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13-001206-CLN-02

***TO: DISTRIBUTION***

***FROM: C NEUMEYER***

***SUBJECT: TF LIMITS vs. TEMPERATURE***

***References***

\[1\] 13-001206-CLN-01, "TF Operation with Water Cooling Absent from
Turn Six"

\[2\] NSTX-CALC-13-2, "TF Coil Parameters"

\[3\] NSTX-CALC-13-18, "TF As-Built Circuit Parameters"

In order to quantify operating limits as a function of allowable
adiabatic temperature rise (as called out in the ref. \[1\]) a
spreadsheet was developed as described herein.

First, the G function is used per ref. \[2\] to determine the ∆J2T which
will heat the coil to the temperature limit, starting from a given inlet
water temperature (nominally 12C). Then, a peak allowable field is
chosen (in this case 3.5kG) which establishes the ∆J2T associated with
current decay, in case a trip occurs at peak field. The final allowable
∆J2T minus the ∆J2T attributable to current decay sets the RIS I2T trip
level. Then, given the trip level, and the I2T associated with current
rise and current fall, the allowable flat top duration at different
field levels can be set such that the current, with power supply ramp
down, goes to zero without raising the I2T to the RIS trip level.

Results are given in the attached tables and figure with 3.5kG and
∆T=20C max. chosen as the governing conditions. It is noted that a flat
top time of order 600mS can be achieved at 3.5kG, including current ramp
down, without an I2T trip. Should an I2T trip occur at the end of flat
top, at any field up to 3.5kG, the maximum allowable temperature rise
will not be exceeded.

These limits are to be enforced in hardware by the RIS and ACP
overcurrent settings, the RIS I2T setting, and in software by the PSRTC
overcurrent, temperature, and I2T settings.

cc:

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

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

R. Hawyrluk P. Heitzenroeder M. Kalish R. Marsala

M. Ono G. Pearson S. Ramakrishnan 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/image2.pct)3.5   41510.00    0.245   0.202   0.595   1.042   26.3       14.3
  -------------------------- ----------- ------- ------- ------- ------- ---------- ----------