Computer Physics Communications 177 (2007) 72–75
Low-pressure plasma generation inside slender tubes
F. Iza, J.K. Lee∗
Department of Electronics and Electrical Engineering, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
Available online 28 February 2007
Low pressure (<50 mTorr) argon discharges inside tubes of a few millimeters in diameter have been studied by means of one- and two-
dimensional particle-in-cell Monte Carlo collision simulations. Magnetically confined DC and microwave discharges have been sustained in
a coaxial configuration. For DC discharges, the magnetic field needs to be strong enough to confine secondary electrons emitted from the cathode,
i.e. the amplitude of the cycloidal motion described by secondary electrons has to be smaller than the discharge gap. For microwave excited
discharges, the power absorption profile depends on the magnitude of the magnetic field. Power absorption beyond the sheath boundary in the
plasma bulk and better confinement for magnetic fields below the ECR condition lead to maximum densities at ωc/ωrf∼ 0.5.
© 2007 Elsevier B.V. All rights reserved.
Keywords: ECR plasma; Coaxial magnetron; Magnetized discharge; Inner wall; Slender tube
Being able to plasma-treat the inner wall of slender tubes is
desirable to improve the performance of tubes and other instru-
ments in biomedical and industrial applications [1,2]. For ex-
ample,treatmentand coating of catheters can improvetheir bio-
compatibility and fouling properties. Similarly, a coating can
improve the lifetime of pipes that will carry corrosive materials.
Various techniques/configurations have been used in the past
to treat the inner wall of tubes. Electro-explosion , ion beams
and movable targets , external discharges , plasma im-
mersion ion implantation , and magnetized discharges 
provide means of treating the inner wall of slender tubes with
different performance in terms of repeatability, uniformity and
This paper studies low-pressure (<50 mTorr) argon dis-
charges inside tubes of inner radii on the order of millimeters.
The discharges are sustained between the tubes and auxiliary
wires introduced inside the tubes, i.e. coaxial configuration.
A detailed description of experimental set-ups can be found in
[8,9]. One- and two-dimensional particle-in-cell Monte Carlo
(PIC-MCC) collision simulations have been performed to study
the plasma characteristics under various magnetic field intensi-
E-mail address: firstname.lastname@example.org (J.K. Lee).
ties and driving schemes. PIC-MCC simulations capture parti-
cle kinetics without the assumptions required in fluid models
and have been successfully used in studies of fundamental and
applied plasma physics . The simulation results provide
a new insight into the underlying physics and are in good agree-
ment with experimental data.
2. Simulation model and device description
The discharges are sustained in a coaxial configuration. The
tube being treated acts as the outer electrode and a thin wire
introduced inside the tube as the inner electrode. For a sputter-
coating application, the thin wire is made of the coating ma-
terial and it is negatively biased so that the ion bombardment
sputters it. DC, pulsed-DC and microwave discharges can be
used to coat metallic and dielectric tubes [8,9]. In order to
effectively accelerate ions against the inner electrode (target)
operation at low pressure is required. Typically, this pressure is
below 50 mTorr and therefore magnetic confinement is needed
to limit the particle loss to the tube walls.
Simulations results are obtained using XPDC1 , an
open-source one-dimensional (1d3v) PIC-MCC code, and
a two-dimensional (2d3v) axisymmetric PIC-MCC plasma
simulator (APPS) developed by the authors. APPS assumes
azimuthal symmetry and solves for the radial and axial pro-
files. A multigrid solver is used to determine the electrostatic
0010-4655/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
F. Iza, J.K. Lee / Computer Physics Communications 177 (2007) 72–75
field and a leap-frog scheme to integrate the particles equations
of motion. The code incorporates an external circuit and Pois-
son’s equation is solved on a uniform grid using superposition
of surface and volume charge densities. A few million particles
and a radially weighted filter are used to minimize numerical
noise. Elastic, excitation and ionization electron-neutral colli-
considered in the models (see [11,13] and references within).
Coulomb collisions are not included in the model and there-
fore the effective electron temperature may be underestimated.
