Lectures on basic plasma physics: Introduction

Transcription

1 Lectures on basic plasma physics: Introduction Department of applied physics, Aalto University Compiled: January 13, 2016

2 Definition of a plasma Layout 1 Definition of a plasma 2 Basic plasma parameters 3 Magnetized plasmas 4 Summary

3 Definition of a plasma What are the four fundamental states of matter?

4 Definition of a plasma Phase transitions A gas is usually converted to a plasma either by a huge voltage difference between two points, or by exposing it to extremely high temperatures. Heating matter to high temperatures causes electrons to leave the atoms, resulting in the presence of free electrons. At very high temperatures essentially all electrons are free, bare nuclei swimming in a sea of electrons.

5 Definition of a plasma Distinguishing features of a plasma Like a gas, plasma does not have definite shape or volume. Unlike gases, plasmas are electrically conductive, produce magnetic fields and electric currents, and respond strongly to electromagnetic forces. Each particle influences many nearby particles leading to collective behaviour This is a distinguishing feature of a plasma

6 Definition of a plasma Various plasmas

7 Definition of a plasma Background check Statistical representation of a gas... Temperature is statistical measure of kinetic energy k B T s = 1 3 m s v 2 s (1) Thermal speed of each species 2kB T s v ts = (2) m s Maxwellian velocity distribution f(v)dv v 2 exp ( v 2) dv Maxwells equations...

8 Basic plasma parameters Layout 1 Definition of a plasma 2 Basic plasma parameters 3 Magnetized plasmas 4 Summary

9 Basic plasma parameters The most fundamental plasma parameters Debye length Plasma frequency Coulomb logarithm

10 The effect of the test charge qδ(r) falls off significantly faster compared to that of an unshielded point charge Lectures on basic plasma physics: Introduction Basic plasma parameters Debye length: Plasma tends to shield out electric field assume plasma species in thermal equilibrium and globally neutral plasma, i.e. N i = N e (as many ions as electrons) n e (r) =n 0 e (eφ(r)/kt ), n i (r) = n 0 e ( eφ(r)/kt ) (3) Introduce an external charge qδ(r) perturbation in the scalar potential δφ (exercise problem) will be δφ(r) = qe r/λ D (4) 4πɛ 0 r where the characteristic length scale is called the Debye length λ D ( ) 1/2 ɛk B T λ D = N j=1 n (5) jqj 2

11 Basic plasma parameters Plasma frequency Lecture assignment: work out the expression for the plasma frequency ω 2 ps = n sq 2 s ɛ 0 m s (6) You may assume: a hydrogen plasma (only protons and electrons), protons are fixed while the electrons are free to move around You should, thus, get the electron plasma frequency, i.e. s = e in the above equation.

12 Basic plasma parameters Solution: When a block of electron plasma is displaced by an infinitesimal distance δx, the electric field at the original position will be (Gauss law) E = qnδx/ɛ 0. Now, the electrons will experience a force: Newton s law md 2 δx/dt 2 = qe. The solution is oscillatory with a frequency of ω 2 = nq 2 /mɛ 0 Hence, the electrons start to oscillate around the static ions. Can you give a reason why we assumed fixed ions?

13 Basic plasma parameters Plasma parameter The number of particles inside a Debye sphere Λ = 4πnλ 3 D T 3/2 n 1/2 (7) cold and dense plasmas are strongly coupled, i.e., individual particles continuously dominated by another s electrostatic influence can be approximated as a charged fluid hot and dilute plasmas are weakly coupled can be described with Fokker-Planck equation (like for neutral gas)

14 Basic plasma parameters Collisions Neutral gas has binary collisions, a few large angle collisions In plasma, charged particles collide with Coulomb collisions, many small angle collisions Typical collision frequency (We will discuss Fokker-Planck equation later) ν c e4 ln Λ 4πɛ 2 0 m1/2 n T 3/2 (8) hot plasmas are less collisional than cold plasmas. WHY? Remember: strongly and weakly coupled plasmas...

15 Magnetized plasmas Layout 1 Definition of a plasma 2 Basic plasma parameters 3 Magnetized plasmas 4 Summary

16 Magnetized plasmas Magnetized plasmas Plasma is called magnetized, if the particle trajectories are governed by magnetic field B All the plasmas we consider, are magnetized (fusion devices, space)

17 Magnetized plasmas Magnetized plasmas Charged particles gyrate around magnetic field line with Cyclotron-frequency Ω = qb m (9) Lecture assignment: What is the expression for gyration radius r L, i.e., Larmor radius? Assume a constant magnetic field and calculate the radius of the gyration.

18 Magnetized plasmas Larmor radius Solution: The Lorentz force acts only on the perpendicular (to the magnetic field) velocity component, i.e. v. Equal the magnitude of the Lorentz force to a magnitude of a centripetal force F c, i.e. F c = mv2 r L = qv B (10) r L = mv qb = v Ω (11)

19 Summary Layout 1 Definition of a plasma 2 Basic plasma parameters 3 Magnetized plasmas 4 Summary

20 Summary Summary Plasma frequency ω p, Debye length λ D and the plasma parameter Λ are the fundamental plasma parameters: Collective plasma behavior on time-scales longer than plasma frequency, which is the highest frequency plasma can sustain Collective plasma behaviour on length-scales larger than Debye-length Statistical character (closer to a liquid or gas) is described by Λ Collisions are important and will be discussed later on All the plasmas we consider are magnetized