L Zani

J.-C Vallet

K Fukui

K Natsume

S Varin

F Bonne

C Hoa

S Nicollet

An update of dynamic thermal-hydraulic simulations of the JT-60SA Toroidal Field coil cooling loop for preparing plasma operation

Keywords:

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In the framework of the Broader Approach, the joint European Japanese superconducting tokamak, JT-60SA, will be commissioned in 2020 in Naka, Japan [START_REF] Davis | JT-60SA TF magnet assembly[END_REF]. The motivation of this work is to have an updated thermal hydraulic modelling of the cryogenic loop supplying the TF coils and coil structures and the associated cryo-distribution to be used for the preparation of the future operation of the tokamak. The cryogenic system has been commissioned in 2016 [START_REF] Kamiya | Commissioning of the JT-60SA helium refrigerator[END_REF], using by-pass lines and heaters to simulate the pulsed heat loads from the cryogenic users. Among the cryogenic users, the superconducting magnets are cooled by two supercritical helium loops at 4.4 K and 5 bar. Loop 1 is dedicated to the Toroidal Field coils (TF) and the cold structures while loop 2 supplies the Central Solenoid (CS) and Equilibrium Field coils (EF). In addition to these two loops, there are a loop 3 supplying the cryopumps at 3.7 K, a loop 4 supplying the thermal shields at 80 K and a loop 5 supplying HTS current leads at 50 K. The performance of the cryogenic system was demonstrated during the acceptance tests by showing that the system could extract the pulsed heat loads due to cycling plasma operation [START_REF] Hoa | Performance of the JT-60SA cryogenic system under pulsed heat loads during acceptance tests[END_REF]. At the time of the specification of the cryogenic system, the pulsed load profiles for the acceptance tests were derived from dynamic thermalhydraulic modelling using Vincenta [START_REF] Lamaison | Determination of heat loads at the interface of the JT-60SA cryogenic system[END_REF]. Several codes have been used to model TF magnets such as 4C [START_REF] Savoldi Richard | The 4C code for the cryogenic circuit conductor and coil modeling in ITER[END_REF] and THEA [START_REF] Bottura | A general model for thermal, hydraulic and electric analysis of superconducting cables[END_REF], in particular for quench studies. Simcryogenics has been developed by CEA for quick dynamic simulations for control with model-based design [START_REF] Bonne | Nonlinear observer of the thermal loads applied to the helium bath of a cryogenic Joule-Thompson cycle[END_REF] and for design optimization through parametric studies [START_REF] Bonne | Simcryogenics: a Library to Simulate and Optimize Cryoplant and Cryodistribution Dynamics[END_REF]. The reliability and optimization of operation become challenging aspects to study with quick dynamic simulations. It requires simplified models for faster-than-real time calculations. Some methodologies have been developed and tested, for example for ITER TF and CS magnets based on Artificial Neural Network requiring training of the neural network on full sets of simulations with detailed models [START_REF] Froio | Design and optimization of Artificial Neural Networks for the modelling of superconducting magnets operation in tokamak fusion reactors[END_REF]. Simcryogenics developed by CEA for the cryo-distribution and the cryoplant is addressing the critical requirement of dynamic simulations for control purposes with simplified models. Recent modelling work with Simcryogenics demonstrated the relevance of the thermal-hydraulic code developed by CEA for modelling the cryodistribution and the cable in conduit conductors (CICC), in order to evaluate the heat load profile to the cryoplant [START_REF] Bonne | Dynamic thermal-hydraulic simulations of the JT-60SA cryogenic system for preparing plasma operation[END_REF]. This work, as well as the present one, is focusing on the supercritical helium loop of the Toroidal Field coils and the structures (loop 1). The present work is an update of the previous modelling, taking into account all the latest information on the TF superconducting coils following manufacturing and the testing in the Cold Test Facility [START_REF] Maksoud | Status of the cold test facility for the JT-60SA tokamak toroidal field coils[END_REF] under cryogenic conditions. Indeed, the available measurements on the 18 TF coils could provide updated friction factor correlations [START_REF] Decool | JT-60SA TF Coils: Experimental Check of Hydraulic Operating Conditions[END_REF]. The model assumptions were detailed and revised with more refined heat load distributions on the TF CICC. These assumptions were also revised in terms of dimensions and materials of the CICC as well as correlations for the convective heat transfer coefficient in the CICC and cryo-distribution pipes. The thermal hydraulic model of the conductors is also improved by taking into account the inter-turn thermal coupling of the pancake-wound conductors. The effect of the inter-turn thermal coupling has been previously studied for TF quench modelling, within the framework of various fusion projects, e.g. JT-60 SA [START_REF] Huang | Numerical Modeling of the Quench Propagation Phase in the JT-60SA TF Coils[END_REF], ITER [START_REF] Zanino | Prediction, experimental results and analysis of the ITER TF insert coil quench propagation tests, using the 4C code[END_REF] and DEMO [START_REF] Coz | Quench Simulation of a DEMO TF Coil Using a Quasi-3D Coupling Tool[END_REF]. The thermal coupling was found to be a relevant phenomenon to model. The impact of these different improvements are highlighted and discussed. The updated profile of the heat load deposited in the thermal damper is presented.

Nomenclature

Description of loop 1 & TF CICC

The TF & Structures loop, also called loop1, uses supercritical helium to cool the 18 Toroidal field (TF) coils and their structures, i.e. TF structures (TF STR), as well as CS structures (CS STR), as shown in Fig. 1. One TF coil consists of a winding pack made of 6 Double-Pancakes (WP) supported by a stainless steel casing. Each Double-Pancake is made of a Cable-In-Conduit Conductor (CICC), whose characteristics are listed in Table 1.

Model description

Description of the Vincenta model

A model of the loop 1 was performed using the Vincenta code V6.0 in 2010 [START_REF] Lamaison | Determination of heat loads at the interface of the JT-60SA cryogenic system[END_REF]. The Vincenta code is a thermal-hydraulic simulation code for superconducting magnets and their cryo-distribution. This code was used to model the dynamic behavior of the supercritical loop HELIOS (Helium Loop for hIgh LOads Smoothing) under pulsed heat loads [START_REF] Vallcorba | Investigations of pulsed heat loads on a forced flow supercritical helium loop: Part B: Simulation of the cryogenic circuit[END_REF]. Since the comparison to experimental results gave very satisfying results [START_REF] Vallcorba | Investigations of pulsed heat loads on a forced flow supercritical helium loop: Part B: Simulation of the cryogenic circuit[END_REF], the Vincenta code was chosen to benchmark the model of the loop 1 performed using the Simcryogenics library [START_REF] Bonne | Dynamic thermal-hydraulic simulations of the JT-60SA cryogenic system for preparing plasma operation[END_REF]. The results obtained using Vincenta in 2010 are considered in the present paper. Since 2010, CEA/dSBT has developed its own modelling tool Simcryogenics, which was chosen for the present modelling work. This tool is more flexible allowing the reduction of the calculation time (typically 10 min for the loop), the study of various dynamic scenarios including the refrigerator (e.g. pulsed heat load scenarios, cool-down scenarios) as well as the analysis of control strategies.

Description of the Simcryogenics models

The loop1 was modelled using the Simcryogenics library for MATLAB/Simulink, as schematically shown in Fig. 2. 1-dimensional pipes, i.e. pipes consisting of volumes distributed along the flow direction, were used to model the supply line, return line, TF CICC as well as TF and CS structures. The two exchangers HX1 and HX2 were considered as perfect heat exchangers, i.e. the outlet temperature was independent of flow conditions and set equal to the bath temperature. These exchangers were immersed into the thermal damper V700, which is a 4.3 K saturated helium bath. The schematic is similar to that presented in [START_REF] Bonne | Dynamic thermal-hydraulic simulations of the JT-60SA cryogenic system for preparing plasma operation[END_REF] even though the library had been updated in order to manage flow reversal [START_REF] Bonne | Simcryogenics: a Library to Simulate and Optimize Cryoplant and Cryodistribution Dynamics[END_REF]. Equivalent parallel channels were only modelled once and then multiplied. Similarly, only one pancake of the TF coil was modelled, as shown in Fig. 3. As the heat load and the pressure drop differ from one pancake to another, a mean friction factor and heat load were applied on the modelled pancake. The modelled pancake was considered a central pancake and the 2-dimensionnal effects of the cooling channels in the casing were therefore neglected. Central pancakes are the most constraining pancake based on the distribution of magnetic fields [24] [23]. Fig. 4 shows the schematic that was used to model the TF & CS structures. One fluid channel is modelled for TF structures and CS structures by a 1-dimensional pipe and a 1-dimensionnal mass. This is a simplified model of the structures where the delay time due to the heat propagation through the cooling pipes as well as the thermal coupling between the TF winding pack and its structure are not considered.

Comparisons that have been performed with and without the modelling of the structure on DEMO TF coil with THEA [START_REF] Coz | Towards a multi-physic platform for fusion magnet design-Application to DEMO TF coil[END_REF] have shown that the differences in terms of temperature margin remain small. Moreover, neglecting the cooling of the structure is a conservative approach concerning the evaluation of the heat load profile to the cryoplant. The purpose of this simplified model of loop 1 is to have an estimate of the heat load arriving at the refrigerator. This model is not accurate enough to provide either refined thermal-hydraulic simulation (temperature margin) or the analysis of an accidental scenario (quench), but can be used to study operating scenarios, such as pulsed heat loads, and the analysis of control strategies. Two distinct models were developed on Simcryogenics. The first one aimed at reproducing the results that were obtained using the Vincenta code. This Simcryogenics model was built using the data that were available in 2010 and will be referred to as SC1 model in the following sections. The second one was an updated SC1 model, which was dedicated to the study of the different modifications in terms of heat transfer coefficient, friction factor, materials properties and non-uniformly distributed heat load distribution on the TF CICC. This model was also modified in order to model the inter-turn thermal coupling, as defined in section 4.6. In the following sections, the updated model will be referred to as SC2 model.

