Modeling and Analysis of Inductively Coupled Plasma Torches
Modeling and Analysis of Inductively Coupled Plasma Torches Glauco George Cipriano Maniçobaa*, Alexandre Magnus Fernandes Guimarãesb, Andres Ortiz Salazara, José Alberto Diaz Amadoc, José Antonio Bernardino de Oliveiraa. a
Departamento de Engenharia de Computação e Automação - DCA, Centro de Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN, Brasil. b Escola de Ciência e Tecnologia- ECT, Universidade Federal do Rio Grande do Norte, Natal, RN, Brasil. c Instituto Federal de Educação, Ciência e tecnologia da Bahia, IFBA, Vitoria da Conquista, BA, Brasil.
In this paper, it is presented a 2D model for the simulation of inductively coupled plasma torches (ICPTs) working at vacuum pressure. The study of the effect and behavior of the plasma generation was solved for formulas used the fluid dynamic models that are generally appropriate for the investigation of inductively coupled plasmas. The governing equations were modeled using the model MHD (magnetohydrodynamic) widely used in several studies for the modeling and simulation of regions of thermal plasma torch are presented where appropriate boundary conditions and nonlinear parameters such as thermal and electrical conductivity gas and energy input used in the simulations. Keywords: plasma torch simulation, modeling, magnetohydrodynamic
1.
Introduction
In recent years, the inductively coupled plasma torches (ICPT), is a type of plasma that is maintained by an external power source, are playing an increasingly important role in many technological processes, since it is a clean and efficient way to produce plasma jets with a high level of enthalpy, which may be used quite in a wide range of applications such as in aerospace, metallurgy and waste treatment, among other1. In a ICPT, a gas at room temperature is heated to a plasma state with extremely high peak temperatures. These torches have a mechanism to provide stable enough energy that will maintain the dynamic balance of the particles formed in the plasma, and its energy conditions will depend on the composition and mixing of the gases.2. In this process the electrons
receive energy the induced magnetic field produced by a coil that generate a nominal frequency oscillation of 450 kHz. From an electrical point of view, the plasma torch behaves as a transformer. A current is applied to the driving coil (the primary) and this induces a current in the plasma (the secondary)2. The plasma then induces an opposing current back in the coil, increasing its resistance. The current flowing in the plasma depends on the current applied to the coil and the reaction kinetics. The total plasma current may vary from no current (plasma not sustained) to the same current as the primary which corresponds to perfect coupling between the coil and the plasma. To describe fully the plasma we used a model of fluid called magnetohydrodynamic (MHD), which treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier-Stokes.
The simulation was conducted to provide a detailed evaluation of the model to experimental studies and the modeling of discharges from a plasma torch. The plasma is formed by inductive heating, consisting of a coil coating the discharge volume. This model simulates a plasma low pressure where the gas temperature cannot be assumed to be constant, then the plasma is still not in local thermodynamic equilibrium. 2.
Description of the Model
Due to the physics that occurs in an inductively coupled plasma be quite complex, resolved start the modeling
project with a simple reaction mechanism. Argon is one of the simplest mechanisms to start and operate the plasma in most plasma torches due to its low heat capacity and temperature ionized and low thermal conductivity3. The electronically excited states can be grouped into a single species, resulting in a chemical mechanism consisting of seven species and three reactions according to Table 1, where the gas has been heated by elastic and inelastic collisions. Through these collisions energy is transferred to other atoms producing more ions and electrons, and thus begins a process of cascade until the formation of plasma4.
Table 1. Important collision parameters in the argon discharge.
Reaction Elastic Excitation Superelastic Ionization Ionization Penning ionization Metastable quenching
In Table 1, the symbols "Ar+"," Ars", and "e" denotes positive ions, metastable atoms and electrons respectively. The neutrals atoms, refer to metastable atom (Ars) to this model, are not of electric charge, and they are completely unaffected by the electromagnetic force. 2.1.
∆ϵ(V) 0 11.50 -11.50 15.80 4.24 -
Formula e+Ar=>e+Ar e+Ar=>e+Ars e+Ars=>e+Ar e+Ar=>2e+Ar+ e+Ars=>2e+Ar+ Ars+Ars=>e+Ar+Ar+ Ars+Ar=>Ar+Ar
Domain Equations
The simulations were performed by argon plasma with the assumptions of axial symmetry, optically thin, laminar flow with negligible viscous dissipation. The governing equations used are as follows:
2.1.1.
