Secondary CLIQ, a robust, redundant, and cost-effective means of protecting high-field accelerator magnets

Secondary CLIQ is a quench protection method where capacitors are discharged over secondary normal-conducting coils that are inductively coupled to superconducting coils. Similar to regular CLIQ, this discharge results in rapid magnetic field oscillations over the superconducting conductors, which gives rise to inter-filament and inter-strand coupling losses in these conductors. Consequently, the superconducting coils quickly and efficiently transitions to normal state. As they develop resistance, a significant amount of stored magnetic energy is inductively transferred to the normal-conducting coils and dissipated there [14].

To limit the scope of this manuscript, the Secondary CLIQ concept is presented here specifically for the case of Nb₃Sn superconducting block-type coils. In general the concept is more broadly applicable, with the main requirement being that the secondary non-superconducting coils are magnetically coupled to the superconducting coils to induce coupling losses effectively.

Figures 1 through 4 illustrate the proposed layout. The secondary coils, comprising insulated copper windings, are located adjacent to the superconducting coils. The secondary coils are subdivided into forward and rear coils (figure 1), which are connected in series with each-other. One of the poles of the CLIQ unit goes to the electrical mid-point in between the secondary coils and the other goes to the electrically opposite side of the secondary coils (figure 2). This particular configuration gives various benefits:

• When the CLIQ unit is discharged, the forward and rear coils oscillate with opposite polarity (figure 3). The secondary coils thus produce a fast-changing dipole field over the superconducting conductors, but with opposite field orientation in the forward and rear coils. As the net dB/dt over the half-turns of the superconducting coil is zero (in spite of significant local dB/dt), the net induced electric field over each half-turn due to the CLIQ discharge is also zero. This means that the discharge of the CLIQ unit does not raise the voltage-to-ground in the superconducting coil at the moment of capacitor discharge except for minor local variations within the half-turns.
• After the superconducting coil transitions to normal state, a significant fraction of the stored magnetic energy is transferred to the secondary coils [14]. For the HD2 example described in section 3 about 25 % of the stored magnetic energy is dissipated in the secondary coils, which constitute 20 % of the total coil volume. This reduces the voltage-to-ground and hot-spot temperature in the superconducting coils [14], but, due to the anti-symmetric connection of the CLIQ unit to the secondary circuit, does not result in a rise in voltage over the CLIQ unit (figure 3). Even though the secondary coils develop substantial currents after the superconducting coils quench, the current through and voltage over the CLIQ unit never exceeds its initial peak and quickly attenuates after the initial CLIQ discharge.
• During the CLIQ discharge, the net field integral induced by the secondary coils is zero. This means that in the case of a spurious CLIQ triggering, the particle beam passing through the magnet is not pushed out of its trajectory, which may otherwise cause severe damage to the particle accelerator [26].

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In addition to subdivision into forward and rear coils, the coils are subdivided into top and bottom coils (figure 4), where the top coils are in Secondary CLIQ circuit #1 and the bottom coils are in Secondary CLIQ circuit #2. Each of the two Secondary CLIQ circuits is connected to a CLIQ unit. The energy stored in the capacitors inside the CLIQ unit is sufficient to bring the magnet to normal state, even when only one of the two CLIQ units is discharging (as demonstrated in section 3). This means that a failure to discharge of one CLIQ unit does not result in an unprotected superconducting magnet. This intrinsic redundancy reduces the required reliability of the triggering system and the CLIQ unit, which would otherwise have to be very close to 100% to provide reliable long-term protection of an accelerator circuit featuring hundreds of accelerator magnets and CLIQ units. Note that CLIQ units are specifically designed with internal redundancies to maximize their fault tolerance. Secondary CLIQ benefits from the fault-tolerance of CLIQ units and in addition requires just one working CLIQ unit out of two to protect the magnet.

