are not quiet, it
is natural to suspect anomalous transport due to turbulence.
Instabilities in magnetrons have been predicted theoretically5
and investigated experimentally.8 However, not all fluctuations are due to plasma wave instabilities. Discharge
“instabilities” like short-duration arcs, called cathode spots9
or anode fireballs10–13 can drastically alter the transport and
thereby the discharge properties.
The present experiment employs the simplest magnetron
using a permanent magnet as cathode and the vacuum chamber
as anode. It does not focus on applications14 but on the discharge physics whose basic characteristics are described in a
companion paper.15 The present paper focuses on different
types of instabilities that have not yet been described. First, a
cathode sheath instability is described which arises when an
ion-rich sheath is formed in a plasma with a restricted supply
of electrons. The sheath oscillates near the ion plasma frequency causing global plasma potential oscillations in the surrounding plasma. Potential oscillations also modulate the
discharge current and produce magnetic oscillations as well as
oscillating inductive electric fields. The ion sheath instability
1070-664X/2013/20(8)/083505/10/$30.00
has been studied in double plasma devices16–21 and gridded
plasma bubbles22–25 but without electromagnetic effects.
Observationally, ion-rich sheaths with a small population of
electrons create copious harmonics.
Second, broadband turbulence is observed for stronger
discharge currents. Its spectrum falls into the ion acoustic regime. Sound waves are weakly damped since the electron to
ion temperature ratio is large. Since the instability is seen
only during the discharge, it can be described as currentdriven ion sound turbulence.
Spiky potential and current fluctuations are observed
and explained by the emission properties of the cathode. The
cathode current increases progressively as the potential drop
across the cathode sheath increases. Thus, a plasma potential
rise increases the cathode current and vice versa. Potential
fluctuations can in turn arise from ionization in the cathode
sheath which increases the space charge density when the
electron mobility exceeds that of the ions. Hence, the mechanism of the spiky discharge current can be described as a
sheath ionization relaxation instability.
The present paper is organized as follows: After reviewing
the experimental setup and diagnostics in Sec. II, the observations of instabilities will be presented in Sec. III and its various
subsections. The findings are summarized in Sec. IV.
II. EXPERIMENTAL ARRANGEMENT
The experimental setup shown schematically in Fig. 1
has already been described in companion papers15,26 and
will only be summarized here. It is a deceptively simple
discharge consisting of a permanent magnet as the cathode
and the chamber wall as anode. A negative voltage of order
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V
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ion conduction currents also depend on plasma potential variations because cylindrical Langmuir probes do not have
constant saturation currents.
All signals are acquired with a 4-channel digital oscilloscope with bandwidth up to 400 MHz and up to 2:5 106
samples are stored.
III. EXPERIMENTAL RESULTS
FIG. 1. Schematic diagram of the discharge setup. The cathode consists of a
permanent magnet pulsed up to 800 V and the chamber wall is the anode.
500 V is applied to the cathode in dc or pulsed mode.
Plasma ions impacting the magnet release secondary electrons which turns the cold magnet into an electron emitting
cathode. The electrons are energized as they traverse the
cathode sheath. The magnet partially confines electrons,
which results in a much higher ionization probability than in
a field-free discharge.
Permanent magnets of different geometries (cylinders,
spheres, bars) and materials (Nd, SmCo, Fe2O3) are used. Dc
operation of magnetrons usually requires a current-limiting
series resistor so as to limit heating and demagnetizing the
permanent magnets. Higher currents are obtained in pulsed
operation at a low duty cycle. The pulse generator employs a
fast high voltage switching transistor and a capacitor charged
by a dc-dc converter of up to 800 V. The magnet current is
obtained from a Rogowski coil or a shunt to ground. The rf
component of the magnet current is obtained from a broadband rf transformer inserted in the line to the magnet.
Langmuir probes are used to determine the plasma parameters. These consist of cylindrical probes (0.125 mm
diam, 2 mm length, Ta) and a plane probe (1 cm 1 cm, Ta).
