ISSN (0970-2083)

^{1}Tomsk Polytechnic University, 634050, Tomsk, Russian Federation

^{2}Institute of Atmospheric Optics SB RAS, 634055, Tomsk, Russian Federation

^{3}Charles University in Prague, 116 36, Prague, Czech Republic

^{4}Tomsk State University, 634050, Tomsk, Russian Federation

**Received date:** 6 July, 2016; **Accepted date:** 18 September, 2016

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The phenomena that cause the experimentally recorded by the dispersed phase temperature distribution in the high-frequency torch (RF) discharge are discussed in this article. The results of calculation of the weight average temperature of the argon-graphite plasma, obtained by solving Elenbaas-Heller equation for the plasma column of cylindrical shape, with varying frequency and voltage on high-voltage electrode were given. Calculation of the temperature of the dispersed phase based on mathematical modeling of the data was conducted. The difference between the plasma gas temperature and the dispersed phase temperature was condensed shown. Assessment of energy losses, leading to an increase in the temperature of the soot during its condensation and reduction of the plasma column temperature was shown. It has been shown that, given the heat loss in argon plasma-graphite is possible to estimate the plasma temperature via temperature of dispersed particles.

Plasma, Temperature distribution, High-frequency torch, Plasma flow, Planck radiation

Low temperature plasma is widely used in the preparation and processing of powders, welding and cutting metals, decomposition of high-molecular compounds, etching of various materials, as well as the synthesis of chemical compounds. In plasma chemical reactions take place at a high rate, and non-equilibrium plasma systems promotes chemical reactions, impossible under normal conditions.

We have studied the isotopic effect in the oxidation of carbon in the plasma processes (Myshkin and Khan, 2015): CО content increases from 1.1% to 1.7% in the products of incomplete oxidation of carbon plasma in a magnetic field.

The plasma technologies are important during processing, time and temperature of the beginning of hardening process of plasma products. The treatment time at given flow rate of plasma gas, determined by the length and temperature field within the reactor. Therefore, for assessing the contribution to the isotope effect as the thermal diffusion and other processes, it is necessary to know the temperature distribution along the axis of the plasma reactor.

High-frequency torch discharge on the properties of is the single-electrode discharge E-type, which is formed based on capacitive coupling of the torchto- earth. To analyze the electrical parameters of the RF torch discharge use the model in the form of an electrical circuit Neumann (Neyman, 1965).

The scientific literature is insufficient data about the distribution of temperature field in the plasma channel of RF torch discharge. Therefore the purpose of this work is the definition of the factors influencing the distribution of the temperature field of a given length in the plasma chemical reactor.

Experimental installation for testing plasma
technologies based on RF torch discharge was
described in the work (Myshkin and Khan, 2015). RF torch discharge was created with graphite
electrode inside the plasma chemical reactor using
a sine wave oscillator frequency of 27.12 MHz and
a power of 4 kW. The length of the plasma channel
in argon in a long quartz tube exceeds 50 cm with
the use of such a generator. In this case on the walls
of the plasma chemical reactor soot formed due to
intensive evaporation of a graphite electrode and a
small amount of oxidant molecules to form CO (CO_{2})
in its gaseous state.

Since a direct measurement of the weight average temperature of the plasma gas is difficult, then assessed the disperse phase temperature, formed by the condensation of carbon vapour. During registration of the spectrum of the plasma channel projected a predetermined area on the entrance slit of the monochromator MSDD1000 company SOLAR. When using a diffraction grating with a number of strokes 1200 lines/mm at the monochromator output plane portion formed of the analyzed spectrum 16 nm wide.

The emission spectrum was recorded over the entire length of torch discharge bounded by quartz tube 45 cm in length. Optical spectrum at the same time contains the flow of Planck's radiation and the line of atomic particles. The radiation intensity at the maximum of the Planck curve is reduced ten-fold axis of the plasma channel with a cross section of 2.5 cm to 12.5 cm section. Later Planck radiation flux varies slightly. The temperature of the dispersed phase T, generated in the evaporation of the graphite electrode and condensation of the carbon atoms calculated from the Wien's displacement law.

**Fig. 1** shows a graph of the temperature distribution
of the disperse phase along the axis of the plasma
channel, which was determined from the Planck
curve.

