Optimizing Secondary CLIQ for Protecting High-Field Accelerator Magnets

Future circular particle accelerators with collision energies significantly beyond the LHC will require magnets with higher magnetic field. Quench protection of such magnets is challenging for two main reasons. First, the high energy density and relatively high margin to quench require a high-performance quench protection system. Second, integration of the protection system in an accelerator machine foreseen to be operated for decades calls for easy-to-integrate, robust, and redundant elements. A new and promising protection method named Secondary CLIQ (S-CLIQ) has recently been proposed. It relies on auxiliary normal-conducting coils that are electrically insulated from the coils to protect but are magnetically coupled to them. Upon magnet quench detection, the coupled coils have dual functionality: first, they introduce high coupling loss in the superconductor, which is sufficient to transfer most of the windings to the normal state in a few milliseconds; second, they extract part of the magnet's stored energy by magnetic coupling. In this work, a S-CLIQ system based on auxiliary coils placed on the top and bottom of a racetrack magnet and made of a thin 1 mm$^{2}$ wire is presented. It is shown that the quench protection performance in terms of hot-spot temperature and peak voltage to ground are superior to alternative methods such as energy extraction, quench heaters, and CLIQ.


Optimizing Secondary CLIQ for Protecting
High-Field Accelerator Magnets E. Ravaioli , T. Mulder , A. Verweij , and M. Wozniak Abstract-Future circular particle accelerators with collision energies significantly beyond the LHC will require magnets with higher magnetic field.Quench protection of such magnets is challenging for two main reasons.First, the high energy density and relatively high margin to quench require a high-performance quench protection system.Second, integration of the protection system in an accelerator machine foreseen to be operated for decades calls for easy-to-integrate, robust, and redundant elements.A new and promising protection method named Secondary CLIQ (S-CLIQ) has recently been proposed.It relies on auxiliary normalconducting coils that are electrically insulated from the coils to protect but are magnetically coupled to them.Upon magnet quench detection, the coupled coils have dual functionality: first, they introduce high coupling loss in the superconductor, which is sufficient to transfer most of the windings to the normal state in a few milliseconds; second, they extract part of the magnet's stored energy by magnetic coupling.In this work, a S-CLIQ system based on auxiliary coils placed on the top and bottom of a racetrack magnet and made of a thin 1 mm 2 wire is presented.It is shown that the quench protection performance in terms of hot-spot temperature and peak voltage to ground are superior to alternative methods such as energy extraction, quench heaters, and CLIQ.Index Terms-Accelerator magnet, coupling loss, quench protection, simulation, superconducting coil.

