**(DRAFT)**

**Engineering for the 14.5Tesla Pulsed Magnet**

**Mechanical Design**

A three segment, layer wound solenoid is proposed for the pulsed magnet.
The conductor is half inch square, cold worked OFHC copper. The coil is
inertially cooled with options for liquid nitrogen or gaseous Helium
cooling between shots. Coolant flows through axial channels in the coil.
The coil will be epoxy impregnated. Wound coils of this small radius,
using cold worked conductor, retain internal elastic stresses from the
winding process, and if not impregnated, require elaborate clamping
mechanisms to have the coil retain it's shape.

Proposed Operational Scenarios:

  ----------- ---------- ------------ ----------- --------- --------------
  Case \#     Peak Field Coolant      T after     T coolant Start Bulk
                                      pulse                 Temp

  1           5T         Helium Gas   90K         66K       84K

  1a          5T         LN2          90K         66K       84K

  2           10T        Helium Gas   96K         66K       74K

  2a          10T        LN2          96K         66K       74K

  3           15T        Helium Gas   78K         22K       30K
  ----------- ---------- ------------ ----------- --------- --------------

Dual operational modes require special design of the cryostat/helium
can. This is discussed in the section on cooldown behavior.

![](media/image1.png){width="3.1277777777777778in"
height="3.571527777777778in"}Insulation design impacts the conduction
cooling behavior:

-   Kapton is the limiting element in the thermal conduction through the
    coil.

-   Kapton initially was expected to be wound around the conductor. This
    produced the equivalent of 5 mils of Kapton between layers.

-   To improve conduction, Kapton is used only between the layers. Turn
    to turn voltage is lower than layer to layer. The turn to turn
    voltage is less than the rule of thumb for He breakdown voltage (1
    volt/mil at 1 atmosphere) for the insulation thickness proposed.
    Note that the He operating pressure is expected to be 15
    atmospheres, the pressures inside the epoxy winding pack may be
    substantially lower, depending on Helium diffusion, making the 1 atm
    breakdown voltage for the conductor, reasonable.

-   The layer to layer voltage exceeds this rule of thumb, however, and
    would need the Kapton if there was an imperfection in the
    epoxy/glass insulation. Half laps of kapton and fiberglass, similar
    to the CS model coil will retain some structural integrity.
    ![](media/image2.png){width="2.1486111111111112in"
    height="1.5381944444444444in"}

-   Once a layer of conductor is wound, a layer of Kapton/glass would be
    wound on the completed layer of conductor. This produces the
    equivalent of 3 mils of Kapton rather than 5 if the conductor were
    wrapped individually. Every 6 to 8th layer some sort of preformed
    channel array would be layed on, then wrapped with glass/Kapton to
    hold it in place, and as the layer insulation for the next layer of
    conductors. .

Experience with Alcator C-Mod indicates that for final magnet
temperatures at or below 100K, the channels will not need "turbulators"
or surface trips to break-up the film boiling layer. This will have to
be reviewed during the design phase. If some form of surface roughness
will be required in the 2mm channels, then the method of forming the
channels with removable strips will have to be re-visited.

**Engineering Tasks**

While the magnet has been conceptualized, with some analytic basis,
detailed engineering will require additional work after the construction
of the magnet is approved. These tasks are outlined below.

-   Identify Voltages for All Operating Scenarios - Choose insulation
    systems. Determine where Kapton is used.

-   Stress Analysis, Assess radial load on channel ligaments, consider
    operation with inner modules energized, and no current in outer
    module

-   Confirm cooldown and pressure drop calculations

-   Analyze thermal contraction/shock of channel -- Avoid separation and
    loss of conduction

-   Design He can for 15 atm. and vacuum operation.

-   Design mandrel and flow plenums

-   Cryostat Design. Is this a Vacuum Cryostat with LN2 Shield, or a
    Gaseous N2?

-   Break-outs and Leads Penetration design -- Design the required
    support to resist loads and torques that result from principally the
    end radial Field.

-   Determine if Eddy Currents in He Can represent a significant load.

-   Design Cryogenic Electrical Breaks

-   Design Supports, Break-outs, He can and Cryostat to Allow Phased
    Construction

Some of the analytic work in support of the present design is now
described:.

**Stress Analysis**

The coil is stress analyzed using ANSYS. Fields and forces are computed
using Elliptic integrals in a code external to ANSYS. The model is
axisymmetrric. The figures show a 3D representation from a symmetry
expansion.