Basic calculations were performed using COMSOL package for physical modelling. Typically, the simulation of low-temperature plasma is possible only in conditions of thermodynamic equilibrium. It is known that low-temperature plasma of RF discharge is the non-equilibrium. Therefore, calculations were performed no for laboratory RF torch discharge, but for the equilibrium low-temperature plasma in a reactor with dimensions taken from the experimental installation. The inner diameter of the plasma reactor was 5 cm, and the length was 45 cm.

Heterogeneity of plasma along the radius of the gas discharge channel with a diameter of 0.3 cm was neglected. As the plasma-forming gas used was argon, supplied to the lower part of the cylindrical shape of the plasma reactor at atmospheric pressure. Flow mode of plasma-forming gas in the plasma reactor shown in work of Myshkin (Myshkin, 2015).

In modeling of plasma phenomena it is also assumed
that the coulomb energy of electrons and ions is small
compared to their thermal energy, and the ionization
and recombination occur on the same path. For the
mathematical simulation of the plasma discharge
channel was used the drift-diffusion approximation
at a pressure close to atmospheric (Wong and
Mongkolnavin, 2016). This approach includes the
Poisson equation for the electrostatic potential and
continuity equations for electrons and ions, which
describe the birth and death of the charged particles.
On this basis, the drift-diffusion fluxes *Г _{e}* and

Where μ_{e} and μ_{i}-the mobility of electrons and ions,
respectively, *D _{e}* and

For a description of charged particle flows continuity equation will be as follows:

(2)Where β–recombination rate, α–ionization ratio that can be calculated from the formula:

(3)Where *p*–pressure of the plasma-forming gas, A,
B-coefficient depending on the ratio *E/P*.

To calculate the electric field inside the plasma chemical reactor plasma torch can be used Poisson equation:

(4)Where φ-potential supply electrode, *q*-volume
charge density, ε_{0}-the permittivity of vacuum.

Between the high-voltage high-frequency RF generator electrode and the ground there is capacitive coupling, which provides a self-sustaining electrical discharge in the absence of the second electrode. This inductive conductivity component is much smaller capacitance. The mathematical model of discharge assumed that the plasma formed by the cord is grounded at the output of the plasma chemical reactor, and the voltage applied to the high voltage electrode, varies according to the law:

(5)where ν–frequency of the supply voltage, *t*-time, *u _{0}*-
amplitude of the voltage on the electrode.

The temperature and therefore the electron density change along the axis of the plasma channel, which in the simulation can be taken into account by setting the parameters varying along the length. Since the discharge is a plasma column of cylindrical shape, in order to calculate the gas temperature of the plasma used equation Elenbaas-Heller (Benilov and Naidis, 2003).

It is assumed that the heat loss is mainly due to conductive flows:

(6)Where radius of the plasma channel, λ-coefficient
of thermal conductivity, *T*-gas temperature of the
plasma, σ-conductivity coefficient.

To determine the ratio of electrical conductivity σ
used data (Zaika, *et al*., 2003).

In this case the heat flux at the plasma axis is absent,
and the discharge temperature at the periphery is
the temperature of the walls of the plasma chemical
reactor *T _{w}*:

When calculated believed that the electron density at
atmospheric pressure of less than 10^{12} cm^{-3}. Transport parameters of charged particles in an argon
plasma taken from Hagelaar paper (Hagelaar
and Pitchford , 2005). Townsend coefficients in
equation (3) for a wide range of pressures are given
in paper of Kruithof (Kruithof and Druyvesteyn,
1937). Wall temperature was determined by means
of a pyrometer and was 700°C.

Numerical modeling in COMSOL environment
(Brezmes and Breitkopf, 2015) calculated the
temperature of the plasma channel, depending on the
magnitude and frequency of the supply voltage at a
distance 1 cm to 2 cm, 2 cm to 9 cm, 3 cm to 17 cm and
4 cm to 25 cm from high voltage graphite electrode
(**Fig. 2**). From **Fig. 2** shows that with an increase
in the voltage across the high-voltage electrode
increases the gas discharge channel temperature.
This is due to the fact that increasing the potential
for increased graphite electrode power deposited in
the discharge. Since the degree of ionization of the
plasma in the discharge capacitance type greatly
depends on the input power, the amount of carriers
increases. Therefore, the total energy of the plasma
system transmitted charged particles from the power
supply increases.