Model assumptions

Initial conditions

On Vincenta and Simcryogenics models, the loop is considered isochoric. In order to be able to compare Simcryogenics results to those obtained with Vincenta, the initial mass of helium was adapted on Simcryogenics so that the initial inlet pressure of the loop was similar to that of Vincenta. This was performed by using a charge or discharge charge valve at the beginning of simulation, modelled by a mass flowrate source or sink, as shown in Fig. 2. Once this adjustment has been performed, the loop is isochoric.

Correlation for convective heat transfer

Constant values were used for convective heat transfer coefficients for both Vincenta and SC1 model. The convective heat transfer coefficient between the helium flowing through the CICC and the CICC material was 25 W/(m 2 .K), while a value of 750 W/(m 2 .K) was chosen for the heat transfer coefficient between the helium and the TF & CS structures. Heat transfer coefficients were calculated on SC2 model using the Dittus-Boelter correlation, as follows:

0.023 . . (1)
JT60-SA TF CICC have also been modelled in previous work using the Dittus-Boelter-Giarratano correlation [START_REF] Huang | Study and modelling of the thermohydraulic phenomena taking place during the quench of a superconducting magnet cooled with supercritical helium[END_REF] and the Colburn-Reynolds analogy [START_REF] Nicollet | Parametric Analyses of JT-60SA TF Coils in the Cold Test Facility with SuperMagnet Code[END_REF], based on the model and tests that were performed for ITER CICC [START_REF] Nicollet | Evaluation of the ITER Cable In Conduit Conductor heat transfer[END_REF]. The Colburn-Reynolds analogy can be written as follows:

f /8 / (2)
Typical values of heat transfer coefficient inside the CICC at 3g/s are respectively about 5.4 10 and 3.1 10 W/(m 2 .K) for the Dittus-Boelter correlation and Colburn-Reynolds analogy. For both methods, the temperature difference between the mass of materials and the fluid is only a few mK, due to the high values of heat transfer coefficient and heat transfer area. Therefore, the choice between Eq. 1 and Eq. 2 have a negligible impact on the results, as shown in section 5.6.

Friction factor

The pressure drop was calculated by using the Darcy-Weisbach equation as detailed in Eq. 3. The Darcy friction factors of pipes, TF CICC and TF & CS structures were calculated accordingly for the different models.

∆ ! L/D $ ρ V /2 (3)
The Darcy friction factors of distribution pipes and TF & CS structures were calculated by using Altshul formula [START_REF] Brkić | Review of explicit approximations to the Colebrook relation for flow friction[END_REF] for the Vincenta and Simcryogenics models:

! 0.11 '68/ ) * . + (4)
On Vincenta and SC1 models, the friction factor of TF CICC was calculated using a modified Katheder correlation [START_REF] Katheder | Optimum thermohydraulic operation regime for cable in conduit superconductors (CICS)[END_REF], which was proposed by Nicollet et al. [START_REF] Decool | JT-60SA TF Coils: Experimental Check of Hydraulic Operating Conditions[END_REF]. The pressure drop inside the TF coils was found to be higher than expected. A new correlation for the friction factor was therefore determined with specific coefficients, i.e. α, β, and γ, for each double-pancakes of each TF coil [START_REF] Decool | JT-60SA TF Coils: Experimental Check of Hydraulic Operating Conditions[END_REF]:

! 3 ) 4 5 (6)
Only one pancake is modelled on Simcryogenics as all pancakes are considered equivalent. In order to update the friction factor on SC2 model, Eq. 6 was used after averaging the experimental coefficients that were measured for each double-pancakes of the TF coil 12 [START_REF] Huang | Study and modelling of the thermohydraulic phenomena taking place during the quench of a superconducting magnet cooled with supercritical helium[END_REF].

Dimensions & materials for the TF CICC

The parameters used to model the TF CICC are shown in Table 2. On SC2 model, the wetted perimeter, the helium cross-section area as well as the type and masses of materials were updated according to [START_REF] Huang | Study and modelling of the thermohydraulic phenomena taking place during the quench of a superconducting magnet cooled with supercritical helium[END_REF]. As for the modified SC2 model dedicated to the study of the inter-turn thermal coupling, the bundle and the jacket with its insulation were modelled as two distinct masses, as described in section 4.6. On Simcryogenics, the material properties of copper, stainless steel and epoxy were calculated using data from NIST. An updated value of 100 was chosen for the RRR of copper based on the measurement that were performed on the CICC copper and NbTi strands, i.e. ranges of 70-90 and 148-233 respectively [START_REF] Zani | Status of European manufacture of Toroidal Field conductor and strand for JT-60SA project[END_REF].

Heat loads

After the Vincenta model of 2010 was established, a contingency of about 14% has been added to the heat load on the TF CICC, TF & CS structures as well as TF joints. The updated load of the latter is 315 W, while the updated dynamic load profiles are shown in Fig. 5 and Table 3. Static losses of about 200 W were added to represent the cryo-distribution losses in the Simcryogenics models and the Vincenta model. Masses of materials for one pancake 425 kg of copper (RRR=300) 157 kg of 316 stainless steel, 182 kg of copper (RRR=100) and 42 kg of NbTi

Inter-turn thermal coupling

The TF CICC is a cable made of NbTi and Cu strands inside a stainless steel jacket, which is insulated against the other conductors using epoxy, as shown in Fig. 7. The CICC in one pancake is wound in 6 turns. The inter-turn thermal coupling is the thermal coupling occurring between the successive turns of the jacket that are in contact. SC2 model was modified in order to investigate the effect of the inter-turn thermal coupling. The CICC was therefore divided between 3 elements: the jacket, the bundle and the fluid channel, as shown in Fig. 6. The thermal coupling was modelled by connecting the different meshed elements of the jacket that were in contact thermally via thermal resistances. The thermal resistance was calculated as follows:

89 2 e :: λ :: ⁄ ) => /λ ?@ (6) With a thickness of stainless steel eSS and glass-epoxy eGE of 2 mm. The thermal conductivity of stainless steel and epoxy was calculated as a function of temperature during simulation for each element of the meshed 1D mass of materials. The thermal conductance associated with inter-turn thermal coupling per meter of CICC ranged from 0.69 to 0.72 W/(m.K) for the simulation described in section 5.5.2. The pancake-to-pancake thermal coupling was not considered in the present study, but would constitute a further improvement of the model. The heat load received by the TF winding pack was distributed along the different turns by applying the distribution profile described in Table 4. This profile is a rough estimate that was extrapolated from DEMO calculations [START_REF] Bonne | Optimization of the cooling capacity of the cryo-magnetic system for EU DEMO at the pre-conceptual design phase[END_REF]. A non-uniformly distributed profile was chosen instead of a uniform one, as this profile is more realistic while being more critical. This allows the smoothing effect of the inter-turn thermal coupling to be illustrated. This heat load was then distributed between the jacket and bundle according to their respective mass ratios.

Results and discussion

Benchmark of Simcryogenics and Vincenta results

Under similar assumptions, the Vincenta code and the Simcryogenics library give similar results [START_REF] Bonne | Dynamic thermal-hydraulic simulations of the JT-60SA cryogenic system for preparing plasma operation[END_REF]. As an update of the Simcryogenics library was performed [START_REF] Bonne | Simcryogenics: a Library to Simulate and Optimize Cryoplant and Cryodistribution Dynamics[END_REF], it was necessary to verify that the results obtained with SC1 model were similar to those obtained with the Vincenta code using the same input parameters. As shown in Fig. 8, both results were in good agreement. For the different curves, the maximum absolute relative difference ranged from 0.6% to 7.5%, while the mean absolute relative difference ranged from 0.1% to 2.3%.

Update of heat loads & heat transfer coefficient

The heat loads were updated as described in section 4.5 on SC2 model, taking into account a 14% contingency. The materials and the dimensions of the CICC were also updated as detailed in section 4.4. The results obtained using SC1 model and SC2 model were compared. As shown in Fig. 9, this update resulted in an increase in temperature for TF & CS structures as well as an increase of the power received by the heat exchanger HX2. An increase in temperature of 0.17 and 0.12 K was respectively observed for the maximum outlet temperature of TF & CS structures. The maximum power received by the heat exchanger HX2 was found to be about 2.8 kW. This power is the power deposited into the thermal damper V700 of the refrigerator. No significant increase in temperature was observed inside the TF CICC.

Update of friction factor and reduced mass flow of 3g/s

The previous results obtained in section 5.2 with SC2 model were modified by reducing the nominal mass flowrate to 3 g/s and using Eq.( 7) in order to calculate the Darcy friction factor. Fig. 10 shows the obtained results. The use of a reduced mass flowrate of 3 g/s, due to the higherthan-expected pressure drop, resulted in an increase of the temperatures of the structures, but did not have a significant impact on the maximum TF CICC inlet or outlet temperature. This can be explained by the high values of heat transfer coefficient for TF CICC at 3 g/s and 4 g/s. Nevertheless, the TF CICC outlet temperature reached its initial value at the end of one heat load pulse after a longer duration. A decrease in the heat load received by the heat exchanger HX2 as well as a smoother heat load profile was observed. The peak heat load received by HX2 was reduced from 2.8 to 2.4 kW. The specific enthalpy of the fluid at the inlet of HX2 was similar in both cases due to the same expansion in the loop and therefore the same increase in temperature resulting from the Joule-Thomson effect. The temperature of the fluid at the outlet of HX2 was set by the temperature of the bath. Hence, a similar variation of specific enthalpy was observed in both cases between the inlet and outlet of HX2. The reduction of peak heat load was therefore caused by the reduction of mass flowrate. These results are consistent with those previously obtained by Bonne et al. [START_REF] Bonne | Dynamic thermal-hydraulic simulations of the JT-60SA cryogenic system for preparing plasma operation[END_REF], even though the latter were obtained under assumptions that differed from the present model, e.g. different values of heat load, heat transfer coefficient and friction factor

Non-uniformly distributed heat load profile

The SC2 model presented in section 5.3. was then updated by assuming a non-uniformly distributed heat load profile along the TF CICC. This profile was estimated from DEMO calculation [START_REF] Bonne | Optimization of the cooling capacity of the cryo-magnetic system for EU DEMO at the pre-conceptual design phase[END_REF] and detailed in section 4.6. This simulation aimed at investigating the effect of a non-uniformly distributed heat load profile and highlighting the influence of the interturn thermal coupling that is studied in section 5.5. As shown in Fig. 11, a non-uniformly distributed heat load profile resulted in an increase of the maximum TF outlet temperature and the maximum power received by the heat exchanger HX2. The assumption of a non-uniformly distributed profile is therefore conservative. A time shift was observed for the maximum values of the TF outlet temperature and HX2 power. This resulted from the reduced mass flow rate and the impact of the nonuniformly distributed heat load on the heat transport along the CICC. .