Coil Build used in the Stress Analysis

  ---------- ---------- ---------- ---------- ---------- ---------- ----------
  Seg#       r          z          dr         dz         nx         ny

  1          .15        0          .098       1.0        16         16

  chan       .2         0          .002       1.0        1          16

  2          .25        0          .098       1.0        16         16

  chan       .3         0          .002       1.0        1          16

  3          .35        0          .098       1.0        16         16
  ---------- ---------- ---------- ---------- ---------- ---------- ----------

For Fusion magnets the inner skin of the solenoid is allowed to reach
the yield - Treating this stress as a bending stress with a 1.5\*Sm
allowable with Sm based on 2/3 Yield.

Interpolated values:, Work hardened copper-, OFHC c10100 60% red

  ----------- ------- ------- ------- ------- ------- ------- ------- ------- -------
  temp deg k  77      90      100     125     150     200     250     275     292

  yield       374     369\.   365\.   356\.   347\.   328\.   317\.   312\.   308\.

  ultimate    476\.   466\.   458\.   439\.   420\.   383\.   365\.   356\.   350\.
  ----------- ------- ------- ------- ------- ------- ------- ------- ------- -------

If the highly cold-worked copper is chosen for the winding, the
conductor allowable near the inside radius of the coil would be 365MPa.
The max stress in the three segment coil is 166 MPa. With this stress
level, it is expected tthat half hard copper could be used, simplifying
the winding process.

![](media/image3.png){width="5.626388888888889in"
height="4.361111111111111in"}

The three segment coil has three operational modes, two of which are
structurally significant. The full performance configuration is limiting
in terms of hoop stress and equivalent stress. It also has some radial
stresses that will have to be mitigated with parting planes at the
segment boundaries, or within the winding.

In the initial operating mode the outer coil segment is not energized.
This induces some differential Lorentz forces and differential
temperatures, that cause shear stresses between segments.

![](media/image4.png){width="5.874305555555556in"
height="4.507638888888889in"}

It may be desirable to build only the initial two inner segments and add
the outer segment at a later time. The coil was analyzed with the outer
segment removed, and the same current density in the other two segments.
The max stress for this case is 85.3 MPa, which is a bit more than with
the outer segment in place, but less than for the fully energized three
segment coil. In all cases the stresses are lower than the expected
allowable for the conductor. It is expected that the degree of cold work
can be relaxed from the full hard condition. The final choice of the
degree of cold work for the conductor will be determined during detailed
design. ![](media/image5.png){width="5.620833333333334in"
height="4.300694444444445in"}![](media/image6.png){width="5.247916666666667in"
height="4.030555555555556in"}

![](media/image7.jpeg){width="5.272916666666666in"
height="4.052777777777778in"}

**Cooldown Between Shots**

Phased implementation of cooling systems is expected for the project.
Within the coil, two cooldown methods are being investigated: and option
using liquid nitrogen and an option which uses helium gas. It is
expected that design of the magnet and cooling channels will allow
either working fluid. Use of liquid nitrogen as the only coolant is
contemplated for the initial operation of the magnet. It is possible to
use the container around the magnet as a vacuum vessel, and sub-cool
liquid Nitrogen to 66K. Helium gas operation uses liquid nitrogen to
cool the helium gas in a heat exchanger, and later allows use of liquid
hydrogen to cool the helium and obtain improved fields and/or pulse
lengths. The heat transfer characteristics of liquid nitrogen operation
have only been conceptualized. Heat transfer calculations using gaseous
helium will be presented here.

![](media/image8.png){width="5.998611111111111in"
height="4.214583333333334in"}

In the LN2 sub-cooling mode, about 50 cubic meter of nitrtogen gas at
standard temperature and pressure must be drawn off by the vacuum pump
to lower both the magnet and the liquid nitrogen to the desired 66K
temperature.

**Cooling time with Helium gas as a Working Fluid**

The solenoid has groups of 6 to 8 layers of 1/2 inch square conductors
separated by set of annular cooling channels. This could model any
linear stack of .5 inch square conductors cooled from the ends of the
stack whether layer wound - then there would be a layer of channels
every sixth layer of conductor, - or pancake wound, where there would be
radial channels every sixth pancake. The solution is a simple finite
difference transient analysis. The ground wrap or cracked
conductor/Kapton tape interfaces have not been modeled

The insulation layer is modeled with five, and as a second option,
three, .001\" thicknesses of Kapton tape. The thermal conductivity of
the tape is about .14 W/(m-K) at 100 k and was taken from \" Thermal
Conductivity of Polymide Film between 4.2 and 300K With and Without
Alumina Particles as Filler\" Rule, Smith, and Sparks, NISTIR #3948.
August 1990

The surface heat transfer coefficient at the channels was taken as 170
W/m\^2 for nitrogen gas at 100K flowing at 40 m/s in a channel with a
2cm hydraulic diameter. This comes from an Oak Ridge CIT report \#
ORNL/FEDC-85-10 Dist Category UC20 c,d October 1986. The Helium gas
coefficient has been calculated from the Nusselt, Reynolds, and Prandle
Numbers using the relation quoted in the Oak Ridge document, and will be
verified during detailed design..

