This work was conducted within the framework of the exploratory French project PEPR SupraFusion, which aims to advance the field of fusion energy by developing High-Temperature Superconductor (HTS)-based demonstrators capable of storing significant energy while operating under high magnetic fields and currents. Ensuring a reliable protection during a quench in Insulated REBCO conductors is challenging : slow normal-zone propagation and validation delays allow the hotspot's temperature to reach damaging levels. We compare (i) conductor protection via copper-stabilizer optimization and (ii) a co-wound, REBCO superconducting quench detector (SQD) that is electrically isolated yet thermally coupled and intentionally deoxygenated to lower $T_{c}$ and $I_{c}$ for an earlier transition. One-dimensional THEA modeling shows that a good choice of stabilizer cross-section makes the protection possible during quench events by keeping the temperature of the hotspot within a safe limit. The simulations also demonstrate that the use of a REBCO SQD enables the quench detection at lower temperatures.

Through a series of experimental sessions, we have characterized pool boiling heat transfer in liquid helium (LHe) around saturation (4.2 K) under reduced gravity conditions ranging from 0.02g to 1g using magnetic forces. The magnetic forces were generated using a 30 T resistive magnet. First, the experimental results confirm and strengthen previous measurements regarding the critical heat flux dependency with respect to reduced gravity. Secondly and more importantly, they provide Nukiyama's curves for liquid helium at 4.2 K and 1 bar at various reduced gravity levels (approximate to 0.02g, approximate to 0.25g, approximate to 0.5g, 1g). Measurements of both nucleate and film boiling regimes are studied and compared with considerations of their theoretically predicted gravity-dependent evolution. The measurements do not show significant degradation of the heat transfer coefficient under reduced gravity only the critical heat flux seems to be drastically impacted by the gravity level.

Abstract With the growing adoption of cryocoolers, there is a demand for efficient thermal links to the cold stages. This demand can be addressed by pulsating heat pipes (PHPs) offering a promising solution at cryogenic temperatures. Despite progress, current literature does not allow precise prediction of PHP performance at cryogenic conditions. To address this gap, we propose a numerical model developed in OpenFOAM. The implementation of the model includes customized conservation equations, thereby incorporating phase change dynamics based on the Volume of Fluid approach. In order to validate this numerical model, a compact PHP has been constructed. A setup has been built to test the designed PHP at different cryogenic temperature ranges. The cooling is provided by a two-stage cryocooler having a cooling capacity of about 28 W at 77 K. The PHP is fabricated from stainless steel tubes with an inner diameter of 1.3 mm. It has projected overall dimensions of approximately 0.19 m x 0.11 m. Nitrogen is used as the working fluid with operating temperatures ranging from 77.3 to 94 K. We also present preliminary results validated against experimental data demonstrating the precision of the implemented model in predicting the thermal performance of cryogenic PHPs.

Abstract Our application seeks cryorefrigeration in liquid neon and liquid helium temperature range. For this purpose, the highest capacity 4K two-stage Giffard-McMohan cryocooler manufactured by Sumitomo (SHI) Cryogenics Group has been employed. At second-stage temperature of 4.2 K, the coldhead RDE-418D4 has refrigeration capacity specifications of 1.8 W @ 50 Hz and 2.0 W @ 60 Hz with first-stage load of 42 W and 50 W respectively. It is operated with F-50SH water-cooled helium compressor embedded with coldhead frequency inverter. This work presents the thermal characterization of the cryocooler second-stage at varying heat loads from 100 mW to 25 W. Different data sets are obtained while maintaining the first stage at no heat load (0W) or under constant heat load conditions (25 W, 50 W, 75 W). Additionally, the cooling capacity data is recorded at different coldhead operating frequency of 40 Hz, 50 Hz, 60 Hz and 70 Hz.