Inter-turn thermal coupling

Comparison between simulation and experimental measurement

TF coils were tested in the Cold Test Facility, whose experimental setup was described by Abdel Maksoud et al. [START_REF] Maksoud | Status of the cold test facility for the JT-60SA tokamak toroidal field coils[END_REF]. In order to study the heat propagation along the CICC and the effect of the thermal inter-turn coupling, an additional test was performed in this facility. This test consisted in testing one TF coil for a fast increase of the inlet temperature of about 1 K and observing the evolution of the outlet temperature.

A model of the experiment was built by using the TF CICC of SC2 model.

The measured profile of inlet pressure, inlet temperature and outlet pressure were set as boundary conditions. Simulations were performed with and without taking into account the inter-turn thermal coupling. The simulated outlet temperature profile was compared to the experimental profile, as shown in Fig. 12. The model with inter-turn thermal coupling was found to be more consistent with the experimental results, thus showing the importance of modelling this phenomenon and validating the calculation of the inter-turn thermal coupling resistance.

Update of Simcryogenics results with inter-turn thermal coupling

The results presented in section 5.4 were updated by modelling the interturn thermal coupling, as shown in Fig. 13. The maximum TF outlet temperature and the maximum power received by the heat exchanger HX2 were reduced by respectively 73 mK and 0.15 kW. The inter-turn thermal coupling was therefore found to have a smoothing effect on the nonuniformly distributed heat load. However, a longer duration was required for the TF CICC outlet temperature to reach its initial value at the end of one heat load pulse.

Comparison between Dittus-Boelter correlation and Colburn-Reynolds analogy

As mentioned in section 4.2, some simulations were also performed by using the Colburn-Reynolds analogy in order to calculate the heat transfer coefficient. The updated SC2 model of section 5.5.2 was run with both the Colburn-Reynolds analogy and the Dittus-Boelter correlation. Fig. 14 shows the obtained results. It can be noted that similar results were obtained, except for the outlet temperature of CS structures for which a higher value was obtained by using the Colburn-Reynolds analogy. An increase of 33 mK was observed for the maximum outlet temperature of the TF CICC. This resulted from higher values of heat transfer coefficient when using the Colburn-Reynolds analogy. As little difference was observed between the two correlations, the results obtained using Dittus-Boelter correlation in section 5.5.2. will be the baseline for future analyses.

Conclusion

A model of the TF & Structures loop (loop 1) was developed using Simcryogenics in order to reproduce the simulations that were performed in 2010 by using the Vincenta code. This previous model, which aimed at determining the pulsed heat load profile, had been used to specify the dynamic refrigeration operation of the JT-60SA cryogenic system. An updated model was built in order to take into account the latest information related to the manufacturing and testing of TF coils. The most significant changes of the model were the consideration of the 14% contingency for the heat load, the update of the friction factor, the reduced mass flowrate, the non-uniformly distributed heat load on the TF CICC and the inter-turn thermal coupling of the TF CICC.

The effect of the inter-turn thermal coupling was found to counterbalance the effect of the non-uniformly distributed heat load. The difference between the updated profile of the heat load deposited in the thermal damper and that obtained in 2010 was therefore mainly due to the update of the heat load and the use of a reduced mass flowrate along with an updated friction factor. The updated profile of the heat load deposited in the thermal damper was found to be smoother than that obtained in 2010.

The modelling work performed using Simcryogenics can be used for preparing the plasma operation of JT-60SA in the coming years. In the future, perfect heat exchangers would be modified in order to model a finite-sized bath and therefore the temperature variation of the bath and hence the variation of the inlet temperature. Similar updates will be performed to simulate CS & EF coils loop (loop 2) in the future. The model can be coupled with the cryogenic system model and can be used for testing the control strategies related to pulse operation as well as investigating cool down scenarios.

Nu 3 V

 3 Nusselt number, -Re Reynolds number, -Pr Prandtl number, -fD Darcy friction factor, -Vf Void fraction, -∆P Pressure drop across the TF CICC, Pa L Length of the TF CICC, m Dh Hydraulic diameter of the TF CICC, m ρ Density of helium flowing through the TF CICC, kg/m Velocity of helium flowing through the TF CICC, m 2 /s Rit Thermal resistance for the inter-turn thermal coupling, m 2 .K/W eSS Thickness of stainless steel of the jacket, m eGE Thickness of glass-epoxy insulation, m λSS Thermal conductivity of stainless steel, W/(m.K) λGE Thermal conductivity of glass-epoxy, W/(m.K) P circ Pressure of the circulating pump, bar TTF Temperature of TF CICC, K TTF str Temperature of TF structures, K TCS str Temperature of CS structures, K Mass flowrate through TF CICC, kg/s QHX2 Power received by the heat exchanger HX2 and deposited into the thermal damper V700, W

Fig. 1 -

 1 Fig. 1 -Simplified Process Flow Diagram of loop 1

Fig. 2 -. 1 .Fig. 3 -Fig. 4 -

 2134 Fig. 2 -Schematic of the Simcryogenics models, which include the heat exchangers HX1 and HX2, cryo-distribution pipes (P1001, P1003, P07a), the circulating pump CP01 as well as the lines detailed in Fig. 3 and Fig. 4. The blue connections are fluid connections while the green ones convey materials properties. The mass flowrates are indicated for a reduced mass flowrate of 3 g/s. The mass flowrate flowing through the structures can be adjusted via by-pass valves, which are not shown in the present figure. The purpose of the element M_adjust is explained in section 4.1.

  fraction Vf of 0.32 Since 2010, new data regarding the friction factor of TF CICC have become available. Decool et al. conducted a characterization program of TF CICC and the measurement of their friction factor

  In order to maintain a pressure drop inside the TF CICC of 1.1 bar despite these higher values of the friction factor, a reduced value of 3 g/s was chosen for the mass flowrate flowing through the TF CICC instead of the previous value of 4 g/s[START_REF] Bonne | Dynamic thermal-hydraulic simulations of the JT-60SA cryogenic system for preparing plasma operation[END_REF].

Fig. 5 -kW can be noted during plasma initialization Table 3 -

 53 Fig. 5 -Overall updated heat load profiles for TF Winding Pack, TF structures and CS structures as a function of normalized time (normalized in relation to the cycle time of 1800 s). For the TF and CS structures, the y-axis has been truncated as a peak of respectively 266.1 kW and 122.6 kW can be noted during plasma initialization

Fig. 6 -Fig. 7 -

 67 Fig. 6 -Schematic used to model the inter-turn thermal coupling

Fig. 8 -

 8 Fig. 8 -Comparison between the results obtained using Vincenta (black curve) and SC1 models (blue curve). Dashed lines and solid lines respectively show the inlet and outlet values.

Fig. 9 -

 9 Fig. 9 -Comparison between the results obtained using SC1 (blue curve) and SC2 model after the update regarding the heat loads and the heat transfer coefficient as described in section 5.2 (magenta curve). Dashed lines and solid lines respectively show the inlet and outlet values.

Fig. 10 -Fig. 11 -

 1011 Fig. 10 -Comparison between the results obtained using SC2 model after the update regarding the friction factor as described in section 5.3 (magenta curve) and those obtained before the update (blue curve). Dashed lines and solid lines respectively show the inlet and outlet values.

Fig. 12 -

 12 Fig. 12 -Comparison between measured TF inlet & outlet temperature profiles (black curves) and Simcryogenics results using SC2 model with inter-turn thermal coupling (blue curve) and without inter-turn thermal coupling (red curve).

Fig. 13 -

 13 Fig. 13 -Comparison between the results obtained using SC2 model after the update regarding the inter-turn thermal coupling as described in section 5.5 (magenta curve) and those obtained before the update (blue curve). Dashed lines and solid lines respectively show the inlet and outlet values.

Fig. 14 -

 14 Fig. 14 -Comparison between the results obtained using SC2 model with Dittus-Boelter correlation (blue curve) and Colburn-Reynolds analogy (magenta curve). Dashed lines and solid lines respectively show the inlet and outlet values.

Table 1 -Characteristics of the TF CICC

 1

	Properties
	Length (m)	113
	Void fraction (-)	0.32
	Strand diameter (mm)	0.81
	Number of superconducting strands	324
	Number of copper strands	162

Table 2 -Data used for the TF CICC on the different models

 2

		Vincenta & SC1 model	SC2 model
	Length (m)	113	113
	Void fraction (-)	0.32	0.32
	Wetted perimeter (m)	1.111	1.108
	Helium cross-section area (m 2 )	1.27e-4	1.25824e-4

Table 4 -Non-uniformly distributed heat load distribution on TF CICC Heat load distribution

 4

	Turn 1	51 %
	Turn 2	21 %
	Turn 3	13 %
	Turn 4	7 %
	Turn 5	4 %
	Turn 6	4 %

Acknowledgements

The authors would like to thank the CTF team for the tests ATA02 and the data regarding coils, in particular Roser Vallcorba for providing the data. The authors would like to thank Manfred Wanner for his advices and fruitful discussions regarding the interpretations of the present results. This work was undertaken under the Broader Approach Agreement between the European Atomic Energy Community and the Government of Japan. The views and opinions expressed herein do not necessarily state or reflect those of the Parties to this Agreement.