Heating of low energy electrons intrinsic to PIC-MCC simula-
tions, however, may partially compensate for physical coulomb
sion coefficient for Ar+ions impinging on the electrodes is set
to 0.2 whereas no secondary electrons are considered in the
microwave case. Finally, the magnetic field is assumed to be
uniform across the discharge.
3. Simulation results
3.1. DC excitation
When the discharge is sustained in DC mode, the tube and
the inner electrode constitute a coaxial magnetron. In the ab-
sence of a magnetic field, most secondary electrons emitted
from the inner electrode transit the discharge gap without col-
liding with the background gas and therefore it is not possible
to sustain a discharge inside the tube. If a sufficiently strong
axial magnetic field is applied, however, electrons are turned
around by the Lorentz force before reaching the tube. Confined
secondary electrons describe circular cycloids spending longer
time inside the tube and increasing the chances of undergoing
collisions. The amplitude of the cycloids increases as the inner
electrode diameter decreases  and therefore, there exists an
optimum inner electrode diameter that minimizes the required
magnetic field to sustain the discharge inside a given tube.
The electron energy probability function measured in the
bulk plasma shows two distinct electron populations: high en-
ergy electrons that have been accelerated across the cathode
fall, and low energy electrons that have been born in the bulk
plasma. The high energy electrons are secondary electrons
emitted from the inner electrode. These electrons ionize the
background gas generating low energy electrons. These low-
energy electrons diffuse very slowly in the radial direction
and as a result, a high-density low-temperature plasma is ob-
Most ions bombarding the inner electrode transit the sheath
without colliding with the background gas, and therefore the
ion energy distribution function presents a single energy peak.
This energy corresponds to the sheath voltage (∼950 V when
the applied voltage is 1 kV). Since the sheath is collisionless,
ions strike the inner electrode almost perpendicularly. Some
secondary electrons are also recaptured by the inner electrode.
See Fig. 1.
Electrons arrive to the tube with a broad angular distribu-
tion and relatively large energy (∼25 V). A small number of
Fig. 1. (a) Angle and (b) energy distribution functions of electrons and ions im-
pinging on the inner electrode. (c) Angle and (d) energy distribution functions
of electrons and ions impinging on the tube.
Fig. 2. Plasma density at the center of the discharge. (a) Simulation re-
sults: Applied voltage 30 V–2.45 GHz. (b) Experimental data : P =
30W −2.45 GHz.
electrons arrive to the tube with energies close to the applied
voltage. These electrons are secondary electrons that have un-
dergone a collision and have been deflected from their cycloidal
Since the axial diffusion of particles is not affected by the
magnetic field, particle losses across the open-ends of the tube
can be even larger than radial losses. Two-dimensional simu-
lations modeling different configurations at the open end show
that despite the slender geometry of the tube the discharge can-
not be sustained without some axial confinement. Axial con-
finement, either electrostatic or magnetic, not only enables the
discharge and higher plasma densities, but it also improves the
uniformity of the plasma treatment .
3.2. Microwave excitation
In this section we present simulation results obtained when
a 2.45 GHz voltage source is used to power up the inner elec-
trode. Fig. 2 shows the plasma density at the center of the
discharge as a function of the magnetic field for an argon dis-
charge in a tube of radius 4 mm and an inner electrode of radius
500 µm. Despite the resonant heating occurring at the electron
cyclotron resonance (ECR) condition (B ∼ 875 Gauss), higher
plasma densities are obtained when weaker magnetic fields are
Under ECR conditions, electrons are resonantly accelerated
and may spiral out of the gap without undergoing collisions.
F. Iza, J.K. Lee / Computer Physics Communications 177 (2007) 72–75
Fig. 3. Potential profiles: Time averaged (thick black line) and instantaneous
profiles (thin colored lines) when the potential of the inner electrode is at its
maximum and minimum value. (For interpretation of the references to color in
this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Time averaged electron power (2πrJe(r,t)·E(r,t)) deposition profiles.