Diodes are placed in series with the secondary coils (figure 2), to prevent inductive transformation of current from the primary coils to the secondary coils during magnet ramping and during a fast circuit discharge of a non-quenching magnet [14]. These diodes are optional, given that for a low ramp rate the ramping loss resulting from inductive transformation to the secondary coils may be insignificant.

Zoom In Zoom Out Reset image size

Accelerator circuits are quite sensitive to the occurrence of shorts-to-ground. For example, a previous event where a short-to-ground appeared in the LHC main dipole circuit lead to the spurious quenching of 22 main dipole magnets, as the quench detection circuitry was suddenly exposed to a circuit potential shift of 400 V [27]. A more serious problem is the occurrence of a double short-to-ground, where the discharge of the circuit is uncontrolled with the potential of severe damage to the circuit [28]. Thus, reducing the likelihood of shorts-to-ground is important for guaranteeing the longevity of an accelerator circuit.

Secondary CLIQ resilience to shorts to ground is given by two ingredients. Firstly, given that heat conduction between the primary and secondary coils is not required for quench protection, the insulation thickness may be designed for robustness. For example, in the HD2 example given in section 3, the conductor insulation thickness between the neighbouring copper conductors in the secondary coils is fixed at 500 µm rather than 220 µm for the superconducting conductors and in addition a 1 mm thick layer of insulation is placed between the primary and secondary coils.

Secondly, since Secondary CLIQ does not require a direct electrical connection from the CLIQ unit to the superconducting coil, a hypothetical short-to-ground inside the CLIQ unit does not directly affect the primary circuit, and thus will not lead to spurious quench detection. In principle the Secondary CLIQ circuit with a single short-to-ground will still operate correctly, albeit without a grounding fuse and with a displaced grounding point.

The protection scheme as presented here considers two CLIQ units per magnet, where each CLIQ unit discharges sufficient energy to efficiently bring the superconducting magnet to normal state over the entire operational current range of the magnet. This means that even when one of the two CLIQ unit fails to trigger, the magnet is still protected. The practical implications of this configuration are discussed extensively in section 3.

To limit the scope of this manuscript, the concept and simulations are applied to a single aperture magnet. In general, the same principle also applies to a double aperture magnet (where the two magnet apertures have a single cold diode in parallel as is the case in the LHC main dipole circuit [29]), with two CLIQ units per aperture and thus four CLIQ units per magnet. Having four CLIQ units per double-aperture magnet further enhances redundancy. The purpose of this paper is to present the concept without considering a variety of magnet configurations. Double-aperture magnets are thus beyond the scope of this paper, but it is nevertheless important to note that applying this method to a double-aperture magnet would further enhance quench protection reliability.

The presence of secondary coils significantly reduces the hot-spot temperature and voltage-to-ground in the superconducting coils, in part because a significant fraction of the stored magnetic energy is dissipated in the secondary coils [14].

The price of Nb₃Sn magnets is expected to be driven by the price of the conductor [30]. In addition to Nb₃Sn, the superconducting conductor comprises a substantial fraction of copper (locally exceeding two-thirds for the FCC-hh baseline designs [9, 31–33]) which undergoes a complex processing route. Unlike the superconducting coil, the secondary coil comprises bulk copper windings, where the associated material costs are orders of magnitudes below that of the superconducting conductor.

It is thus evident that for magnets in which the design is driven by quench protection considerations, i.e. internal voltages and hot-spot temperature during a quench, Secondary CLIQ reduces the need for copper in the superconducting coils, and thus gives the magnet designer the option of lowering the mass and cost of the superconducting coils.

A series of simulation studies were performed to determine the implications of Secondary CLIQ in terms of hot-spot temperature, peak voltage-to-ground, and redundancy. A 14 m long version of HD2 is taken as reference magnet, for the theoretical case where it is powered at an operating current of 18.6 kA to produce 16 T (figure 5).

