**Conceptual Design Study for**

**ITER Divertor Interferometer Diagnostic**

***D.L. Brower***

***University of California at Los Angeles***

**14 December 2005**

**Conceptual Design Study for**

**ITER Divertor Interferometer Diagnostic**

> **Diagnostic Requirements:**

The ITER design report calls for a measurement of the divertor electron
density. Specifications given for this measurement are

1.  density range from 10^19^ to 10^22^ m^-3^, no density resolution is
    specified but a minimum of 1% should be required.

2.  time response of 1 msec, and

3.  spatial resolution of 5 cm along the leg and 3 mm across the
    divertor leg.

4.  Realtime density output is not specified but presumed necessary for
    ITER operations

These specifications were originally put forward when various
reflectometer systems were envisioned for each divertor leg. At present,
for the ITER divertor interferometer system, the lines of sight planned
are shown in Fig. 1, which shows 5 chords (\~10 cm spacing) on the outer
leg and 3 chords (\~20 cm spacing) on the inner leg. This is considered
to be the maximum number of chords that will be available. Other
possibilities put forward in ITER documents are 4 outer and 2 inner
chords or even a reduced set of 2 outer and 1 inner chord is possible.

**Regarding the density range:** The density range anticipated for the
ITER divertor and the range which must be covered by the interferometer
spans three orders of magnitude. For any interferometer system envisaged
for ITER, no single wavelength can cover the entire density range from
10^19^ to 10^22^ m^-3^, with the density resolution of 1%. It is not
specified whether the peak density of 10^22^ m^-3^ would occur
continuously in time or be limited to discrete events such as giant ELMs
which would last \~1-10 msec. If the peak density were only reached
during discrete short duration events, then it might be possible to lose
phase during the event (and density information) and have the
interferometer recover immediately after the event. This would
considerably reduce the design constraint. More on this later. The
anticipated electron density distribution for a standard ITER discharge
scenario is shown in Fig. 2, where the density profile is provided for 8
different lines of sight along the outer divertor leg. The maximum
density is expected to occur along path 2 (1.8 x 10^21^ m^-3^) and
minimum along path 8 (1.8 x 10^20^ m^-3^). A minimum density of \~10^19^
m^-3^ would then occur near the wall. Divertor path lengths are
relatively short and vary from 0.05 m (Path 2) to 0.45 m (Path 8). For
purposes of this conceptual design study, we will take this discharge
scenario \[covering from 1x10^19^ m^-3^ edge(or wall) to 1.8 x 10^21^
m^-3^ core\] as the baseline for designing the interferometer system.
This discharge corresponds to an ITER divertor case with 75 MW into SOL.
For the maximum density put forward in the ITER design specifications,
we will simply scale each profile by a factor of \~5 so that the peak
density along path 2 reaches 10^22^ m^-3^. On this basis, the local
density distributions shown in Fig. 2 can be converted into line
integrals along each sight line for both the ITER divertor baseline
\[Fig. 3(a)\] and maximum density \[Fig. 3(b)\] cases.

If the divertor interferometer does actually require a capability to
measure a peak density of 10^19^ m^-3^ (assuming it is along path 8),
then all the profiles shown in Fig. 2(b) must be scaled down by a factor
of \~18. This will require longer interferometer wavelengths to obtain
the specified resolution. This situation will only be treated briefly in
this report. It is anticipated that divertor reflectometer systems
operating at frequencies up to 155 GHz (private communication with G.
Vayakis) will be able to accommodate densities from the lowest density
range up to 3 x 10^20^ m^-3^.

By comparing Fig. 1 with Fig. 2, it can be deduced that for the outer
divertor leg, path 4 most closely corresponds to the interferometer
chord labeled O1 in Fig. 1(b). This is the interferometer chord that
will see the highest peak density in the divertor. Paths 5-8 would then
correspond to chords O2-O5, respectively, in Fig. 1(b).

**Regarding the time response:** Existing interferometers systems can
easily obtain time resolution of 1 msec and even 1 μsec is readily
feasible. Interferometers with optimum time response will have the added
measurement capability of looking at both equilibrium and fluctuating
quantities. This may be important for the divertor region where density
structures (or 'blobs') may be moving down the divertor leg. A high time
response interferometer would be able to resolve these structures. Time
delay measurements from chord-to-chord would also allow determination of
the propagation velocity as well as size. Consequently we recommend
decreasing the time response to 1-10 μsec.

**Regarding spatial resolution:** For any line-of-sight interferometer
measurement, there will be ***no*** spatial resolution across the
divertor leg. Interferometers only measure
$»\lambda\int_{}^{}{n_{e}(r,t)}\text{dl}$ along a given chord (λ is the
radiation wavelength and dl is the path length in the plasma). Spatial
resolution along the divertor leg will be limited to the number of
chords. As shown in Fig. 1, this spacing is currently set at \~10-20 cm
for a very limited number of chords. Inversion of interferometry data to
obtain local density should not be considered likely due to the limited
number of chords and the lack of symmetry in the divertor region.
Meeting the spatial resolution requirements with the number of chords
specified is not possible.

> **Interferometer Diagnostic Issues to be addressed:**

1.  **optimum diagnostic technique:**

    -   standard interferometry

    -   two-color system to compensate for vibrations and thermal
        expansion

    -   single or multiple pass systems

    -   dispersion interferometer

    -   Cotton-Mouton effect interferometer

Due to the harsh environment in the ITER divertor region, a standard
single-frequency interferometer system would not be suitable. The
two-color interferometer system typically employed by the fusion
community to compensate for optical system vibrations is feasible for
ITER as it would also compensate for mechanical stresses and thermal
expansion which are expected to be significant. Due to the anticipated
large thermal expansion, perhaps up to a centimeter, development may be
required to be able to make the correction and provide realtime density
output from the phase measurement. Changes in pathlength will be much
greater than the source wavelength generating huge phase errors (many
fringes) that must be removed from the measurement. However, it is also
important to note that fringe skips are still possible (due to plasma or
instrument instability) which would result in loss of the phase
information.

A potential resolution to this problem would be to employ a
Cotton-Mouton interferometer in the divertor. In this instance, one is
measuring a phase directly proportional to
$»\lambda^{3}\int_{}^{}n_{e}(r,t)B_{{\hat{}}^{2}\text{dl}}$, where
$B_{\hat{}}$ is the perpendicular magnetic field or, for the case of
ITER, the toroidal magnetic field which is known. Using this approach,
the total measured phase is always \<\<2π thereby removing the problem
of fringe skips. In this approach, two probe beams are employed with
orthogonal polarizations (O- and X- mode). The phase difference between
the two probe beams, upon traversing the plasma, is the Cotton-Mouton
effect. Since both beams experience the same vibrations, mechanical
stresses and thermal expansion, errors induced by these effects
automatically cancel when evaluating the phase difference. If fringe
information is temporarily lost, for instance due to a giant ELM, the
correct phase is automatically recovered after the event. This type of
system has been successfully demonstrated on the WVII-AS stellarator
(Fuchs and Hartfuss, Phys. Rev. Lett. **81**,1626(1998)).

Both the two-color interferometer and Cotton-Mouton effect
interferometer systems have their strengths and weaknesses. These will
be outlined in the following section. Before proceeding, it should be
noted that the dispersion interferometer approach was considered but
eliminated due to lack of a demonstrated track record for performance
and reliability. However, if a 10.6 micron interferometer is used for
the divertor, commercial components do exist for implementing the
dispersion interferometer approach. Should future development work prove
successful, this technique can potentially be applied by inserting the
proper optical components in the probe and signal beam paths in the
diagnostic hall. Interferometer design should be kept sufficiently
flexible to allow for potential future modification. For any
interferometer approach applied, it has also been determined that a
single pass system would be most appropriate due to the harsh
environment (bad for retroreflecting optics) and refractive effects
(double pass). For some wavelength choices (e.g., 10.6 microns),
multiple passes would be useful for increasing the total phase shift,
but the downside considerations outweigh the advantages. This will be
addressed later in the discussion of wavelength choices.

2.  **wavelength selection**

Proper choice of source wavelength depends on the density range being
measured, refraction due to transverse gradients, and density resolution
required. Since the measured interferometer \[Cotton-Mouton
interferometer\] phase is proportional to the source wavelength
λ \[λ^3^\], longer wavelength is desired to increase the phase and
improve resolution. However, refractive effects are proportional to λ^2^
leading to beam deflection problems as one increase the wavelength. In
order to balance these two competing effects, the wavelength must be
chosen to maximize the total phase while experiencing acceptable beam
refraction.

For ITER densities and chord lengths, three wavelengths fall into a
range that appears potentially suitable. These wavelengths are 10.6, 57
and 118 μm which span the spectrum from the infrared to far-infrared.
Each of these sources corresponds to frequencies well above any cutoff
effects. Laser sources exist at each of these wavelengths. Using the
density profiles provided for the 8 paths shown in Fig. 2, the
calculated phase at each wavelength is shown in Fig. 4(a) for the
baseline ITER divertor case. At each wavelength, the largest phase is
measured for path 2 where the density is maximum \[although path length
is minimum\]. However, the variation from chord to chord is only a
factor of two. For the baseline ITER divertor scenario, the range of
phase is from 400-800 degrees at 118 μm, 200-400 degrees at 57 μm, and
35-70 degrees at 10.6 μm. If we scale the density such that the peak
density along path 2 is 1 x 10^22^ m^-3^, the maximum density case, the
measured phase at each wavelength would increase as shown in Fig. 4(b).
Here, the range of phase is from 2000-4000 degrees at 118 μm, 950-2000
degrees at 57 μm, and 180-360 degrees at 10.6 μm. An expanded view of
the phase plots is also shown in Fig. 4.

Since the phase noise of an interferometer is typically around 1-2
degrees at best (worse depending on vibration compensation, etc.), and a
resolution of 1% is desired, it appears from the modeling of Fig. 4,
that 57 microns (or longer wavelength) is the best choice of source
radiation wavelength. For the case of Fig. 4(a), 1% resolution would
correspond to 2-4 degrees or just above the phase noise limit for 57
microns. For the case of Fig. 4(b), 1% resolution would correspond to
10-20 degrees or well above the phase noise limit. For source wavelength
of 10.6 microns, the total phase change is too small for the Fig. 4(a)
case to obtain the desired resolution. At 118 microns, the total phase
is large in both cases, but as we'll see in the following, beam
refraction may be too large at this longer wavelength.

As mentioned earlier, employing a Cotton-Mouton (CM) interferometer
involves the measurement of the phase *difference* between the
extraordinary (X) and ordinary (O) refractive indices. In this setup,
there would be two collinear, orthogonal probe beams at offset frequency
of a \~1 MHz. Since both beams traverse the same optical path and
experience the same thermal expansion (and other mechanical stresses on
optics plus vibrations), the phase difference between the two would be
immune to these effects. This would be a huge advantage in the difficult
ITER environment. Minimum phase resolution obtainable in such a
configuration would be \~50-100 times better than for a conventional
interferometer. This has been demonstrated by the Faraday rotation
system on MST where R and L wave were used instead of X and O \[Brower,
Ding, et al., Rev. Sci. Instrum. **74**,1534-1540(2003)\].

For the same three wavelengths identified previously, plots of the
anticipated Cotton-Mouton effect phase in the ITER divertor are shown in
Fig. 5, for the baseline and maximum density cases, respectively. This
was done for the same two cases provided in Fig. 4 and the toroidal
field was taken as B~T~=6 T (outer divertor leg). For the inner divertor
leg, B~T~=7 T giving a 59% increase in the CM induced phase shift. The
range of CM phase is from 2-4 degrees at 118 μm, 0.2-0.4 degrees at 57
μm, and 0.001-0.002 degrees at 10.6 μm. If we scale the density traces
from Fig. 2 such that the peak density along path 2 is 1 x 10^22^ m^-3^,
the measured phase at each wavelength would increase as shown in Fig.
5(b). This is considered to be the maximum density scenario for the ITER
divertor. Here, the range of phase is from 10-20 degrees at 118 μm, 1-2
degrees at 57 μm, and 0.005-0.01 degrees at 10.6 μm. Existing Faraday
rotation systems can readily resolve profile information with maximum
phase shifts in the range of a few degrees. The MST Faraday rotation
system operating at 432 microns has 0.05 degree resolution with 20 kHz
bandwidth. Similar resolution should be expected for a CM
interferometer. From the above estimates, making the CM interferometer
work at wavelengths of 118 or 57 microns appears feasible. The CM effect
at 10.6 microns is too small to be measurable by existing standards for
any anticipated ITER divertor density.

If we consider the ITER discharge scenario where the maximum density in
the lowest density path (i.e., path 8) is 1x10^19^ m^-3^, then by simple
scaling the peak density in path 2 would be 1x10^20^ m^-3^. The
calculated phase shifts for this discharge are shown in Fig. 6. Only a
conventional two-color interferometer at 118 (possibly 57) microns could
be expected to provide useful density data for this low density
scenario. Phase shifts for the CM measurement would be too small to
resolve.

**Refraction:**

Another critical consideration for each of these wavelengths is the
effect of refraction. No detailed ray tracing has been done to evaluate
this effect but a simple (crude) estimate has been performed. Here x is
taken the direction perpendicular to the chord and y is the path along
the chord. The equation used to estimate the refractive effects is

$\alpha_{\text{Re}f}»\int_{0}^{L}\frac{1}{2\left( n_{c} - n_{e}(r) \right)}\frac{\text{dn}_{e}}{\text{dx}}\text{dy}»\frac{L}{2\left( n_{c} - n_{e0} \right)}\frac{{Dn}_{e}}{Dx}$,

where n~c~ is the critical density for a given wavelength and n~e0~ is
taken as the peak density along the chord. In this calculation, the
density is treated as a constant along the chord (making the estimate an
upper bound) and the transverse gradient is estimated by simply taking
the perpendicular gradient, dn/dx, for adjacent paths shown in Fig. 2.
This serves only as a crude estimate (perhaps within a factor of 2) and
more detailed ray tracing is required to evaluate this parameter more
accurately.

The results for ITER density cases used in Figs. 4 and 5 are shown in
Table 1. This refraction angle leads to a deflection of the beam which
causes a displacement at the receiver waveguide as compared to the *no
plasma* case. The displacement depends on the path length and is maximum
for paths 6-7 where the chord length is longer. The transverse gradient
is roughly constant from path to path. Since the waveguide being
considered presently are 1x2 and 1x1 cm in dimension (these dimensions
are subject to change), a displacement of \~1/10 the waveguide dimension
is taken as being tolerable. The displacement of the beam, δ, at the
exit waveguide entrance is also calculated and shown in Table 1. Here we
see that the 118 micron radiation may potentially work for the baseline
density case (depending on waveguide size) but at high density,
refractive effects are too large and the interferometer would fail. For
λ=57 μm, refractive effects are manageable at the baseline density but
may become borderline for maximum density scenario. To evaluate this
more accurately, detailed ray tracing must be done. However, to first
order, it looks like 57 microns is workable at the high density. At 10.6
microns, refraction does not pose a problem.

  -------------- --------------- ------------- --------------- -------------
                 **Baseline                    **Maximum       
                 Case**                        Density Case**  

                                                               

                 ne=1.8x10\^21                 ne=1x10\^22     
                 m\^-3                         m\^-3           

                                                               

  λ (microns)    α (deg)         δ (cm)        α (deg)         δ (cm)

                                                               

  118            0.65            0.17          4               1.05

                                                               

  57             0.15            0.04          0.9             0.24

                                                               

  10.6           0.005           0.005         0.03            0.008
  -------------- --------------- ------------- --------------- -------------

*Table 1. Refraction angle estimates for various wavelengths in the ITER
Divertor interferometer (caution: this is a crude estimate). The
displacement, δ, is computed for path 8 where it is maximum.*

Based on the these estimates, it seems that when one takes into account
both the total phase measured and refractive effects, that 57 microns
would provide the best wavelength for an ITER divertor interferometer.
At 118 microns beam refraction is potentially too large while at 10.6
microns the total phase measured is too small to obtain sufficient
resolution.

A two-color interferometer using 57 microns requires a second
wavelength. Japanese researchers have already found a suitable laser
line at 48 microns that could be used (Kondoh et al., Rev. Sci. Instrum.
**75**,3420(2004)). This wavelength should be useful in all anticipated
density regimes. Another possible choice would be to use 10.6 microns
for the expansion/vibration compensation instead of 48 microns. This
would actually be best for the two-color system accuracy since 10.6
would have the smallest plasma phase change (∼λ) but a very large shift
due to thermal expansion (\~1/λ). For a two-color interferometer, the
line-integrated density is equal to

> $\int_{0}^{L}{n_{e}(r)\text{dy} =}\frac{\left( f_{1}\lambda_{1} - f_{2}\lambda_{2} \right)}{\left\lbrack e^{2}4\text{pe}_{0}m_{e} \right\rbrack\left( \lambda_{1}^{2} - \lambda_{2}^{2} \right)}$,

where λ~1~, λ~2~ and φ~1~, φ~2~ are the wavelengths and measured phase
for the two colors. The further λ~1~ and λ~2~ are separated the more
accurate the cancellation of vibrations and thermal expansion effects.

However, it also may be useful to use 118 microns, especially for lower
density divertor plasmas (see Fig. 6). The reason for including 118
microns is to allow for better resolution in lower density ITER divertor
plasmas. This may be especially useful during commissioning phases of
the ITER device before actual burning plasma operation. In addition,
with 118 microns, making a CM measurement can be achieved at lower
densities while the 57 microns can be used at the higher density. Having
the ability to make the CM effect measurements lends critical
flexibility to the interferometer system which may be crucial to its
success on ITER. Using a two-color interferometer to deal with thermal
expansion of up to 1 cm results in a phases error correction of many
fringes. As mentioned earlier, a CM interferometer system would not be
subject to this limitation. In addition, if the maximum density of
10^22^ m^-3^ is only reached during discrete giant ELM events (\~1-10
msec in duration), the loss of signal/phase due to refraction would only
be temporary. Since the CM effect phase is \<\< 180 deg, the correct
phase information would be quickly recovered after the ELM event. If
this scenario held true for the bulk of ITER plasmas, a CM
interferometer would be vastly superior to the two-color system. As is
being done for the tangentially-viewing interferometer system where both
two-color interferometry and Faraday effects will be measured to obtain
the density, it is recommended the same be done in the divertor. Only in
this instance, the CM effect should be used to replace the Faraday
effect. In addition, a two-color interferometer using 57 and 118 micron
sources would be an excellent choice for low density divertor plasmas.

Finally, due the importance of each discharge during ITER operation, the
reliability of the interferometer system is a critical issue. Ideally, a
separate laser system should be provided for each channel. Redundancy
would optimize the chances of obtaining at least some useful information
for each ITER plasma. If this argument is supported, then one can
imagine having separate laser systems at 10.6(9.27), 57(48) and 118
microns. For 118 microns, the source would be dedicated to chord (O5),
57 microns for chords O2-O4, and 10.6 microns for chord O1 (see Fig.
1(b)). In this configuration, the divertor interferometer system could
handle essentially any ITER discharge scenario by providing at least
some information from one of the chords. The WG used for 57(48) and 118
microns can most likely be made the same so plumbing of this radiation
to various chords could be modified on a shot-to-shot basis from the
diagnostic hall. The following represents a few example scenarios. CASE
1: For the low-density divertor scenario (Fig. 6) you might lose data
from O1 because the phase shift would be too small (at 10.6 microns) but
the 57-118 micron systems would provide data from the other paths using
both the two-color interferometer and C-M measurements. CASE 2. For the
baseline divertor density (Fig. 4(a)), the 118 micron might fail but the
57 micron chords will have provide useful information along with the
10.6 micron chord for paths O1-O4. CASE 3. Finally, for the maximum
density case, under almost any scenario, the 10.6 micron system should
be operational providing information along path O1. In addition, the 57
micron system would likely be functional in most high density cases for
chords O2-O4. Consequently, having separate laser systems for individual
chords provides sufficient redundancy to optimize availability as well
as making the system sufficiently flexible to be useful for all
anticipated ITER divertor scenarios.

3.  **Single pass or double pass with retro-reflectors:**

I see no advantage to double pass if both launch and receive antennae
are available. Double refraction with double pass is a problem for long
wavelengths. For 10.6 μm, double pass would give a larger phase shift
but the environment for the retro-reflecting mirror is especially harsh
at this wavelength. The issue of mirror survivability in the divertor
region where heat and neutron flux may be large should not be
discounted. Sensitivity to these effects is increased as the wavelength
is reduced. This would then argue for using the 57 μm source compared to
10.6 μm. Future mirror development work should be closely monitored to
determine viability of materials for mirrors in the divertor region.

4.  **Diagnostic Layout**

A rough schematic of the diagnostic layout for the combined two-color
interferometer and Cotton-Mouton interferometer is shown in Fig. 7.
Here, a 57 micron laser source serves as the primary interferometer and
CM-effect system and vibration compensation is provided by the second
color at 48 microns. If more density range were desired at the lower
densities, a third source at 118 microns could also be added to replace
the 57 micron source. While this could not all be accomplished
simultaneously, depending on the ITER operation scenario, different
wavelength source radiation could be optically connected to the
waveguide system in the diagnostic hall. The overmoded waveguide would
be designed to efficiently pass radiation at 48, 57 and 118 microns
while maintaining the polarization integrity.

The 48 micron mixers would provide the reference and probe waveforms at
the beat frequency of 1 MHz. Phase electronics would then provide
signals proportional to the line-integrated plasma phase plus any
vibration/expansion effects. The 57 micron mixers would simultaneously
carry information at three frequency bands (1.5, 1.0 and 0.5 MHz)
multiplexed into a single time series trace. Phase electronics would
then provide signals of the O- mode index, X- mode index and their
difference (CM effect). These outputs would then be combined to provide
two independent measures of the electron density along the chord.

Depending on anticipated ITER divertor plasma conditions, having an
extra 118 micron source in the Diagnostic Hall would offer flexibility
to swap wavelengths. For instance, the 48 micron laser could be kept for
vibration compensation and the 118 micron laser used to measure plasma
density and CM effect in place of the 57 micron source. This would be
done for lower density cases. This need to switch sources should be
incorporated into the diagnostic design so that it could be accomplished
between ITER discharges.

5.  **Does divertor cassette provide adequate space**

    -   optics,

    -   waveguide

    -   real-time alignment hardware

    -   

I do not have much information on this matter but it is a crucial issue.
Space for waveguide must be maximized. Close interaction with ITER
mechanical design considerations is required. End result has a large
impact on the next section (Sec. 6).

6.  **Radiation propagation from diagnostic hall to plasma and back**

For any interferometer system, a significant unknown is the beam
propagation (waveguide) techniques required to transmit the source
radiation from the diagnostic hall to the launch antenna and from the
receive antenna back to the diagnostic hall where the detectors will be
located. In addition, since the signal mixer will likely be located in
the diagnostic hall, \~30-40 m from the divertor plasma, even small
deviation of the beam from its optical path (due to refraction or optics
shift due to expansion, etc.) must be considered in detail. Ideally, for
the use of 118 and 57 microns, overmoded waveguide that can accommodate
both wavelengths is desired. This seems to be feasible but detailed
testing needs to be done, especially under ITER environment conditions
where mechanical stresses may be high, thermal expansion is large, and
vibrations exist. R&D is required to develop a waveguide test facility
and confirm that broadband, overmoded waveguide can pass radiation at
48, 57 and 118 microns while maintaining polarization integrity and
minimizing losses. Tests must also be conducted to ensure that no index
sensitive effects occur within the waveguide system or vacuum windows
which would act to add error to the density measurement.

Current ITER diagnostic plans call for two types of beam transmissions
systems as shown in Fig. 8. One would take the radiation from the
diagnostic hall, where the sources are located, to inside the vacuum
vessel between the blanket and vessel wall. This is referred to as the
*transmission waveguide*. At this point, ITER drawings call for a
conversion box where the radiation would be transferred from the
*transmission waveguide* to the *cassette waveguide* to cover the final
distance to the actual plasma. This final distance appears to be \~4 m.
When the beam is in the *transmission waveguide*, from the diagnostic
hall to conversion box in the divertor cassette, there is ample room for
overmoded waveguide (say \~75 mm diameter) to transport the beams at 57
and 118 microns. Waveguide is not necessary at 10.6 microns under any
scenario, as will be shown shortly. Once conversion has been made to the
*cassette waveguide,* space constraints are much more demanding and
present drawings call for metallic waveguide, 1x2 cm rectangular. This
waveguide was chosen for the original design which called for divertor
reflectometer systems, not laser interferometer systems. This *cassette
waveguide* would then be used to transfer the radiation the final \~4 m
to the plasma as well as the 4 m path back to the conversion box for the
signal beam. A roundtrip distance of at least 8 m is anticipated. In the
divertor cassette, waveguide may be needed depending on beam size and
wavelength of the source.

Simple calculations can be made to provide information on potential
waveguide needs. If at the conversion box we take a source radiation
beam with waist diameter d~o~ (at the e^-1^ point of the intensity
distribution), wavelength λ, and propagate it some distance z, the beam
diameter at that distance is given by

$d = \left( d_{o}^{2} + \left( \frac{2\lambda z}{{pd}_{o}} \right)^{2} \right)^{12}$.

Below, in Table 2, is a chart showing how the beam diameter varies with
wavelength and distance. We will examine source radiation using two
different initial beam waists.

This first thing to note from Table 2 is that at 10.6 microns, beam
divergence is always negligible for path lengths in the divertor
cassette. This is also true for the longer transmission path from the
diagnostic hall to the conversion box in the divertor cassette (\~ 30
m). However, any type of protective cover to maintain the integrity of
the beam path would need to have a diameter at \~3 times the beam size.
This cover would not act as a waveguide. Also, any optical element, such
as a mirror, would need to have a diameter at least 2 times the beam
diameter. For 57 microns, if the initial beam waist is 2 (1) cm, beam
expansion from the conversion box to the plasma is small but the return
path to the conversion box would result in a beam diameter expansion to
2.5 (3.6) cm. This may still be manageable, depending on the actual
space available, for the d~o~=2 cm case. It is most likely though that
waveguide will be need at this wavelength. At 118 microns, the need for
transmission waveguide is increased.

  -------------- ------------ --------------- -------------------------- --
  **Table 2**                                                            

                                                                         

  λ (microns)    z (m)        do (m)          d (m)                      

                                                                         

  10.6           4            0.02            0.02                       

                                                                         

  57             4            0.02            0.0214                     

                                                                         

  118            4            0.02            0.025                      

                                                                         

  10.6           8            0.02            0.02                       

                                                                         

  57             8            0.02            0.025                      

                                                                         

  118            8            0.02            0.036                      

                                                                         

  10.6           8            0.01            0.01                       

                                                                         

  57             8            0.01            0.032                      

                                                                         

  118            8            0.01            0.061                      
  -------------- ------------ --------------- -------------------------- --

*Table 2. Change in source radiation beam size with distance.*

**Divertor Cassette Waveguide:** \~4 m length both to and from the
divertor region:

-   at present 1x1 and 1x2 cm metallic waveguide.

-   For interferometer system, \~2 cm ID circular waveguide would be
    better for 57 and 118 micron sources (design work required).

-   10.6 micron (and possibly 57 micron) radiation would need no
    waveguide. Requires optics \~ 2-4 cm dia. Even if waveguide is not
    required, due to restricted space and safety, some type of enclosure
    will be required for the laser beam and its dimensions need to be
    considered.

**Transmission Waveguide:** from inside the vacuum vessel to the
diagnostic hall, \~30 m:

-   use overmoded waveguide at 57 and 118, space restrictions much less
    severe

-   10.6 micron would still not require waveguide

Once final the wavelength choice is made and actual ITER optical path
(and space) is known (both are connected), then the waveguide design can
be proposed and tested. It is a critical step to test the waveguide
under conditions where large expansion (thermal or otherwise) occurs.
Real-time alignment may prove necessary to keep radiation on the optical
path of the waveguide otherwise unacceptable losses may occur.

-   realtime alignment

Due to both refractive effects and possible movement of optical elements
due to thermal expansion, plus the large distance from the plasma to the
actual signal mixer in the diagnostic vault, real-time alignment of the
beams (especially the signal beam after plasma) will most likely be
required. This type of control could be used to offset beam drifts due
to thermal expansion as well as plasma refractive effects. Since the
thermal expansion effect on the optical system is largely unknown at
this time, it is feasible that the beam could be entirely lost from the
optical path due (unless the optics are made so large as to accommodate
any likely misalignment). Even at 10.6 microns, where refractive effects
can be safely neglected, it may still be necessary to have real time
alignment control in order to compensate for the unknown thermal
expansion (or structure movement) effects. This realtime control would
need to included on both the source beam going out to the plasma as well
as the signal beam returning to the diagnostic hall.

7.  **Source and Receiver Technology**

Suitable laser sources are readily available at wavelengths of 10.6
(9.27) and 118 μm. These sources have been used for many years in plasma
diagnostic applications comparable to those expected in ITER. High-speed
detector technology is also commercially available for the receiver. The
same is not true at 57 (48) μm. Development work in this wavelength
region has only been initiated fairly recently by Japanese researchers
\[Okajima et al., Rev. Sci. Instrum. **72**,1094-1097(2001)\]. Output
power up to 1.6 W has been measured at 57 μm and 0.8 W at 48 μm for the
CH3OD molecular gas laser \[Kawahata et al., Rev. Sci. Instrum.
**75**,3508-3510(2004)\]. Non-optimized Schottky barrier diode mixers
with high time response have been successfully used to measure radiation
at 57 μm. Since this a fairly recently identified wavelength, detector
technology remains to be optimized at both 57 and 48 μm. Schottky
barrier diode mixers are a possibility along with He-cooled InSb
detectors and Ge:Ga photoconductor detectors. Since responsivity for
these short wavelengths is known to be poor, detector development work
will be required.

8.  **What are the \"high leverage\" issues that would be part of such a
    development? What R&D would be wise to invest in?**

\- Waveguide testing at 57 (48) and 118 microns

\- high speed detector development at 57 and 48 μm.

\- Effect of heat expansion on alignment and phase (index effects)

-   Movement of launch and receive waveguides/horns due to thermal
    expansion or any other effect.

-   Ray-tracing in the divertor region at each wavelength

-   Window materials (diamond?)

-   Real-time alignment tests to compensate for both thermal expansion
    and refraction (using the waveguide). This can and should be mocked
    up and tested in great detail.

**Conceptual Design Study Conclusions for ITER Divertor Interferometer
Diagnostic System:**

1.  Realtime information on the divertor density is important for the
    plasma control and safety in ITER. Any interferometer system must be
    robust and have suitable redundancy and reliability. It is
    recommended that each chord be an independent system with separate
    source, optics, receiver and waveguide. This allows better
    optimization of source to task, makes the interferometer system
    useful under any divertor plasma scenario, and provides sufficient
    redundancy in case of source failure. Source radiation at 10.6
    (9.27), 57 (48) and 118 microns appears best suited for the ITER
    divertor. The shortest wavelength source would be used for chord O1,
    the longer wavelengths would be used for chord O2-O5. Since the same
    waveguide can be used for all wavelengths \>40 microns and separate
    waveguide is used for each chord, the actual radiation wavelength
    for chords O2-O5 can be changed in the diagnostic hall to
    accommodate specific experimental needs.

2.  Both a two-color interferometer combined with a Cotton-Mouton effect
    interferometer should be used to make the density measurement. This
    is analogous to using a combined two-color interferometer and
    Faraday measurement for the tangential-view system, which is already
    planned for ITER.

3.  Source and receiver technology is available for all wavelengths
    under consideration. Currently, no US research facility has
    familiarity with laser sources at 57 and 48 μm. A prototype
    diagnostic should be developed using these wavelengths. Detectors
    for wavelengths of 57 and 48 μm need to be optimized. Schottky
    barrier diode detectors are a possibility or perhaps InSb He-cooled
    detectors.