I. INTRODUCTION
Q UENCH protection of Nb 3 Sn high magnetic field ac- celerator magnets poses significant challenges.On the one hand, the high stored energy density and relatively low quench propagation velocity make it difficult to quickly spread the normal zone to the entire winding pack, which is often a requirement to maintain the hot-spot temperature and peak voltage to ground within acceptable levels.On the other hand, the integration of the quench protection system in an accelerator machine foreseen to work for decades mandates a high level of robustness and reliability.
Existing quench protection systems have limitations that can make them unsuitable or impractical to effectively protect high-field magnets inserted in a circuit containing dozens of similar magnets.Energy extraction (EE) [1] would require a prohibitively high voltage to protect a high energy-density magnet in series to many others, or the installation of one EE unit per magnet, which would be exceedingly expensive.Quench heaters (QH) [1], [2], [3], [4] attached to a magnet by-passed by a diode allow to selectively quench and protect one magnet within a circuit.However, in order to initiate a transition to the normal state in a few milliseconds, the insulation between QH strips and conductor needs to be very thin, hence increasing significantly the risk of electrical failure.Furthermore, it is technically very challenging to cover all turns with QH strips, especially those located in the magnet inner layer.CLIQ [5], [6] relies on an effective power deposition mechanism based on inter-filament coupling loss [7], [8], [9], [10], [11], which offers fast quench initiation without the need of thermal contact between magnet coil and protection elements.However, by principle it requires to be electrically connected to the magnet circuit.While it is relatively easy to integrate a few CLIQ units in a circuit [12], [13], including hundreds of units in future accelerator circuits appears complicated.
A new quench protection system named Secondary CLIQ (S-CLIQ) was recently proposed [14], which relies on two sets of normal-conducting auxiliary coils that are electrically insulated from the coils to protect, but strongly magnetically coupled to them.The magnet and auxiliary coils are schematically illustrated in Fig. 1.
S-CLIQ offers similar or better performance with respect to CLIQ in terms of power deposition and hence normal-zone initiation capability without relying on any electrical connection to the circuit, nor on thermal diffusion.
In previous work, it was shown that auxiliary coils placed outwards of the magnet coils and corresponding to about 20% of the magnet coils' cross-section were sufficient to effectively Fig. 2. Simplified electrical scheme of the circuit including a magnet protected by S-CLIQ.The magnet circuit includes a power supply (PS), a switch (SW) that opens when PS is switched off, a crowbar composed of a resistor R crow and a diode D crow , warm circuit resistance R circuit , and magnet with its inductance L m and resistance R m .Each S-CLIQ circuit includes auxiliary coils with their inductance and resistance, a CLIQ unit grounded in the middle, and back-to-back diodes (D dir1 , D rev1 , D dir2 , D rev2 ).Mutual coupling between L m and L 2a , L m and L 2b , L 1a and L 2a , and L 1b and L 2b , is present but not shown.Mutual coupling between L 1a and L 1b , and L 2a and L 2b can be neglected in first approximation.
protect a 16 T block-coil magnet [14].In this publication, a S-CLIQ auxiliary coil design to protect a block-coil magnet, with a cross-section of less than 8% of that of the coils to protect, is explored through simulations.S-CLIQ quench protection performance is also compared to that of other protection systems.

II. S-CLIQ WORKING PRINCIPLE
The S-CLIQ system includes two auxiliary coil sets L 1a +L 1b and L 2a +L 2b , each made of two coils arranged longitudinally (see Fig. 1).Both coils are symmetrically placed with respect to the magnet coil L m , such that their mutual coupling with it are identical, i.e.M m,1a =M m,1b =M m,2a =M m,2b .A CLIQ unit including a capacitor bank of capacitance C [F] charged to a voltage U 0 [V] is connected across one coil of each set, as shown in Fig. 2. Each unit is grounded at the middle points of its capacitor bank to halve the peak voltage to ground imposed on the auxiliary coils.Upon quench detection, the power supply is switched off and both CLIQ units are triggered simultaneously introducing oscillating currents in the four coils.Due to the system's symmetry, the voltages induced by S-CLIQ on each magnet turn are compensated, and therefore the magnet transport current I m [A] is unaffected by the initial auxiliary current oscillations.Such oscillations generate high magnetic-field change on the magnet conductor, which results in high inter-filament coupling loss.As a consequence, most of the magnet winding pack is quickly turned to the resistive state and the magnet coil resistance R m [Ω] increases considerably.The resistive voltage build-up causes a decrease of I m and consequently an increase of all four auxiliary coil currents.During this phase, part of the magnetic energy stored in the magnet is inductively transferred to the auxiliary coils and dissipated therein, thus effectively extracting energy from the magnet.

