Quench protection analysis integrated in the design of dipoles for the Future Circular Collider

The EuroCirCol collaboration is designing a 16 T ${\mathrm{Nb}}_3\mathrm{Sn}$ dipole that can be used as the main bending magnet in a 100 km long 100 TeV hadron-hadron collider. For economic reasons, the magnets need to be as compact as possible, requiring optimization of the cable cross section in different magnetic field regions. This leads to very high stored energy density and poses serious challenges for the magnet protection in case of a quench, i.e., sudden loss of superconductivity in the winding. The magnet design therefore must account for the limitations set by quench protection from the earliest stages of the design. In this paper we describe how the aspect of quench protection has been accounted for in the process of developing different options for the 16 T dipole designs. We discuss the assumed safe values for hot spot temperatures and voltages, and the efficiency of the protection system. We describe the developed tools for the quench analysis, and how their usage in the magnet design will eventually ensure a secure magnet operation.

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Figure 1

Estimation of heater delays at nominal current.

Figure 2

Cross sections and magnetic field distribution of one aperture of (a) block and (b) $\mathrm{Cos}\theta$ design. For the CC design, (c), both apertures are shown. The coils are not to scale relative to each other. The color map gives an approximate value for the different field regions. In parentheses we show the coil design version identifiers for relating them to subsequent literature.

Figure 3

Maximum peak temperature vs protection quench delay.

Figure 4

Quench delay and heater delay at 105% of $I_{\mathrm{nom}}$ in the $\mathrm{Cos}\theta$ design.

Figure 5

Quench delay and heater delay at 105% of $I_{\mathrm{nom}}$ in the block design.

Figure 6

Quench delay and heater delay at 105% of $I_{\mathrm{nom}}$ in the common-coil design.

Figure 7

Final temperature ($\mathrm{t}=600\mathrm{ms}$). Left: Uniform 40 ms delay; right: distributed heater delay.

Figure 8

Final temperature ($\mathrm{t}=550\mathrm{ms}$). Left: Uniform 40 ms delay; right: distributed heater delay.

Figure 9

Final temperature ($\mathrm{t}=600\mathrm{ms}$). Left: Uniform 40 ms delay; right: distributed heater delay.

Figure 10

Voltage to ground in the $\mathrm{Cos}\theta$ design at $\mathrm{t}=180\mathrm{ms}$. Left: Uniform 40 ms delay; right: distributed heater delay.

Figure 11

Resistive and inductive voltages across the coil half turns at $\mathrm{t}=180\mathrm{ms}$. Left: Uniform 40 ms delay; right: distributed heater delay.

Figure 12

Voltage to ground at $\mathrm{t}=160\mathrm{ms}$. Left: Uniform 40 ms delay; right: distributed heater delay.

Figure 13

Resistive and inductive voltages across the half turns at $\mathrm{t}=160\mathrm{ms}$. Left: Uniform 40 ms delay; right: distributed heater delay.

Figure 14

Voltage to ground in the common coil. Left: Uniform 40 ms delay, $\mathrm{t}=200\mathrm{ms}$; right: distributed heater delays, $\mathrm{t}=160\mathrm{ms}$. Only upper halves of coils are shown (see Fig. 2).

Figure 15

Resistive and inductive voltages across the half turns. Left: Uniform 40 ms delay, $\mathrm{t}=200\mathrm{ms}$; right: distributed heater delays, $\mathrm{t}=160\mathrm{ms}$.

Figure 16

Schematic of a CLIQ unit connected to a superconducting magnet. ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ represent two different electrical parts of the magnet.

Figure 17

Considered CLIQ connection scheme.

Figure 18

Currents in different coil sections after a CLIQ discharge. The coils sections are described in Fig. 17.

Figure 19

Final temperature ($t=500\mathrm{ms}$) with CLIQ protection system.

Figure 20

Voltage-to-ground ($t=140\mathrm{ms}$) with CLIQ protection system.

Figure 21

Final temperature ($t=500\mathrm{ms}$) with CLIQ and quench heater protection systems.

Figure 22

Voltage to ground ($t=140\mathrm{ms}$) with CLIQ and quench heater protection system.