A confinement argument, however, cannot explain the rapid
increase of plasma density as the magnetic field approaches
ωc/ωrf ∼ 0.5 nor the density decrease when the magnetic
field is increased above the ECR condition. Here ωc is the
electron cyclotron frequency and ωrf the excitation frequency
Fig. 3 shows the radial potential profile for various magnetic
field intensities. Similarities can be found with the more studied
case of magnetically enhanced reactive ion etchers (RIE) .
As the magnetic field increases, the cross-field electron mo-
bility decreases and the plasma becomes more resistive. The
reduction of electron mobility results in a reduction (in absolute
value) of the bias voltage. With high magnetic fields (see the
1050G case in Fig. 3), the inner electrode can reach instanta-
neously voltages above the plasma potential and large voltage
drops are sustained across the bulk plasma. Nonetheless, an im-
portant difference with respect to magnetically enhanced RIEs
should be noted. Besides the geometrical configuration, mag-
netically enhanced RIEs operate typically with magnetic fields
well above the ECR condition. In this paper, however, the mag-
netic field intensity is such that the electron cyclotron frequency
is also smaller than the excitation frequency.
Fig. 4 shows the time averaged electron power absorption
profile as a function of the radial position. The electron power
is defined as Je·E, where Jeis the electron current density and
E the electric field. Significant changes can be observed in the
power absorption profiles.
For high magnetic fields (1050G, above the ECR condition),
the electron heating takes place at the sheath–plasma bound-
ary near the inner electrode (Fig. 4). The time resolved data
(not shown) indicates that the electron current is almost 90 de-
grees out of phase with respect to the electric field and that
the current leads the electric field, i.e. the bulk plasma behaves
capacitively. Although unmagnetized low pressure plasmas be-
have inductively due to the electron inertia, in a magnetized
discharge above the ECR condition (ωc> ωrf) the Lorentz
force makes particles turn before the electric field reverses. This
leads to the capacitive behavior. Since electrons cross-field mo-
bility is limited, stochastic heating at the sheaths is negligible
and the net power absorption observed in Fig. 4 is due to colli-
sional heating (no power is absorbed if collisions are artificially
removed in the simulation). Although the average power depo-
sition profile is similar for the ECR condition (B = 875G), the
is absorbed collisionlessly (power is absorbed even if the colli-
sions are artificially removed in the simulation). For magnetic
fields such that ωc/ωrf≈ 0.5–1, the power deposition profile
presents a radial standing wave pattern with alternating layers
of positive and negative power absorption. As a result, power
is absorbed beyond the sheath–bulk interface. It is believed that
the power absorption inside the bulk plasma is responsible for
the enhanced plasma density observed in the simulation and
experimental data (Fig. 2). As the magnetic field is reduced
to 300G, electrons gain mobility and the discharge recovers
the typical characteristics of an unmagnetized capacitive dis-
Low pressure (<50 mTorr) plasma generation inside tubes
of a few millimeters in diameter has been studied by means
of one- and two-dimension particle-in-cell Monte Carlo colli-
sion simulations. The large particle loss to the tube wall at low
pressure requires the use of magnetic confinement. DC and mi-
crowave argon discharges operated in a coaxial configuration
have been analyzed and good agreement is found with existing
experimental data. Despite the resonant heating occurring at the
electron cyclotron resonance (ECR) condition, this is not the
best operation point for discharges inside slender tubes. Poor
particle confinement under the ECR condition and enhanced
power absorption in the bulk plasma at lower magnetic fields
result in higher plasma densities at ωc/ωrf∼ 0.5. For magnetic
fields such that ωc/ωrf= 0.5–1 a radial standing wave pattern
in the power absorption profile has been shown. Although not
all the elements of this profile are yet understood, this power
absorption profile indicates that power is delivered beyond the
sheath–plasma interface into the bulk plasma.
This work was supported by the Korean Ministry of Ed-
ucation through its Brain Korea 21 program and the Korean
Science and Engineering Foundation under Grant No. R11-
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