Electromagnetic equations
In solving electromagnetic field equations could be used the Maxwell's equations ,in the case of two-dimensional axisymmetric ICP model, where these have been reduced in the form of the magnetic vector (A), and thus the distribution of the electromagnetic field is obtained : ∇ A+ ε ε ω A = −J
(1)
Where Js is the current density in the coil, μ0 is the vacuum permeability, μr the relative permeability, ε0 the permittivity in a vacuum, relative permittivity εr,∇ the operator is divergence and ⍵= 2пf , where f is the frequency of oscillation.
2.1.2.
Mass conservation equation
For ions, electrons and neutral the transport equations were used to describe which all follow conservation of mass equations. The details are as follows: i.
For íons:
= 0=
− ∇.
and "Pind" represents the inductive heating that is the power deposited into the plasma. The fifth and sixth terms are the energy loss in inelastic-elastic collisions between electrons and neutral species, respectively. "E" is the electric field induced by static ambipolar-diffusion and "Tg" is the gas temperature.
(2) 2.1.4.
Where ni e Ji are the ion number density and the ion flux, respectively. Considering this model as static constant, we let ni / t = 0. And Si is the ion source, which is the source of energy needed to produce íons. ii.
For electrons:
= ∑
Using the MHD model, considering the laminar flow, the modeling of this flow has been described by the Navier-Stokes equations (equation 6), which are differential equations describing the outflow of the flow. − ∇. (∇ + ∇ )
(3)
Where ne is is the electron number density, which is equal to the total summation of all ions number densities.
Navier-Stokes equation
∇ = 0
+
.∇ ∇ =
, (6)
Where Dn, un, e nn são: are the diffusivity, convection, velocity convection, and number density of the neutral species. In Equation 4, Sn indicates all sources related reactions with neutral species.
Where , η, u represent gas density, dynamic viscosity and velocity vector respectively, and p is pressure, and F is force. In this case the force is equal to zero. The boundary condition of inlet and outlet are set to velocity inlet type and pressure outlet respectively and the wall boundary condition is simply defined with the Dirichlet condition, that ∇u=0, since there is no energy transport particles or the walls.
2.1.3.
2.2.
iii.
For neutrals:
= 0=
− ∇. (−
∇
+
) (4)
Electron energy equations
There are several theories about energy equations for electrons under different conditions5-6. For this model, we consider the energy balance of the electrons described by: +3 0
3 2 n kv
+ ∇. T − T
+
.
−
+ n N∑ K T ε =
(5)
Where the second term is the divergence of the total energy of the electron energy flux, the third term represents the joule heating
Torch Geometry
The physical behavior of the plasma was modeled fully dimensional and was implemented in the COMSOL Multiphysics®. The scheme of plasma torch used is shown in Figure 1. A summary of the dimensions of the torch and the operating conditions are given in Table 2. The gas used was pure argon at a pressure of 10 mTorr (~1.33Pa).
Figure 1. Inductively plasma torch. Table 2.Torch characteristic dimensions and operation conditions.
Dimensions and operating conditions L1 130mm L2 176mm R0 75mm R1 100mm 3mm w Operation Frequency 450kHz Current in the coils 100A 3.
Results
The governing equations along with the operation conditions are solved through resolution by infinite elements. This model insures a real of the existing phenomena, since it is based on a simultaneous solution of partial differential equations (PDE). The electron density peak shown in Figure 2, occurs in the outer region of the
torch (vacuum chamber) due to a shift of the thermodynamic equilibrium caused by the symmetry of the coil by changing the energetic distribution regions. The electron temperature, as shown in Figure 3, is greater in the central channel of the torch where it is stored most of the energy supplied by the coil. The Figures 4 and 5 show the profiles of the electric field, and the magnetic vector applied. The distributions of electric and magnetic vector field along the axial direction of the torch indicate that the majority of the power transferred from the RF generator to the plasma by the induction coil is dissipated in the central region of the coil. The Figure 6 shows the velocity profile well accentuated between the axis of the torch and the walls of the torch which is where the rotational power is provided by the electromagnetic inductive coil laminar flow is absorbed. The Figure 7 shows the graph of the power dissipated by the coil over time. Initially, the power dissipated in the coil is maximum (~ 50kW). After, over a period of 2 microseconds, start the ignition of the plasma neutral gas atoms that is split into electrons and ions, this electrons begin to absorb more energy, causing either lower the coil power at about 1,4kW. In this case, the total power absorbed by both the coil is fixed at 48,6kW. When modeling inductively coupled plasmas it is generally best to specify the total power as a setting for the coil rather than the coil current or voltage.
Figure 2. Plot of the electron density.