This paper reports the development and the successful testing of the first operational high-temperature superconductor (HTS) magnet cooled with a single two-stage cryocooler using two cryogenic pulsating heat pipes (PHP) as thermal links. The superconducting magnet is a metal-as-insulation (MI) REBCO double-pancake "10 T class magnet" built in-house and was operated at neon temperature (around 30 K). The superconducting magnet, the current leads, the cryogenic cooling system and scheme, the pulsating heat pipes and the overall experimental facility are detailed in length. The operational working limit, quench, alternating current (AC) losses and heat dissipation evaluations as well as constant current stability tests were performed and are methodically discussed. A maximum magnetic field of 4.24 T was reached during ramp-up, while a field of 1.72 T was maintained in direct current (DC) conditions for more than six hours with the neon PHPs evidently active. Numerous tests have verified that the cryogenic system, which includes the cryocooler, PHPs, thermal links and power regulation system, is sufficiently dynamic to cope with the transient heat generated by the superconducting magnet. The AC tests demonstrated that this test setup, with the aid of cryogenic PHPs and its power regulation system, can serve as an evaluation tool for power dissipation due to AC losses.

This study presents a CFD-based analysis of pulsating heat pipes operating under cryogenic conditions with nitrogen as the working fluid. Simulations were conducted in OpenFOAM for single-and double-loop geometries. The numerical model employs a compressible, turbulent two-phase formulation using the Volume of Fluid method with fully temperature-dependent thermophysical properties. The phase change is modeled via an adaptive version of the Lee model, in which the condensation coefficient is dynamically updated on the basis of local saturation parameters. This study extends a previous implementation limited to a single geometry and constant properties by introducing a comprehensive multiphase model for cryogenic conditions, incorporating fully temperature-dependent parameters, conjugate heat transfer, and adaptive phase-change coupling. The temperature difference between the condenser and the evaporator varies between 77.85 and 115 K. Validation against experimental data demonstrates thermal prediction below 5% in difference for a wide range of heat inputs (1-35 W), accurately capturing transient oscillatory behavior and pressure-temperature forecasting. The numerical results are compared to published data and the simulated flow structures are consistent with the experimental observations, reproducing key regimes such as Taylor bubbles, annular films and based on plug-slug flow. The developed model offers a robust framework for the analysis of transients and geometry-specific optimization of cryogenic PHPs.

This study presents new numerical procedures for simulating cryogenic pulsating heat pipes (PHPs) developed in OpenFOAM. Using a multiphase flow approach, the numerical model incorporates a combination of Lee and Min phase change models and also features conjugate heat transfer between the solid wall and fluid. Turbulence effects are modeled using the k-s turbulence model, with wall functions implemented to capture heat transfer dynamics more accurately. The model was validated against experimental data reported in literature on a nitrogen single- loop configuration. Our code captures the overall experimental thermal performance and pressure evolution within less than 3% difference. In addition, this study demonstrates that turbulence enhances heat transfer, with turbulent diffusion contributing substantially to the overall effective thermal conductivity and thus should not be neglected. The findings also indicate that cryogenic PHP simulations must consider pressure- and temperature- dependent properties to achieve reliable predictions for different operating scenarios. This work provides a promising basis for advancing the numerical modeling of cryogenic PHPs.

The main objective of this study is to reproduce the heat and mass processes in He II forced flows in steadystate condition using a modified simplified two-fluid model with an open source CFD environment. The model is derived from the so-called two-fluid model by assuming that the dominant terms in the superfluid momentum equation are the thermo-mechanical, the Gorter-Mellink mutual friction and the pressure gradient terms. From this simplification, a new system of equations describing the heat and mass transfer in He II is obtained with a conventional continuity equation, a modified momentum equation for the total fluid, and an energy equation revealing the unique counter-flow heat transport mechanism as in other simplified models, but here with the addition of the pressure gradient effect in He II. The model has been validated and compared with other models available in the literature, such as the original two fluid model and simplified models, as well as experimental data. Our model has been implemented using the OpenFOAM software and we have demonstrated here its good accuracy with experimental results and shorter computational time by 2-6% compared to the two-fluid model.