Zoom In Zoom Out Reset image size

Similar studies were previously done on this magnet where a regular CLIQ protection scheme was considered. These studies were done with the simulation code TALES and reference results are available elsewhere [7, 34–36]. The material properties are well-known and the simulations described here use identical parameters as used previously [34, 35], see table 1. The influence of conductor $\mathrm{RRR}$ is also investigated here where $\mathrm{RRR}$ values of 100 and 300 are considered. The magnetic field map and inductive properties of the HD2 magnet with secondary coils were calculated with Roxie [37] (figure 5).

Table 1. Magnet and conductor parameters.

Parameter	Value	Parameter	Value
Nominal current $\mathrm{I}_{\rm{nom}}$ [kA]	18.6	Bare cable width [mm]	22
Bore field at $\mathrm{I}_{\rm{nom}}$ [T]	16.0	Bare cable height [mm]	1.4
Peak conductor field at $\mathrm{I}_{\rm{nom}}$ [T]	16.9	Insulation thickness [mm]	0.11
Operating temperature [K]	1.9	Cu:non-Cu ratio	0.85
Differential inductance at $\mathrm{I}_{\rm{nom}}$ [mH]	68	Filament twist pitch [mm]	14
Stored magnetic energy at $\mathrm{I}_{\rm{nom}}$ [MJ]	11.8	Secondary bare cable width [mm]	10.6
Strands per Rutherford cable	51	Secondary bare cable height [mm]	2.8
Strand diameter [mm]	0.8	Secondary insulation thickness [mm]	0.25

The quench simulation model needed to simulate Secondary CLIQ is relatively complex, with multiple galvanically insulated but inductively coupled circuits. The Secondary CLIQ simulation uses a co-simulation [38, 39] of two LEDET [40] models and a PSPICE electrical circuit [41]. The two LEDET models calculate the quench behaviour of the forward and rear part of the magnet simultaneously (See figure 1 'LEDETf' and 'LEDETr'). The inductive coupling between the circuits is internal to the LEDET simulations and a PSPICE network provides the electrical connections inside the various circuits, thus also connecting the forward and rear halves of the magnet together. The resulting voltages-to-ground at all parts of the magnet are calculated with a post-processing step. Both the co-simulation framework [39] and LEDET [40] are part of the STEAM project [38].

To gain confidence that the simulations were configured correctly, multiple cross-checks were done. Firstly, a LEDET standalone simulation of HD2 is cross-checked against the previously executed TALES simulation of the same magnet. Subsequently, a co-simulation comprising two LEDET models and PSPICE is compared to the standalone LEDET model, where the considered PSPICE circuit implements a regular CLIQ configuration (figure 6). These simulation results are discussed in section 3.2.

Zoom In Zoom Out Reset image size

Subsequently, Secondary CLIQ simulation results are presented in sections 3.3, 3.4, and 3.5. A comparison of the hot-spot temperature of peak-voltage-to-ground of the regular CLIQ and Secondary CLIQ, including fault condition evaluations, is given in section 3.6.

This section discusses comparisons of simulations on the HD2 magnet (figure 5) without secondary coils, powered at 18.6 kA, and protected with a regular CLIQ configuration (figure 7). Previously published TALES simulations [34, 35], standalone LEDET simulations [40], and a co-simulation combining two LEDET models and PSPICE are compared. In the co-simulation model, the secondary coils are present but held at zero current so that they do not affect the discharge of the superconducting coils, and the PSPICE circuit is set up in the regular CLIQ configuration, where the top coils oscillate against the bottom coils during the magnet discharge (figures 6). The CLIQ unit capacitance is 100 mF and the charging voltage is 1000 V.

