5.4.1 Categories of thermal loads  

The thermal management of the MACE Demonstration Unit must contend with a number of thermal loads. Some thermal loads are constant, or “steady state” loads, whereas other thermal loads are transient and involve heating of conductors during the triggering of the MACE Experimental Demonstrator. These various thermal loads are depicted as a schematic in Figure 29.

Figure 29

Figure 29.  Schematic representation various heat loads of the MACE Experimental Demonstrator. Steady-state loads that represent constant heat flux into the device are depicted as red arrows. Transient heating of specific components that occurs during device firing are depicted as blue ovals.

With steady state thermal loads, there is a constant heat flux into the device across insulation layers which must be actively cooled by the cryogenic system. These steady state loads include:

1) heat flux from the 300 K ambient temperature outside the Unit into the 30 K compartment of the MACE Experimental Demonstrator;

2) heat flux across the primary leads from the 77K (70K) liquid nitrogen Dewar to the 30 K compartment; and

3) heat flux across the secondary leads from the 300 K exterior to the 30 K compartment.

The transient thermal loads occur during device triggering and are related to resistive heating of normal (non-superconducting) conductors as current passes through the device. These transient thermal loads include:

1) I2R heating of the secondary coil during firing;

2) I2R heating of the secondary current leads during firing; and

3) heating of the quenched HTS switch in the 70 K compartment during firing.


5.4.2 Temperature Specification and Operating Characteristics of MACE Demonstration Unit Determine Cryogenic Approach

Choice of thermal design, including insulation strategy and cryogenic components is largely determined by the operating temperature of the primary and secondary coils of the MACE Demonstration Unit. Because the primary coil must operate at 30 K, far below liquid nitrogen temperatures, the logical approach to cooling is to use conduction cooling from the cold head of a cryocooler. For the purposes of making a lab-scale prototype, conduction cooling is simpler, cheaper, and more robust compared to other options such as liquid helium-based cooling.

Furthermore, because the MACE Demonstration Unit generates a magnetic field of approximately 2 Tesla, which is significantly lower than the expected MACE Field Prototype, it is impossible to maintain an insulated gap between the primary coil (which must operate at 30 K) and the annular secondary coil without significantly impacting overall energy transfer efficiency. At higher field strengths, such as are expected in the MACE Field Prototype, a 1-2 cm insulated gap will not significantly impair device efficiency.

Thus, both the primary and secondary coils in the MACE Demonstration Unit must be maintained at 30 K, despite the secondary coil being subject to steady state and transient loads which could easily be cooled with liquid nitrogen. Paradoxically, perhaps, MACE becomes easier to cool as it scales up from the Experimental Demonstrator to the Field Prototype.

5.4.3 Thermal Design of Main Vessel

Because MACE is a superconducting Pulsed Power Transformer, it is important to minimize the presence of metal structural elements which could inductively couple to the primary and secondary coils. This design consideration limits the use of metal to create the main vacuum vessel (aka the 30 K compartment), the use of metal to create metallic standoffs to position the coil within the vessel, and even the use of standard thermal design elements such as metallic thermal shielding.

Figure 30 shows the basic design of the main vessel, which consists of an evacuated HDPE plastic vessel that contains the main MACE coils (primary and secondary), the cryocooler cold head, and associated copper heat sink. Also shown is the liquid nitrogen Dewar that contains the HTS switch. The main MACE coils (primary and secondary) are supported in a packed bed of evacuated perlite thermal insulation (in a 2-cm width layer) which provides both thermal insulation and structural support during operations. Evacuated perlite has a thermal conductivity of 1 x 10-3 W K-1 m-1 and a packed bed compressive strength of 80 psi, or well in excess of the 20-psi outwards hoop stress expected during operation of the coil.

Figure 30

Figure 30. Thermal design of the main vessel. The MACE main coils (primary and secondary, as well as cryocooler cold head and heat sink materials are contained within a HDPE vessel. Vessel lid is shown as transparent, and the packed perlite fill is not shown. Cross section diagram of the MACE secondary and primary coil structures located within the main vessel. The coils are supported with a packed bet of evacuated perlite fill.

With the above design, under steady-state conditions, ISIT can expect a continuous heat load of 11 W into the secondary coil from the ambient exterior well within the cooling capacity of the cryocooler (see Section 5, Page14). 