Figure 3. Plot of the electron temperature.
Figure 4. Plot of the norm of the electric field due to the induction currents.
Figure 5. Plot of the contours of the magnetic vector potential.
Figure 6. Plot of the Velocity Field in the torch.
Figure 4.Plot of total power versus time in the coil
4.
Conclusions
The work aimed at an overview of the analysis and modeling of an asymmetric twodimensional model of an induction plasma
torch operating at a pressure around 1.33Pa (10mTorr). The model represents the coupling between Navier-Stokes and electromagnetic equations. This work presents a finite element formulation, based on a direct solution of a system of dynamic, non-linear and coupled
equation for the discharge in inductively coupled plasma torch (ICPT). The plasma gas is taken as argon at vacuum. As for evaluation of technical performance can be concluded that the analysis of the used torch was very efficient. It was made a study of the behavior of inductive torch, detailing through simulations a model close to the real. Acknowledgments We are thankful to PPGEE/CT, Petrobras, CNPq and CAPES for the financial support. References 1.
Mékideche, M. R. and Féliachi, M. An axisymmetric finite element model for the electromagnetic behavior in an RF plasma device, IEEE. Trans. On Mag, Vol.29. N°.6,pp. 2476, Nov.1993.
2.
Maniçoba, G. G. C.; Salazar, A. O.; Amado, J. A. D.; Oliveira, j. A. B.; Dubut, j. P.; Lock, A. S.; Quintaes, F. O. Estudo e Simulação de uma Tocha de Plasma Térmico com Acoplamento Indutivo. In: Congresso Nacional de Engenharia Mecânica, 2012, São Luís. Engenharia em destaque, 2012.
3.
Hagelaar, G. J. M. and Pitchford, L. C., Solving the Boltzmann Equation to Obtain Electron Transport Coefficients and Rate Coefficients for Fluid Models, Plasma Sources Sci. Technol, vol. 14, pp. 722–733, 2005.
4.
Lymberopoulos D. P., Economou D. J. Modeling and simulation of glow discharge plasma reactors. J Vac Sci Technol A, 1994, 12(4): 1229.
5.
Jaeger, E. F.; Berry L. A.; Tolliver, J. S., et al. Power deposition in high-density inductively coupled plasma tools for semiconductor processing. Phys Plasmas, 1995, 2(6): 2597.
6.
Rauf S., Kushner M. J. Model for noncollisional heating in inductively coupled plasma processing sources. J Appl Phys, 1997, 81(9): 5966.
Departamento de Engenharia de Computação e Automação - DCA, Centro de Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN, Brasil. b Escola de Ciência e Tecnologia- ECT, Universidade Federal do Rio Grande do Norte, Natal, RN, Brasil. c Instituto Federal de Educação, Ciência e tecnologia da Bahia, IFBA, Vitoria da Conquista, BA, Brasil.
In this paper, it is presented a 2D model for the simulation of inductively coupled plasma torches (ICPTs) working at vacuum pressure. The study of the effect and behavior of the plasma generation was solved for formulas used the fluid dynamic models that are generally appropriate for the investigation of inductively coupled plasmas. The governing equations were modeled using the model MHD (magnetohydrodynamic) widely used in several studies for the modeling and simulation of regions of thermal plasma torch are presented where appropriate boundary conditions and nonlinear parameters such as thermal and electrical conductivity gas and energy input used in the simulations. Keywords: plasma torch simulation, modeling, magnetohydrodynamic
1.
Introduction
In recent years, the inductively coupled plasma torches (ICPT), is a type of plasma that is maintained by an external power source, are playing an increasingly important role in many technological processes, since it is a clean and efficient way to produce plasma jets with a high level of enthalpy, which may be used quite in a wide range of applications such as in aerospace, metallurgy and waste treatment, among other1. In a ICPT, a gas at room temperature is heated to a plasma state with extremely high peak temperatures. These torches have a mechanism to provide stable enough energy that will maintain the dynamic balance of the particles formed in the plasma, and its energy conditions will depend on the composition and mixing of the gases.2. In this process the electrons
receive energy the induced magnetic field produced by a coil that generate a nominal frequency oscillation of 450 kHz. From an electrical point of view, the plasma torch behaves as a transformer. A current is applied to the driving coil (the primary) and this induces a current in the plasma (the secondary)2. The plasma then induces an opposing current back in the coil, increasing its resistance. The current flowing in the plasma depends on the current applied to the coil and the reaction kinetics. The total plasma current may vary from no current (plasma not sustained) to the same current as the primary which corresponds to perfect coupling between the coil and the plasma. To describe fully the plasma we used a model of fluid called magnetohydrodynamic (MHD), which treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier-Stokes.
