等离子体物理基础(英)全册精品完整课件.ppt
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1、等离子体物理基础等离子体物理基础(英文)全册英文)全册 精品完整课件精品完整课件 Chapter 1 Introduction 1.1 Definition of plasma A plasma is a quasineutral gas of charged and neutral particles which exhibits collective behavior. 1.2 Characterization of plasma 1.2.1 Plasma density e n ei nn Electron density Ion density Quasineutral conditi
2、on i n 1.2.2 The temperature of plasma 32 2 ( )()exp() 2 2 m mv fn kT kT v 2 13 22 mvkT Maxwellian distribution at thermal equilibrium The mean kinetic energy e T i T g T Electron temperature Ion temperature Gas temperature 2 3 ee kT 2 1 2 eee m 1eV e kT The electron temperature at nonequilibrium is
3、 defined as , 1eV = 11600 K . It is called as kinetic temperature. The temperature in units of energy eV for example 1.3 Classification of plasma 1.3.1 Cold plasma The plasmas can be generated by a direct current glow discharge, a high frequency or a microwave discharges at low pressures. The plasma
4、 is called a nonequilibrium plasma. Plasma in a processing reactor (computer model, by M. Kushner) 1.3.2 Thermal plasma The plasmas are generated by the arc discharges with the temperature eig TTT :p : e n 163 10 cm : e T The plasma is at thermal equilibrium. over 100 Torr 2000K50000K ,: ei T T The
5、plasma used for controlled thermonuclear fusion 104 eV (108K) Plasmas are also classified as low temperature plasma and high temperature plasma. 1.4 Debye shielding and Debye length Let us introduce a negative charge into a plasma having equilibrium densities . We assume immobile ions, such that 0ei
6、 nnn 0i nn Poissons equation after the charge is introduced. 2 0 ( )() ie e rnn (1-1) From the Boltzmann relation, we set 0 exp() e e e nn kT (1-2) i e Substituting for ne and ni in Eq(1-1), we have 2 0 0 ( )(1) e e kT en re (1-3) exp() e e kT e ekT Expanding in a Taylor series for , Eq(1-3) becomes
7、 2 2 0 2 0 1 () e ndde r r drdrkT (1-4) ( ) DD rr AB ree rr ,0r 0 0, 4 q r r The general solution is (1-5) 0 ( ) 4 D r q re r 1 0 2 D 2 0 () e kT n e the solution becomes (1-7) (1-6) where The quantity D D is called the Debye length. Using the condition 3 7.0 10 cm D D We find for glow discharge n0
8、=1010cm-3 and kTe =1 eV that The Debye length serves as a characteristic scale to shield the Coulomb potential in plasma. D D It is also the characteristic scale of the quasi-neutrality region in plasma. Imagine that the neutrality is disturbed in some volume of the plasma. We assume for simplicity
9、that this disturbance is due to the displacement of a plane layer of electrons. 1.5 Plasma oscillations Fig.2-1 e n ex e o n ex E The surface density of the charge on the plates is (1-8) The electric field E is determined (1-9) The electron motion equation has the form 22 2 e e o n e xd x m dt (1-10
10、) It describes harmonic oscillations with a frequency of 2 12 () e pe oe n e m (1-11) The frequency is accordingly called the plasma frequency or electron plasma frequency. Therefore the time scale of charge separation in a plasma is determined by 12 2 1 () oe D pee m n e (1-12) 8980 2 pe pee fn Hz
11、The frequency in practical units can be written (ne in cm-3 ) (1-13) Plasma frequencies for discharges are typically in the microwave region (1-10GHz). If the assumption of infinite mass ions is not made, then the ions also move slightly, we obtain the plasma frequency 1 22 2 () ppepi 2 12 () o pi o
12、 e n M (1-14) where (1-15) is the ion plasma frequency. For Mm, ppe . 1.6 Criteria for plasma D L D 1 3 0D n The dimensions L of a system are much larger than The three conditions a plasma must satisfy are: 1. 2. The picture of Debye shielding is valid only if there are enough particles in a “Debye
13、sphere”. If there are only one or two particles in the region, Debye shielding would not be a statistically valid concept. 3. pc We require the third condition for the gas to behave like a plasma rather than a neutral gas. exp() j jo j q nn kT 1 2 2 () oei D eio kTT TT n e D Show that the shielding
14、distance is then given approximately by and that is determined by the temperature of the colder species. Problem 1-1 In a strictly steady state situation, both the ions and the electrons will follow the Boltzmann relation. Chapter 2 Single particle motions 2.1 Uniform magnetic field d mq dt v vB In
15、this case, the equation of motion for a particle is (2-1) zB()BzB Taking to be the direction of , we have 0 x y d mqB dt 0 y x d mqB dt 0 z d m dt (2-2a) (2-2b) (2-2c) Differentiating (2-2a) and (2-2b), we obtain 2 2 00 2 y x x d dqBqB dtmdtm 22 00 2 y x y d qB dqB dtmdtm (2-3a) (2-3b) 2.1.1 Particl
16、e motion with E=0 00 cos xct 00 sin yct 0zz where Solving (2-3) and (2-2), we find (2-4a) (2-4b) (2-4c) 0 c qB m (2-5) o 0 B 0 is the cyclotron frequency, and is the speed perpendicular to , and is an arbitrary phase. 00 sin o c c xtx 00 cos o c c yty /0 ztz Integrating (2-4) yields the particle pos
17、ition (2-6c) (2-6a) (2-6b) 22 2 00c xxyyr 0 oo c c m r q B Using (2-6a) and (2-6b), we have (2-7) where (2-8) is defined the Lamar radius. The direction of the gyration is always such that the magnetic field generated by the charged particle is opposite to the externally imposed field. Plasmas are d
18、iamagnetic. Fig.2-1 2.1.2 Finite E EB d mq dt v EvB The equation of motion in uniform and (2-11) (2-9) EEE BWe take . We obtain a uniform acceleration along . d mqq dt v vBE c D vvv The equation for the transverse motion is (2-10) We let Putting (2-11) into (2-10), we have d mqqq dt c cD v vBvBE (2-
19、12) c v 0qq D vBE Since is the velocity of gyration, we obtain (2-13) 2 B DDD E BBvBvB vB Taking the cross product with B, we have (2-14) 2 B D EB v The electric drift velocity is (2-15) D v EB is perpendicular to both and is independent of the mass and charge of the particles. It is important to no
20、te that and , Fig.2-2 2.1.3 Gravitational field qE FF The foregoing result can be applied to other forces by replacing in the equation (2-15) by a general force is then . The drift caused by 2 1 qB f FB v (2-16) F mg 2 m qB g gB v In particular, if is the force of gravity , there is a drift (2-17) g
21、 vB The drift is perpendicular to both the force and but it changes sign with the particle charge. , There is a net current density in the plasma given by 2 n Mm B gB j (2-18) Fig.2-3 2.2 Non-uniform magnetic field 2.2.1 Gradient drift ( ) d mq dt v vB r ( )( )( ) 0c0 B rB rrB r The equation of moti
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