A pair of cylindrical probes, movable in radial and vertical
direction is used for cross-correlation measurements. Rf
oscillations are usually detected with coaxially fed cylindrical Langmuir probes. The grounded coaxial outer conductor
has to be carefully insulated so as to avoid drawing electrons
in regions of negative plasma potential. Alternatively, differential rf probes have been used which consist of two 1 mm
diameter semirigid coaxial cables connected to a balanced
broadband rf transformer (0:2 350 MHz). The insulated
transformer avoids ground currents and the differential
arrangement measures electric or magnetic wave fields while
canceling large common-mode potential variations in pulsed
discharges. Magnetic rf probes are made of 1 mm diameter
coaxial cables, bent into an 8 mm loop with a break in
the outer shield. By rotating the probe, two field components
can be measured or the proper probe response Vprobe / cos /
verified.
Special attention has been paid to the interpretation of
probe signals in a pulsed plasma. Fast current fluctuations
can be displacement currents due to plasma potential variations and the sheath capacitance, I ¼ CdV=dt. Electron and
Discharges are subject to various instabilities, particularly when a magnetic field is transverse to the cathodeanode direction. Commonly discussed are current driven
plasma instabilities8 but cross-field discharges also exhibit
sheath and ionization instabilities due to secondary electron
emission, sputtering, and arc formation. Observations of several types of instabilities will be discussed below.
A. Ion sheath instability
An ion rich sheath can become unstable when the electron
supply is limited and cannot balance the expansion of the ion
sheath. An ion sheath instability has been observed in double
plasma devices16,19,21,27 and plasma bubbles formed by spherical grids with negative bias in an ambient plasma.22–25 The
sheath oscillates near the ion plasma frequency.
Such a situation also arises at the cathode of the present
magnetron discharge. Secondary electrons emitted from the
cathode by impact of Ar ions of <1 keV have a yield of typically 0.1.28,29 Electrons from the ambient plasma are prevented from approaching the sheath due to a strong
transverse magnetic field and an opposing electric force.
Thus, the ion charge density in the cathode sheath leads to a
sheath expansion which is not balanced by electrons. The
inertia of ions provides a positive feedback for an oscillation
of the sheath near the ion plasma frequency where the ion
transit time corresponds to an rf plasma period, fpi1 . A similar transit time instability exists at the electron plasma frequency in electron-rich sheaths.30 Oscillations of the sheath
charge density affect the potential drop across the sheath
which creates an oscillating plasma potential in the ambient
plasma for a constant electrode potential.
In the present experiment, the sheath oscillation instability is observed for low dc discharge voltages or in the early
phase of pulsed discharges. The latter is displayed in Fig.
2(a) showing the pulsed discharge current, Imagnet;dc , and
coherent oscillations in the magnet current, Imagnet;rf , as well
as in two rf probes, Iprobe;rf , located at different radial and
axial positions. All signals oscillate at the same frequency,
f ’ 1:5 MHz, which is close to the ion plasma frequency in
Argon at a density n ’ 2 109 cm3 . The magnet voltage
(600 V) is applied at t ¼ 0 which produces a low density
discharge plasma followed by the delayed onset of the magnetron discharge. Prior to the rise of Imagnet;dc , there may be a
positive space charge layer which reflects the ions. Such a
“virtual anode” is unstable21 and oscillates near the ion
plasma frequency.
Figure 2(b) shows waveforms of Imagnet;rf and Iprobe;rf for
two different vertical positions z. The signals are conditionally averaged, i.e., the oscilloscope is triggered from Imagnet;rf
and both signals are averaged over many repeated
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FIG. 2. Oscillations for a pulsed discharge on a thin cylindrical Neodymium
magnet (5 cm diameter, 0:5 cm height, magnetized along height, forming a
thin disk plasma disk around the magnet side wall). (a) Magnet and rf probe
currents showing coherent oscillations prior to discharge onset. (b)
Conditional averages of rf magnet oscillations (trigger source) and probe
current. Both signals are well correlated with long coherence times. When
the rf probe is moved radially away from the magnet, the amplitude
decreases but the phase does not change. The probe signal is not due to a
propagating wave but indicates a global plasma potential oscillation.
Phys. Plasmas 20, 083505 (2013)
discharges. The same oscillations in both traces indicate that
they have a long temporal coherence.
One obtains the spatial coherence by moving the probe.
No phase shift is observed in the z-direction (kB), nor in
r-direction (?B). Thus, the plasma potential oscillates
globally, supporting the conclusion that the sheath is the
source of the instability. The oscillations are not due to propagating ion acoustic waves. The oscillation amplitude decays
outside the plasma layer, implying that there is a rf electric
field. The movement of the probe perturbs the electron confinement causing small frequency shifts. Since the plasma
potential oscillates at a high frequency (’ fpi ), the oscillating
magnet current is predominantly a displacement current
rather than an ion current.