![](media/image11.wmf){width="4.197916666666667in" height="2.59375in"}

![](media/image12.wmf)

Present Operational Scenarios:

  --------- ----------- ---------- --------- -------------- ---------------
  Case \#   Peak Field  T after    T coolant Start Bulk     Guestimated
                        pulse                Temp           Time

  1         5T          90K        66K       84K            \~200 sec

  2         10T         96K        66K       74K            \~800 sec

  3         15T         78K        22K       30K            \~1500 sec
  --------- ----------- ---------- --------- -------------- ---------------

![](media/image13.png){width="2.660416666666667in"
height="3.4319444444444445in"}

Typical results for 66K He cooling, .1kg/sec, 100 K end of pulse temp.
85K target Magnet start temp. The cooldown time is 600 sec. to reach 85K
bulk temp, but not thermal equilibrium.

Number of Atmospheres Operating Pressure ;10

Enter Channel Heigth in mm ;2

Rinner, radial build 0.1000000 7.6200157E-02

inner coil start temp 100.0000

outer coil start temp 100.0000

inner coil radius 0.1000000

model cell energy 1644.685J (100 to 85K bulk)

model cell volume 5.5099601E-05

volume cpp 1989954.

nlength, naxial, 120 5

Mass flow rate= 4.1666666E-05kg/sec

Volume flow rate= 5.5507730E-06

flow velocity= 2.120239

Hydraulic Diameter= 2.8944151E-03m

Velocity Head= 1.721665 Pascal

Pressure Drop= 31.46283 Pascal

Pressure Drop= 3.1041747E-04Atmospheres

Helium density= 7.506462 kg/m\^3

Helium viscocity= 2.6448268E-07

Prandl #, Reynolds \# 4.0756337E-02 174174.1

Heat transfer coefficient 115984. 9

From mdot\*cp\*deltaT for a 20 deg inlet-outlet difference the cooldown
time is about 950 sec. The simulation with a finer time step
(dtime=.0001 rather than .001) yields a 600 sec cooldown . The inlet
outlet delta T ranges from 26K to 16K. The Energy balance or difference
between the conduction heat flux and the channel heat flux. Is good at
the finer time step

**30K Coolant, Cooldown from 100K**

![](media/image14.png){width="1.55in" height="0.8784722222222222in"}

![](media/image15.wmf){width="4.875in" height="3.6305555555555555in"}

Bulk temp Is computed as the average temperature at mid axial build - It
bottoms out before the down stream end. In the plot above, the channel
outlet temperatures are better indicators of when the magnet reaches 30K

tout 1 and tout2 are Outlet Temperatures

Analyses to date: Time to target bulk temp from 100K. ½ inch Copper
Conductor.

+--------------------------+-------+-------+--------+--------+--------+
|                          | T     | T     | Cond   | !      | Time   |
|                          | after |       |        | [](med | to 30K |
|                          |       | co    | Layers | ia/ima | sec    |
|                          | pulse | olant |        | ge14.p |        |
|                          |       |       |        | ng){wi |        |
|                          |       |       |        | dth="1 |        |
|                          |       |       |        | .55in" |        |
|                          |       |       |        | heig   |        |
|                          |       |       |        | ht="0. |        |
|                          |       |       |        | 878472 |        |
|                          |       |       |        | 222222 |        |
|                          |       |       |        | 2222in |        |
|                          |       |       |        | "}Time |        |
|                          |       |       |        | to 85K |        |
|                          |       |       |        | sec    |        |
+--------------------------+-------+-------+--------+--------+--------+
| Equiv 5 Kapton .001in    | 100K  | 66K   | 6      | 600    |        |
| wrap                     |       |       | layers |        |        |
+--------------------------+-------+-------+--------+--------+--------+
| Equiv 5 Kapton .001in    | 100K  | 66K   | 8      | \>850  |        |
| wrap                     |       |       | layers |        |        |
+--------------------------+-------+-------+--------+--------+--------+
| Equiv 3 Kapton .001in    | 100K  | 66K   | 8      | 450    |        |
| wrap                     |       |       | layers |        |        |
+--------------------------+-------+-------+--------+--------+--------+
| Equiv 5 kapton .0001in   | 100K  | 30K   | 6      |        | 2000   |
| wrap                     |       |       | Layers |        |        |
+--------------------------+-------+-------+--------+--------+--------+