BALLET Je ́rôme, BAZIN Boniface K Komena
email: boniface_komena@yahoo.com

Damien Bazin
email: damien.bazin@gredeg.cnrs.fr

Alassane Ouattara Of Bouake

BALLET Je ́ro ̂me Phone+33(0)5 56 84 25 75

downscaling of existing

1

Introduction

Academic and professional interest in how innovations spread in society has long historical roots, going back to the work of [START_REF] Ryan | The diffusion of hybrid seed corn in two Iowa communities[END_REF] and [START_REF] Rogers | Diffusion of innovations[END_REF] on the adoption and diffusion of innovations. Today, such processes of adoption or diffusion are generally labelled as the scaling of innovations. Innovations can be technologies, products, services and practices, but also organizational and institutional arrangements. Scaling refers to the increased use of innovations beyond the group involved in its initial design and testing.

Scaling is considered important in the context of global investments in research and development to address societal challenges related to health, agriculture, and the environment. The scaling of innovations is particularly relevant to research for development (R4D) organizations that have a mandate to develop, test and validate innovations to achieve Sustainable Development Goals (SDGs) and to demonstrate to donors that their research innovations are adopted in society to show return-on-investment [START_REF] Renkow | The impacts of CGIAR research: A review of recent evidence[END_REF].

Experience shows that achieving impact at scale is more complex and difficult than anticipated in intervention proposals [START_REF] Alvarez | Participatory impact pathways analysis: a practical method for project planning and evaluation[END_REF][START_REF] Thornton | Responding to global change: A theory of change approach to making agricultural research for development outcome-based[END_REF]. Earlier conception that innovations could simply be transferred by intermediaries and change agents (e.g., extension officers or health educators) and then diffuse within communities of individual beneficiaries [START_REF] Rogers | Diffusion of innovations[END_REF] has been largely refuted [START_REF] Röling | Extension science: Information systems in agricultural development[END_REF][START_REF] Leeuwis | Communication for rural innovation: rethinking agricultural extension[END_REF]. Historians of technology, for example, argue that scaling of innovation involves competition between supporters of different technological solutions, and those who defend interests and sunk investment associated with incumbent technological systems [START_REF] Geels | Typology of sociotechnical transition pathways[END_REF][START_REF] Schot | Strategic niche management and sustainable innovation journeys: theory, findings, research agenda, and policy[END_REF]. Others stress that the scaling of one innovation (e.g., using a new seed variety) depends on the simultaneous upscaling of other complementary practices (e.g., weeding, pesticide-use, distribution of inputs, credit provision) and the intervening and navigating complex interdependencies that influence the intervention's ability to achieve impact at scale. The approach presented in this paper -Scaling Readinessis centred around the ambition to assess the readiness of innovations to achieve specific impact at scale, within a specific context, and develop, implement and monitor scaling strategies to achieve those scaling objectives. Although developed and published in the context of the agricultural R4D sector, it has been designed to support other R4D sectors as well (e.g., health, environment, education). The notion of "readiness" refers to whether an innovation has been tested and validated for the role it is intended to play in society. The concept resonates with levels of technology readiness that have been proposed by the National Aeronautics and Space Administration (NASA) of the United States, the European Commission (EU) and technology studies scholars to assess advancements in technology development, commercialization, and transition pathways (European Commission, 2014;[START_REF] Sauser | From TRL to SRL: The concept of systems readiness levels[END_REF][START_REF] Kobos | Timing is everything: A technology transition framework for regulatory and market readiness levels[END_REF]. Thus, to accommodate these ideas, we use the term "Scaling Readiness" in two ways: (1) as a brand name for a decision-support process that we are developing and describing in this paper (capitalized), and (2) as a key variable and measure for assessing the maturity and scalability of an innovation (not capitalized).

Scaling Readiness contributes in meaningful ways to other frameworks and approaches that have been proposed in relation to readiness and/or scaling (inter alia [START_REF] Kuehne | Predicting farmer uptake of new agricultural practices: A tool for research, extension and policy[END_REF][START_REF] Wigboldus | Systemic perspectives on scaling agricultural innovations. A review[END_REF]. First, Scaling Readiness not only assesses the maturity of technological innovations, but also of other types of innovations (including social, institutional and political innovations), which enable a significant broadening of scope when compared to technological readiness [START_REF] Sauser | From TRL to SRL: The concept of systems readiness levels[END_REF]. Second, Scaling Readiness extends conventional readiness assessments by incorporating a measure of the actual use of the innovations in the locations where scaling is desired and thereby grounds readiness in the specific local context. Third, the scope of Scaling Readiness goes beyond the PRactice-Oriented Multi-level perspective on Innovation and Scaling (PROMIS) assessment from [START_REF] Wigboldus | Systemic perspectives on scaling agricultural innovations. A review[END_REF] by providing a hands-on and action-oriented process that fosters collective decision-making, learning and strategizing. Furthermore, Scaling Readiness reduces complexity into a single metric indicator that can also be used to assess changes in scalability over time. Fourth, the emphasis on decision-support and complex interdependencies distinguishes Scaling Readiness from the ADOPT approach proposed by [START_REF] Kuehne | Predicting farmer uptake of new agricultural practices: A tool for research, extension and policy[END_REF], which essentially predicts adoption of a specific innovation based on Rogers's (1983)

Key concepts of Scaling Readiness

This section presents key concepts that underlie Scaling Readiness and which guided the design of our approach in terms of its requirements and measures. The key concepts of Scaling Readiness are a combination of adapted, existing concepts and new concepts introduced by the authors. We group them under five sub-sections that are linked to the five steps proposed in Section 4.

Scaling is subject to a specific spatial and temporal context

A consistent finding across different sectors (e.g., health, agriculture, and the environment) is that scaling is influenced by contextual conditions, and that 'one-size-fits-all' approaches are unlikely to be effective [START_REF] Schut | Towards dynamic research configurations: A framework for reflection on the contribution of research to policy and innovation processes[END_REF][START_REF] Sartas | Factors influencing participation dynamics in research for development interventions with multistakeholder platforms: A metric approach to studying stakeholder participation[END_REF][START_REF] Shelton | Evidence-based public health: not only whether it works, but how it can be made to work practicably at scale[END_REF][START_REF] Thornton | Adapting to climate change: Agricultural system and household impacts in East Africa[END_REF][START_REF] Levin | Ecosystems and the Biosphere as Complex Adaptive Systems[END_REF][START_REF] Innes | Consensus building and complex adaptive systems[END_REF]. The innovation systems literature conceptualizes innovation as the outcome of (changes in) interactions between networks of interdependent actors and stakeholders, the socio-technical context in which they operate, and the rules and institutions that govern their interactions [START_REF] Klerkx | Adaptive management in agricultural innovation systems: The interactions between innovation networks and their environment[END_REF]. This finding suggests that an innovation that may be appropriate and scalable in one context, may not fit another context.

Secondly, an intervention strategy that may effectively support the scaling of innovation in one context, may not be effective in another context.

A range of different spatial conditions play a role here, including agro-ecological conditions [START_REF] Douthwaite | Ecoregional research in Africa: learning lessons from IITA's benchmark area approach[END_REF] and the socio-institutional features of the innovation system in question [START_REF] Klerkx | Adaptive management in agricultural innovation systems: The interactions between innovation networks and their environment[END_REF]Schut et al., 2016a). As well, several studies have noted that the success of similar R4D interventions may vary considerably over time [START_REF] Abrahams | Changing the debate about health research for development. International Health Research Awards Recipients[END_REF][START_REF] Baur | Impact assessment and evaluation in agricultural research for development[END_REF][START_REF] Delisle | The role of NGOs in global health research for development[END_REF][START_REF] Henderson | Evaluating the impact of forestry research for development[END_REF][START_REF] Laws | Research for development: A practical guide[END_REF][START_REF] Sartas | Factors influencing participation dynamics in research for development interventions with multistakeholder platforms: A metric approach to studying stakeholder participation[END_REF]. For example, in agriculture, the 'green revolution' is a good example of how the scaling of uniform high input use in farming (e.g., fertilizers, improved crop varieties) had differential impact over space and time [START_REF] Evenson | Assessing the impact of the green revolution, 1960 to 2000[END_REF][START_REF] Hazell | The Green Revolution reconsidered: the impact of high-yielding rice varieties in South India[END_REF].

Taken together, these studies imply that we cannot usefully make generic statements about whether an innovation is ready for scaling or not. Thus, Scaling Readiness must assess maturity and scalability in specific spatial and temporal contexts and provide context-specific decision support to develop meaningful scaling strategies.

Taking the scaling context and objectives of R4D interventions as starting point

Stating that an evaluation of scaling readiness must be contextual opens the question of what and whose boundaries of context should be considered. This question relates not only to the geographical location (space) and temporal horizon (time) to be taken into account but also requires defining what may usefully scale and for what underlying objective. For instance, an R4D intervention that aims to decrease vitamin A deficiency in rural communities in tropical areas by scaling of vitamin A rich crops could consider supporting the development of three alternative cropping systems and value chains (e.g., rice, banana and sweet potato) to address the vitamin A deficiency problem 1 . However, each crop has a different set of resource requirements and will lead to different impacts depending on the context. Under similar conditions, the same amount of vitamin A can be produced with the least amount of land if rice is used, with the least amount of water if sweet potato is used, and with the least amount of labour if banana is used. Thus, a scaling strategy for decreasing vitamin A deficiency needs to consider other objectives and conditions as well. Yet another dimension of context concerns who are the expected beneficiaries from the scaling of the innovation. For example, if women are defined as the main target group, then scaling an innovation that reduces labour by women may make most sense.

