4.1.1 LT-SPICE Results

Excellent coupling is achieved between the MACE multi-turn SC energy storage coil (inner conductor of coax) and the single-turn copper load coil (outer conductor of the coax) by using a coaxial conductor arrangement. Good coupling in a pulse transformer typically results in good energy transfer and extraction since there is little uncoupled magnetic field leakage energy.  

The MACE SC switch transfers energy from the SC storage coil to the load when the SC switch is quenched and driven to its OFF state.  This enables the primary SC coil to be maintained in its low temperature state and only the small SC switch needs to be recooled.  The voltage developed across the SC switch resistance drives a changing flux linkage in the SC coil that decreases the current; since the SC coil is magnetically coupled to the load coil, the changing flux linkage drives an increase in the current in the load coil.  Because it is the total amp-turns in the coil that determines the flux linkage, the current induced single turn load coil is (ideally) N-times the initial current in the SC coil if the turns ratio is N to 1.  Because of magnetic leakage flux internal to the SC coil and in the radial gap between the SC and load coil conductors, there is <100% energy transfer, but the excellent coupling of the coaxial construction helps to minimize this.

However, our circuit simulation and analysis has shown that for the SC MACE system the OFF-state resistance of the SC switch has a significant impact on the system performance.  

In the OFF-state, a typical mechanical switch exhibits a resistance that is essentially infinite (unless there is a voltage breakdown), but a SC switch has an OFF-state resistance determined by the matrix or backing material used in its construction.

This SC, if used as-is in our switch, would have an OFF-state resistance of 20 Ω, so the resistance for the 188-turn storage coil that appears across the load coil terminals is 20/1882 or 0.566 mΩ (assuming 100% coupling and no leakage inductance).   This means that the transient part of the circuit solution should be identical in its amp-turns response for both the load coil and the energy storage coil, since both coils are connected to equivalent resistances.  A simple LTSpice simulation demonstrates this. 

Figure 1

Figure 1. Circuit diagram of one configuration of the MACE Demonstration unit.

The LTSpice circuit is shown in Figure 1, with the load resistance set to 0.566 mΩ and the SC switch OFF resistance set to 20 Ω. Inductance parameters were determined from FEMM finite element calculations based upon the circular MACE coil geometry. Initial current in the SC coil is set to 800 A, and the load coil current is set to 0 A.

The simulation results for the voltages and currents at both the SC coil and the load coil terminals after opening the SC switch are shown in Figure 2. Note that some quantities are scaled by the turns ratio (188) in order to properly represent them on the same scale.

Figure 2

Figure 2. Simulated voltages (top panel) and currents (bottom panel) of the terminals of the SC coil and Secondary Coil

The scaled voltages and currents track almost exactly during the transient part of the curves. This case shows that nearly equal energy is delivered to the load and SC switch resistances. Circuit theory indicates that in order to get more current (and energy) delivered to the load, the load resistance should be much smaller than the transformed switch resistance. If the load resistance is set to 0.0566 mΩ (one-tenth of the initial value), (Figure 3) the energy delivery shifts to the load and away from the switch.

Figure 3

Figure 3. Simulated voltages (top panel) and currents (bottom panel) of the terminals of the SC coil and Secondary Coil when load resistance is set to 0.0566 mΩ

Conversely, the load resistance is 5.66 mΩ (10 times the initial value), most of the energy is deposited in the SC switch resistance (Figure 4).

Figure 4

Figure 3. Simulated voltages (top panel) and currents (bottom panel) of the terminals of the SC coil and Secondary Coil when load resistance is set to 0.0566 mΩ

In the switch configuration currently under study, the MACE circuit is inherently a closely-coupled air-core coil set and the currents which flow during any circuit transient are governed by the impedances seen at the terminals of each winding reflected through the turns ratio.  This sets fundamental limits on load impedance values that maximize energy transfer to the load and minimize energy deposition in the SC switch. Thus, some modification to the original electric circuit is required.  Alternative arrangements for the SC switch are a topic for future research.

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