5.4.4 Thermal Design of Secondary Leads

The leads from the secondary coil in the 30 K compartment to the exterior (i.e. 300 K) of the vessel represent a significant thermal design challenge. The leads must be large enough to carry the expected current (up to 150,000 A) without excessive heating while simultaneously not being so large as to allow significant heat flux from the exterior of the vessel into the 30 K compartment and conductively heating the secondary and primary coils excessively. Additionally, to minimize heat flux into the 30 K compartment and to avoid conductively heating the secondary and primary coils, it seems necessary that the external leads (connected to an external load such as a railgun) should remain physically unconnected (except at time of firing) to the leads within the 30 K compartment that are connected to the secondary coil.  To accomplish these design objectives, ISIT has designed a demountable secondary lead system shown in the diagram in Figure 31.  Although this design has not been brought into the CAD design as yet, ISIT believes it represents a viable method to satisfy all the design criteria for the secondary leads. 

Figure 31

Figure 31.  Thermal Design of Secondary Leads. To avoid excess heat flux from 300 K exterior into the 30 K interior compartment, the secondary leads can be quickly attached and detached from the external leads by means of an expandable bellows.

The secondary lead design specifies the use of 10 cm-long  Litz wire  leads which  connect to  copper terminals on the secondary coil at one end and connect to bullet-type terminal pins at the other end that reside within the 30 K compartment (i.e. they are not physically connected to any outside leads).  At 1 second before firing, a bellows holding the external leads is collapsed so that the bullet pins of the secondary leads are mated with a matching connector that terminates the external leads to the external wall of the main vessel. After firing, the bellows are expanded and the secondary leads are uncoupled from the connector containing the external leads.  Thus, a physical connection from the 30 K region via the secondary leads to the 300 K region is only maintained for a few seconds during firing, and conductive heat losses are minimized. 

The Litz wire leads (each of which has a cross-sectional area of 1-cm) are encased in an epoxycomposite form to add rigidity to the structure.


5.4.5 Thermal cycling times for primary and secondary coil 

The thermal cycling time for the main vessel of the MACE Experimental Demonstrator is  equation where, T is time in seconds, E is the thermal energy deposited into the structure during firing, and P is the available thermal cooling power provided by the cryocooler. During firing of the MACE Experimental Demonstrator, approximately 950 J of thermal energy is deposited into the secondary coil structure due to I2R losses of current passing through the 30 K coil and 330 J of thermal energy is deposited in the secondary leads attached to the secondary coil for a total of 1250 J of thermal energy which must be removed before the system returns to its pre-firing state. The available thermal power from the cryocooler is estimated to be 45 W(th), which equates to its 60 W(th) capacity (at 30 K) minus the steady-state losses of approximately 15 W(th) due to heat leakage into the 30 K compartment. Thus, expected cycling time will require at least 1250 J / 45 (J/s) = 27.8 s.

5.4.6 Thermal cycling times for persistent high temperature superconducting switch

The HTS switch is expected to experience the highest transient thermal loads at time of firing since the switch must dissipate approximately 10% of the total stored energy in the MACE Experimental Demonstrator, or approximately 1.9 kJ of energy, it is expected the switch will experience a significant rise in temperature (ΔT = 75 K).  However, since the HTS switch coil (described in Tech Report 3) is mounted within a perforated copper coil form which allows the free circulation of sub-cooled liquid nitrogen (T = 70 K) to bathe the HTS switch coil, it is expected that the liquid nitrogen will remove the excess heat within seconds. Liquid nitrogen has a high heat of vaporization of 200,000 J / kg.  Thus, removing 1920 J of heat from the HTS switch will consume only about 1 g of LN2. Also, LN2 can remove heat from a material at a rate of 10 W/cm2 of material being cooled.  Since the area of HTS tape in contact with LN2 is 80 cm2, it is expected that the thermal cycling time of the HTS switch will be 1920 J / (80 * 10) (J/sec) = 2.4 s.


5.4.7 Cryocooler equipment, cryogen, and thermal insulation requirements

ISIT thermal management design will use standard, commercially available components and materials.  For example, the cryocooler will most likely be a Cryomech AL230 (Figure 32), which provides approximately 60 W(th) cooling power at 30 K. 

Figure 32

Figure 32. [A] The Cryomech AL230 cryocooler. [B] The cooling capacity of the AL230 at different temperatures. Credit for both images: www.cryomech.com


.: Management and Organization

The Institute's focus areas. Click on a specific area for more information.