Sheath oscillations can become strongly nonlinear as
demonstrated in Fig. 3(a) where the Fast Fourier Transform
of Imagnet;rf is shown. The spectrum displays multiple harmonics. The second harmonic amplitude exceeds that of the
fundamental, which suggests that the first line is a subharmonic of the second. Similar effects have been observed in
earlier sheath instability investigations.24 The frequency
increases with jVmagnet j since the discharge current, hence
density and ion plasma frequency, increases with jVmagnet j
[Fig. 3(b)]. Close inspection of Fig. 3(a) also shows that the
frequency increases as the discharge current grows in time.
The harmonics are above the ion plasma frequency and cannot excite ion acoustic waves.
A magnetron discharge has a threshold voltage for the
onset of Imagnet . The sheath oscillations arise just below the
threshold for ignition of the magnetron discharge. It shows that
a background plasma is needed to ignite the magnetron magnetron discharge. Figure 4(a) shows the fluctuations and net current to the magnet for a pulsed voltage below threshold. The
magnet current exhibits a capacitive transient at t ’ 0:02 ms
when the magnet voltage is switched on, but a negligibly small
discharge current develops, Imagnet;dc ’ 1 mA. However, due to
the oscillating plasma potential there is a rf displacement
FIG. 3. Spectral features of the magnet
current oscillations at discharge onset.
(a) Frequency spectrum showing narrow harmonic lines of which the
second line has the largest amplitude.
(b) Voltage dependence of the spectrum. The frequency increases with
magnet voltage.
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FIG. 4. Sheath instabilities in low density magnetron discharges. (a) Magnet current shows only a capacitive spike at the turn-on of the magnet voltage with no
significant dc current but a pronounced rf current. (b) Time-resolved spectrum of the rf magnet current showing a frequency and amplitude maximum where
the discharge starts when the discharge voltage is raised. (c) Magnet voltage and current waveform and oscillations observed on a transformer-coupled
Langmuir probe. Inserts show the spectra at different times. Line spectra with second harmonics occur before and after the magnet current and in the afterglow.
Broadband turbulence arises during the magnet current pulse. The fundamental frequencies are at or below the ion plasma frequency.
current flowing from the magnet to ground, Imagnet;rf . Its amplitude and frequency exhibit a peak, caused by density variations
since the magnet voltage is constant. The time resolved spectrum displayed in Fig. 4(b) shows that the oscillation has a pronounced second harmonic. If Vmagnet is raised, the onset of
Imagnet occurs at the peak of the oscillation.
When the magnetron discharge occurs, the instability
changes its character. Figure 4(c) shows magnet current and
voltage waveforms, the oscillation from the rf probe and their
spectra in several inserts. Prior to the onset and after the end
of Imagnet;dc , the oscillations are again sheath-plasma instabilities with narrowband lines and a harmonic. Broadband turbulence is created during the Imagnet pulse and its properties
are described below.
B. Current-driven turbulence
When a strong discharge current of several Amperes
flows, the plasma exhibits broadband turbulence in the ion
acoustic frequency range. Typical waveforms of the discharge current and the probe signal are displayed in
Fig. 5(a). The oscillations exhibit random waveforms which
occur only in the presence of the discharge current. Thus,
cross-field electron drifts (E B; rB), which also exist in
the afterglow plasma, are not the cause for the noise, as
speculated in Ref. 8. The time-resolved spectrum of the
probe signal [Fig. 5(b)] shows that the center frequency of
the broadband noise and the noise amplitude decrease as the
discharge current decays in time.
The spatial and temporal coherencies of the turbulent
oscillations are obtained by conditionally averaging two
movable probe signals. For this case, the trigger level
“condition” is typically chosen at half the peak oscillation
amplitude of the stationary probe signal. An ensemble average is formed over many repeated discharges of both probe
signals. The temporal coherence is judged by the decay of
the average in time, the spatial coherence is given by the
decay with probe separation. Coherent signals are sinusoidal,
incoherent signals decay rapidly in space and time. The latter
is observed in the present case.
