Fanny Le Gloux
email: fanny.le-gloux@inrae.fr

Pierre Dupraz

Alice Issanchou

Carole Ropars-Collet

Payments for environmental services with provision thresholds: farmers' preferences for a conditional bonus

Keywords: Water quality, choice experiment, collective action, payment for environmental services, conditional bonus C25, Q15, Q18, Q25, Q28, Q53

The effectiveness of payment schemes for delivering agri-environmental public goods with provision thresholds (biodiversity, water quality) depends on reaching enough farmland enrolment at the landscape scale. Supporting the development of collaborative approaches with a financial bonus conditioned to a collective element on top of an individual basic payment is a promising way to favour participation and continuity of environmental commitments in an area. However, little is known on farmers' attitudes towards such mixed-payment mechanisms. Using a choice experiment, we measure farmers' preferences towards an individual bonus for sponsoring peers, which can be combined with a collective bonus for improving the ecological quality of rivers in northwestern France. Applying a mixed logit model, we find that respondents have a positive willingness to accept contracts with a sponsor bonus, but a negative willingness to accept a sponsor bonus combined with a bonus for reaching a collective environmental objective. We characterize respondents' heterogeneity with a latent class model and identify 3 different attitudes towards the bonus options: (i) negative preferences for both, particularly for the combined bonus, (ii) indifference, (iii) positive preferences for both, even higher for the combined bonus.

Introduction

Payment for environmental services (PES) are initiatives supporting farmers voluntary interventions contributing to the preservation of ecological functions [START_REF] Duval | Paiements pour services environnementaux et méthodes d'évaluation économique: Enseignements pour les mesures agro-environnementales de la politique agricole commune[END_REF][START_REF] Wunder | Payments for environmental services: some nuts and bolts[END_REF]. They emerged in the early 1990s, in response to the growing awareness of the value and shortage of agri-environment-climate public goods (AECPGs). In the European Union (EU), the most widely implemented PES are the agri-environmental schemes (AES) of the common agricultural policy. Over the past decades, the low environmental additionality, participation rates and cost-effectiveness of AES have been highlighted in the literature, in particular because of underfunded and poorly designed measures [START_REF] Cullen | Agri-Environment Scheme Design: Past Lessons and Future Suggestions[END_REF][START_REF] Dupraz | Effets des mesures agri-environnementales[END_REF][START_REF] Espinosa-Goded | Identifying additional barriers in the adoption of agri-environmental schemes: The role of fixed costs[END_REF][START_REF] Zavalloni | Agri-environmental Policies and Public Goods: An Assessment of Coalition Incentives and Minimum Participation Rules[END_REF]. Dedicated PES involving other contractual arrangements and financial contributors are also implemented on a smaller scale. Examples include schemes funded by water bottlers such as the Vittel Company, or by municipalities such as the water authorities of Munich and New York city [START_REF] Déprés | Contracting for environmental property rights: The case of Vittel[END_REF][START_REF] Grolleau | Designing watershed programs to pay farmers for water quality services: Case studies of Munich and New York City[END_REF].

Designing efficient incentive mechanisms for AECPG provision is a challenge that often involves trade-offs between environmental ambition and large acceptance by farmers. Conditionality rules must define an effort that reaches the environmental objective(s), but remain attractive enough to ensure significant participation. When the objective is to improve water quality or biodiversity, high participation and spatial continuity of environmental commitments at the landscape scale are necessary to observe environmental improvements [START_REF] Dupraz | Threshold effect and co-ordination of agrienvironmental efforts[END_REF]. Developing instruments favouring collaboration among land managers, coordination of actions and high uptake within a same area are promising ways to increase the environmental effectiveness of farmers' actions, as well as the cost-effectiveness of incentive schemes. In addition to supporting to meet ecological thresholds, collective approaches provide other advantages, such as fewer transaction costs for the buyers of environmental services, and building of social capital for farmers [START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: The role of a collective bonus[END_REF][START_REF] Lefebvre | Agricultural landscapes as multi-scale public good and the role of the Common Agricultural Policy[END_REF][START_REF] Pretty | Social Capital and the Collective Management of Resources[END_REF].

Collective approaches can take different forms of contractual arrangements and therefore payment conditionality [START_REF] Kuhfuss | Should agri-environmental schemes aim at coordinating farmers' pro-environmental practices? A review of the literature[END_REF]. Some involve a collective payment. In this case, the contracting party receiving the payment is a group of farmers, which distributes the amount to participants according to rules defined by the collective. The Netherlands provide a large amount of examples of successful collective AES, in which participants are local groups of farmers organised in environmental cooperatives [START_REF] Franks | The collective provision of environmental goods: A discussion of contractual issues[END_REF]. Cases from other EU countries are scarce. One can cite the collective AES for preserving the European Hamster (Cricetus cricetus) habitats in France [START_REF] Eichhorn | Deliverable D2.1 of the CONSOLE project: catalogue of descriptive factsheets of all European case studies[END_REF]. Other approaches are based on individual contracting, but condition the distribution of the payment to the achievement of a collective objective (minimum participation or land enrolment at the landscape scale, reaching an environmental goal…) or collective action (coordination of management practices, agglomeration of the plots enrolled…). These conditionality rules can apply to all or part of the payment. In the latter case, the collective component of the contract takes the form of a conditional "reward" or "bonus". An example of mixed-payment scheme is the Swiss network bonus (agglomeration bonus) [START_REF] Krämer | The agglomeration bonus in practice-An exploratory assessment of the Swiss network bonus[END_REF].

