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Open Research Online The Open University’s repository of research publications and other research outputs Electro-acoustic coupling in a plasma gas Thesis How to cite: Sutton, Yv onne (2011 ). El ec tro- acoustic couplin g in a plasma gas . PhD thes is The Open Univer si ty. For guidance on citations see  FAQs. c 2011 The Author Version: Version of Record Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owne rs. F or more information on Open Researc h Online’s data  policy on reuse of materials please consult the policies page. oro.open.ac.uk

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8/17/2019 yvonne_sutton_thesis Electro-acoustic coupling in a plasma gas.pdf

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Open Research OnlineThe Open University’s repository of research publicationsand other research outputs

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.

For guidance on citations see FAQs.

c 2011 The AuthorVersion: Version of Record

Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or othercopyright owners. For more information on Open Research Online’s data policy on reuse of materials pleaseconsult the policies page.

oro.open.ac.uk

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%

%

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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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%

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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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±

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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

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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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