State doctoral exam topics

Plasma Physics

Introduction to plasma physics

1. Criteria for the definition of plasma. Plasma frequency, cyclotron frequency, collision frequency, mean free path, Debye length, magnetic pressure, beta parameter.
2. Temperature. Saha equation, ranges of temperature and electron density for plasma. General properties of various types of plasma. 
3. Plasma dielectric constant. Polarization, magnetization. Plasma polarization tensor.
4. Motion of charged particles. Equation of motion, adiabatic invariants, drifts.  Motion in magnetic dipole and in magnetic mirror.   
5. Transport equations.  Ohm´s, Fick´s and Fourier´s law. Onsager reciprocal relations.  Diffusion, mobility, ambipolar diffusion. Diffusion across magnetic field, effect of collisions on diffusion in magnetic field, plasma resistivity.
6. Statistical description of plasma. Boltzmann equation, Fokker-Planck equation. Higher moments of the distribution function. 
7. Collisions in plasmas. Cross sections.  Coulombic collisions. Coulomb´s logarithm. Runaway solution.  Chandrasekhar's function.
8. Foundation of magnetohydrodynamics. Continuity equation, equation of motion, equation for magnetic field. Frozen in and diffusion magnetic field.  
9. Thermonuclear fusion. Basic reactions. History, presence and future.  Lawson criterion. Tokamak and stellarator. Inertial fusion.
10. Waves in plasma. Alfvén magnetoacoustic wave complex. Electromagnetic waves in plasma (O, X, R, L wave). CMA diagram.
11. Plasma instabilities. Kelvin-Helmholtz, Rayleigh-Taylor instabilities, instabilities of plasma column – sausage, kink, and m > 2 instabilities. Two-stream (Buneman) instability.
12. Force free configuration. Helicity, helical structures, conservation of helicity, examples of helical structures, conditions for violation of the helicity conservation law.

Electrical discharges, applications

1. General classification of electrical discharges. Self-sustained and non- self-sustained discharge. Current voltage characteristic of discharge at low pressure. Silent discharge, glow discharge and arc. 
2. Application of electrical discharges.  Plasma technologies. Direct and indirect plasma treatment.  Applications of discharge products.    
3. Elementary processes on electrodes and in discharge volume.  Thermal emission, secondary emission, cold emission, explosive electron emission, photoemission. Excitation, dissociation and ionization, formation of radicals. Thermal and non-thermal plasma. Afterglow.
4. Townsend theory and breakdown voltage.  Physics of electron avalanches,description of an avalanche, breakdown, applications.  Condition for initiating a self- sustained discharge.  Breakdown voltage and engineering estimation of breakdown voltage.  Paschen´s law.
5. Glow discharge at low pressure.  Characteristic regions and physics of glow discharge. Effect of various parameters on glow discharge. Reactions taking part in glow discharge.
6. Discharges at atmospheric pressure. Positive, negative and bipolar corona discharge. Trichel pulses. Warburg´s law.  Dielectric barrier discharge. Gliding arc. Stabilization and homogenization of discharges at atmospheric pressure.
7. High frequency and microwave discharge. Discharge properties.  Microwave sources of plasma. Sliding discharges. Applications of microwave plasma.
8. Arc discharge and spark.  Definition and characteristic features of these discharges, description and applications. Description of lightning discharge and its peculiarities.
9. Z-pinch. Bennett equilibrium and plasma pressure formula p(r), Bennett formula for pinch temperature. Reverse pinch. Cylindrical instability modes, Kruskal stability condition. Electromagnetic collapse.
10. Self-organization of plasma structures in the discharge. Minimum magnetic energy condition and its relationship to helical structures and self-organization.

Plasma diagnostics and simulations

1. Measurements of current, voltage and potential. Methods of measurements. Langmuir probe, Rogowski coil.
2. Measurements of magnetic fields. Faraday rotation, Zeeman effect, direct measurement of magnetic fields, magnetometers.
3. Foundations of spectroscopy. Optical emission spectroscopy, spectral lines, measurement of temperature, density, rotational and vibrational spectra, plasma constituents and other plasma characteristics. Heat capacity of vibrational and rotational states.
4. Visualization diagnostic techniques. Interferometric and schlieren methods for measurements of electron densities and gradients of electron densities.
5. Microwave and corpuscular diagnostics.Overview of methods and detecting plasma parameters, neutrons detection.
6. Measurement of plasma density. Overview of basic methods, determination of density from propagation of electromagnetic waves, significance of plasma frequency. 
7.  X-ray diagnostics of hot plasma. Mechanism of production of X-ray emission. Detection of X-ray emission. Parameters determinable by X-ray diagnostics.
8. Numerical simulation basics. Numerical solution of ordinary and partial differential equations (basic principles). Examples of difference schemes. Convergence and stability of the scheme. Hybrid methods.
9. Particle and field solvers. Equation of motion solvers (Boris-Buneman, Leap-frog, Runge-Kutta). Partial differential equation solvers (difference schemes, finite elements, multigrid and FFT solvers).
10. Selected numerical methods in plasma physics. Monte Carlo simulations – probability distribution realization, Metropolis method, optimization methods (simulated annealing). Perturbation theory. Series expansion. PIC simulations (basic steps of PIC algorithm).