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13-001212-CLN-01

***TO: DISTRIBUTION***

***FROM: C NEUMEYER***

***SUBJECT: TF OPERATION AT 4.5kG WITH WATER COOLING ABSENT FROM TURN
6A***

***References***

\[1\] 13-001206-CLN-02, "TF Limits vs. Temperature"

\[2\] 13-001206-PJH-01, "Results of Cooling and Shear Stress Analysis
for NSTX TF Center Stack with No Active Cooling on Turn Six and
Resulting Operational Limitations"

\[3\] 13-001208-HMF-01, "Stress Analysis of Loss of Coolant on Cool Down
of TF Coil Inner Leg"

Present TF operational limits were set in ref. \[1\] based on a
prospective adiabatic ∆T of 20C in the TF inner legs, which would lead
to a 0.7\*20C = 14C ∆T between turn 6A and the other turns of the bundle
during cooldown. According to projections made at that time this would
cause a shear stress of 1400 psi in the turn insulation, which would be
48% of the ultimate shear strength of 2942 psi assumed at that time.

Since then the follow-on work in ref. \[2\] and ref. \[3\] has shown
that:

-   indeed at a ∆T of 20C between turns the insulation shear stress is
    of order 2ksi (actual max. value projected to be 2.07ksi);

-   shear strength, even at zero compression, is considerably larger
    (5883 psi) than that assumed earlier (2942 psi).

The above findings, along with the possibility of resurrecting the
Rochester Instrument System (RIS) "1/2LI\^2" module, improve the
prospects for operating at 4.5kG under the present conditions.

The 1/2LI\^2 module introduces a variability into the RIS trip setting
which continuously anticipates the additional I2T which would be
deposited into the coil should an L/R decay occur from the current at
that moment (the equivalent square wave (ESW) of an L/R decay from an
initial current I~o~ is I~o~\^2\*τ/2, where τ = L/R and is adjustable on
the module). This feature allows an extension of the available flat top
from that otherwise available according to the following logic:

Without the feature, the trip setting I2T~trip~ is chosen such that, in
case of a trip at full current, the final value of I2T will not exceed
the maximum allowable I2T~max~. Then in order to avoid trips on each
shot, the end of flat top (EOFT) I2T is limited such that, after the
current is ramped down, the additional I2T~ramp~ added to the prior
accumulation of I2T will not exceed the trip value, i.e. I2T~EOFT~ +
I2T~ramp~ \< I2T~trip~.

With the feature, the trip point varies with current, increasing as the
current decreases according to I2T'~trip~ = I2T~max~ - I~o~\^2\*τ/2.

The effect of the module is illustrated in the following feature which
depicts the per unit TF current and I2T for three cases, namely 1) L/R
decay at EOFT after I2T reaches I2T~trip~, which ultimately deposits
I2T~max~ = 1.0 p.u. into the coil, 2) Ramp down of current at EOFT such
that the at the completion of ramp down the total I2T is equal to a
constant trip (CT) I2T~trip~ and therefore no trip occurs, and 3) Ramp
down of current at EOFT such that the variable trip (VT) I2T'~trip~ is
never exceeded and no trip occurs. It is evident from this figure, which
was run for the 4.5kG case, that an additional ≈ 100mS of flat top can
be gained.

![](media/image2.pct)

The following table summarizes the options, assuming that we want ≈
500mS flat top at 4.5kG:

+------------------+------------+-----------+------------+-----------+
|                  | 3.5kG w/o  | 3.5kG     | 4.5kG w/o  | 4.5kG     |
|                  | RIS Module | w/RIS     | RIS module | w/RIS     |
|                  |            | module    |            | Module    |
+------------------+------------+-----------+------------+-----------+
| Max Flat Top     | 595        | 663       | 505        | 497       |
| Time (ms)        |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| ## Fault         |            |           |            |           |
|  Condition...... |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| ∆T Adiabatic     | 20         | 20        | 33         | 30        |
| (degC)           |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| ∆T Turn-Turn     | 14         | 14        | 23.1       | 21        |
| (degC)           |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| Shear (psi)      | 1449       | 1449      | 2390.85    | 2173.5    |
+------------------+------------+-----------+------------+-----------+
| Shear            | 24.6%      | 24.6%     | 40.6%      | 36.9%     |
| (%Ultimate)      |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| ## No-fault      |            |           |            |           |
|  Condition...... |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| ∆T Adiabatic     | 14.3       | 14.3      | 23.4       | 23.1      |
| (degC)           |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| ∆T Turn-Turn     | 10.01      | 10.01     | 16.38      | 16.17     |
| (degC)           |            |           |            |           |
+------------------+------------+-----------+------------+-----------+
| Shear (psi)      | 1036       | 1036      | 1695       | 1673      |
+------------------+------------+-----------+------------+-----------+
| Shear            | 17.6%      | 17.6%     | 28.8%      | 28.4%     |
| (%Ultimate)      |            |           |            |           |
+------------------+------------+-----------+------------+-----------+

