等离子体基本特征I-美国某高校等离子体讲义系列

2 2 ne ne d W = ∫ e y0 dy0 = ε ε0 2 0 0 d
Mean Thermal Energy
kTe ne λ = 2 ε0 2
2
2 D
Ey =
ε0
y0
ε 0 kTe λD = 2 ne
1/ 2
Te = 69 n
ρ ∇⋅ E = ε0
dE y dy = ne
+ + - + + - Ey + + - + + - 0
+ + + + -
+ + + + -
+ + + + -
+ + + + -
+ + + + -
+ + + + y
+ + - + + - Ey + + - + + - 0
+ + + + + + + + y0
qe − 2r / λD Φ(r ) = 4πε0r
Page 131
[ n ∆ x = ( n + δ n ) { x 1 + ξ ( x 1 ) ] − [x + ξ ( x ) ]}
∆x
before
ne x x1
dξ ≅ ( n + δ n ) x1 + ξ ( x ) + ∆ x − [x + ξ ( x ) ] dx dξ = ( n + δ n ) 1 + ∆x dx
1/ 2
Solid 0
Sheath x
Φ(x)
Plasma
ne=ni=n for x>>λD λ
Φ0
d 2Φ ρ ( x) 1 ne − =− = − (ni ( x) − ne ( x)) = − (e 2 dx ε0 ε0 ε0
Taylor Expansion:
eΦ ( x ) kT
−e
eΦ ( x ) kT
EE 403/503 Introduction to Plasma Processing
October 19, 2004
105
Thermonuclear Plasmas
104
Average Electron Energy, [eV]
Electron Beam
103
Solar Corona
102
101
Glow Discharge Arc Discharge MHD Generator
100
Ionosphere
ν p = 8.97 × ne
Solid
Hz
10-1 100 102 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024
Electron Number density, [cm-3]
Interstellar Gas Gaseous Nebulae
Glow Discharge Arc Discharge MHD Generator
100
Ionosphere Solid
10-1 100 102 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024
1/ 2
[m]
Solid 0
Sheath x
Φ(x)
Plasma
ne=ni=n for x>>λD
Φ nve ekT0 Γe = n ∫ v x f e (v x )dv x = e 4 vx >vx 0
Φ0
nvi Γi = 4
1 2 me v x 0 ≡ −eΦ 0 2
Γ e = Γi
kT ve kT mi − Φ0 = ln = ln e e me vi
=
ω
p
2π
= 8 . 97 ×
ne
[sec-1]
after
ξ(x)
ξ(x1)
n − ndξ / dx dξ δn = −n = ≅ −n dx 1 + dξ / dx 1 + dξ / dx
Assuming dξ/dx << 1
n+δn(x)
dξ δn ≅ − n dx
∆x
before
dE x eδn ne dξ =− = dx ε0 ε 0 dx Ex ( x) = ne
)
d 2Φ ne eΦ eΦ 2ne 2 2 (1 − − 1− +...) ≅ Φ= 2 Φ 2 = − dx kT kT ε0 ε0 kT λD
Approximate Solution
Φ( x ) = Φ 0e
−
2x
λD
Particle
Sheath r
q
Plasma
eΦ ( r ) 1 d 2 dΦ ne − eΦ ( r ) − (r ) = − (e kT − e kT ) r 2 dr dx ε0
e
ν radiation > ν P
ionosphere
ωp = 2πνp
To the highest part of atmosphere
Reflection
Earth
2 ω P = 56 . 36 n e ⇔ n critical = 0 . 0124 ⋅ ν radiation
25 miles
Debye Length
λD = 69 ×
Te ne
[m]
104
Average Electron Energy, [eV]
103
νP = 100 MHz
νP = 10 GHz
νP = 1 MHz
102
νP = 100 Hz
νP = 1 THz
Plasma Frequency
101
Interstellar Gas Gaseous Nebulae
ne
+ + + + -
+ + + + d
+ + + + -
+ + + + y
ne
Ey = 0
Ey =
ε0
y
Ey =
ε0
y0
ε0
+ + - + + - Ey + + - + + - 0
+ + + + + + + + y0
ne
+ + + + -
+ + + + d
+ + + + -
+ + + + y
The work necessary to move each electron an additional distance d is:
Two fundamental Plasma Parameters Debye Length
Te λD = 69 × ne
Plasma Frequency
[m]
ωp νp = = 8.97 × ne 2π
[sec-1]
105
Thermonuclear Plasmas Electron Beam Solar Corona νP = 10 KHz
ν radiation < ν P
A fluctuation in electrons charge density set up an electric field
∇ ⋅E = −
3.
n
ε0
∂ 1. × ∂t
eE ∂ue = − me ∂t 2. ∂n + ∇ ⋅ ( nu e ) = 0 ∂t
Electron Number density, [cm-3]
Debye Length, λD
Link
1- Charge Neutrality 2- Plasma Sheaths 3- Shielded Coulomb Potential Plasma Frequency, νp or ωP Plasma Response Time
ne2 ∂ 2 δn = 0 2 δ n + ∂t ε0m e
Charge density fluctuation will oscillate with frequency ωP
Debye Length
λ D = 69 ×
Te ne
[m]
Plasma Frequency
ν
p
ε0
ξ ( x)
ne x x1
d 2ξ ne 2 me 2 = − eE x ( x + ξ ) ≅ − eE x ( x ) = − ξ dt ε0
Harmonic motion
after
ξ(x)
ξ(x1)
n+δn(x)
ωP =
ne = 56 .36 n e ε0me
2
ne<ncritical ne ne>ncritical