Figure 6 shows conditional averages of Iprobe;rf vs time in
the azimuthal (a) and radial direction (b). The temporal coherence has a halfwidth of Dt ’ 0:5 ls corresponding to the
inverse bandwidth of the broadband signal. The spatial coherence in both azimuthal and radial directions has similar halfwidths of Dr ’ 7 mm. A small shift of the contours indicates a
preferential propagation in the E B direction and radially
inward direction, the direction of thepion
ffiffiffi drift. The propagation
speed is vphase ’ ð0:7 cm=0:5 lsÞ= 2 ’ 1 cm=ls, while the
sound speed is cs ’ 0:5 cm=ls in Ar for 10 eV electrons.
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The above observations are consistent with properties of
current-driven ion sound turbulence. The current is due to
counter-streaming electron and ion drifts. Magnetized electrons drift azimuthally around the equator of the magnet
except when scattered radially away from the magnet in the
radial electric field. Unmagnetized ions are accelerated toward the magnet. Sound waves drift with the ions and grow
along the electron drift. No turbulence arises without discharge current. After the end of the discharge, there remains
an afterglow plasma with cross-field electron drifts but these
are insufficient to maintain the broadband turbulence.
Other investigators have studied instabilities in planar
magnetrons and concluded that they are drift waves in the
E B direction.31 Since both E and B are spatially varying,
it is not obvious why eigenmodes with discrete frequencies
are formed. In the present experiment, the instability exhibits
no discrete spectral lines and the spatial coherence length is
much shorter than the azimuthal circumference, hence forms
no drift wave eigenmodes. To our knowledge, the present
observation of ion sound turbulence in magnetrons is novel.
C. Magnetic oscillations
FIG. 5. Broadband turbulence in a magnetron discharge. (a) Waveforms of
the discharge current and probe fluctuations whose amplitude and frequency
scale with discharge current. (b) Time-resolved frequency spectrum of the
probe signal which indicates broadband turbulence.
FIG. 6. Spatial and temporal coherences of broadband rf plasma fluctuations
obtained by conditional averaging the signals from two Langmuir probes.
(a) Conditional averages of probe current fluctuations vs azimuthal direction
around the magnet and time (see insert). The fixed reference probe, whose
signal is used to trigger the oscilloscope at s ¼ 0 is located at the origin,
Dr ¼ D/ ¼ 0. The temporal correlation is approximately the inverse of the
noise spectral width. The spatial correlation width of ’ 7 mm yields an average propagation speed in the range of ion acoustic waves. (b) Conditional
average vs time and radial position yielding similar correlation times and
lengths and a drift toward the magnet. The correlation measurements characterize the fluctuations as ion sound turbulence.
For large discharge currents, the sheath instability modulates the discharge current leading to magnetic oscillations.
These have been detected with magnetic probes and shown
not to be propagating electromagnetic waves but instabilities
of the cathode emission.
Figure 7(a) displays the waveform of a short but strong
discharge current pulse produced with a 2 lF charged capacitor and a small series resistor (R ¼ 1 X). As the magnet current rises, it exhibits small oscillations whose frequency
increases with current (f ¼ 40–90 MHz), hence are not transient ringing effects. The same oscillations are observed with
a magnetic probe near the magnet [Fig. 7(b)]. Since the amplitude and phase fluctuate from pulse to pulse, the probe
signal has been conditionally averaged [Fig. 7(c)]. The probe
signal is gated to a desired time, then the oscilloscope is triggered at a chosen amplitude level (the “condition”) and the
signal is averaged over typically 100 repeated discharge
pulses. The temporal coherence extends only over a few
cycles. Together with the magnetic probe signal, the fluctuations in the magnet current are averaged [Fig. 7(d)]. The
“dc” current is subtracted so as to display only the fluctuations. Not surprisingly, the current and magnetic oscillations
correlate. The magnetic probe signal increases as the probe
is moved closer to the feed wire of the magnet but exhibits
no phase shift with distance inside the plasma. Thus,
although the oscillation frequency falls into the whistler
mode regime, it is not a plasma eigenmode but an electromagnetic oscillation of the discharge current.