While we realize that different views may exist on what the relevant geographies, objectives and beneficiaries should be for a specific scaling initiative, the starting point of our approach is to assess the scaling readiness of innovations based on the expected goals and impacts of a specific R4D intervention [START_REF] Kuehne | Predicting farmer uptake of new agricultural practices: A tool for research, extension and policy[END_REF][START_REF] Cohen | Harnessing Complexity[END_REF]. We take this as a practical and legitimate starting point given our purpose is to provide decision support to R4D interventions. At the same time, we expect that the need to explicate such parameters will foster critical reflection in situations where boundaries, scaling objectives and target beneficiaries are not clearly defined. Those considerations will trigger further reflection within R4D interventions on whether scaling is indeed feasible, desirable and responsible.

Innovations scale as part of packages

As indicated, innovation systems literature emphasizes that the upscaling of specific innovations (e.g., a new crop variety) may simultaneously require the upscaling of other innovations (e.g., a seed multiplication and distribution system), or the downscaling of existing practices (e.g., use of the currently dominant crop variety) [START_REF] Kilelu | Unravelling the role of innovation platforms in supporting co-evolution of innovation: Contributions and tensions in a smallholder dairy development programme[END_REF][START_REF] Wigboldus | Systemic perspectives on scaling agricultural innovations. A review[END_REF]. These dynamics imply that innovations cannot be usefully scaled in isolation but must be regarded as part of a collection of innovations, or an innovation package. The innovation package then becomes the unit of analysis for assessing scaling readiness.

Packages include core and complementary innovations

R4D interventions often focus on scaling a specific core innovation (e.g., a new drug or new crop variety) that is assumed to contribute to a societal benefit. These core innovations often form the heart of an R4D intervention. However, the scaling of core innovations is influenced by interactions with other innovations or conditions that can be either enabling or constraining. We refer to these other innovations as complementary innovations. For instance, scaling a new animal vaccine (the core innovation) also requires (1) new vaccine dosage and application practices; (2) certification from vaccine control agencies; (3) establishing or improving vaccine delivery systems; and (4) education about vaccine characteristics and use (the complementary innovations) [START_REF] Curry | Scaling up depot medroxyprogesterone acetate (DMPA): a systematic literature review illustrating the AIDED model[END_REF][START_REF] Paina | Understanding pathways for scaling up health services through the lens of complex adaptive systems[END_REF].

What constitutes a meaningful and viable innovation package depends again on the context, which implies that packages can change over time and are likely to differ across locations.

Similarly, the composition of an innovation package may need to vary for different beneficiary groups. Using the animal vaccine example again, for countries where resource poor populations are impacted by a specific animal disease, subsidized vaccine distribution through public veterinary services may be an important complementary innovation to ensure equitable and affordable access.

In sum, Scaling Readiness needs to take into account interdependencies between core and complementary innovations and needs to support the characterization and definition of innovation packages that are specific to the R4D intervention: its context, objectives, users and beneficiaries.

The scaling readiness of an innovation is a function of innovation readiness and innovation use

As mentioned in Section 1, the technology readiness levels proposed by NASA and the EU are, in essence, a measure of the maturity of a technology wherein maturity is defined as a demonstrated capacity to perform a specific function or contribute to a specific objective within a specific research or development environment (e.g., in the laboratory, under controlled conditions or under uncontrolled conditions). Levels of readiness range from an 'unproven idea' to 'innovation that is validated for use in an uncontrolled environment' with in-between gradations of 'proof of concept', 'tested prototype' and 'demonstrated under controlled conditions'.

However, in spite of this elaboration, the maturity scale is not sufficient for understanding the potential of a core innovation and/or an innovation package as a whole and its readiness to go to scale and contribute to the desired objectives. Many documented ready innovations have failed to be used at scale, such as improvements to child and maternal health [START_REF] Althabe | Strategies for improving the quality of health care in maternal and child health in low-and middle-income countries: an overview of systematic reviews[END_REF] and agroforestry management practices that use fodder shrubs or improve tree fallows [START_REF] Franzel | Scaling up the impact of agroforestry: Lessons from three sites in Africa and Asia[END_REF]. In addition, not every innovation may have a demonstrated capacity to perform a specific function or have a desired impact. For example, multi-stakeholder innovation platforms have been increasingly utilized in the agricultural R4D sector to advance innovation and scaling, but evidence of their effectiveness to achieve impact is scarce [START_REF] Biermann | Multi-stakeholder partnerships for sustainable development: does the promise hold?[END_REF][START_REF] Cole | Implementing a national health research for development platform in a low-income country -a review of Malawi's Health Research Capacity Strengthening Initiative[END_REF]Sartas et al., 2018a;[START_REF] Servaes | How "sustainable" is development communication research?[END_REF][START_REF] Warner | Multi-stakeholder platforms: integrating society in water resource management?[END_REF]. To put it more simply, innovations with a low potential for achieving impact are sometimes used at scale, whereas innovations with a high potential for achieving impact are not necessarily used at scale. Thus, while it is important to capture the maturity of innovations that are part of an innovation package (i.e., innovation readiness), it is also necessary to incorporate additional variables if we want to fully understand and assess scaling potential.

Inspired by innovation scholars [START_REF] Geels | Typology of sociotechnical transition pathways[END_REF][START_REF] Leeuwis | Rethinking communication in innovation processes: creating space for change in complex systems[END_REF] and network science [START_REF] Hermans | Social network analysis of multi-stakeholder platforms in agricultural research for development: Opportunities and constraints for innovation and scaling[END_REF]Sartas et al., 2018b), we argue that the scaling potential of a core innovation and/or innovation package is -at a given point in time -also shaped by the social networks in which the innovations are embedded, supported and used. In other words, whether or not an innovation is likely to scale depends on who and how many users are already using it, and how such users are positioned in the social network. Thus, it makes sense to distinguish between network environments in which the innovation still receives considerable support and protection (e.g., a project or intervention), and network environments in which it has been used without any form of support (e.g., as part of livelihood systems). This thinking aligns with the literature on strategic niche management, which points to the importance of gradually reducing protection of innovation initiatives (niches) over time and the ability of niche-level innovations to reconfigure dominant policies, procedures and practices (regimes) [START_REF] Hommels | Techno therapy or nurtured niches? Technology studies and the evaluation of radical innovations[END_REF][START_REF] Smith | What is protective space? Reconsidering niches in transitions to sustainability[END_REF].

If innovations are used only by R4D intervention teams, their partners and beneficiaries who are directly linked to or incentivized by the intervention, then the scaling potential is still low, irrespective of the number of team members, partners and direct beneficiaries using those innovations. When we frame the intervention in these terms, it creates a different perspective on claimed scaling achievements such as "this new crop variety is used or adopted by 25,000 farmers in Zambia". Such statements do not reveal much about the performance of the R4D invention unless we are provided with information on who these farmers are and what was their relation to the intervention. In other words, numbers tell only part of the story (Woltering et al., 2019). Instead, the position of those using innovations in the innovation network is a much better indicator of the innovation's scaling potential. Such a variable also captures whether the innovation users operate within a protected space (controlled environment), or whether they use the innovation in more unprotected conditions (uncontrolled environment) [START_REF] Smith | What is protective space? Reconsidering niches in transitions to sustainability[END_REF]. Therefore, we propose a scaling readiness variable that indicates in what type of networks an innovation or innovation package is already being used. We will refer to this concept as innovation use.

Scaling readiness then becomes a function of innovation readiness and innovation use. In our approach, we use these variables to generate diagnostic information relevant to scaling strategy development. We will further elaborate and operationalise these variables in Section 3.

Identify bottlenecks for scaling strategy development

When we acknowledge that innovations scale as part of innovation packages, then the next step is to try to understand which of the innovations limits the scaling of the innovation package and what is the most resource-efficient strategy to overcome such bottlenecks.

Innovations with low innovation readiness and use constitute bottlenecks for scaling

Liebig's Law of the Minimum is a good way to explain the focus on the innovation package as the unit of analysis for assessing its scaling potential. According to Liebig, plant growth is limited by the nutrient in shortest supply [START_REF] Austin | Species distribution models and ecological theory: A critical assessment and some possible new approaches[END_REF][START_REF] De Baar | von Liebig's law of the minimum and plankton ecology (1899-1991[END_REF][START_REF] Van Der Ploeg | On the origin of the theory of mineral nutrition of plants and the Law of the Minimum[END_REF]. Therefore, to analyse plant growth, it is necessary to know the relative availability of all nutrients necessary for the growth of the plant, and to assess which of the (micro-) nutrients is constraining efficient nutrient uptake. Similarly, the scaling of innovations is limited by the core or complementary innovation in the innovation package that are least developed, or, in other words, form the bottleneck. This dynamic is illustrated in the adapted version of 'Liebig's barrel' [START_REF] Whitson | Soils and soil fertility[END_REF] presented in Figure 1. Each individual innovation can be considered as a stave in the barrel. Just as the capacity of a barrel with staves of unequal length is limited by the shortest stave, so is the scaling potential of an innovation package determined or limited by the innovation with the lowest readiness and use. Different staves are combined by a hoop (the R4D approach) that binds staves as an innovation package. The length of each stave corresponds with innovation readiness, and width of the stave corresponds with innovation use. The higher and wider the staves are, the more water the barrel can hold. In other words, the higher the readiness and use of the innovations, the higher the capacity of the innovation package to achieve impact at scale.

