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8/17/2019 yvonne_sutton_thesis Electro-acoustic coupling in a plasma gas.pdf
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Electro-acoustic coupling in a plasma gas
ThesisHow to cite:
Sutton, Yvonne (2011). Electro-acoustic coupling in a plasma gas. PhD thesis The Open University.
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z
µ
µ
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Lp
µ Ls
C s
%
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R
X
r
r
Rp X p
R0 X 0
r
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z
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z
rms ±
rms
z
I
rms
%
z
z
%
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z
t
µ
µ
µ
z %
%
%
%
z
z
%
%
z
T r
T v r
z
%
z
z
%
%
z
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yi
z
%
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z
r
I rms ua
z
z
r
z
I rms
z
z
I rms
z
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T g
T r
z
z
%
r
t
z
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2
2
2+
T r
T v
T g
ua
ub
uc
U
n
(n− 1)
ε
a
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&
&
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tys
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∆P = ∆ngkT g + ngk∆T g
∆P
∆T g
T g
k ng N/V
N
V
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%
%
%
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RI 2
∇2 p−
1
c2
∂ 2 p
∂t2 =
(γ − 1)
c
∂H
∂t −divF
γ
c
H = (4me
mn)(mev
2e
2 )nenn(σ)
ve
m
n
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H
ne
H
I 2R
R
τ
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L
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Lp Ls C s
p−p
p−p
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Lp
µ Ls
C s
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Ω
π
f rms = 1
b− a b
a [f (t)]2
dt
f rms
f (t)
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AMsignal = [A+ f (t)] cos(ωct)
ωc
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V mod
I dmod = C dV mod
dt
C
±
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%
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µ
SPL = 20 log P eP ref
P e
P ref
µ
µ
&
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&
&
&
&
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rms rms
±
±
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THD =
(n
(i=1) V 2
i )
V 0
V i
i
V 0
%
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%
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τ TD
τ T D = L2
αair
αair
κair
ρairC air
C air
ρair
κair
L
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Z r = ρ0cS cos θae jθa
ρ0
c
S
θa ka
k
a
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R
X
r
r
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Rp X p
R
0 X
0
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r
r
o
o
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±
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±
µ
%
%
%
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±
µ
µ
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3Πg
3Πu
∆
2
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µ
2
z
µ
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2
2
2
3Πg
2
3Πg
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E
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z
p−p
σ
σ = I
V
l
πr2
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I
V
l
r
ne
ne = σmeν
e2
e
me
ν
ν
vngσN
ng
v
σN
17
−3
17
−3
P ∝ I 2
%
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z
z
2
2
2+
2+
3Πg
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2 2
v
2
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%
%
z
2
2 2
γ
2
2
2
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z
2
2
2 2
3Σu+
3Πg
2
2
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z
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z
rms
±
→
2
3 →
2
2
γ
x
T r
T v
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rms z
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T r
T v
T r
T g
T g
T v
T v
T v
T v
E
T v
T r T v
T r
T r
T v
T v
T r
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T g
T r
T v
±
T r
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x
x 2
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x
x
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I
rms
T v
2
2
2
2
2
2
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±
±
±
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T v
T r
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∆t
T
µ
∆t
µs
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y
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P (t) = V (t)I (t)
V (t)
I (t)
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%
µ
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o
o
o
%
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z
z
%
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E
z
E
E
E
µ
%
z
I
IntVIS
IntN2C
µ
Int
vis
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z
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±
o
RVIS
±
%
RUV
±
%
2
2
%
2 %
%
