TD C5 - Correction 1 Propagation d`une onde dans le plasma

ωp2=c2K2
k
k2>0ω > ωp
k=±√ω2−ωp
2
c
vφ=ω
|k|=ω c
ω2−ωp2vφ=c1 + K2
k2
vg
2k k =2ω ω
c2vφvg=c2
vg=c
1 + K2
k2
δt =t2−t1=L
vg2−L vg1
=L
c
1 + λ22K2
4π2−1 + λ12K2 4π2
ω1≫ωpω2≫ωp
δt =K2L
8π2cλ22−λ12

t x = cste
−→
uxωt −kx
t
−→
E //⃗ k
−→
B=
⃗
k∧−→ E
ω
−→
E−→ k−→ B=−→ 0
m−→
ve
t=−e−→
E
−→
j=−n0e−→ ve
∂−→ j
∂t =−n0e∂−→
ve
∂t
∂−→ j
∂t =n0e2 m−→
E
−→−→
B=µ0−→ j+µ0ε0
∂−→ E
∂t
−→
j+ε0
∂−→ E
∂t =−→
0
−→
E
∂2−→ E
∂t2+n0e2 ε0m−→
E=−→ 0
−→
E
ω2=ωp2ωp=n0e2
ε0m
ω
vg=ω
k= 0

u+ec= cste
ε0∂−→
E
∂t
−→
j=γ−→ E
||ε0
∂−→ E
∂t ||
||γ−→ E|| =ε0ω
γ=2πε0ν γ
10−18
1014
||ε0
∂−→ E
∂t ||
||γ−→ E|| ≪1
(MT )ik−→ ux·−→ B= 0
(MG)ik−→ ux·−→ E= 0
(MF )ik−→ ux∧−→ E=iω−→ B
(MA)ik−→ ux∧−→ B=µ0γ−→ E

−→
B
−→
B=k
ω−→
ux∧−→ E
ik2
ω−→
ux∧−→ ux∧−→ E=mu0γ−→ E
−ik2
ω=µ0γ
k2=iµ0γω
k=±eiπ
4√µ0γω =±(1 + i)µ0γω
2=±1 δ+i δ
δ=2
µ0γω
x
−→
E=E0exp −x
δexp [i(k0x−ωt)] −→
uz
k0=1
δδ
δ