A cryogenic pulsating heat pipe (PHP) whose capillary tube diameter does not satisfy the classical Bond number (Bo) criterion has been experimentally tested and showcased in this work. Helium is the working fluid employed and the PHP diameter is similar to 1.75 times its recommended critical diameter of 0.57 mm. All the investigations reported till date on helium PHP have adhered to tube diameter of 0.5 mm evidently meeting the Bo < 4 criterion. However, this helium PHP corresponds to Bo = 12 at 4.2 K and, in fact, is the first cryogenic PHP demonstrating its functionality at such a high Bond number for helium. The motivation for such an investigation is initially presented with a deliberation on different PHP critical diameter criteria. A hypothesis emphasizing on the need to re-evaluate the upper limit of tube diameter for cryogenic PHPs is proposed. In support of this, a closed-loop PHP constructed from a 1 mm inner diameter stainless steel tube is utilized. It is composed of 20 parallel channels and has a projected length of 0.4 m. The functionality of this large diameter helium PHP is validated by experimentally characterizing its thermal performance and pressure as a function of heat load up to 1.5 W within an exhaustive range of filling ratios (10 to 90 %). This is conducted both in vertical and horizontal orientation. Zones where the PHP quickly surpasses the helium critical temperature and pressure values and still functioning are identified. Finally, its reliability is exhibited by 65 h stability test conducted at constant operational conditions.

Cryogenic pulsating heat pipes (PHP), also termed oscillating heat pipes, are passive thermal links that transfer heat by oscillatory motion of two-phase cryogen confined in serpentine-shaped capillary tubes. It is composed of three sections, namely, the condenser (cold sink), the evaporator (heat source) and the adiabatic part that can range from several centimetres to few metres. In spite of longer lengths, PHPs hold an advantage that their weight does not radically increase in comparison to counterparts like metallic thermal straps. The aim is to present cryogenic PHPs as one of the potential thermal links aiding in distant cooling of superconducting devices from active cryocoolers. A 0.4 m long neon PHP with 1 mm capillary tube diameter has been recently developed characterized by one of the highest thermal conductance reported till date both in vertical and horizontal orientation. An innovative modification in the construction of PHP evaporator is showcased in this article. This would considerably enhance the flexibility of PHPs in terms of their employment geometrically within the targeted application. Pilot experimental results for neon PHP coupled with the altered evaporator is presented for heat load up to 18 W.

The Metal as Insulation and more generally the No-Insulation windings are promising for the protection of DC and slow ramping HTS magnets. The modeling of the thermal behavior during a quench in order to design the protection of a magnet is highly dependent on parameters set by materials and fabrication. The electrical resistance between turns has been widely studied worldwide, but the turn-to-turn thermal conductivity of MI windings stays relatively unknown. Turn-to-turn thermal conductivity may have a significant role in the dynamics of a quench and on the hot spot temperature. This motivated us to develop a specific apparatus for evaluating this turn-to-turn thermal conductivity. Because we are working with HTS dry stacks the thermal conductivity depends not only on temperature but also on radial pressure. This paper present the design of an apparatus to evaluate the thermal conductivity of an HTS stack under different radial compression and at different temperature. The measurements are made with an isoperibolic cell using the steady-state differential method. This article details the mechanical and thermal design and the fabrication steps of the first thermal samples. We also present the first results of thermal conductivity obtained at 20 MPa and 5.5 K, which is close to our theoretical prediction.

An experimental campaign was conducted to investigate heat and mass transfer phenomena in superfluid helium (He II) in two rectangular cross-section channels of high aspect ratios and different thickness resembling the space between steel collars in the LHC superconducting magnets. The experiments consisted of clamped heat flux tests at atmospheric pressure, in which a heater strip suddenly releases a constant heat load into the channel that is open to a helium bath on one side. The difference in thickness between the two channels allowed exploring the effect of the geometrical confinement on the propagation of both phase change fronts: i) the He II-He I A-transition front; ii) the He I-vapour first-order transition front. The observations show that, in the thinner channel, it is possible to distinguish different behaviours of the phase fronts depending on the extent of the heat flux. For increasing heat flux values, the A-front speed successively increases sharply, decreases, and increases weakly. This sequence is determined by the presence of the vapour film, which either diminishes the He II-He I transformation rate by lowering the heat transfer or pushes the A-front while expanding. In the thicker channel, the intermediate behaviour is absent as the level of confinement is lower and the He I phase never expands considerably along the highest dimension of the channel.