The simulation was conducted to provide a detailed evaluation of the model to experimental studies and the modeling of discharges from a plasma torch. The plasma is formed by inductive heating, consisting of a coil coating the discharge volume. This model simulates a plasma low pressure where the gas temperature cannot be assumed to be constant, then the plasma is still not in local thermodynamic equilibrium. 2.
Description of the Model
Due to the physics that occurs in an inductively coupled plasma be quite complex, resolved start the modeling
project with a simple reaction mechanism. Argon is one of the simplest mechanisms to start and operate the plasma in most plasma torches due to its low heat capacity and temperature ionized and low thermal conductivity3. The electronically excited states can be grouped into a single species, resulting in a chemical mechanism consisting of seven species and three reactions according to Table 1, where the gas has been heated by elastic and inelastic collisions. Through these collisions energy is transferred to other atoms producing more ions and electrons, and thus begins a process of cascade until the formation of plasma4.
Table 1. Important collision parameters in the argon discharge.
Reaction Elastic Excitation Superelastic Ionization Ionization Penning ionization Metastable quenching
In Table 1, the symbols "Ar+"," Ars", and "e" denotes positive ions, metastable atoms and electrons respectively. The neutrals atoms, refer to metastable atom (Ars) to this model, are not of electric charge, and they are completely unaffected by the electromagnetic force. 2.1.
∆ϵ(V) 0 11.50 -11.50 15.80 4.24 -
Formula e+Ar=>e+Ar e+Ar=>e+Ars e+Ars=>e+Ar e+Ar=>2e+Ar+ e+Ars=>2e+Ar+ Ars+Ars=>e+Ar+Ar+ Ars+Ar=>Ar+Ar
Domain Equations
The simulations were performed by argon plasma with the assumptions of axial symmetry, optically thin, laminar flow with negligible viscous dissipation. The governing equations used are as follows:
2.1.1.
Electromagnetic equations
In solving electromagnetic field equations could be used the Maxwell's equations ,in the case of two-dimensional axisymmetric ICP model, where these have been reduced in the form of the magnetic vector (A), and thus the distribution of the electromagnetic field is obtained : ∇ A+ ε ε ω A = −J
(1)
Where Js is the current density in the coil, μ0 is the vacuum permeability, μr the relative permeability, ε0 the permittivity in a vacuum, relative permittivity εr,∇ the operator is divergence and ⍵= 2пf , where f is the frequency of oscillation.
2.1.2.
Mass conservation equation
For ions, electrons and neutral the transport equations were used to describe which all follow conservation of mass equations. The details are as follows: i.
For íons:
= 0=
− ∇.
and "Pind" represents the inductive heating that is the power deposited into the plasma. The fifth and sixth terms are the energy loss in inelastic-elastic collisions between electrons and neutral species, respectively. "E" is the electric field induced by static ambipolar-diffusion and "Tg" is the gas temperature.
(2) 2.1.4.
Where ni e Ji are the ion number density and the ion flux, respectively. Considering this model as static constant, we let ni / t = 0. And Si is the ion source, which is the source of energy needed to produce íons. ii.
For electrons:
= ∑
Using the MHD model, considering the laminar flow, the modeling of this flow has been described by the Navier-Stokes equations (equation 6), which are differential equations describing the outflow of the flow. − ∇. (∇ + ∇ )
(3)
Where ne is is the electron number density, which is equal to the total summation of all ions number densities.
Navier-Stokes equation
∇ = 0
+
.∇ ∇ =
, (6)
Where Dn, un, e nn são: are the diffusivity, convection, velocity convection, and number density of the neutral species. In Equation 4, Sn indicates all sources related reactions with neutral species.
Where , η, u represent gas density, dynamic viscosity and velocity vector respectively, and p is pressure, and F is force. In this case the force is equal to zero. The boundary condition of inlet and outlet are set to velocity inlet type and pressure outlet respectively and the wall boundary condition is simply defined with the Dirichlet condition, that ∇u=0, since there is no energy transport particles or the walls.
2.1.3.
2.2.
iii.
For neutrals:
= 0=
− ∇. (−
∇
+
) (4)
Electron energy equations
There are several theories about energy equations for electrons under different conditions5-6. For this model, we consider the energy balance of the electrons described by: +3 0
3 2 n kv
+ ∇. T − T
+
.