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t
µ
µ
µ
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z
%
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%
S rad
2 ne
S rad
µ µ
%
%
z
z
T r
T v
T r
T v
P
T r
T v
T r
±
±
%
T v
±
±
%
T r T v
%
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%
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%
z
z
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P
±
%
P
T v
µ T v
T r µ
µs T r
ν
ν = vngσ
v
ng
σ
T r
v =
2
me
me
σ
−23
2
ν
7
−1
∼ µ
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σ
−24
2
∼ µ
T v
P
T v
%
%
z
T v
T r %
T r
T v r
T r
T v
z
r
±
r
z
%
T v
T g
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%
z
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T r
T v r
z
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T v
T g Q
Q
T v
µ T v
T g µ
Q
T v
T v
±
%
±
%
z
T g
T r T g ± %
±
%
z
T r T g
T r
T g
%
T v
%
%
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%
%
z
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o
U = P acz s
P ac
z
U
RUV
Z r = ρ0cS cos θae jθa
ρ0
c
S
θa
ka
k
a
Z r
z
z s = Z rS
S
θ
kr
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θ → 0
kr
π
π
%
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%
δp
p =
γ
γ − 1
δT
T
p
δp
T
δT
δT r
±
T r
±
T v
T g
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±
±
Intac
Intac = P 2rms
cairρair
P rms
cair ρair
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εy
n
εy ∝ ∂n
∂y
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εy
∆a
∆a = f focεy
f foc
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a
∆a
a
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n− 1
if i ni − 1
ni
f i
i
(n− 1)e = − 1
4πε0
e2λ2
2πmec2ne
(n− 1)+,N = 1
4πε02α+,N (λ)n+,N
ne
n+,N
λ
α+,N
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18
−3
23
−3
con f
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col f
foc f foc
y
x
im f
µ
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a
±
± %
a
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±
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%
%
%
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λ
±
%
±
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∆E
E
y
E
∆a
a =
∆E
E
ε = a
f foc
∆E
E
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yi
yi
n(r)
ε(y) = 2y
∞
y
d(n− 1)
dr
dr
(r2 − y2)1/2
n(r)− 1 = −1
π
∞
r
ε(y) dy
(y2 − r2)1/2
n(r)
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n(r)− 1 = κρ(r)
κ
−3
3
T (r) = pρ(r)Rs
p
Rs
R/M
R
M
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%
±
Ω
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%
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r
r
±
z
r
±
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z
r
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r ≥
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r
r
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I rms
ua
r
z
ua
z
±
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z
8/17/2019 yvonne_sutton_thesis Electro-acoustic coupling in a plasma gas.pdf
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z
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r
z
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I rms
z
I rms
z
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z
y
r
z
I rms
z
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z
I rms
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2
z
r
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T g
T r
z
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z
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(n− 1)
%
%
T
µ
%
%
z
(n− 1)
(n− 1)
z
(n − 1)
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z
z
(n− 1)
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±
z
r
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o
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E
ne
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2 2
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p− p
p− p
±
f
I rms
ne
17
3 I rms
z
I rms
T v
z
I rms
T r
z
I rms
z
I rms
% f
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± ub
uc
U
k
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Ω
±
%
Ω
±
%
±
%
±
%
±
%
p−p
%
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%
±
ub
ub
uc
U
k
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±
ub
ub
uc
U
k
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E (x) = I 2π R0 σ(x, r)rdr
,
∂
∂x (ρu) +
1
r
∂
∂r (rρv) = 0,
ρu∂u
∂z + ρv
∂u
∂r = −∂p
∂z − ρg,
ρu∂v
∂z + ρv
∂v
∂r = 0.
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σ
σ
eµe e µe
ρ
εV
ρuC ∗p∂T
∂z + ρvC ∗p
∂T
∂r = ηTσE
2 + QVT + 1
r
∂
∂r
χ∗r∂T
∂r
,
nN2u∂εV∂z
+ nN2v∂εV∂r
= ηVσE 2 −QVT +
1
r
∂
∂r
nN2DVr
∂εV∂r
,
k
∂
∂z (nku) +
1
r
∂
∂r (rnkv) =
1
r
∂
∂r
Dkr
∂nk∂r
+ F k.
χ∗
nN 2 DV
2 ηT
ηV
2 Dk
k
De
F k
QV T
2
ηT
ηV
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2 2
+
− 2
− 3
−
2 2
ωδν
ω ν ν
Kexp(−Bn/E )
<
>
K amp
E amp π
1/2
E amp
K amp
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−
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&
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