This paper presents an experimental thermal and hydraulic characterization of a pulsating heat pipe (PHP) at neon temperature. In the search for efficient alternative cooling techniques, with a cryocooler as the cold source, this particular heat pipe is considered a potential candidate for passive thermal link to cool high-temperature superconducting devices. This wickless heat pipe is 0.4 m long with 0.1 m enclosed within the evaporator and condenser. It consists of 20 turns of 1.0 mm inner diameter stainless tube. A systematic study of the thermal performance and pressure of this PHP is presented as a function of thermal load and orientation covering the widest range of filling ratios (10 to 90 %). The cryocooler capacity limit is 18 W for which the PHP functions successfully. This cryogenic PHP has the best thermal performance ever measured with neon showcasing a thermal resistance as low as -0.17 K/W in vertical and -0.27 K/W in horizontal orientation. The limits of the operating conditions (start-up and dry-out) are also studied as well as the non-homogeneity in evaporator heat load. Finally, a 100 h stability test at constant operating conditions is also demonstrated.

The MAgnetized Disc and Mirror Axion eXperiment (MADMAX) project aims at detecting axion dark matter in the mass range of 100 μeV. To do so, a dipole detector magnet producing 100 T 2 m 2 is needed. In the framework of an innovation partnership with the Max Planck Institute, CEA Paris-Saclay designed this large-scale magnet producing 9 T in a 1.35-m bore. The magnet is made of a cable in-conduit conductor, operating at 1.8 K. One of the main challenges of this novel design is to guarantee the magnet's safety toward quench management. In order to validate the magnet and conductor designs, a mock-up coil with a quench behavior scalable to MADMAX was designed, manufactured, and cold-tested. This article gives an overview of the main guidelines followed to design the prototype fully representative of the MADMAX quench behavior. The experimental facility, instrumentation, and protocol are presented. The main experimental results are given and extensively analyzed with empirical, analytical, and numerical approaches. This article presents the first experimental observation of the existence of the thermohydraulic quench back phenomenon in stagnant superfluid helium.

A dimensional study of the momentum equations of superfluid helium is presented together with a parametric analysis of newly derived dimensionless numbers. The study is performed with a focus on the role of forced flows in the Gorter-Mellink regime. The dimensionless numbers are derived in such a way they become dependent solely on the total fluid velocity, heat flux, and thermophysical properties in order to facilitate their application to engineering problems where the velocity of the single fluid components might be difficult to measure directly. With a similar approach, a novel form of the superfluid Reynolds number is obtained. This form takes into account the velocity of a forced flow and allows to make considerations about the contribution of both forced flow and heat flux to the establishment of the ordinary turbulence in the normal fluid component. It is also presented a formula for a channel critical dimension at which the critical heat flux for the onset of superfluid turbulence causes ordinary turbulence too.

The characterization of Critical Heat Flux (CHF) under magnetic compensation of gravity in liquid helium (LHe) is particularly important for the design of the future very high magnetic field superconducting magnets. Through a series of experimental sessions, the critical heat flux in LHe pool boiling has been determined under various gravity conditions ranging from 0.03g to 2.2g using magnetic forces. It is the largest range of gravity variation, from reduced to hyper-gravity, ever studied in a single facility so far. The study was conducted in a very high magnetic field up to 30 T. The magnetic compensation of gravity does not allow for perfect resulting gravity homogeneity. Nevertheless, for the first time, the magnetic field configuration is considered in the experimental results analysis. The relative resulting gravity inclination with respect to the heat exchange surface is also taken into account. The experimental results are compared with the well-known CHF correlation in LHe pool-boiling and show a very good behavior agreement. For our experimental gravity level, the CHF is ranging from 3000 W/m2 to 12000 W/m2.

In the dark matter Axion research context, the MADMAX project acts as a figurehead in the physics research field. The goal of the project is to discover axion as dark matter. For this, it is necessary to design and manufacture a dipole, composed of 18 coils, that generates a Figure of Merit of 100 T2m 2. The MADMAX coils have several specific features though, as the use of Cable-In-Conduit-Conductor (CICC) with a copper profile that serves as thermal stabilizer and the use of stagnant superfluid helium inside the CICC conduit. With a 28 mm2 helium cross-section and a conductor of several hundred meters before reaching the helium bath, the quench dynamics appear then as a challenge of the design phase. To experimentally investigate the quench propagation in the MADMAX coils, we designed a MADMAX-like solenoidal prototype based on numerical simulations made with THEA (R) called MACQU (MAdmax Coil for Quench Understanding). This numerical study allowed analysing the physics behind the quench phenomenon and define the relevant current range for the experimental quench studies. Nevertheless, as THEA (R) has never been used for a CICC filled with superfluid helium, the results will have to be benchmarked by the quench testing campaign on MACQU. The different calculations made with THEA (R) show that the quench propagation is divided into two different phases: after the initiation, the propa-gation is at a constant speed of around 5 m/s, followed by an acceleration phase where the propagation speed reaches 40 m/s, at 17 kA. Among the different possible phenomena, we have found that the friction forces term, as defined in the THEA code, are responsible for this two-phase propagation because they initiate the pre-heating of the magnet before the quench, reducing then the local temperature margin.