Figure 1.

Scaling Readiness Barrel to illustrate how innovation(s) with the lowest readiness limit an innovation package's capacity to achieve impact at scale. 13 Notably, Figure 1 has clear implications for strategy development and R4D investment. For example, the scaling of a drought tolerant crop variety may be limited by the absence or poor performance of a seed delivery system. One can continue to invest in plant breeding to improve a drought tolerant crop variety, but as long as the seed delivery system is not being improved, such an investment will not result in any impact at scale. In Figure 1, this innovation bottle next is illustrated by the water drops that drip into the barrel (the R4D scaling investment) and leak from the lowest stave. Thus, bottleneck analysis can form the basis for prioritizing resource allocation and investment in R4D interventions and can inform strategic and operational decision-making for scaling. Accordingly, Scaling Readiness must be able to support the identification and prioritization of those innovations in a package that form the bottleneck that prevents achieving a defined impact at scale objective.

Strategies for overcoming bottleneck innovations must be realistic and resource-efficient

Once bottleneck innovations are identified, R4D interventions can pursue different options to overcome the bottleneck and increase the impact potential of the innovation package. It is important that strategies for overcoming bottleneck innovations should be realistic in view of available time, human and financial resources. Here, we borrow from the organizational science literature that provides various options for organizations to improve their effectiveness and efficiency when faced with a constraint. Depending on the situation, they can substitute some inputs for others [START_REF] Wolf | Between data and decisions: the organization of agricultural economic information systems[END_REF][START_REF] Brach | Ten attributes of health literate health care organizations[END_REF], outsource operations [START_REF] Roberts | A review of outsourcing of services in health care organizations[END_REF][START_REF] Gunasekaran | Performance measures and metrics in outsourcing decisions: A review for research and applications[END_REF], choose to invest in design and improvement [START_REF] Tidd | Managing innovation: integrating technological, market and organizational change[END_REF], Snapp & Pound, 2017), or change the locations where they operate (Lin et al., 2016[START_REF] Reis | Scaling up physical activity interventions worldwide: stepping up to larger and smarter approaches to get people moving[END_REF]. We recognize that applying such options in R4D interventions may cause tension, as it can require a degree of flexibility that R4D projects and programs, bounded by their context-specific objectives, may not have (e.g., [START_REF] Leeuwis | Rethinking communication in innovation processes: creating space for change in complex systems[END_REF], Schut et al., 2016aand Woltering et al., 2019). Nevertheless, it is important that Scaling Readiness facilitates critical reflection, discussion and prioritisation on a variety of strategic options to overcome bottlenecks to reach the expected objectives.

Scaling requires multi-stakeholder agreement and coalition formation

innovations or practices in a package, which implies that scaling inherently includes multiple stakeholders. R4D interventions, therefore, cannot realize their scaling ambitions on their own, but are dependent on other actors in the innovation system [START_REF] Eastwood | Dynamics and distribution of public and private research and extension roles for technological innovation and diffusion: Case studies of the implementation and adaptation of precision farming technologies[END_REF].

However, these other actors may not necessarily recognize this interdependence and may pursue different and potentially even conflicting goals and interests [START_REF] Wigboldus | Systemic perspectives on scaling agricultural innovations. A review[END_REF]Sahay & Walsham, 2016;[START_REF] Galaz | The Problem of Fit among Biophysical Systems, Environmental and Resource Regimes, and Broader Governance Systems: Insights and Emerging Challenges[END_REF], and, therefore, may not necessarily agree on a proposed scaling strategy. For example, the most efficient short-term strategy for addressing a bottleneck innovation related to the scaling of a drought-tolerant crop variety may be to bypass working with government extension and/or seed systems that face severe capacity constraints. However, this option may not be acceptable for other partners, or have negative consequences for the long-term sustainability, credibility and impact of the R4D organisation in that specific location or context. As a result of such tensions and interdependencies in innovation systems and the inability of a single stakeholder group to scale innovations in complex livelihood systems, scaling of innovation requires forging agreements and accommodations among interdependent actors. There is a growing body of evidence from different sectors that demonstrates this is a process that requires active facilitation [START_REF] Leeuwis | Communication for rural innovation: rethinking agricultural extension[END_REF][START_REF] Giller | Competing claims on natural resources: what role for science?[END_REF].

Coalition formation requires facilitated learning and negotiation

Forging agreement among interdependent actors about scaling ambitions and scaling strategies amounts to building effective coalitions for change [START_REF] Biggs | Beyond methodologies: coalition-building for participatory technology development[END_REF]. A coalition is a network of stakeholders that actively supports change in a particular direction (Aarts & Leeuwis, 2010). The stakeholders may support the change for different reasons and objectives, and there may be a continuation of tensions and disagreements on specific issues.

Two intertwined processes need to be facilitated. First, stakeholders need to learn about one another's context and perspectives, discover how they depend on one another to fulfil their ambitions, develop common starting points to build upon, and develop mutual relationships and trust [START_REF] Kahan | Theories of coalition formation[END_REF]. Second, in the process of reaching agreement, there is likely to be tension and conflict, and typically these differences need to be settled through negotiation. Negotiation is essentially a process of giving and taking amongst the participants with regard to the proposed scaling objectives, pathways and desired outcomes.

In this context, Scaling Readiness must anticipate that scaling strategies cannot be usefully imposed by R4D interventions on rational grounds (e.g., bottleneck assessments) and need to offer facilitated spaces where interdependent innovation system actors can reach agreement regarding the actions and strategies that can support effective scaling of innovation.

Scaling is an emergent and unpredictable process of change

Scaling is a complex process and R4D interventions operate under real and uncontrolled conditions. This combination implies that stakeholders and intervention teams are likely to be confronted with unforeseen developments and with activities that give rise to unintended consequences and outcomes [START_REF] Geels | Typology of sociotechnical transition pathways[END_REF][START_REF] Schot | Strategic niche management and sustainable innovation journeys: theory, findings, research agenda, and policy[END_REF]. Moreover, the scaling context is bound to change continuously. Thus, R4D interventions require mechanisms to capture and navigate the ever-changing environment in which they operate.

Scaling processes require reflexive monitoring and learning

Interactions among the innovations in an innovation package evolve with time [START_REF] Hall | What do complex adaptive systems look like and what are the implications for innovation policy[END_REF][START_REF] Pahl-Wostl | The implications of complexity for integrated resources management[END_REF][START_REF] Paina | Understanding pathways for scaling up health services through the lens of complex adaptive systems[END_REF][START_REF] Van Den Bergh | Environmental innovation and societal transitions: Introduction and overview[END_REF]. The addition of an innovation to an innovation package, or the improvement of an innovation with low readiness for scaling, interacts with and influences other innovations in the package either positively or negatively. As a consequence, scaling processes cannot be simply designed or engineered at the onset of an R4D intervention by projecting the outcomes assuming linear growth [START_REF] Klerkx | Adaptive management in agricultural innovation systems: The interactions between innovation networks and their environment[END_REF][START_REF] Paina | Understanding pathways for scaling up health services through the lens of complex adaptive systems[END_REF]. For instance, a new soybean variety introduced to a village by an R4D intervention can be used at scale and lead to an initial increase in the income of farmers producing soybeans since they can sell their produce (positive outcome). However, the success of this initial scaling of the soybean variety may, over time, lead to the collapse of the soybean price and an eventual decrease in the income of the farmers as overproduction results in a market glut (negative outcome) [START_REF] Gilbert | Food price volatility[END_REF]. Sustaining that income growth may require additional innovations (e.g., enabling access to export markets or local value addition) to continue ensuring positive impact, which may not always be possible. In addition, the relations among partners in a scaling coalition may change over time due to internal and external developments.

Scaling Readiness must be sensitive to emergent and unpredictable dynamics in two respects.

First, it needs to consider short-term horizons for the design and implementation of scaling strategies by focusing on overcoming the key bottleneck innovations through concrete activities and partnerships. Second, Scaling Readiness should promote continuous and reflexive monitoring, evaluation and learning [START_REF] Van Mierlo | Reflexive monitoring in action. A guide for monitoring system innovation projects[END_REF] to assess whether the scaling strategies had the desired effect over a long-term horizon, and to determine if the bottleneck innovations were addressed. The diagnosis of a reconfigured innovation package may result in the identification of new bottlenecks that require additional strategies and further agreement between stakeholders.

Measures of Scaling Readiness

In this section we explain how to operationalise and measure the variables in our approach: innovation readiness, innovation use and scaling readiness. As indicated in Section 2 these variables can only be assessed contextually; that is, in connection with specific R4D intervention goals that are pursued in a particular time and space. This condition implies that an innovation may have a high level of readiness in one location, or at a specific moment in time, or for a specific goal, but at the same time have a low readiness in a different location, moment in time, or when directed toward a different goal. We do not elaborate in detail on how these contextual features may be defined and characterised; however, there exist standard ways of mapping innovation systems for specific sectors, such as for agriculture (Schut et al., 2015).

Innovation readiness measurement

In the R4D literature, there are different scales for measuring the maturity of an innovation.

