![](media/image1.pct){width="5.973611111111111in"
height="0.4576388888888889in"}

72-030203-CLN-01

TO: DISTRIBUTION\
FROM: C NEUMEYER\
SUBJECT: RESISTIVE WALL MODE SYSTEM SCOPING STUDY

***\
Reference:*** 72-030123-JM-01 ***"***Preliminary Requirements For NSTX
Resistive Wall Mode And Error Field Feedback Coils And Power Supplies",
J. Menard, S. Sabbagh

[Summary]{.underline}

The purpose of this memo is to 1) identify the design issues, 2) develop
the design concepts and 3) outline the tasks related to the
implementation of a Resistive Wall Mode (RWM) and error field correction
system on NSTX.

Since a GA/PPPL collaboration has already deployed an RWM system on
DIIID it is advantageous and cost effective for NSTX to build upon this
experience and utilize coil and power supply concepts already developed.
Therefore a starting point for this study is to determine to what extent
the GA coil and power supply designs can be adopted for NSTX duty.

It is concluded herein that the DIIID internal coil design could be
adopted on NSTX, and that the Switching Power Amplifiers (SPAs) are
suitable.

A decision on internal or external coil location needs to made soon,
based upon a trade-off between costs and benefits. Toward this end, the
next steps are to 1) quantify the performance difference (VALEN code)
and 2) quantify the cost/schedule difference. The results given herein
should provide the necessary input to these steps.

#### Requirements

Per the reference memo and discussions with J. Menard et al the proposed
NSTX system requirements are as follows.

  ----------------------------------- -----------------------------------
  Number of Coils                     6

  Coil Location                       Centered about midplane

  Coil Connections                    Diametrically opposite coils
                                      connected in anti-series forming 3
                                      independently controllable circuits

  Coil height                         Approximately equal to gap between
                                      passive plates \~ 1 m.

  DC Field at r=R0+0.6\*a             50 gauss

  AC Field at 1kHz, r=R0+0.6\*a       10 gauss

  Maximum Ripple                      +/- 2% of full load DC

  Pulse Length                        5 sec

  Repetition Period                   300 sec
  ----------------------------------- -----------------------------------

#### GA RWM System

# Internal and External Coils

GA started their RWM experimental program with a coil system consisting
of a set of 6 external coils centered about the midplane[^1]. The coils
were wound using 4 turns of 750MCM cable carrying up to 5kA for 10s.
These were designed to produce 30 gauss at the plasma edge. The were
located at approximately R=2.56m, or 0.22m from the plasma edge. See
figure 1.

![](media/image2.jpeg){width="6.0in" height="4.5in"}

*Figure 1 -- DIIID External Coils*

More recently an internal coil system has been added which consists of
12 coils, 6 above and 6 below midplane[^2]. See figure 2.

![](media/image3.jpeg){width="5.9875in" height="4.490277777777778in"}

*Figure 2 -- DIIID Internal Coils*

The coils are approx. 0.5 m tall by 2.0 meter wide, single turn water
cooled tubular copper conductors (14.4mm OD, 8.6mm ID) wrapped with one
half-lapped layer of polyamide (0.5mm (0.002") thickness Kapton)
insulation, a 1.7 mm thick Vespel spacer, and an additional layer of
Kapton tape, all encased in a 304SS tube (19mm OD). The coils are
capable of 7kA continuous with 5.5m/sec water cooling. Because a fully
assembled coil cannot be passed into the vessel, the coil is fabricated
outside the vessel in three pieces; a lower conductor assembly, an upper
conductor assembly and a 35 mm diameter concentric lead assembly. Leads
are brought out from two coils at a time through 10" diameter openings.

The design requires in-vessel joining of copper with three induction
brazes and six orbital welds of the stainless vacuum jacket. The coils
are installed under PFC tiles and are baked to 350°C. The design
provides a double barrier of copper and stainless steel against water
leakage into the machine. In order to detect water leaks in the copper
or leaks through the stainless into the vessel, the insulation space is
sealed in two places outside the vessel using machined polyamide and "O"
rings. During the initial bake of the vessel, this space is vacuum
pumped to remove moisture and gases that evolve. After cool down, dry
nitrogen gas is back filled to about 0.7 bar, and sealed off. The
pressure in this trapped volume is monitored to detect either water
leaks through the copper (higher pressure) or stainless sheath leaks to
the vacuum (lower pressure). During vessel baking, the cooling water in
the coils is replaced with dry nitrogen in order to limit oxidization of
the copper.

An extensive R&D program was conducted in '00 and '01 which led to the
installation of two prototype coils in DIIID. After their removal they
were hipot tested (to destruction) and found to withstand 5kV.

The 12 production coils were fabricated during the first 6 months of '02
and then installed during a 3 month opening. So far there have been no
leaks or any other problems with the coils.

The total cost associated with the fabrication and installation of the
12 production coils was \$2M, most of which was for labor costs. However
this figure includes costs for a significant amount of PFC tile removal,
modification, and re-installation, along with the relocation and
replacement of some magnetic diagnostics. So the cost associated with
the coils themselves was perhaps of the order of \$1.5-\$1.8M or approx.
\$100K-\$150K per coil.

If NSTX elects to install internal coils, the GA design could be
adapted, taking advantage of their prior R&D and experience. Furthermore
the coils could be fabricated by GA and they could lead in the
installation task, especially the in-vessel brazing and welding
operation. In fact the NSTX installation would be simpler and less
demanding due to the lower bakeout requirement (the coils would be
attached to the vessel wall at 150°C), simpler geometry (the coils on
the midplane would conform to the cylindrical shape of the vessel), and
lower fields (and forces). It may be possible to install the coils
through Bay K on NSTX (future NBI port) and avoid much of the in-vessel
fabrication, which would be a great simplification. Similarly, if the
coils were installed during a center stack removal then would be
possible to pass them into the vessel via the opening at the top of
NSTX. One additional challenge presented by NSTX is the CHI operation
which places a 1kV bias on center stack casing. But part of the voltage
can appear on the resistive grounded outer VV. So RWM coils mounted on
the outer VV of NSTX should be designed for a hipot of 2\*1+1=3kV. GA
tests of their insulation scheme, to destruction, indicate a dielectric
strength of 5kV.

*Power Supplies*

The power supplies consist of two parts, a rectifier DC source and an
IGBT chopper "Switching Power Amplifier" (SPA)[^3]. One DC source can be
connected to supply one or more SPA units.

The SPA choppers are subdivided into three parallel modules which can be
controlled separately and connected to three independent loads or
combined in parallel to drive one load. The DC inputs to the three
chopper modules are connected in parallel, and each to chopper module
input includes an input filter capacitor and output filter induictor.
See figure 3.

![](media/image4.pct){width="5.992361111111111in"
height="6.680555555555555in"}

*Figure 3 -- DIIID DC Supply and SPA Configuration*

The SPAs were specified and procured by PPPL and manufactured by
Robicon. The DC source supplies were obtained from LLNL surplus. SPA
characteristics are given in the following table.

+-----------------------------------+----------------------------------+
| Pulse Current per Module          | 1.667kA                          |
+-----------------------------------+----------------------------------+
| Pulse Current (3 parallel module) | 5kA                              |
+-----------------------------------+----------------------------------+
| Pulse Duration                    | 10 sec                           |
+-----------------------------------+----------------------------------+
| Pulse Period                      | 180 sec                          |
+-----------------------------------+----------------------------------+
| Input Voltage                     | 300Vdc                           |
+-----------------------------------+----------------------------------+
| Switching Frequency               | 3.5kHz (first version)           |
|                                   |                                  |
|                                   | 7.0kHz (second version)          |
+-----------------------------------+----------------------------------+
| Input Filter Capacitance (3       | 0.2835 millifarad, 800V          |
| parallel module)                  |                                  |
+-----------------------------------+----------------------------------+
| Output Filter Inductor (per       | 11 microhenry                    |
| module)                           |                                  |
+-----------------------------------+----------------------------------+
| Output Filter Inductor (3         | 3.67 microhenry                  |
| parallel module)                  |                                  |
+-----------------------------------+----------------------------------+

The SPA IGBTs consist, in each bridge arm, 2 parallel IGBT devices
(EUPEC 400A/1200V).

If NSTX elects to procure the same SPA units then there is a possibility
that they could be operated at a somewhat higher voltage. For the DC
source, therefore, it may be possible to utilize PPPL Transrex
rectifiers which at present produce a DC voltage of 1012.85Vdc at
alpha=0. It would be necessary to either supply the Transrex units with
a lower AC input voltage (480Vac would yield 650Vdc) or control them to
a lower voltage with suitable accessories to prevent overvoltage.
Alternativly, new DC source power supplies could be procured or obtained
from surplus TBD.

[Analysis of Implementation Options]{.underline}

A spreadsheet analysis was performed for several NSTX design options.
This was helpful in identifying the issues. The GA internal and external
coil designs were also analyzed so as to provide a benchmark.

The complexities of the magnetics (mutual coupling to VV and resultant
eddy current effects) were not included in the model. However, skin
effect was accounted for. In arriving at the results in the GA cases,
the physical dimensions, circuit resistances and inductances, including
choke values, were based on information extracted from several GA
publications^1,2^,[^4]. In the NSTX cases the choke value was chosen so
as to limit the peak-to-peak ripple to 4% of the total amp-turns.

The following table provides a summary of the cases studied.

+-------+------------+-----------+------------+-----------+-----------+
|       | GA         | GA        | NSTX       | NSTX      | NSTX      |
|       |            |           |            | External  | External  |
|       | Internal   | External  | Internal   |           |           |
|       |            |           |            | Coil      | Coil      |
|       | Coil       | Coil      | Coil       |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| #     | 1          | 4         | 1          | 1         | 2         |
| Turns |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Peak  | 5k         | 5kA/      | 5k         | 5kA       | 5kA/      |
| DC    | A/5kA-turn | 20kA-turn | A/5kA-turn | /5kA-turn | 10kA-turn |
| Cu    |            |           |            |           |           |
| rrent |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Rcoil | R0+a=2.34m | 2.56m     | 1.68m      | 1.85m (6" | 1.85m     |
|       | (see note  |           | (5/8"      | outside   |           |
|       | 1)         |           | inside VV  | VV wall)  |           |
|       |            |           | wall)      |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| d     | 1.02m      | 1.6m      | 1.0m       | 1.0m      | 1.0m      |
| Zcoil |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| R     | R0+0.      | 2.07m     | R0+0.      | 1.26m     | 1.26m     |
| point | 6\*a=2.07m |           | 6\*a=1.26m |           |           |
| (t    |            |           |            |           |           |
| arget |            |           |            |           |           |
| for   |            |           |            |           |           |
| f     |            |           |            |           |           |
| ield) |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Br @  | 9.6e-3     | 6.65e-3   | 9.05e-3    | 6.98e-3   | 6.98e-3   |
| R     | gaus       | gauss     | gaus       | gauss     | gauss     |
| point | s/amp-turn | /amp-turn | s/amp-turn | /amp-turn | /amp-turn |
| (see  |            |           |            |           |           |
| note  |            |           |            |           |           |
| 2)    |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Br @  | 48.1 gauss | 133.0     | 45.2 gauss | 34.9      | 69.8      |
| R     |            | gauss     |            | gauss     | gauss     |
| point |            |           |            |           |           |
| @     |            |           |            |           |           |
| Peak  |            |           |            |           |           |
| DC    |            |           |            |           |           |
| Cu    |            |           |            |           |           |
| rrent |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Br @  | 4.8 gauss  | 1.1 gauss | 6.3 gauss  | 4.9 gauss | 4.9 gauss |
| R     |            |           |            |           |           |
| point |            |           |            |           |           |
| @     |            |           |            |           |           |
| 1kHz  |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Coil  | GA         | 750MCM    | GA         | 500MCM    | 250MCM    |
| Cond  |            | cable     |            | cable     | cable     |
| uctor |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Coil  | Rdc=1.33mΩ | R         | Rdc=1.1mΩ  | R         | R         |
| Impe  |            | dc=1.64mΩ |            | dc=0.54mΩ | dc=1.86mΩ |
| dance | L=6.6µH    |           | L=5.1µH    |           |           |
|       |            | L=128µH   |            | L=5.25µH  | L=22.6µH  |
+-------+------------+-----------+------------+-----------+-----------+
| #S    | 2          | 2         | 2          | 2         | 2         |
| eries |            |           |            |           |           |
| Coils |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| DC    | Rdc=6.33mΩ | R         | 2x250'     | 2x250'    | 2x250'    |
| Feed  |            | dc=6.33mΩ | 500MCM     | 500MCM    | 500MCM    |
| Cable | L=32.8µH   | L=32.8µH  | cable      | cable     | cable     |
|       |            |           |            | R         | R         |
|       |            |           | Rdc=35.1mΩ | dc=35.1mΩ | dc=35.1mΩ |
|       |            |           |            |           |           |
|       |            |           | L=56.3µH   | L=56.3µH  | L=56.3µH  |
+-------+------------+-----------+------------+-----------+-----------+
| SPA   | 3.5kHz     | 3.5kHz    | 7.0kHz     | 7.0kHz    | 7.0kHz    |
| Swit  |            |           |            |           |           |
| ching |            |           |            |           |           |
| Freq  |            |           |            |           |           |
| uency |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| SPA   | 300V       | 300V      | 300V       | 300V      | 300V      |
| Vo    |            |           |            |           |           |
| ltage |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| L     | 50µH       | 0         | 1.4µH      | 1.2µH     | 0         |
| choke |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+
| Peak  | 5.7        | 1.9%      | 4.0        | 4.0%      | 4.0%      |
| -peak | %/2.8gauss | /2.5gauss | %/1.8gauss | /1.4gauss | /2.8gauss |
| r     |            |           |            |           |           |
| ipple |            |           |            |           |           |
| (see  |            |           |            |           |           |
| note  |            |           |            |           |           |
| 3)    |            |           |            |           |           |
+-------+------------+-----------+------------+-----------+-----------+

Notes:

1)  GA Internal coils consist of 2 sets, one above and one below mid.
    This radius chosen to simulate such coils using 1 set centered
    around the midplane.

2)  Br estimated based on planar, anti-series coil pair

3)  \% based on amp-turns

The following curves depict the dependence of current, field, and pulse
length on frequency for the various case, considering the variation in
inductive impedance as well as the skin effect on resistance.

![](media/image5.pct){width="4.570138888888889in"
height="5.143055555555556in"}

*Figure 4 -- Available Peak Current (amp-turns) vs. Frequency*

![](media/image6.pct){width="4.9840277777777775in"
height="3.9451388888888888in"}

*Figure 5 -- Radial Field vs. Frequency*

![](media/image7.pct)

*Figure 6 -- Available Equivalent Square Wave vs. Frequency for Cable
Formed Coils*

Based on the analysis performed, the following observations are made.

1 -- All of the designs come close to meeting the requirement for 50
gauss under DC conditions. However they all fall short of the
requirement for 10 gauss at 1kHz, even with the simple model used which
does not simulate the demagnetizing effect of the eddy currents in the
VV. It appears that 10 gauss is only available up to around 500Hz.

2 -- The necessity of the additional choke, and higher switching freq
uency for the new GA internal coils so as to keep the ripple down,
appears evident.

3 -- At least for the simple model used herein, the ripple requirement
dictates the minimum allowable circuit inductance for a given driving
voltage. This imposes, therefore, a fundamental limit on system
performance. It may actually be advantageous to reduce the base DC
voltage (nominally 300 volts) under certain conditions to reduce the
ripple.

4 -- The effect of the VV is probably very important in determining the
ripple response. Considering that the NSTX VV is 5/8" (0.625") thick
304SS, and the skin depth at 1kHz is only 0.550" in 304SS (resistivity =
7.7e-7 ohm-m), the VV may serve as an effective ripple filter, reducing
or eliminating the need for external inductance (choke).

5 -- If the VV does serve effectively as a ripple filter, then the noise
pick-up on in-VV magnetic diagnostics would be reduced in the case of
external RWM coils.

6 -- For NSTX, it would appear that the resistive and inductive
impedance of a cable run from the NTC to FCPC, assumed here to be 250',
can be tolerated, allowing the equipment to be installed at FCPC. If
closer study finds too small a margin in this regard, perhaps the DC
source voltage can be increased above 300V to compensate.

7 -- For the cable formed coils (the GA external coil from 4 turns @
750MCM, the NSTX external coil from 2 turns @ 250MCM, the NSTX coil from
1 turn @ 500MCM) the available pulse length (equivalent square wave) is
a function of frequency. For the 500MCM and 750MCM conductors, the
allowable pulse length at peak DC current exceeds 5 seconds with a 300
second repetition rate (rated NSTX pulse length and duty factor).
However, if a 250MCM cable is used (e.g. to conserve space and allow a 2
turn external coil to be formed) then the pulse length at the low end of
the frequency range would be less than 5 seconds as shown in figure 6.

8 -- Since the water cooled GA conductor is designed for 7kA continuous
then, as long as the DC feeds, etc., are 500MCM or larger, then the RWM
could run at rated current for the full 5 second pulse.

9 -- The net field available from 3 coil pairs will be higher than that
available from one. Figure 7 shows the spatial variation of Br (at
r=R0+0.6\*a) on the midplane for the case of the 1 turn NSTX external
coil when all three coil pairs are identically operated. The ratio of
multi-coil to single coil field in this case is 2.37.

![](media/image8.pct){width="6.002777777777778in"
height="3.902083333333333in"}

*Figure 7 -- Spatial Variation of Br at r=R0+0.6\*a on Midplane for 1T
External Coil*

cc:

M Bell J Bialek D Gates R Marsala M Ono

S Ramakrishnan R Raman S Sabbagh A Von Halle M Williams

[^1]: "Resistive Wall Mode Feedback System on DIIID", J. Scoville et al,
    18^th^ SOFE, Albuquerque, Oct. 1999

[^2]: "Design, Fabrication, Installation and Testing of In-Vessel
    Control Coils for DIIID", P. Anderson et al, 22^nd^ SOFT, Helsinki,
    Sept 2002

[^3]: Operating & Maintenance Manual, PU PO#S-04108-G, Robicon
    SO#1-64739

[^4]: "Modeling and Design of A Resistive Wall Mode Stabilization System
    with Internal Field Coils In DIIID", G. Jackson et al, 44^th^ APS,
    Orlando, Nov. 2002