4.  Detailed ray-tracing is needed to fully assess refractive effects on
    probe beams. In addition, access to equilibrium field data/modeling
    will be necessary to evaluate toroidal field in the divertor region.

5.  A significant technological challenge is faced when propagating
    source radiation from the diagnostic hall to the plasma and back
    while maintaining alignment and minimizing losses. Conventional
    waveguide or free space propagation techniques can be used from the
    D-Hall to the vacuum vessel and conversion box interface (\~30 m
    path length). Beyond this point, space for waveguide is extremely
    restricted (\~4-5 meter path length, each way to and from the
    plasma). R&D needs to be performed to establish whether low-loss
    waveguide can be used that satisfies both space and environment
    requirements. No waveguide is needed at 10.6 microns. It should be
    possible to accommodate both 57 and 118 micron radiation in the same
    waveguide.

6.  It should be confirmed that the density range for which this
    feasibility study was conducted is valid. In particular, at the
    low-density range of 10^19^ m^-3^, I assumed that this referred to
    the edge density along each chord where the peak was of order 10^21^
    m^-3^. For the originally planned reflectometry measurements, where
    the density profile was to be measured across the divertor leg, a
    density resolution of 10^19^ m^-3^ would be needed. For an
    interferometer measurement, I'm assuming it is no longer necessary
    to meet this constraint. However, including the wavelength choice of
    118 microns might be necessary to cover the low-density range of
    ITER divertor plasmas as well as enhancing the CM-interferometer
    measurement capability at higher densities.

7.  Once the conceptual design of the diagnostic is established, strong
    interaction should be immediately sought with ITER design engineers
    to ensure that access for beam lines, optics and waveguides is
    maximized. Also, identifying proper mirror materials is a critical
    issue (especially at 10.6 μm).

8.  If forced to choose a single system, it would be a combined
    two-color interferometer and Cotton-Mouton effect polarimeter system
    operating at 57 (48) and 118 microns. The two-color interferometer
    could operate using either 57 and 48 or 57 and 118 microns. The CM
    effect would be measured using either 118 or 57 microns. All three
    wavelengths could use the same waveguide and radiation choice for a
    given chord could be selected in the diagnostic hall on a
    shot-to-shot basis. Realtime alignment mirrors (for probe and signal
    beams) would be used to correct for movement of the optics due to
    thermal expansion or movement of the beam due to refraction. This
    type of system would provide reliable density information over the
    largest range of ITER divertor parameters.

![](media/image1.jpeg){width="4.8180555555555555in"
height="3.4055555555555554in"}

\(a\)

![](media/image2.jpeg){width="4.782638888888889in" height="3.38125in"}

\(b\)

Figure 1. Divertor interferometer chords planned for ITER, (a) inner
leg; three chords shown with spacing \~20 cm, (b) outer leg; five chords
shown with spacing \~10 cm.

![](media/image3.png){width="4.804861111111111in"
height="3.6381944444444443in"}

![](media/image4.pct){width="5.99375in" height="2.433333333333333in"}

Figure 2. Modeled density distribution for ITER divertor (outer divertor
leg).

![](media/image5.pct){width="5.590277777777778in"
height="7.027083333333334in"}

Figure 3. Anticipated line-integrated densities for (a) baseline \[path
2, peak 1.8x10^21^ m^-3^\] and (b) maximum density \[path 2, peak
1x10^22^ m^-3^\] cases.

![](media/image6.pct){width="5.518055555555556in" height="7.03125in"}

Figure 4. Wavelength dependence of computed phase for peak density
\[path 2\] (a) baseline case: 1.8x10^21^ m^-3^, and (b) maximum density
case: 1x10^22^ m^-3^.

![](media/image7.pct){width="4.728472222222222in"
height="6.026388888888889in"}

Figure 4. Expanded view

![](media/image8.pct){width="4.800694444444445in"
height="6.042361111111111in"}

Figure 5. Computed Cotton-Mouton phase for peak density \[path 2\] (a)
baseline case: 1.8x10^21^ m^-3^, and (b) maximum density case: 1x10^22^
m^-3^.

![](media/image9.pct){width="4.800694444444445in"
height="6.0256944444444445in"}

Figure 6. Computed (a) standard interferometer phase and (b)
Cotton-Mouton phase for peak density \[path 2\] equal to 1x10^20^ m^-3^.
This is the low density ITER divertor scenario.

![](media/image10.pct){width="5.052777777777778in"
height="3.682638888888889in"}

Figure 7. Combined two-color interferometer and Cotton-Mouton
interferometer experimental setup using nominal laser wavelengths of 48
and 57 microns.

![](media/image11.pct){width="4.864583333333333in" height="2.45625in"}

Figure 8. ITER design schematic showing transmission waveguide,
conversion box inside the vacuum vessel, and cassette waveguide to the
plasma.