The three different simulation types give consistent results, where at an operating current of 18.6 kA and a CLIQ discharge delay of 16 mss (accounting for the time required to detect and validate a quench, and subsequently to trigger the CLIQ unit) after the quench onset the resulting adiabatic hot-spot temperature is 349 K and the peak voltage-to-ground is 1610 V. Figure 9 shows the temperature distribution inside the magnet. The consistency between the three different model types (figures 7 and 8) gives confidence that the Secondary CLIQ calculations are not affected by unintentional errors in the modelling implementation.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As a side-note, it was previously shown [34, 35] that the manner in which the CLIQ unit is connected to the primary circuit affects the hot-spot temperature and voltage-to-ground, so that optimization beyond the regular CLIQ configuration shown in figure 6 is possible. The most optimal regular CLIQ connection scheme (where different layers inside the top and bottom coils oscillate against each-other) gives a hot-spot temperature of 280 K and a peak voltage-to-ground of 1.2 kV [34, 35].

Figure 11 shows the discharge behaviour of the HD2 magnet protected with Secondary CLIQ without fault conditions (figure 10). The CLIQ units are charged at 1200 V, and the capacitance is 100 mF.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The discharge of the CLIQ unit results in current oscillations in the secondary circuits (figure 11) with a peak CLIQ current (equal to the difference in currents between the forward and rear secondary coils) of 7.7 kA. The current in the secondary coils rises to about 25 kA after 0.16 s, at which point the current through the CLIQ units is 0.8 kA. The resulting adiabatic hot-spot temperature and peak voltage-to-ground are 248 K and 610 V. Figure 12 shows the temperature distribution inside the magnet, not including the adiabatic hot-spot zone which reaches a temperature of 248 K. Except for the adiabatic hot-spot zone, the maximum temperature in the primary and secondary coils is 153 K.

Zoom In Zoom Out Reset image size

For an accelerator circuit comprising hundreds of magnets with multiple CLIQ units per magnet, the correct discharging of all CLIQ units with 100 % reliability cannot reasonably be guaranteed. For this reason, it is useful to consider what happens when a CLIQ unit fails to discharge.

Figure 13 shows the result of a simulation where one of the two CLIQ units fails to discharge. As only half the energy is discharged into the magnet, quench protection is now less effective. This results in an elevated hot-spot temperature of 263 K (figure 13) instead of 248 K (figure 11), and an elevated peak voltage-to-ground of 840 V (figure 13) instead of 610 V (figure 11). Figure 14 shows the temperature distribution inside the magnet with a maximum temperature of 162 K, not including the adiabatic hot-spot zone.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In spite of less efficient quench protection, the magnet is still protected when only one of the two CLIQ units discharges. Note that, even when one of the CLIQ units fails to discharge, the associated secondary circuit will still passively absorb stored magnetic energy from the quenching superconducting coils (figure 13).

Figure 15 once again considers the quench behaviour of the magnet where one of the CLIQ units fails to discharge, but now at an operating current of 2 kA. At this low operating current, the current sharing temperature of the superconducting conductor is substantially higher so that more energy is needed to bring the magnet to normal state.

Zoom In Zoom Out Reset image size

The simulation result indicates that even at this low current and with just one of the two CLIQ units discharging, sufficient energy is dissipated into the superconducting magnet to bring it to normal state with a resulting adiabatic hot-spot temperature well below 100 K and a peak voltage-to-ground well below 100 V (figure 15). The peak temperature in the magnet excluding the adiabatic hot-spot zone is 25 K (figure 16).

Zoom In Zoom Out Reset image size

Note that the peak voltage-to-ground is much lower than the charging voltage of the CLIQ units (1200 V). As explained in section 2, upon discharge of the CLIQ unit, the secondary coils oscillate with opposite polarities, so that the inductive voltage over each half-turn of the superconducting coil is not affected by the CLIQ discharge. In principle the charging voltage of the CLIQ unit may be raised to an arbitrarily large value without raising the voltage-to-ground in the superconducting coil upon discharge, except for a minor local voltage variation along the length of each half-turn. The secondary coil insulation (which is more robust than that of the superconducting coil) does of course have to be robust enough to handle the CLIQ discharge. For the simulations presented here it was found that the peak voltage-to-ground in the secondary coil is equal to the CLIQ charging voltage, and rapidly diminishes after the CLIQ discharge, staying below 200 V after 100 ms.