III. S-CLIQ AUXILIARY COIL SETS
The quench protection of the SMC magnet [15], [16], whose parameters are summarized in Table I, is analyzed.It is composed of two racetrack coils made of Nb 3 Sn Rutherford cable.Although the SMC magnetic length is 0.3 m and there is no  current plan to build a longer version of it, a 15 m long SMC magnet is considered here in order to demonstrate the S-CLIQ quench protection performance on a full-scale magnet.
The cross-section of the magnet and auxiliary coils is shown in Fig. 3: one coil is placed on top of the magnet coil, and the other is placed at its bottom.Each auxiliary coil consists of 46 turns of 1 mm by 1 mm copper wire, with 0.1 mm kapton insulation.The total cross-section of the two coil sets including insulation Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.amounts to less than 8% of that of the magnet coil.The magnetic coupling factor between the magnet coils and each auxiliary coil set is about 86% when the coils of each set are powered in series.
It is assumed that a quench occurs at t=0 in the highest magnetic-field turn while the magnet is at the nominal current I nom = 14500 A. Two 50 mF, 1 kV CLIQ units are triggered at t = 16 ms to account for detection, validation, and triggering time.Just after the S-CLIQ triggering, the currents in the L 1a and L 2b coils are opposite to those in the L 1b and L 2a coils (see Fig. 3(a)).The massive applied magnetic-field change, which reaches a peak of 400 T/s, introduces such high inter-filament coupling loss that all magnet coil turns are quenched within 2 to 7 ms (i.e.18 ms<t<25 ms).As a consequence, the coil resistance increases causing a rapid decrease of the transport current.Moreover, due to magnetic coupling a significant positive current change is imposed on all four auxiliary coils (see Fig. 3(b)), which adds to the S-CLIQ induced current change for two coils (L 1a , L 2b ) and subtracts to that of the other two coils (L 1b , L 2a ).Subsequently, the magnet and auxiliary coil currents are discharged and about 10% of the magnet's stored energy is inductively transferred to the auxiliary coils and dissipated there.During the transient, a peak current of about 2 kA is reached in the auxiliary coils.
The voltages to ground in the magnet coil turns, which are plotted in Fig. 4(b), reach a peak amplitude U g [V] lower than 700 V.This remarkable performance for such a long Nb 3 Sn magnet can only be achieved by rapidly quenching most of the winding pack.The peak voltage to ground in each auxiliary circuit occurs at the moment of the triggering and is ±U 0 /2=±500 V.
The simulated temperature T [K] profile at the end of the discharge in the "a" cross-section is shown in Fig. 5.The hot-spot temperature T h [K] is maintained below 290 K. Excluding the turn where the quench occurred and a few turns physically close to it, all turns reach a temperature between 105 K and 175 K, which implies a relatively low thermal gradient considering the significant effect of magneto-resistance.The auxiliary coil temperature is between 105 K and 230 K.
Similar simulations were performed assuming an initial current I 0 [A] in the range of 10% to 90% of I nom .As shown in Fig. 6, where the simulated currents are plotted, S-CLIQ successfully discharges the magnet at all current levels.The simulated T h remains well below the value reached at I nom .Interestingly, the currents in coils L 1b and L 2a reach higher peak absolute values for lower I 0 .This can be explained by observing that the current-change reversal occurring around t=20 ms is driven by the resistive voltage build-up in the magnet coils, which is significantly lower for lower I 0 since both R m and I m are smaller.
V. COMPARISON TO OTHER PROTECTION METHODS S-CLIQ quench protection performance is compared to those of alternative protection systems, which are listed in Table II.All simulations assume the same conductor, initial operating conditions, and a detection, validation, and trigger time of 16 ms.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 6.Simulations of a S-CLIQ discharge transients at different initial current levels between 10% and 100% of the nominal current.Current in the magnet (continuous lines) and auxiliary coils (dashed lines for I L 1a =I L 2b , and dotted lines for I L 1b =I L 2a ), versus time.