−
+ n N∑ K T ε =
(5)
Where the second term is the divergence of the total energy of the electron energy flux, the third term represents the joule heating
Torch Geometry
The physical behavior of the plasma was modeled fully dimensional and was implemented in the COMSOL Multiphysics®. The scheme of plasma torch used is shown in Figure 1. A summary of the dimensions of the torch and the operating conditions are given in Table 2. The gas used was pure argon at a pressure of 10 mTorr (~1.33Pa).
Figure 1. Inductively plasma torch. Table 2.Torch characteristic dimensions and operation conditions.
Dimensions and operating conditions L1 130mm L2 176mm R0 75mm R1 100mm 3mm w Operation Frequency 450kHz Current in the coils 100A 3.
Results
The governing equations along with the operation conditions are solved through resolution by infinite elements. This model insures a real of the existing phenomena, since it is based on a simultaneous solution of partial differential equations (PDE). The electron density peak shown in Figure 2, occurs in the outer region of the
torch (vacuum chamber) due to a shift of the thermodynamic equilibrium caused by the symmetry of the coil by changing the energetic distribution regions. The electron temperature, as shown in Figure 3, is greater in the central channel of the torch where it is stored most of the energy supplied by the coil. The Figures 4 and 5 show the profiles of the electric field, and the magnetic vector applied. The distributions of electric and magnetic vector field along the axial direction of the torch indicate that the majority of the power transferred from the RF generator to the plasma by the induction coil is dissipated in the central region of the coil. The Figure 6 shows the velocity profile well accentuated between the axis of the torch and the walls of the torch which is where the rotational power is provided by the electromagnetic inductive coil laminar flow is absorbed. The Figure 7 shows the graph of the power dissipated by the coil over time. Initially, the power dissipated in the coil is maximum (~ 50kW). After, over a period of 2 microseconds, start the ignition of the plasma neutral gas atoms that is split into electrons and ions, this electrons begin to absorb more energy, causing either lower the coil power at about 1,4kW. In this case, the total power absorbed by both the coil is fixed at 48,6kW. When modeling inductively coupled plasmas it is generally best to specify the total power as a setting for the coil rather than the coil current or voltage.
Figure 2. Plot of the electron density.
Figure 3. Plot of the electron temperature.
Figure 4. Plot of the norm of the electric field due to the induction currents.
Figure 5. Plot of the contours of the magnetic vector potential.
Figure 6. Plot of the Velocity Field in the torch.
Figure 4.Plot of total power versus time in the coil
4.
Conclusions
The work aimed at an overview of the analysis and modeling of an asymmetric twodimensional model of an induction plasma
torch operating at a pressure around 1.33Pa (10mTorr). The model represents the coupling between Navier-Stokes and electromagnetic equations. This work presents a finite element formulation, based on a direct solution of a system of dynamic, non-linear and coupled
equation for the discharge in inductively coupled plasma torch (ICPT). The plasma gas is taken as argon at vacuum. As for evaluation of technical performance can be concluded that the analysis of the used torch was very efficient. It was made a study of the behavior of inductive torch, detailing through simulations a model close to the real. Acknowledgments We are thankful to PPGEE/CT, Petrobras, CNPq and CAPES for the financial support. References 1.
Mékideche, M. R. and Féliachi, M. An axisymmetric finite element model for the electromagnetic behavior in an RF plasma device, IEEE. Trans. On Mag, Vol.29. N°.6,pp. 2476, Nov.1993.
2.
Maniçoba, G. G. C.; Salazar, A. O.; Amado, J. A. D.; Oliveira, j. A. B.; Dubut, j. P.; Lock, A. S.; Quintaes, F. O. Estudo e Simulação de uma Tocha de Plasma Térmico com Acoplamento Indutivo. In: Congresso Nacional de Engenharia Mecânica, 2012, São Luís. Engenharia em destaque, 2012.
3.
Hagelaar, G. J. M. and Pitchford, L. C., Solving the Boltzmann Equation to Obtain Electron Transport Coefficients and Rate Coefficients for Fluid Models, Plasma Sources Sci. Technol, vol. 14, pp. 722–733, 2005.
4.
Lymberopoulos D. P., Economou D. J. Modeling and simulation of glow discharge plasma reactors. J Vac Sci Technol A, 1994, 12(4): 1229.
5.
Jaeger, E. F.; Berry L. A.; Tolliver, J. S., et al. Power deposition in high-density inductively coupled plasma tools for semiconductor processing. Phys Plasmas, 1995, 2(6): 2597.
6.
Rauf S., Kushner M. J. Model for noncollisional heating in inductively coupled plasma processing sources. J Appl Phys, 1997, 81(9): 5966.