It appears that an increase to 4.5kG, 500mS flat top time is feasible
without substantial increase in risk from the insulation shear
perspective. The incorporation of the extra RIS module would slightly
reduce the exposure to temperature and stress but probably not enough to
justify the cost and effort of implementation.

E. Baker M. Bell W. Blanchard A. Brooks

J. Chrzanowski L. Dudek H. Fan R. Hatcher

R. Hawyrluk P. Heitzenroeder M. Kalish R. Maingi

R. Marsala M. Ono G. Pearson S. Ramakrishnan

E. Synakowski A. Von Halle M. Williams NSTX File

  ---------------------------------------- ------------ ------------------
  Allowable Adiabatic ∆T                   20           deg C

  T0                                       12           deg C

  G0                                       2.53E+15     (A/m\^2)\^2-sec

  Tmax                                     32           deg C

  Gmax                                     6.47E+15     (A/m\^2)\^2-sec

  ∆Gmax=J2Tmax                             3.93E+15     (A/m\^2)\^2-sec

  L                                        4.37E-03     Henry

  Rcircuit (cold)                          7.81E-03     Ohm

  Rcircuit (hot)                           8.19E-03     Ohm

  Rpsequiv                                 4.03E-03     Ohm

  ∑R (cold)                                1.18E-02     Ohm

  ∑R (hot)                                 1.22E-02     Ohm

  CSA inner leg                            6.74E-04     m\^2

  Bt                                       3.5          kG

  Iflat                                    4.15E+04     Amp

  J2T L/R decay                            1.06E+15     (A/m\^2)\^2-sec

  J2T Trip (RIS)                           2.87E+15     (A/m\^2)\^2-sec

  I2T Trip (RIS)                           1.31E+09     A\^2-sec

  Trise                                    0.245        sec

  J2T Rise                                 3.62E+14     (A/m\^2)\^2-sec

  Tfall                                    0.202        sec

  J2T Fall                                 2.55E+14     (A/m\^2)\^2-sec

  J2T Flat                                 2.26E+15     (A/m\^2)\^2-sec

  Tflat                                    0.595        sec

  Gfinal                                   5.41E+15     (A/m\^2)\^2-sec

  Tfinal                                   26.3         deg C

  ∆Tfinal                                  14.3         deg C

  Gfinal (fault)                           6.47E+15     (A/m\^2)\^2-sec

  Tfinal (fault)                           31.8         deg C
  ---------------------------------------- ------------ ------------------

  -------------------------- ----------- ------- ------- ------- ------- ---------- ----------
  Bt                         Iflat       Trise   Tfall   Tflat   ∑T      Tfinal     ∆T

  (kG)                       (Amp)       (sec)   (sec)   (sec)   (sec)   (deg C)    (deg C)

  3.0                        35580.00    0.198   0.179   0.897   1.274   26.3       14.3

  3.1                        36766.00    0.207   0.184   0.826   1.217   26.3       14.3

  3.2                        37952.00    0.216   0.188   0.761   1.166   26.3       14.3

  3.3                        39138.00    0.225   0.193   0.702   1.120   26.3       14.3

  3.4                        40324.00    0.235   0.197   0.646   1.079   26.3       14.3

  ![](media/image3.pct)3.5   41510.00    0.245   0.202   0.595   1.042   26.3       14.3
  -------------------------- ----------- ------- ------- ------- ------- ---------- ----------