Lecture 2. Introduction to plasma physics. Dr. Ashutosh Sharma
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1 Preparation of the concerned sectors for educational and R&D activities related to the Hungarian ELI project Ion acceleration in plasmas Lecture 2. Introduction to plasma physics Dr. Ashutosh Sharma Zoltán Tibai 1
2 Contents 1. Definition of Plasma 2. Theoretical Background 3. Three Approaches to Plasma Physics Hydrodynamic Theory Kinetic Theory Particle Theory 4. Occurrence of Plasmas 2
3 Plasma The plasma state (4th state of matter) is a gaseous mixture of positive ions and electrons. Plasma can be fully ionized, as the plasma in the Sun, or partially ionized, as in fluorescent lamps, which contain a large number of neutral atoms. "A plasma is a 'quasineutral' gas of charged and neutral particles which exhibits 'collective' behavior. Any ionized gas cannot be called as plasma, of course; there is always some small or low degrees of ionization in any gas. 3
4 Plasma Neutral GAS PLASMA A gas is characterized by the number of particles per unit volume (n). Plasma is a mixture of two different gases, light electrons and heavy ions. electron density (n e ) ions density (n i ) Thermodynamic equilibrium state and gas temperature given as T. Non-equilibrium state with different temperature T e and T i. In a normal gas, sound waves propagate via intermolecular action of collisions. In a plasma, waves can propagate when collisions are negligible because of coulomb interaction of the particles. 4
5 Plasmas are Quasi-Neutral (2.1) (2.2) 5
6 SLAB The resulting force on the charges tending to expel whichever species is in excess. If n i > n e E field causes decreasing n i, increasing n i, reduce the charge. Enormous restoring force!!! 6
7 Theoretical Background (2.3) 7
8 Theoretical Background The temperature of plasma can be defined in terms of kinetic energy via Maxwellian distribution function (for a thermodynamic equilibrium) (taking into account electrons only) (2.4) (2.5) (2.6) m e mass of the single electron, n e electron density, k B Boltzmann constant. Since m i / m e >> 1, v ti << v te (for T T e T i ). 8
9 Plasma density of Electrostatic Potential (2.7) 9
10 Debye Shielding (2.8) (2.9) 10
11 Debye Shielding (2.10) (2.11) (2.12) (2.13) 11
12 Debye Shielding (2.14) (2.15) 12
13 Response Time and Frequency (2.16) (2.17) 13
14 Response Time and Frequency Similarly the request for dynamic collective behavior can be quantified by the plasma frequency. The simplest collective motion is the oscillation of the (fast) electrons against the ion background (assumed to be at rest). Taking ions stationary; perturb a slab of plasma by shifting electrons a distance δ. Displacement of a sheet of electron creates an electric field (2.18) δ is a function of time. 14
15 Response Time and Frequency The equation of motion of the electron sheet is (2.19) where From (the previous) equations (2.20) 20) 15
16 Response Time and Frequency 16
17 Classification of Plasmas Fig
18 Classification of Plasmas (Coulomb potential ) (2.21) 21) (2.22) 18
19 Three approaches to plasma physics Three Basic Approaches to plasma physics: Hydrodynamic Kinetic Particle description description description 19
20 Hydrodynamic description Conservation laws of mass, momentum and energy coupled with Maxwell Equations. Local thermodynamic equilibrium (LTE) and the knowledge of the equation of state (relations between pressure, temperature, energy, entropy, etc.) required. Fluid theory is a good approximation for many phenomena in the interaction of plasma with relatively low laser intensities and relatively long laser pulse. System thatt are not in LTE (such as plasma interacting ti with intense femtosecond laser pulse). 20
21 21 Kinetic description
22 Particle description The particle theory approach Equations of motion for the individual plasma particles. Plasma is described by electrons and ions moving under the influence of the electric and magnetic fields due to their own charge and of the laser fields. 22
23 Equations of Plasma Physics 23
24 24 Self Consistency
25 Plasma-Solid Boundaries When a plasma is in contract with a solid, the solid acts as a sink draining i away the plasma. Recombination of electrons and dions occur at surface. Then: 1. Plasma is normally charged positively with respect to the solid. 2. There is a relatively thin region called sheath, at the boundary of the plasma where main potential variation occurs. 25
26 Occurrence of Plasmas Gas Discharges: Fluorescent Lights, Spark gaps, arcs, welding, lighting Controlled dfusion Ionosphere: Ionized belt surrounding earth Interplanetary Medium: Magnetospheres of planets and starts. Solar Wind. Stellar Astrophysics: Stars. Pulsars. Radiation--processes. Ion Propulsion: Advanced space drives, etc. & Space Technology Interaction of Spacecraft with environment Gas Lasers: Plasma discharge pumped lasers: CO 2, He, Ne, HCN. Materials Processing: Surface treatment for hardening. Crystal Growing. Semiconductor Processing: Ion beam doping, plasma etching & sputtering. Solid State Plasmas: Behavior of semiconductors. 26
27 Problems Q2.1. A2.1. Is plasma a good conductor or bad conductor? Good Conductor. Q2.2. A2.2. Calculate the Debye length of plasma created in laser solid interaction with an electron temperature t of 1keV and an electron density of cm -3. Debye length = 7.5 Angstrom. Q2.3. Calculate plasma frequency if plasma electron density of cm -3. A cm -3. Q2.4. A2.4. On what parameters the quasineutrality of plasma depends? Density and Temperature. Q2.5. A2.5. True or False. The Vlasov equation is reversible. True. 27
28 Problems Q2.6. A2.6. Q2.7. A2.7. Q2.8. A2.8. Q2.9. A2.9. True or False. The Vlasov equation describes the conservation of particles in self consistent phase space flow. True. Mention the three most fundamental plasma parameters? Plasma Frequency, Debye Length and Plasma Parameter. True or False. In an isotropic plasma (in absence of magnetic field) electromagnetic wave can propagate with a frequency below the plasma frequency. False. How do you explain the Vlasov equation? A differential equation which describe the evolution of the distribution function of plasma particles with long range Coulomb interaction. Q2.10. Why electrons move faster than ions in plasma? A2.10. Mass difference. 28
29 References 1. F. F. Chen, Introduction to Plasma Physics, (Plenum Press, New York, 1974). 2. R. J. Goldston and P. H. Rutherford, Introduction to Plasma Physics, (Institute of Physics Press, Bristol, 1995). 3. P. M. Bellan, Fundamentals of Plasma Physics, (Cambridge University Press, Cambridge, 2006). 29
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