Chemistry Reference
In-Depth Information
The integral on the right-hand side is the so-called line-integrated density or simply
the line density, the quantity aimed at. If ϕ has been measured, the line density can
readily be evaluated from (6.13). The approximation is usable for ω
/
ω
pe
≥
2.
To gain local information
N
e
(
)
a number of sightlines through the plasma and
model assumptions on the density distribution are necessary. In case of circular
density distribution Abel inversion on the basis of multi sightline measurements is
possible [94,103].
r
6.2.3 E
XPERIMENTAL
A
RRANGEMENTS
6.2.3.1 Mach-Zehnder Interferometer
The basic microwave interferometer in Mach-Zehnder arrangement is given in
Figure 6.4. The signal generated by a microwave source with angular frequency
ω is launched into the plasma with a horn antenna and collected with another one
then guided to the phase meter. The reference path is generated by splitting and
combining a part of the signal with the aid of directional couplers, guiding it along
a path of equal length to the phase detector as well. Using in this basic arrangement
a detector diode as the simplest phase meter, the combined microwave signal and
reference amplitudes at the diode
V
D
=
(
−
)
+
A
S
cos
ω
t
ϕ
A
R
cos ω
t
,aremixedby
−
V
characteristic
I
D
=
a
0
+
a
1
V
D
+
a
2
V
D
+
...
the quadratic term of the diodes
I
,to
give a dc diode current component proportional to
A
S
A
R
cos ϕ from which the phase
can basically be determined [93,103,105]. Phase and amplitude adjustments for max-
imum phase sensitivity can be made in the reference path. The phase measurement is
improved by introducing another diode detector with the reference signal shifted by
90
◦
to generate a dc diode current proportional to
A
S
A
R
sin ϕ. From cos ϕ and sin ϕ,
the phase ϕ can uniquely be determined [106-109].
6.2.3.2 Heterodyne Interferometer
Direct phase measurement is possible by operating the probing and the reference path
at slightly different frequencies after mixing the two as shown in Figure 6.5.
The signal
A
S
cos
carrying the phase information as introduced by the
plasma is mixed with the reference signal
A
R
cos ω
2
t
in a microwave mixer M
S
generating the intermediate frequency (IF) signal
A
IF
cos
(
ω
t
−
ϕ
)
(
ω
IF
t
−
ϕ
)
at frequency
ω
IF
=
ω
2
[105,110,111]. The mixing process is phase preserving. The phase
shift ϕ introduced at the signal frequency ω
1
by the plasma transit is transferred
to the intermediate frequency. Typically the IF frequency is chosen in the range of
several tens of MHz that standard radio frequency techniques can be applied for
accurate phase measurements (see below). The reference for the phase measurement
is generated by directly mixing the signals of the two oscillators at ω
1
and ω
2
in
reference mixer
M
R
. In the mm-wave range at probing frequencies of the order of
100 GHz, the two separate oscillators are typically locked to each other in a so-called
phase locked loop (PLL) using a stable quartz oscillator at difference frequency
ω
IF
as the reference, to keep the difference frequency constant. The offset signal
at ω
2
can also be derived from the probing oscillator signal at ω
1
introducing the
frequency shift by applying single sideband modulation (SSBM) techniques [111],
or by introducing it as a Doppler shift with the classical Veron-wheel [103,112,113].
ω
1
−