Although not all of them refer to the term readiness, these scales do capture the capacity of innovations to perform a specific function, or contribute to a specific objective within a specific context. Examples include service innovation readiness [START_REF] Yen | Service innovation readiness: Dimensions and performance outcome[END_REF] and technology readiness [START_REF] Parasuraman | Technology Readiness Index (TRI) a multiple-item scale to measure readiness to embrace new technologies[END_REF][START_REF] Richey | Firm technological readiness and complementarity: capabilities impacting logistics service competency and performance[END_REF][START_REF] Sauser | A systems approach to expanding the technology readiness level within defence acquisition[END_REF][START_REF] Sauser | From TRL to SRL: The concept of systems readiness levels[END_REF]. We chose to build our measure of innovation readiness on the technology readiness index developed by NASA [START_REF] Parasuraman | Technology Readiness Index (TRI) a multiple-item scale to measure readiness to embrace new technologies[END_REF][START_REF] Sauser | A systems approach to expanding the technology readiness level within defence acquisition[END_REF] which has also been adopted by the Horizon 2020 Programme of the European Union (European Commission, 2014). This readiness index is one of the oldest available and has been used for assessing the readiness of technological innovations, and for making strategic research investments. We modified the index categories to make them suitable for assessing both technological and non-technological innovations, thus transforming the technology readiness index into a scale for assessing the readiness of all types of R4D innovations (Table Table 1:

Innovation use measurement

Innovation use measures the current use of the innovations that compose the innovation package in the specific spatial-temporal context where the R4D intervention aims to reach its goals. This metric maps the use of core and complementary innovations by various groups of stakeholders against their position in an innovation network (Figure 2). If only the intervention team is using the innovation (that it has designed and tested), then the scalability potential of the innovation is low. If other intervention teams and partners or aspired endusers start using use the innovation (without being actively involved in its design and testing) then the scalability potential is higher. Different types of innovations (e.g., products, practices, services, organizational and institutional arrangements) may have different user groups. For example, a farmer would be the typical end-user of a new crop variety, whereas a seed multiplier would be the typical end-user of a system that promotes certified seed multiplication. It is important to mention that typical end-users of R4D innovations, such as farmers, can also be part of the intervention team or its effective partners if they are directly engaged in the design and testing of the innovation, or incentivized by the R4D intervention to use the innovation. The next progression is the use of the innovation(s) by stakeholders who influence the R4D intervention and its activities although they are not directly involved. We refer to this group as innovation network stakeholders. They are typically the management of R4D organizations and the effective partner organizations, such as Ministers and high-level officials, directors of non-governmental organizations, CEOs of companies, or established opinion leaders.

A next progression is the use of the innovation(s) by stakeholders who are not collaborating directly with the R4D intervention teams, effective partners, nor innovation network stakeholders. These stakeholders do not have any direct connection with or influence on the R4D intervention activities. However, their own work can have important implications for scaling the innovation, as they are also in the business of developing, testing and validating R4D innovations that can be complementary to or competing with the innovation. We refer to them as stakeholders in the innovation system with are typically other R4D intervention teams and their effective partners operating in the same spatial-temporal context.

A final progression towards scaling is the use of the innovation(s) by stakeholders who were not involved in any R4D interventions or activities and had no influence on the R4D activities. We refer them as stakeholders in the livelihood system since they include all the remaining actors who are not part of innovation systems. Innovation use by stakeholders or beneficiaries in the livelihood system is a key outcome for many R4D interventions that aim to scale innovations for achieving impact. Similar to innovation readiness, innovation use is measured using a 9-level scale (Table 2).

Table 2. Innovation use scores, levels and their basic description.

Scaling readiness measurement

While innovation readiness and innovation use are assessed separately for different (core and complementary) innovations in a package, the unit of analysis for assessing scaling readiness is the innovation package as a whole. Following Liebig's Law of the Minimum (Figure 1, Section 2.3.1), the overall potential of the innovation package to have impact at scale is determined by the innovation in that package with the lowest innovation readiness and innovation use score. As indicated earlier, this is assessed by multiplying the two separate scores for each innovation in the package. The lowest score is referred to as the scaling readiness score of the innovation package.

Innovation packages of which all innovations have been proven to work in real, uncontrolled environments (innovation readiness level 8 or 9), and of which all innovations are already used by many livelihood stakeholders (innovation use levels 8 or 9) have a high potential to achieve impact at scale. We propose that innovation readiness and innovation use have the same weight in determining the potential impact at scale of an innovation package. Having one simple measure of scaling readiness allows for comparison and aggregation across a portfolio of innovation packages and R4D interventions. The various measurements discussed so far can be visualized as a two-dimensional graph (Figure 3) that presents all the key concepts and measures of Scaling Readiness, using a stylised innovation package with a new crop variety as the core innovation. This graph, in particular, represents the different real-life innovation packages in root, tuber and banana cropping systems that have significant coordination issues amongst stakeholders [START_REF] Bentley | Understanding root, tuber, and banana seed systems and coordination breakdown: a multi-stakeholder framework[END_REF]. We are currently applying Scaling Readiness in several R4D interventions that aim to scale agricultural innovations, including the scaling of crop varieties, post-harvest technologies, digital decision-support tools, and crop management practices. In Figure 3 the overall scaling readiness of the innovation package is 2 based on the innovation with the lowest product of innovation readiness and use -novel seed quality assurance policy (innovation readiness = 2 * innovation use = 1). This innovation forms the bottleneck for this innovation package to contribute to impact at scale in a defined space and time and for a specific objective.

Scaling readiness diagnosis merits independent and evidence-based assessment

important to reflect briefly on how and by whom such assessments may be made. In R4D, the design and scaling of health, agricultural, environmental and other societal innovations often depend on continuous coordinated support from donor-funded interventions (Sartas, 2018a).

Sustaining this support depends on, among other factors, the perceived potential and impact of the innovations at scale, and the progress achieved by researchers and innovation developers during previous interventions. Therefore, such closely involved parties are likely to have an interest in overstating innovation impact potential towards donors. This possibility can create a conflict of interest when assessing innovation readiness and innovation use [START_REF] Suri | Purposeful sampling in qualitative research synthesis[END_REF][START_REF] Vera-Cruz | Virtues and limits of competitive funds to finance research and innovation: the case of Mexican agriculture[END_REF]. In Scaling Readiness, therefore, documented evidence (e.g., scientific papers demonstrating proof-of-concept, data collected through rigorous and/or independent monitoring and evaluation systems) are required to support claims of innovation readiness and innovation use levels. Whenever such documents are not accessible by the R4D interventions, experts are requested to provide their judgements. We seek to minimize selfreporting biases by encouraging the assessment of innovation readiness and innovation use by independent experts (Grinstein & Goldman, 2006).

Proposed practical uses of Scaling Readiness

In this section we discuss how Scaling Readiness and its key concepts and measures can be used in practice to contribute to more efficient scaling interventions in R4D. Our discussion is informed by initial testing and validation of the key concepts of Scaling Readiness through several pilot cases (Sartas et al., 2017b). better-informed scaling strategies for R4D interventions [START_REF] Sartas | Scaling Readiness: Concepts, Practices, and Implementation[END_REF].

One of the aims of Scaling Readiness is to support a complexity-aware, decision-making process that assists R4D interventions in developing, implementing and monitoring scaling strategies in a structured and evidence-based way. To this end, we propose an iterative cycle of five steps that builds on key concepts, measures and requirements discussed so far (Figure 4).

Step 1: Characterization -This first step is to characterize the innovation system in the spatial and temporal context in which scaling is to deliver impact. Characterization supports R4D intervention teams by clearly defining their goals, available resources (time, budget) and scaling objectives. This step also supports unpacking innovation packages by identifying the core and complementary innovations that are required to contribute to impact at scale. The failure to unpack innovation packages has frequently been reported as a key constraint for enhancing scaling and impact in the R4D sector [START_REF] Mangham | Scaling up in international health: what are the key issues?[END_REF][START_REF] Moore | Scaling out, scaling up, scaling deep: Strategies of non-profits in advancing systemic social innovation[END_REF][START_REF] Paina | Understanding pathways for scaling up health services through the lens of complex adaptive systems[END_REF]. In Scaling Readiness, visualizations of different innovations and their interdependency are used in both conceptual and empirical ways, which was highly appreciated by R4D intervention teams involved in the initial testing and validation of Scaling Readiness.

Step 2: Diagnosis -Diagnosis supports independent and evidence-based assessment of the individual innovations in the package in terms of their innovation readiness and innovation use. This step subsequently helps to identify bottleneck innovations that keep the innovation package from contributing to the defined goals and impact in a particular context. Schut et al.

(2016a) reported how R4D actors and organisations are often unable or unwilling to work on the real (often institutional) bottlenecks for innovation and scaling, as they perceive this to be outside of their organisation's mandate or their personal comfort zone. Stronger evidencebased identification of bottlenecks for innovation and scaling may translate into real action by R4D establishments to invest in activities and partnerships to overcome these bottlenecks.

Step finding improved conditions for the intervention as a whole and in a different space (relocate), objective (reorient), or time (postpone). Strategic option 7 is a last resort when finding better conditions is not possible.

Step 4: Agree -The proposed draft scaling strategy needs to be shared and agreed upon with the broader R4D intervention partners and other stakeholders, such as donors. This step ensures sufficient buy-in for the proposed strategy and validates whether the implementation of the strategy is technically feasible and socially and politically acceptable. If the draft scaling strategy is found unfeasible or undesirable, then the strategic options mentioned above should be reconsidered, and the team moves back to Step 3. When the scaling strategy is agreed upon, then a scaling action plan needs to be developed to provide details of the types of partnerships and activities to address the core bottleneck(s). Available time and financial resources will determine whether overcoming the bottleneck within the boundaries of the R4D intervention is realistic, and if it merits additional resource mobilization efforts.

Step 5: Navigate -If agreement is reached on a scaling strategy and a scaling action plan, the implementation and monitoring of the agreed-upon activities begins. Scaling Readiness facilitates and monitors the scaling strategy and action plan implementation through a process of reflexive monitoring and learning. This process requires that R4D intervention teams periodically reflect on the implementation of the scaling strategy and action plan and update these plans, if necessary, to guide implementation towards the desired results. Monitoring can be based on short-term feedback loops that guide the implementation of the scaling action plan, but also on long-term feedback loops to see if the scaling strategy has had the desired effect in terms of increasing the scaling readiness score. This long-term loop would require going through another Characterization (Step 1) and Diagnosis (Step 2) effort.