A new generation magnetic spectrometer in space will open the opportunity to investigate the frontiers in direct high-energy cosmic ray measurements and to precisely measure the amount of the rare antimatter component in cosmic rays beyond the reach of current missions. We propose the concept for an Antimatter Large Acceptance Detector In Orbit (ALADInO), designed to take over the legacy of direct measurements of cosmic rays in space performed by PAMELA and AMS-02. ALADInO features technological solutions conceived to overcome the current limitations of magnetic spectrometers in space with a layout that provides an acceptance larger than 10 m2 sr. A superconducting magnet coupled to precision tracking and time-of-flight systems can provide the required matter–antimatter separation capabilities and rigidity measurement resolution with a Maximum Detectable Rigidity better than 20 TV. The inner 3D-imaging deep calorimeter, designed to maximize the isotropic acceptance of particles, allows for the measurement of cosmic rays up to PeV energies with accurate energy resolution to precisely measure features in the cosmic ray spectra. The operations of ALADInO in the Sun–Earth L2 Lagrangian point for at least 5 years would enable unique revolutionary observations with groundbreaking discovery potentials in the field of astroparticle physics by precision measurements of electrons, positrons, and antiprotons up to 10 TeV and of nuclear cosmic rays up to PeV energies, and by the possible unambiguous detection and measurement of low-energy antideuteron and antihelium components in cosmic rays.

Pulsating heat pipes (PHPs) are two-phase flow, thermal transport carriers characterized by ease of fabrication, flexibility of compactness and variable heat transfer capability. Conventionally, cooling of superconducting magnets is realized by using cryogen cooling system. Cryogenic PHPs are emerging as the new-age economical alternative that can passively contribute in efficient transport of generated heat to active cryocoolers. Nevertheless, a number of challenges must be addressed to materialize this union. For this objective, a multipurpose experimental test-rig has been developed which will allow different critical parameters of cryogenic PHPs to be investigated. The preliminary tests are conducted using neon as the working fluid. The PHP capillaries, made of SS304, have an outer diameter of 2.5 mm and a projected length of 400 mm with the adiabatic part having twice the length as compared to that in the condenser and evaporator. It consists of 20 parallel tubes forming a closed-loop and are tested in gravity-assisted environment. Employing the Sumitomo RDE-418D4 4K Cryocooler, the condenser temperature is controlled at the neon saturation temperature, around 27 K. The thermal performance of this cryogenic PHP is recorded at different evaporator heat load conditions. We report here the temperature evolution of PHP evaporator, and condenser as well as the pressure oscillations with time.

We explore steady state and transient heat transfer from a narrow, rectangular stainless steel heater strip cooled from one side by an open bath of He II. Setup validation is done by fitting the Kapitza heat transfer expression Q = a_K( T_s^n_K - T_b^n_K) to steady state measurements, finding fit parameters within the expected range; a_K = 1316.8±10% Wm^-2K^-1, n_K = 2.528±10%. We find critical heat flux in line with estimates from literature, and the time between a step in heating and the onset of film boiling follows the expected ∝ Q^-4 dependence. During the first millisecond after a step in applied heating power density our measurements show a slower thermal rise time than that found by a time-dependent one-dimensional model of our setup using the steady state Kapitza heat transfer expression as the cooling boundary condition. However, the results compare favourably with transient measurements in literature. After the first millisecond, agreement between measurement and model is excellent. We do not find conclusive evidence of an orientation dependence of the Kapitza heat transfer mechanism, nor heat transfer differences that can be attributed to local surface variations along the same heater.