In order to confirm that the high frequency probe signal
is a magnetic oscillation, the angular probe response has
been checked. Figure 7(e) shows conditionally averaged
traces of two identical magnetic probes, one movable and
the other stationary. The latter provides the trigger for conditional averaging, i.e., a reference phase. The movable probe
is then rotated around its axis by an angle H and exhibits a
sign change when H ¼ 180 [Fig. 7(f)]. The rotation
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FIG. 7. Magnetic oscillations at the start of a strong magnetron discharge. (a) Magnet current with oscillations during the current rise (full waveform in the
insert). (b) Magnetic probe signal whose frequency rises in time (41 to 94 MHz). (c) Conditionally averaged magnetic oscillations showing temporal coherence
limited to a few rf periods. (d) Simultaneous conditional average of the magnet current and its fluctuations which are obtained by subtracting the mean current
waveform. Fluctuations in the magnetic current and the magnetic field correlate. (e) Conditionally averaged signals from two magnetic probes which are correlated when closely aligned. (f) The signals are anticorrelated when one probe is rotated by 180 , indicating that the signals properly detect 60 MHz magnetic
field oscillations. (5 cm diameter Nd magnet, 2 lF capacitor charged to 500 V, Rseries ¼ 1 X, 5 mbar Ar).
indicates that the magnetic field is azimuthal to the wire connected to the magnet.
Initially, the frequency of the magnetic oscillations
increases with discharge current. The latter has been raised to
its limits by discharging the capacitor without a series resistor
for a few shots, reaching currents up to 400 A in 2 ls pulses.
Figure 8(a) shows the oscillations in the current waveform
and magnetic probe signal. The time-resolved frequency
spectrum of the probe signal [Fig. 8(b)] shows the frequency
increase during the rise of Imagnet up to 200 MHz followed by
an abrupt drop to 20 MHz approaching the current peak. The
initial oscillation is consistent with the ion plasma frequency
of a dense plasma (n ’ 4 1013 cm3 ). However, the sudden
frequency drop with rising current indicates a different mechanism such as a ringing effect due to a cathode spot as
described in the previous companion paper.26 All frequencies
are well below the electron cyclotron frequency of the strong
Nd magnet (Bmax ’ 4 kG; fce ¼ 11 GHz).
D. Probe displacement currents
The signal of rf probes is frequently found to consist
of pulses rather than sinusoidal oscillations. In order to
interpret these features, the probe response has been first
investigated.
When the discharge is turned on, the floating potential
of Langmuir probes drops rapidly to a large negative value
and subsequently decays gradually. Figure 9(a) displays the
discharge current, Fig. 9(b) the rf probe signal, and Fig. 9(c)
the floating potential on a Langmuir probe attached to a high
impedance oscilloscope probe. The rf probe is a cylindrical
probe connected to a grounded broadband rf transformer and
a matched 50 X coaxial cable to the oscilloscope. Its signal
is a negative pulse closely resembling the derivative of the
floating potential waveform. Since the probe is grounded and
the floating potential is negative, the probe should also collect electrons. However, the probe current peaks prior to the
most negative floating potential, after which it reverses sign,
rather than decay slowly with the floating potential, all
inconsistent with an electron current to a probe. The rf transformer can transform a pulse of 5 ls duration, albeit with
some droop. Thus, the probe current is best explained by a
displacement current due to the time varying plasma potential and the sheath capacitance, I ¼ Csheath dVplasma =dt. When
the probe current is integrated, its waveform is proportional
to the floating potential and can be fitted by a constant factor
[Fig. 9(c)]. Since the electron temperature is small compared
to the potential drop (kTe ejVfloat j), it is not unreasonable
to assume that the plasma potential behaves like the floating
potential. From the scaling factor (1.66) and the probe
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shows the simultaneously recorded probe signals for two different probe separations along the electron drift direction of
a bar magnet. The probe signals are in phase irrespective of
the probe position, implying that the signal is not due to a
propagating wave but to a global potential oscillation of the
plasma layer with respect to ground or the constant cathode
potential.
E. Spiky discharge fluctuations
FIG. 8. Oscillations in the magnet current of a strong discharge. (a) Discharge
current waveform and magnetic probe signal. (b) Time-resolved frequency
spectrum of the magnetic oscillations. The frequency rises rapidly which confirms that it is an instability and not a transient ringing effect. A sheath instability modulates the cathode current at the ion plasma frequency which yields an
estimate of the ion density near the cathode (n ’ 4 1013 cm3 ). The abrupt
frequency drop near the peak current suggests a transient oscillation triggered
by a cathode spot. (5 cm diameter Nd magnet, 2 lF capacitor charged to
800 V; Rseries ¼ 1 X, 5 mbar Ar).
termination impedance (200 X), the probe-plasma coupling
capacitance (24 pF) is determined.