Proposition 2: Scaling Readiness can support the management of R4D portfolios and investments

Many organizations involved in the R4D sector manage not just one, but multiple R4D interventions as part of their portfolio. With increasing pressure to show returns on investment and impact at scale [START_REF] Renkow | The impacts of CGIAR research: A review of recent evidence[END_REF], Woltering et al., 2019), these R4D organizations can use the key concepts and measures of Scaling Readiness to monitor and manage their R4D portfolio and guide investments to increase the overall scaling readiness of their innovation and scaling investments. This can be accomplished in two ways.

First, through its standardized measures, Scaling Readiness can support comparison of different innovation packages for particular spatial and temporal contexts and goals.

This advantage can help R4D organizations identify the innovation packages with the highest potential to achieve impact at scale. It can also be useful for R4D portfolio managers and decision-makers to consider impact potential at scale zones to compare different innovation packages (Figure 5) and the type of investments that may be required to further improve its scaling readiness. Innovation packages with same scaling readiness scores might need very different strategies and partnerships to improve their readiness or use. For example, in Figure 5, although bottlenecks in innovation packages III and VI are positioned in the medium impact potential at scale zone, the required strategies to bring them to the high impact potential at scale zone can be different for each package. For innovation package III, investments with a focus on dissemination to increase the innovation use are required, whereas for innovation package VI, investments with a focus on developing and increasing innovation readiness are desirable. This comparative analysis may facilitate resource allocation decisions or prioritisation of investments in R4D organizations that have both research (increase innovation readiness) and delivery (increase innovation use) mandates. focussed investment in improving innovation may be prioritised (Figure 5).

Second, using Scaling Readiness continuously can reveal if the scaling readiness of an innovation package increases, stays the same, or decreases over time as a result of R4D investments. This information can help portfolio managers make smarter decisions about where to prioritise their investments. For example, innovations packages with rapidly increasing scaling readiness could be allocated extra investment. Innovations packages with significant investment but without significant progress in terms of their innovation readiness and/or use can be put on hold or stopped. This use of Scaling Readiness can also facilitate socalled stage-gate management of an innovation portfolio in which the scaling readiness scores can inform decision-makers and/or R4D donors whether or not an investment has resulted in the desirable increase in innovation readiness and/or innovation use.

Here it is important to emphasize that the scaling readiness of individual innovations and innovation packages can increase or decrease due to a variety of factors. Readiness and use of complementary innovations in an innovation package -for example innovations that provide access to finance or to markets -may change as a result of a financial crisis or the bankruptcy of an important agricultural processor in a specific region. Although such factors are beyond the direct influence of the R4D intervention team, they need to be taken into account as they may form new bottlenecks for scaling innovation which may require a reorientation of resources, activities and partnerships.

Conclusion

Scaling of innovations is the outcome of complex dynamics in innovation and livelihood systems. Realistic scaling strategies need to recognise the characteristics of complex systems dynamics. To connect the science and the practice of scaling, there is a need to develop complexity-aware models that can guide operational and strategic decision-making on scaling of innovation in R4D. Scaling Readiness incorporates key concepts and measures to:

  perceived attributes of innovations (i.e., trialability, observability, relative advantage, etc.) and several population characteristics in a given context. In summary, Scaling Readiness aims to advance and complement other tools, approaches, and frameworks by: (1) paying attention to both technological and non-technological innovations; (2) considering contextual conditions; (3) providing hands-on decision support to address scaling bottlenecks; and (4) by striking a balance between analytical complexity and practical applicability. This contribution is structured in five sections. Section 2 presents the key-concepts underlying Scaling Readiness. Section 3 explains how Scaling Readiness key-concepts are operationalized, measured and made actionable. Section 4 sketches the Scaling Readiness process as we propose it and its potential use in the R4D sector. Conclusions and reflections are presented in Section 5.

  Innovation readiness levels, basic descriptions and the type of science and evidence to support readiness level claims 425 capacity of the innovation to meet specific goals within a controlled environment that reflects the specific spatial-temporal context in which the innovation is to contribute to achieving impact. capacity of the innovation to meet specific goals within a controlled environment that reflects the specific spatial-temporal context in which the innovation is to contribute to achieving impact. of the innovation to meet specific goals or impact in natural/real/uncontrolled conditions in the specific spatial-temporal context in which the innovation is to contribute to achieving impact with support from capacity of the innovation to meet specific goals or impact in natural/real/uncontrolled conditions in the specific spatial-temporal context in which the innovation is to contribute to achieving impact without support from

Figure 2 .

 2 Figure 2. Stakeholder typology for those involved in innovation development, scaling and use, based on a network approach.

  used for achieving the objective of the intervention in the specific spatial-temporal context where the innovation is to contribute to used by effective partners who are involved in the R4D intervention 4 Innovation network (rare) Innovation has some use by stakeholders who are not directly involved in the R4D intervention but are connected use by stakeholders who work on developing similar, complementary or competing innovations but who are not directly connected to the Innovation system used by stakeholders who are not in any way involved in or linked to the development of the R4D innovation

Figure 3 .

 3 Figure 3. Stylized example of an innovation package (with 8 innovations) that have been assessed for their innovation readiness (y-axis) and innovation use (x-axis) specific to space, time and R4D intervention goals.

Figure 4 .

 4 Figure 4. Scaling Readiness proposes a stepwise approach to support the development of

  3: Strategize -The diagnosis of the innovation package and the identification of scaling bottlenecks is meant to kick-start a process of scaling strategy development. The position of the bottlenecks in the Scaling Readiness graph provides valuable information on what kinds of investments, activities and partnerships are required to improve its innovation readiness and/or innovation use. For each innovation with low readiness or use (Figure3) the intervention team can discuss how the innovation can be moved along the x-axis (e.g., What strategies can be used to access and engage other innovation networks?) or along the y-axis (e.g., How can we generate further evidence about the innovation's capacity to contribute to impact?). Similarly, the strategic options listed below support critical reflection of how to best overcome the bottlenecks to scaling, and the type of partnerships that can effectively support these actions:1. Substitute: Can the bottleneck be replaced by another innovation with higher readiness and/or use in the given context? 2. Outsource: Are there any organizations or external experts that can more efficiently improve the Scaling Readiness of the bottleneck? 3. Develop: Can the intervention team improve the readiness and/or the use by investing available intervention capacities and resources? 4. Relocate: Can the intervention objectives be realized more effectively if the intervention is implemented in another location where innovations have higher readiness and use levels? 5. Reorient: Can the objective or outcome of the intervention be reconsidered if addressing the bottleneck is not possible and relocation is not an option? 6. Postpone: Can scaling the innovation package be achieved at a later point in time? 7. Stop: If none of the above strategic options are feasible, should the team consider stopping the intervention? These strategic options are ranked in terms of the resources necessary to implement them from the least to most resource demanding. To achieve maximum efficiency, R4D interventions are advised to use the least resource demanding option to address bottleneck innovations. Strategic options 1-3 focus on addressing the core or complementary innovation with the lowest innovation readiness or use (the bottleneck). Strategic options 4-6 focus on

Figure 5 .

 5 Figure 5. Impact at scale zones that indicate the relative position of innovation packages and their scaling readiness specific to space, time and R4D intervention goals.

  (1) characterize innovation systems, R4D interventions and their scaling goals, and innovation packages; (2) diagnose the scaling readiness of innovation packages as a function of their innovation readiness and innovation use; (3) support strategy development to overcome the main bottlenecks for scaling; (4) guide stakeholder agreement and coalition formation to overcome bottlenecks to scaling; and (5) navigate R4D interventions in effective scaling action through reflexive monitoring and adaptive management. In doing so, Scaling Readiness has the potential to enhance the scaling performance of R4D interventions and can support portfolio management of innovations and scaling investments. The initial testing and validation of Scaling Readiness key concepts, measures and practices within pilot projects in the agricultural R4D sector has been very promising and R4D intervention teams, to date, have greatly appreciated the stepwise and action-oriented process that Scaling Readiness facilitates. A next step for Scaling Readiness is the development of Scaling Readiness methods, processes and tools to improve strategic and operational decision-making in R4D interventions. Documenting the rigorous application of Scaling Readiness in R4D interventions and analysing its contribution to the intervention's scaling

For example through the Vitamin A rich golden banana(Buah, Mlalazi, Khanna, Dale, & Mortimer,

[START_REF] Servaes | How "sustainable" is development communication research?[END_REF][START_REF] Paul | Golden bananas in the field: elevated fruit pro-vitamin A from the expression of a single banana transgene[END_REF], golden rice[START_REF] Paine | Improving the nutritional value of Golden Rice through increased pro-vitamin A content[END_REF][START_REF] Welch | Breeding for micronutrients in staple food crops from a human nutrition perspective[END_REF] or orange flesh sweet potato[START_REF] Low | A foodbased approach introducing orange-fleshed sweet potatoes increased vitamin A intake and serum retinol concentrations in young children in rural Mozambique[END_REF][START_REF] Van Jaarsveld | Beta-carotene-rich orange-fleshed sweet potato improves the vitamin A status of primary school children assessed with the modified-relative-dose-response test[END_REF].

Acknowledgement

We would like to acknowledge the contributions to our development of Scaling Readiness by Michael Friedmann, Vivian Polar, James Legg, Pieter Pypers, Boudy van Schagen, Anne Rietveld, Dietmar Stoian, Claudio Velasco, Jorge Andrade, Peter Kromann, Thomas Van Mourik, Jonathan Newby, Eric Delaquis, Seerp Wigboldus, Bernard Vanlauwe, Jens Andersson and Ana Lucia Vasco Carrillo.

Funding

This work was carried out as an integral part of the CGIAR Research Program on Roots, Tubers and Bananas (RTB). We would like to acknowledge the CGIAR Fund Donors (https://www.cgiar.org/funders/) for their provision of core funding without which this work would not have been possible.