Supply voltage frequency significantly affects the
temperature of the plasma of electric discharge. **Fig. 3** shows that with increasing frequency there
is a growth of the gas temperature in the discharge
channel. When using a chain of Neumann as a
computational model does not take into account the
inductive component of the plasma channel.

It is known that the frequency of collisions of
particles in the gas phase depends on temperature
and pressure. Therefore, we carried out the
calculation of the gas temperature of the plasma
channel, depending on the initial pressure in the plasma reactor (**Fig. 4**). **Fig. 4** suggests that with
increasing pressure the gas temperature in the
discharge channel decreases. This is due to the fact
that the degree of ionization of the plasma decreases
with increasing pressure (O’Connell, *et al*., 2008). At
the same time, the cooling of the plasma leads to a
decrease in the concentration of charged particles
that carry energy from the electromagnetic field to
the plasma particles.

The contribution of carbon atoms and oxygen molecules in a plasma heating process is neglected due to their small content. Influence of the dispersed phase for various processes in the simulation is also neglected due to the fact that the maximum concentration of atomic carbon and oxygen in the plasma channel does not exceed 0.001 mole fraction.

In the photographs of the plasma discharge channel of RF torch discharge recorded a small number of bright tracks along the entire length. On the walls of the reactor, in the area of about 10 cm above the electrode, soot is formed. Therefore we suggest that the dispersed phase comprises two components: the nanoparticles are formed in the electrode region by vapor condensation of carbon and graphite electrodes fragments. In RF torch discharge occurs oxidation of carbon by oxygen impurities in the plasma-forming gas, which penetrates into the reactor due to leaky joints. The decrease in the intensity of the maximum of the Planck curve is due to the oxidation of ultradispersed particles. Large fragments do not have time to oxidize and reaches the end of the reactor.

A decrease in temperature of the plasma along the
axis of the channel does not contradict the data
presented earlier in Manual of Tartu University.
At the end of the channel of RF torch discharge is
lowering particulate matter temperature to 2700
K. Sufficiently high temperature of the dispersed
phase due to the following processes. In the area of
electrode pair of carbon have a temperature of the
gas phase. Condensation of carbon is accompanied
by release of vaporization energy, which heats
the soot particles formed above the gas-phase
temperature. In what follows the high temperature is
maintained by the energy released by the oxidation
of the dispersed phase. Therefore, an ultra-dispersed
soot temperature slightly above the temperature of
the gas phase and has a maximum, in contrast to the
gas phase (Kee, *et al*., 2003).

The ratio of energy emitted by the dispersed particles and atoms was evaluated as the area ratio in the spectrum. Therefore, in the electrode region energy loss of the plasma channel is much higher due to Planck's radiation. The heat capacity change due to changes in the composition of components and temperature change due to energy release of oxidation of carbon plasma system, under these conditions, due to a slight change in the gas mixture in the plasma flow is neglected. However it is possible to analyze the processes leading to heat losses.

The temperature distribution in each cross section along a flow axis defined by a balance between the energy supplied by RF field and losses. In energy balance in the plasma channel of RF torch discharge in different sections of the axis along the plasma channel, the following physical and chemical processes must take into account the relative contribution of that change:

• heating of the plasma by RF field associated with the heating of electronic components and power transmission heavy particles–equation (1), (2), (4);

• heat release during the formation of the dispersed phase and the preferential heating of the soot by that heat (717.7 kJ/mol at 208.16 K);

• The release of energy by the oxidation of particulate carbon (110 kJ/mol).

Processes leading to cooling the plasma flow:

• Heat loss due to heat transfer from the discharge channel to diffuse shell;

• Radiation losses due to soot and gas phase:

(8) (9)Other types of energy losses, the value of which cannot be an accurate assessment, make a minor contribution.

An analysis of the processes occurring in the plasma flow of RF to rechdischarge evaporating carbon electrode shows that the temperature of the ultra-dispersed particles is the upper bound of the gas temperature. These particles are formed by vapor having a temperature of the plasma gas. As a result, the carbon condensation releases heat, which is consumed, including for heating of ultrafine particles. Indeed, the dispersed phase temperature determined from the experimental data, the higher the gas temperature calculated for the equilibrium of the plasma of electric discharge.

The condensed phase, if present, to a large extent determines the loss of plasma channel energy by Planck radiation. Proposed in the calculation model is suitable for the determination of the electrical parameters of the equilibrium plasma.

The reported study was funded by RFBR according to the research project No. 16-38-00382 mol_a.

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