Furthermore, the scaling factor also permits one to
obtain the amplitude of potential fluctuations quantitatively,
an example of which is shown in Fig. 9(d). There are small
fluctuations in the discharge current and floating potential
and are shown on an expanded time scale together with the
rf probe signal and its integral. It is worth noting that the
oscillations in the discharge current and the plasma potential
are in phase. Again, the rf probe signal for short pulses is a
displacement current whose integral follows the plasma
potential and is in phase with the floating potential. When
the plasma potential increases, the sheath potential drop at
the cathode increases, which in turn enhances the ion energy,
the secondary electron emission, ionization, and ion current
to the cathode. This feedback may explain the unstable discharge properties discussed below.
Using two identical rf probes, the spatial properties of
the potential oscillations have been explored. Figure 9(e)
Ionization instabilities can produce fluctuations in a discharge which are far stronger than microinstabilities in the
plasma. One of these effects was shown in a companion
paper26 which described the formation of pulsating “fireball”
discharges on a positively biased probe. It modulates the discharge current, the plasma potential, and most probe signals.
Another example is the unstable current-voltage characteristic of a cold cathode with secondary electron emission.
Figure 10 presents examples of spiky potential and current oscillations in a magnetron discharge. The discharge
current has an initial pulse due to the capacitive power supply, followed by a low current, slowly decaying discharge
[Fig. 10(a)]. In the low-current regime, the potential exhibits
repetitive sub-microsecond pulses [Fig. 10(b)]. These are not
plasma waves but global plasma potential fluctuations. The
potential is obtained by integrating the displacement current
of the rf probe. It is positively correlated with fluctuations in
the discharge current, i.e., the current increases when the
potential increases [Fig. 10(c)].
When the discharge voltage is increased, the discharge
current is increased [Fig. 10(d)]. The frequency of the rf probe
pulses increases and their spacing becomes so close that the
spikes go over into a continuous oscillation [Fig. 10(e)]. Still,
the signal remains a global potential oscillation but it is not a
sound wave. During the current decay, the frequency decreases
as shown in the time resolved FFT of Vprobe; rf [Fig. 10(f)].
Spikes are also observed in the discharge current
[Fig. 10(g)]. Since they correlate with the potential oscillations, their frequency also decreases when the magnet current decreases. Note that while the peak current increases the
low level current may decrease. The current spikes of the
middle trace are shown on an expanded time scale in Fig.
10(h). The spikes are all positive, very short, and reach a significant fraction of the dc discharge current (dI=I ’ 0:3).
The magnetic probe signal confirms that the current spikes
create magnetic field spikes inside the plasma. When the discharge voltage is further increased, the discharge develops
cathode spots, i.e., short duration arcs which produce high
current discharge pulses but little subsequent spikes. The
high current discharge mode has been described in more
detail in a companion paper.26
One cannot distinguish between cause and effect of the
phenomenon from the simultaneity of current and potential
spikes alone. However, the steep current-voltage characteristics of the magnetron discharge provide additional information. As the cathode voltage is increased, the ion energy
increases which raises the secondary electron emission yield.
The increased electron current and energy increase ionization
and ion collection, hence the discharge current rises
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FIG. 9. Response of a rf probe to fast potential variations. (a) Magnet current waveform for a discharge voltage supplied by a charged 2 lF capacitor and a
25 X series resistor. (b) Rf probe voltage. (c) Floating potential of a Langmuir probe and a scaled integral of the rf probe voltage, showing that the probe current is a displacement current. (d) Fluctuations in the magnet current, floating potential, and rf probe signal on an expanded time scale. The scaled integral of
the probe signal yields the potential fluctuations quantitatively. Current and potential fluctuations correlate positively. (e) Probe signals from two identical rf
probes with different probe spacings. The lack of a phase shift indicates that the potential fluctuations are not due to propagating waves but global potential
variations of the plasma layer.
progressively. The ions acquire their energy mainly from the
potential drop of the cathode sheath. For a constant magnet
voltage, the plasma potential rises, the sheath potential drop
increases, and the same feedback arises as when the magnet
voltage is made more negative. Thus, a potential rise produces a current increase. However, the positive feedback
between potential and current is limited by the requirement
that the return current to the chamber wall has to vary exactly
as the cathode current. Since the wall collects electrons, a
potential rise decreases the electron collection, unless compensated by a density increase. Thus, the potential and current
spikes are limited in amplitude and duration. The spacing of
spikes increases when the ionization rate decreases, i.e., for
low discharge voltages and currents. At high discharge voltages, a spike may trigger the short-duration arcs (spots)
which alter the discharge physics dramatically.
The feedback between potential and current is independent of pulse polarity. Thus, a decrease in potential causes a
loss of current or a negative current spike, an example of
which is displayed in Fig. 11. The rf probe signal starts with
a negative pulse followed by a positive polarity which upon
integration yields a negative potential pulse [Fig. 11(a)]. The
magnet current also exhibits negative spikes, consistent with
the integrated magnetic probe trace [Fig. 11(b)]. The magnet
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Phys. Plasmas 20, 083505 (2013)
FIG. 10. Properties of spiky discharges. (a) Magnet current waveform. (b) Rf probe waveform with spikes. (c) Expanded time scale with rf probe signal, magnet current spikes, and potential spikes obtained by integrating the probe displacement current. (d) Magnet current waveform for larger charging voltage than
in (a). (e) Rf probe waveform with higher spike frequency compared to (b). (f) Time resolved spectrum of the oscillations in (e), showing a frequency decrease
as the discharge current decays in time. (g) Three magnet current waveforms with different levels of spikes. The bottom waveform (saturated) shows very high
discharge current pulses due to the formation of cathode spots. (h) Current spikes of the middle trace on an expanded scales. Magnetic probe signal correlates
with the derivative of the current or magnetic field spikes. (27 cm long bar magnet, 9 mbar Ar).
current is not a displacement current since its waveform
differs from that of the rf probe. The rf probe current is not
differentiated by the rf transformer which passes microsecond pulses without distortions. When negative and positive
spikes are closely spaced such as in Fig. 10(e) they are
difficult to distinguish from wave signals, unless spatial
cross-correlations are performed.
IV. CONCLUSION
FIG. 11. Example of spikes with negative polarity. (a) Rf probe current is a
displacement current whose integral is proportional to the plasma potential.
(b) Negative spikes in the magnet current and magnetic field which correlate
with the potential spikes. (27 cm long bar magnet, Vcharge ¼ 500 V, no
cathode spots).
Instabilities in a cross-field discharge of the magnetron
type have been investigated. The cathode sheath was found
to be a primary source of the instabilities. For low secondary
electron emission, the ion-rich sheath is unstable to ion
transit time effects which cause oscillations near the ion
plasma frequency. The space charge in the sheath,
ðni ne Þe ¼ 0 r2 U, determines the sheath thickness and
potential drop U and the latter is observed to oscillate. The
oscillations are detected with a rf probe whose current is
shown to be a displacement current due to the sheath capacitance and potential oscillation. The ion density near the
sheath has been estimated from the oscillation frequency.
Correlation measurements reveal global potential oscillations
and no wave propagation.
The sheath oscillations affect the ion current collected
by the cathode. Significant electromagnetic effects arise at
high discharge currents. Magnetic probes detect oscillating
fields below the electron cyclotron frequency but no whistler
waves. Periodic current and potential bursts have been
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Stenzel et al.
observed which may arise from ionization events in the
sheath. Potential and discharge current are positively correlated which results from the cathode current-voltage characteristics. The current rises steeply with the potential drop
across the cathode sheath, i.e., the difference between cathode and plasma potential.
Current-driven ion sound turbulence, which can produce
anomalous cross-field electron transport, has also been
observed. It exhibits short correlation times and lengths
which distinguish it from sheath oscillations. Very large discharge currents, triggered by impulsive arcs (cathode spots),
produce high frequency transient ringing in probes and the
discharge circuit.
Thus, the cross-field discharge is not a quiescent plasma
but its afterglow eliminates most of the instabilities.
Knowledge of the instabilities is important for applications
of plasma-surface interactions.
ACKNOWLEDGMENTS
This work was supported in part by NSF/DOE Grant
DE-SC0004660 and in part by the Austrian Science Fund
(FWF) under Grant No. 19901. Additional support by the
University of Innsbruck is acknowledged.
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