An analysis on transmission microwave frequency spectrum of cut- off probe D. W. Kim, S. J. You, B. K. Na, J. H. Kim, and H. Y. Chang Citation: Appl. Phys. Lett. 99, 131502 (2011); doi: 10.1063/1.3634022 View online: http://dx.doi.org/10.1063/1.3634022 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v99/i13 Published by the American Institute of Physics. Related Articles Techniques for the measurement of disruption halo currents in the National Spherical Torus Experiment Rev. Sci. Instrum. 82, 103502 (2011) Charge resolved electrostatic diagnostic of colliding copper laser plasma plumes Phys. Plasmas 18, 103104 (2011) Electron density measurement of inductively coupled plasmas by terahertz time-domain spectroscopy (THz-TDS) J. Appl. Phys. 110, 073303 (2011) A synchronized emissive probe for time-resolved plasma potential measurements of pulsed discharges Rev. Sci. Instrum. 82, 093505 (2011) Electrical time resolved metrology of dust particles growing in low pressure cold plasmas Phys. Plasmas 18, 093701 (2011) Additional information on Appl. Phys. Lett. Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors Downloaded 20 Oct 2011 to 203.254.160.241. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
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An analysis on transmission microwave frequency spectrum of cut-off probeD. W. Kim, S. J. You, B. K. Na, J. H. Kim, and H. Y. Chang Citation: Appl. Phys. Lett. 99, 131502 (2011); doi: 10.1063/1.3634022 View online: http://dx.doi.org/10.1063/1.3634022 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v99/i13 Published by the American Institute of Physics. Related ArticlesTechniques for the measurement of disruption halo currents in the National Spherical Torus Experiment Rev. Sci. Instrum. 82, 103502 (2011) Charge resolved electrostatic diagnostic of colliding copper laser plasma plumes Phys. Plasmas 18, 103104 (2011) Electron density measurement of inductively coupled plasmas by terahertz time-domain spectroscopy (THz-TDS) J. Appl. Phys. 110, 073303 (2011) A synchronized emissive probe for time-resolved plasma potential measurements of pulsed discharges Rev. Sci. Instrum. 82, 093505 (2011) Electrical time resolved metrology of dust particles growing in low pressure cold plasmas Phys. Plasmas 18, 093701 (2011) Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors
Downloaded 20 Oct 2011 to 203.254.160.241. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
An analysis on transmission microwave frequency spectrum of cut-off probe
D. W. Kim,1 S. J. You,2,a) B. K. Na,1 J. H. Kim,2 and H. Y. Chang1
1Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea2Center for Vacuum Technology, Korea Research Institute of Standards and Science, Daejeon 305-306, Korea
(Received 30 June 2011; accepted 16 August 2011; published online 27 September 2011)
We investigated the formation mechanism of transmission microwave frequency (TMF) spectrum of
cut-off probe using a simple circuit model to elucidate the physics behind the TMF spectrum. The
result showed that the overall shape of the TMF spectrum of cut-off probe (N – shape spectrum) is
well reproduced with our proposed circuit model and can be understood as the combined result of
two different resonances caused by the elements between two probe tips (a sheath, a plasma, and a
vacuum which is filled by the plasma). Furthermore, based on this simple modeling, a more precise
method to find the plasma frequency by taking account with the e-n collision frequency and the
pressure limitation of the cut-off probe application is established. VC 2011 American Institute ofPhysics. [doi:10.1063/1.3634022]
A number of diagnostic methods which is available
even in complex plasma condition have been developed,
such as oscillation probe, absorption probe, impedance
probe, and cut-off probe.1–4 Among these diagnostic tools,
the cut-off probe using the physical phenomenon of cut-off
which is known to be reflected in the transmission micro-
wave frequency (TMF) spectrum is believed to be one of the
most promising diagnostic tool. The cut-off probe has many
advantages as following: The probe system is very simple
and robust. The calculation of electron density (ne) from the
measured plasma frequency (xpe) is not complicated
ðne ¼ x2pe�0me=e2Þ which is one of the simplest relation of
the plasma physics with less assumption.5 The theoretical
error bar is known to be small.6 In spite of these advantages
and wide applications of the probe, there is a little under-
standing about the TMF spectrum used in the determination
of the cut-off frequency. This TMF spectrum of the cut-off
probe corresponds to the IV-curve of Langmuir probe, dis-
closing the detail physics for the formation of the TMF spec-
trum is very important to optimize the cut-off probe.
In this letter, to elucidate the physics behind the TMF
spectrum of cut-off probe, we investigated the formation
mechanism for the TMF spectrum of cut-off probe using a
simple circuit model and an E/M wave simulation (CST
Microwave Studio). The results showed that the overall
shape of the TMF spectrum of cut-off probe (N – shape spec-trum) is well reproduced with the proposed circuit model
and can be understood as the combined result of two differ-
ent resonances caused by the elements between two probe
tips (a sheath, a plasma, and a vacuum which is filled by the
plasma). Furthermore, based on this simple modeling, a
more precise method to find the plasma frequency by taking
account with the e-n collision frequency and the pressure
limitation of the cut-off probe application were established.
In order to understand the physics on the TMF spectrum
of cut-off probe, two complementary simulation models
were used: One is a commercially available E/M wave simu-
lation which is direct numerical solver for the Maxwell equa-
tions for given boundary conditions.7–9 The other is a circuit
simulation using lumped circuit elements that we proposed.
The two simulations help our analysis for the cut-off probe
in a complementary way. The former simulation is a com-
plete solver of Maxwell equation in 3-dimensional space at
the given boundary conditions. This simulation is known to
be very accurate not only having a good agreement with
experiment but also having no frequency limitation for the
application. However, sometimes it is not suitable for the
speculation of the underlying physics because the simulation
includes lots of physical considerations and is too compli-
cated. The later simulation is very simple simulation which
cannot capture lots of physical considerations (e.g., wave
radiation, interference, diffraction, and cavity resonance) and
can apply in the limited range of frequency (low frequency),
but is good for the speculation of the underlying physics.
Kwon et al. reported that a sheath path between two
probe tips is insignificant to form the TMF spectrum.6,10
Therefore, we can model the cut-off probe as the interaction
between separated two cylindrical probe tips immersed in
the plasma medium.3,9,11
When we assume that the plasma is uniformly distrib-
uted in the presence of background gas that is driven by a
small amplitude of bulk plasma electric field of which wave-
length (k) is much larger than the plasma size (Ls), k� Ls,
most of the field associated with the system are confined to
the vicinity of the system.12 In this condition, elements near
cut-off antennas consume most of the power, thus the circuit
simulation to describe a localized plasma system around cut-
off antennas is possible. The plasma (bulk) can be treated as
an assemble of lumped elements having an admittance
Yp¼ ixC0þ 1/(ixLpþRp), where Lp is the inductance of the
bulk plasma ðx�2pe C�1
0 Þ, Rp is the resistance of the bulk
plasma (mmLp), and C0 is the vacuum capacitance (�0A=d for
the case of the slab geometry of bulk plasma).11 The sheath
connected to the bulk plasma in series can be also treated as
capacitor (Cs) in the simulation, because a conduction cur-
rent is negligible at high frequency.11 Therefore, the cut-off
probe can be modeled as shown in Figure 1. For more reality
in the calculation, we used two cylindrical capacitancea)Electronic mail: [email protected].
0003-6951/2011/99(13)/131502/3/$30.00 VC 2011 American Institute of Physics99, 131502-1
APPLIED PHYSICS LETTERS 99, 131502 (2011)
Downloaded 20 Oct 2011 to 203.254.160.241. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions