![](media/image1.png){width="5.954861111111111in"
height="0.41597222222222224in"}

52-960306-CLN-01

***TO: DISTRIBUTION***

***FROM: C NEUMEYER\
SUBJECT: PRELIMINARY ANALYSIS OF TF PERFORMANCE***

A preliminary analysis of the TF system performance was conducted in
order to verify the latest selection of TF conductor cross sections and
overall dimensions. Simulations were performed using crude models of the
C-site MG sets, which are planned to be used for the power supply for
the TF system.

*Coil Description*

The latest coil dimensions were provided by A. Brooks, along with a
value for inductance. These are summarized in the following spreadsheet,
along with some derived parameters.

  ------------------------------- ------------------- -------------------
  \# TF Coils                     12                  

  \# Turns/coil                   6                   

  Ro                              0.8                 m

  B @ Ro                          0.32                T

  I                               17777.77778         amp

  Inductance                      0.017               henries

  Stored Energy                   2.69E+06            Joule

  Inner Leg Cu CSA per Coil       0.00212             m\^2

  Inner Leg Cu CSA per Turn       0.000353333         m\^2

  Inner Leg Length                5.04                m

  Outer Leg Cu CSA per Coil       0.0232              m\^2

  Outer Leg Cu CSA per Turn       0.003866667         m\^2

  Outer Leg Length                7.03                m

                                                      

  Conductor resistivity @ 20C     1.7240E-06          Ω-cm

  Conductor res temp coeff        0.0041              1/degC

  Conductor heat capacity         0.386               J/gm-degC

  Conductor density               8.94                gm/cc

                                                      

  Total Inner Leg Res @ 20C       0.017705805         Ω

  Total Outer Leg Res @ 20C       0.002256775         Ω

  Total Coil Res @ 20C            0.019962581         Ω

                                                      

  Total Inner Leg Heat Capacity   442458.4228         Joule/deg C

  Total Inner Leg Heat Capacity   6753818.408         Joule/deg C

                                                      

  Initial Temperature             20                  deg C
  ------------------------------- ------------------- -------------------

The coils are water cooled; however the water cooling is intended only
to remove the heat between pulses. For all practical purposes it is
adiabatic during the pulse. No credit for the water is taken in the
simulations.

Since the operation is assumed adiabatic, and since the coils consist of
two discrete constant cross section elements (the inner and outer legs),
an equation for resistance vs. ∫i\^2(t)dt may be derived and used in
general to compute resistance during a simulation run.

The following figure depicts the resistance and temperature rise of the
inner and outer legs, as well as the total coil resistance, vs.
∫i\^2(t)dt.

![](media/image2.pct){width="5.895833333333333in"
height="4.295138888888889in"}

A equation fit to the above curve is as follows:

R = 0.019968 + 2.8728e-12 \* X + 2.7813e-22 \* X\^2

where:

R = total coil resistance

X = ∫i\^2(t)dt

At the moment no information is available concerning the inner/outer leg
joint resistance; it is assumed equal to zero.

*Power Supply*

The C-site MG sets are separately DC generators. The excitation is
generated via cascade rotating machines acting as magnetic amplifiers. A
feedback control system is provided to close the loop on load current.
The voltage response of the generators is relatively slow since the
generated voltage is proportional to the field current, and the time
constant of the field circuit is on the order of seconds. At the same
time the time constant of the load circuit is less than one second. This
makes the feedback control problematic.

An initial attempt was made to model the generators, their excitation
systems, the feedback control, and the coils via a simulation. Although
the simulation is working the precise machine parameters are not yet
available to the writer, and the simulation is really not ready for use.
Further work is required.

In addition, a very detailed simulation developed some years ago by the
MG Section is available, and needs to be run with the above coil model
to refine the results described herein and provide further insight into
the development of a simplified model as described above for general
purpose NSTX use.

To approximate the behavior of the system a linear ramp voltage source
was used. A ramp rate of 1000 volts/second per generator was used for
both up and down ramps. This rate is somewhat less than known to be
achievable in practice. The voltage was ramped up, and then switched to
ramp down in such a way that the coil current reached its flat top value
just as the generator voltage had ramped down to the coil I \* R drop.

No bus bar resistance was included in the simulations.

Two series sets of two parallel generators were assumed. Since the
simple ramp voltage model (independent of load current and generator
speed) was used, the only effect of the inclusion of parallel generators
was to include the appropriate net armature resistance and inductance.

Results for the 3.2 and 6.4kG simulations are given in the following
figures.

![](media/image3.pct){width="5.895833333333333in"
height="4.273611111111111in"}

![](media/image4.pct){width="5.895833333333333in"
height="4.273611111111111in"}

![](media/image5.pct){width="5.895833333333333in"
height="4.273611111111111in"}

![](media/image6.pct){width="5.895833333333333in"
height="4.273611111111111in"}

The results are summarized in the following spreadsheet:

  ------------------------- ----------------- ----------------- -----------
                            3.2kG             6.4kG             

  Flat Top Current          17777.8           35555.6           amp

  Flat Top Time             5.0               0.6               sec

  ∫i\^2(t)dt                1.769E+09         1.802E+09         A\^2-sec

  ESW                       5.597E+00         1.425E+00         sec

  Max Inner Leg Temp        101.6             103.3             deg C

  Max Outer Leg Temp        20.6              20.6              deg C

  Peak Energy               4.780E+07         4.997E+07         Joule

  Dissipated Energy         4.700E+07         4.801E+07         Joule
  ------------------------- ----------------- ----------------- -----------

The above results show that the baseline 5 second flat top pulse can be
achieved with a maximum temperature slightly over 100C (a 120C allowable
has been mentioned), as well as a double field, 0.6 second flat top
pulse.

With a 5 minute repetition period the rms current and average power
would be:

  ------------------------- ----------------- ----------------- -----------
                            3.2kG             6.4kG             

  Repetition Period         300               300               sec

  Irms                      2428.3053         2450.8502         amp

  Pavg                      156666.67         160033.33         watt
  ------------------------- ----------------- ----------------- -----------

The above results (peak current, rms current, peak energy) would imply
that one generator parallel would be sufficient for the 3.2kG, but two
would be required for the 6.4kG.

*Action Items:*

*M Awad requested to run the detailed MG simulation using the coil
parameters described above, including the variation of resistance with
∫i\^2(t)dt.*

M Awad A Brooks P Heitzenroeder R Myslinski M Ono

J Spitzer NSTX File