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TRANSITION TO CHAOS IN PLANAR GAS DISCHARGE-SEMICONDUCTOR SYSTEM IN NITROGEN: EFFECT OF FLUID MODELLING APPROACH

Authors:
TRANSITION TO CHAOS IN PLANAR GAS
DISCHARGE-SEMICONDUCTOR SYSTEM IN
NITROGEN: EFFECT OF FLUID MODELLING
APPROACH
Cihan Yeşil
Department of Physics
Middle East Technical University
Supervisor: Prof. Dr. İsmail RAFATOV
What is Plasma ?
What is Plasma ? Gas discharge system
Retrieved from http://www.cpepphysics.org/
~fusion-samples.html.
Gas Discharge Modelling
Fluid Models
- Simple Fluid Model
- Extended Fluid Model
Kinetic Particle Models
- PIC/MC Methods
Hybrid Models
A diagram illustrating a correct physical model for a
plasma system as functions of system size and pressure
Retrieved from V.Kolobov and R. Arslanbekov, Microelectron. Eng., 69, 606615, 2003.
Pattern Formation in Gas Discharge Plasma
The group of Purwins
(Münster, Germany)
The group of Astrov (St.
Petersburg, Russia)
Planar DC gas discharge system with high ohmic cathode
Retrieved from https://www.uni-muenster.de/~Physik.AP/Purwins/DC/index-en.html.
Experimentally Observed Patterns and
Oscillating Modes
2D Patterns Oscillating Modes
Retrieved from https://www.uni-muenster.de/~Physik.AP/Purwins/DC/index-en.html.
Retrieved from C. Strümpel, Yu. A. Astrov and H.G. Purwins, Phys. Rev. E, 65, 066210, 2002.
Governing Equations
Boltzmann Equation

  
 
  

It is supplemented with Maxwell’s Equations.
Zeroth moment produces the contiunity
equation:

    
First moment produces the momentum
equation:
 
     
Second moment gives the energy equation:


 
    
Drift-diffusion approximation
Two-fluid equations with drift-diffusion
approximation

    

    
To have a self-consistent model, Poisson’s
equation for electric potential is added
 

 and  reduces
momentum equation into a simpler form
with


 
Simple Fluid and Extended Fluid Models
Set of Equations

   
 
    
  
Local-field approximation (LFA)
By adding electron energy equation to
the simple fluid equations

 
 


where  ,  
 
Local-mean-energy approximation (LMEA)
Simple Fluid Model Extended Fluid Model
Basic Plasma Chemical Reactions
Phelps and pitchford. http://www.lxcat.net.
Discharge parameters:
p = 30 Torr, d = 1.4 mm,   ,  
Verification of models were done in given
reference:
I. Rafatov, C. Yesil, "Transition from
homogeneous stationary to oscillating
state in planar gas discharge
semiconductor system in nitrogen: Effect of
fluid modelling approach", Phys. Plasmas,
vol. 25, no. 8, pp. 082107, 2018.
Numerical modelling of the GDSS in nitrogen

    
Stationary
solution
Obtaining Stationary Solutions
  Load Line:
Subnormal
Regime
CVC curve:   
Nonlinear oscillations occur in Subnormal Regime
Plasma medium length is very small
Bifurcation diagram
of
vs.
Stable and unstable regions
and signature of Hopf
bifurcation
Different types of oscillations
limit cycle, period doubling etc.
Points where chaotic
oscillations initiate
Chaos initiated
Chaos initiated
: limit cycle
: period-doubling
: oscillation with four period
: Chaos
*
vs. diagram
A B
c
D
AB C D
A: 665 V C: 725 V
B: 708 V D: 827 V
Lorenz map
Lorenz maps (the (n + 1)th local
maximum of the discharge current j(t)
versus its nth maximum) obtained for the
regimes corresponding to voltages Ut =
665 V, 708 V, 725 V and 827 V.
Showing universal trend but with
different current density values
Conclusion:
Two developed one dimensional discharge models
- Simple Fluid approach
- Extended Fluid approach
Two bifurcation diagrams are obtained
-Determination of locations
-Classification of oscillations
Future works
- Lyapunov exponents
- 2D and 3D models
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