TABLE II PERFORMANCES OF VARIOUS QUENCH PROTECTION METHODS
Furthermore, the QH, CLIQ, and S-CLIQ systems store the same amount of energy in their capacitor banks, i.e 100 kJ, and are charged to the same voltage of 1 kV.For each system, the simulated T h and U g are reported, as well as the fraction of extracted energy f ex and the time t 90% [s] required to transfer 90% of the winding pack volume to the normal state.
It can be seen that EE cannot effectively protect this magnet even when a voltage of 2 kV is allowed across its resistor, since T h approaches 400 K. Due to quench back induced by coupling losses, the fraction of extracted energy is limited to 30%.Activating a 1 kV EE system would result in T h well above 500 K, and the magnet internal voltages would exceed 2 kV.
Two QH systems are considered with two insulation designs: one including only 50 µm of kapton insulation between QH strip and coil insulation, and one including an extra 100 µm G10 layer.In both designs, the QH strips are assumed to cover more than 90% of the magnet turns and to have heating stations covering 12.5% of their length in order to achieve a peak power density of 298 W/cm 2 .While the two QH designs induce a quench in 11 and 16 ms, respectively, it takes them a significantly longer time (70 and 82 ms) to quench 90% of the winding pack volume by quench propagation between heating stations.As a result, T h >380 K and U g >1. 5 kV even in the case of the thin-insulation design.
A CLIQ system can protect this magnet, although T h and U g would approach 340 K and 1.4 kV, respectively.This barely acceptable performance is achieved even with a very effective system that turns 90% of the winding pack volume to the normal state in less than 10 ms.
This comparison highlights the excellent performance of S-CLIQ, which can be attained thanks to its dual function of quickly quenching the winding pack (t 90% = 6 ms) and extracting part of the magnet energy (f ex = 10%).Indeed, the obtained T h and U g approach the performance of an ideal system capable to quench all magnet turns at the very instant when it is triggered, i.e. at t = 16 ms.
While the performance described in this section by no means applies directly to other magnet designs and operating conditions, it shows that the S-CLIQ technique is a promising solution for the protection of high-field magnets.Since S-CLIQ relies primarily on inter-filament coupling loss, its effectiveness would be reduced in the case of magnets designed to operate at high field-change, for example those made of a superconductor with a CuMn matrix.Integrating thin copper coils in the magnet crosssection is a complication, but it seems certainly feasible for most magnet designs.Careful analysis of the electro-magnetic forces developed in the magnet and auxiliary coils is an important step in the complete S-CLIQ system design, and will be the object of future study.

VI. CONCLUSION
Secondary CLIQ is a recently developed quench protection method that relies on auxiliary normal-conducting coil sets that are strongly coupled with the magnet coils.S-CLIQ working principle is based on fast quench initiation induced by very high coupling loss due to auxiliary coil current oscillations, and on the extraction of part of the magnet's stored energy by magnetic coupling.It does not rely on thermal contact between magnet coil and protection elements, nor on electrical connection to the magnet circuit.Both are attractive features for a magnet to integrate in a future accelerator circuit.
A S-CLIQ design protecting a racetrack magnet is introduced, which includes auxiliary coils made of 1 mm 2 copper wire with a total cross-section corresponding to less than 8% of that of the coils to protect.Electro-magnetic and thermal simulations of quench transients performed with the software tools of the STEAM framework are presented.Simulation results demonstrate that the S-CLIQ system can initiate a quench more quickly and achieve lower hot-spot temperature and peak voltage to ground with respect to alternative protection methods, such as energy-extraction, quench heaters, and CLIQ.
Although the presented results are not generally applicable to other magnet designs without dedicated studies, they show that S-CLIQ is a very promising technology for protecting the next generation of high magnetic field, high energy density superconducting magnets.

Fig. 1 .
Fig. 1.Schematic representation of a magnet protected by S-CLIQ.The two auxiliary coil sets L 1a +L 1b and L 2a +L 2b , each made of two coils "a" and "b", are placed on the top and bottom of the magnet coils L m .

Fig. 3 .
Fig. 3. Cross-section "a" of the SMC magnet and S-CLIQ auxiliary coils.The conductor coloring indicates the current polarity during the S-CLIQ induced oscillations phase, when the current polarities in L 1a and L 2a differ (a), and during the extraction phase, when the current polarities in 1 and 2 are equal (b).

Fig. 4 .
Fig. 4. Simulation of a S-CLIQ discharge transient including a quench at nominal current and the activation of two 50 mF, 1 kV CLIQ units.(a) Current in the magnet and auxiliary coils, versus time.(b) Voltage to ground in each of the magnet's coil turns, versus time.

Fig. 5 .
Fig. 5. Simulation of a S-CLIQ discharge transient.Temperature distribution at the end of the discharge in the 2D cross-section of the magnet and auxiliary coil turns.It is assumed that the quench occurs in the highest magnetic field turn of the top right quadrant.

TABLE I SMC
[17]ET AND CONDUCTOR MAIN PARAMETERS[17]