Tables 2 and 3 give the quench integral QI, adiabatic hot-spot temperature $\mathrm{T}_{\rm{Adiabatic}}$ (See [42] for an explanation of these two terms), and peak voltage-to-ground $\mathrm{V}_{\rm{Gnd,\textrm{max}}}$ for regular and Secondary CLIQ, where for Secondary CLIQ low current discharges and fault scenarios are considered as well. The RRR of the superconducting conductor is varied between 300 (table 2) and 100 (table 3). The copper in the secondary coils has an conservatively chosen RRR of 100, where a higher RRR was found to moderately raise the effectiveness of the Secondary CLIQ in terms of the hot-spot temperature and peak voltage-to-ground in the superconducting coils. In particular, for a conductor RRR of 300, nominal current and nominal quench protection gives a hotspot temperature of 248 K and a peak voltage-to-ground of 610 V when the RRR of the copper conductor in the secondary coil is 100, and 246 K and 600 V when the RRR of the copper conductor is 300. The presence of magnetic field and higher temperature significantly reduces the difference in resistivity between copper with RRRs of 100 and 300, which explains this modest difference in performance.

Table 2. Resulting hot-spot temperatures and voltages-to-ground for variety of scenarios, where the superconducting conductor RRR is fixed to 300. Here $\mathrm{I}_{\rm{Op}}$ refers to the operating current of the superconducting magnet, QI refers to the quench integral in the superconducting conductor from the moment of quench origination, $\mathrm{T}_{\rm{Adiabatic}}$ refers to the adiabatic hot-spot temperature, and $\mathrm{V}_{\rm{Gnd,\textrm{max}}}$ is the maximum voltage-to-ground found in the superconducting coils.

Scenario	$\mathrm{I}_{\rm{Op}}$ [kA]	$\mathrm{QI}$ [MA2s]	$\mathrm{T}_{\rm{Adiabatic}}$ [K]	$\mathrm{V}_{\rm{Gnd,\textrm{max}}}$ [V]
Regular CLIQ	18.6	34.6	349	1610
Secondary CLIQ, nominal	18.6	27.9	248	610
Secondary CLIQ, fault	18.6	28.7	263	840
Secondary CLIQ, fault	2.0	11.3	58	lt; 100

Table 3. Resulting hot-spot temperatures and voltages-to-ground for variety of scenarios, where the superconducting conductor RRR is fixed to 100. Here $\mathrm{I}_{\rm{Op}}$ refers to the operating current of the superconducting magnet, QI refers to the quench integral in the superconducting conductor from the moment of quench origination, $\mathrm{T}_{\rm{Adiabatic}}$ refers to the adiabatic hot-spot temperature, and $\mathrm{V}_{\rm{Gnd,\textrm{max}}}$ is the maximum voltage-to-ground found in the superconducting coils.

Scenario	$\mathrm{I}_{\rm{Op}}$ [kA]	$\mathrm{QI}$ [MA2s]	$\mathrm{T}_{\rm{Adiabatic}}$ [K]	$\mathrm{V}_{\rm{Gnd,\textrm{max}}}$ [V]
Regular CLIQ	18.6	32.5	334	1420
Secondary CLIQ, nominal	18.6	25.5	221	553
Secondary CLIQ, fault	18.6	26.3	233	810
Secondary CLIQ, fault	2.0	7.0	40	lt; 100

Figure 17 shows the adiabatic hot-spot temperature and peak voltage-to-ground over a wide current range, considering the most conservative case where only one of the two CLIQ units is discharged and the superconducting conductor RRR is 300. It is shown that the worst-case adiabatic hot-spot temperature and voltage-to-ground of 263 K and 840 V occur at the highest considered current of 18.6 kA. This adiabatic hot-spot temperature and voltage-to-ground under fault conditions compares favorably with the nominal protection provided by the already very efficient regular CLIQ configuration (figures 7, 8, tables 2, 3).

Zoom In Zoom Out Reset image size