The literature suggests farmers are reluctant when collective requirements are conditioning the full payment, but favourable to a reward conditioned to collective action on top of an individual basic payment. [START_REF] Villanueva | Heterogeneity of farmers' preferences towards agri-environmental schemes across different agricultural subsystems[END_REF] showed that individual contracting tends to be preferred to collective contracting of at least five farms from a same municipality, especially among older farmers with little experience of participating in cooperatives. Interestingly, Ben-Othmen and Ostapchuk (2019) found an opposite result, with positive preferences for collective contracting of at least three farms from the same municipality. However, the two studies differed in the way collective participation was defined. In the study of [START_REF] Ben-Othmen | Farmers' preferences for grassland restoration: Evidence from France. 172nd EAAE Seminar 'Agricultural policy for the environment or environmental policy for agriculture[END_REF], it was made clear that farmers could form a group with whom they trust the most, and that only free-riding farmers would be sanctioned in case of noncompliance with management requirements, not the whole group. It therefore suggests that a key factor of collective AES acceptance is well-defined group governance and monitoring, what is often emphasized by researchers studying successful Dutch case studies of environmental cooperatives [START_REF] Barghusen | Motivations of farmers to participate in collective agri-environmental schemes: the case of Dutch agricultural collectives[END_REF][START_REF] Franks | The collective provision of environmental goods: A discussion of contractual issues[END_REF][START_REF] Uetake | Agri-environmental Management Through Collective Action[END_REF]. Le [START_REF] Coent | Compensating Environmental Losses Versus Creating Environmental Gains: Implications for Biodiversity Offsets[END_REF] looked at farmers preferences for biodiversity offsets with the full payment conditioned to a minimum of 20% of participation of farmers from the area. They found that farmers anticipate transaction costs for reaching the participation threshold and prefer contracts without. Another study measuring preferences for an AES requiring the coordination of the location of tree planting with neighbouring farms also concluded that farmers were reluctant to the collective approach due to transaction costs and beliefs that other farmers would not be willing to cooperate [START_REF] Villamayor-Tomas | Bringing the neighbors in: A choice experiment on the influence of coordination and social norms on farmers' willingness to accept agro-environmental schemes across Europe[END_REF]. However, they identified a peer effect, with the finding that farmers were more likely to choose an agri-environmental measure recommended by other farmers. When it comes to collective bonus options, a study by [START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: The role of a collective bonus[END_REF] reveals positive preferences for a conditional bonus if at least 50% of the eligible area is enrolled in the scheme after five years.

Apart from this last study by [START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: The role of a collective bonus[END_REF] among vine growers, there is still little evidence on farmers' attitudes towards mixed-payment mechanisms promoting collective approaches. Further analyses would confirm or nuance the acceptability of these nudges in other contexts, and provide recommendation for designing successful schemes. This present study aims at providing new elements on the acceptability among farmers of a collective component in PES, designed to meet high participation rates and environmental efforts. We develop a choice experiment (CE) to measure preferences for a contract targeting the improvement of rivers ecological quality in northwestern France. CE are particularly relevant to elicit preferences for specific contract characteristics that do not yet exist [START_REF] Louviere | Stated Choice Methods: Analysis and Applications[END_REF]. Two types of bonuses were tested to explore new elements on the design of payment mechanisms: an individual bonus for sponsoring a peer, and a sponsor bonus combined with a collective result bonus distributed equally to all participants.

The paper is organised as follow. In section 2 are presented the choice modelling and experimental design. The survey data are described in section 3. Section 4 presents and discusses the results. Section 5 provides some concluding remarks and policy recommendations.

Method

Discrete choice experiment approach

A CE is a survey-based method to elicit stated preferences of individuals. Respondents are successively asked to choose their preferred option among a small number of hypothetical alternatives, which differ according to several attributes. CE techniques are based on Lancaster's theory that consumption decisions are determined by the utility derived from the attributes of the good being consumed [START_REF] Lancaster | A new approach to consumer theory[END_REF] and the random utility theory decomposing utility into a deterministic part and a random part [START_REF] Mcfadden | The measurement of urban travel demand[END_REF]. They are particularly useful to estimate ex-ante the marginal utility of different characteristics of policy design. The application of CE methods already provided a lot of useful policy recommendations for agri-environmental contracts design, for instance regarding farmers preferences for contract length [START_REF] Bougherara | Farmers ' preferences over conservation contract flexibility and duration : an estimation of the effect of transaction costs using choice experiment[END_REF][START_REF] Christensen | Determinants of farmers' willingness to participate in subsidy schemes for pesticide-free buffer zones-A choice experiment study[END_REF][START_REF] Latacz-Lohmann | Using choice experiments to improve the design of agri-environmental schemes[END_REF][START_REF] Ruto | Investigating farmers' preferences for the design of agrienvironment schemes: a choice experiment approach[END_REF], payment sequences [START_REF] Bougherara | Do farmers prefer increasing, decreasing, or stable payments in Agri-environmental schemes?[END_REF] and conditional bonuses [START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: The role of a collective bonus[END_REF][START_REF] Vaissière | Preferences for biodiversity offset contracts on arable land: A choice experiment study with farmers[END_REF].

Model specification

Under the random utility theory, the utility 𝑈 𝑛𝑗𝑡 that individual 𝑛 obtains from choosing alternative 𝑗 out of 𝐽 alternatives in the choice set 𝑡 out of a series of 𝑇 choice sets, is made of an observed component 𝑉 𝑛𝑗𝑡 (deterministic part) and a stochastic error term 𝜀 𝑛𝑗𝑡 (random part) (1).

𝑈 𝑛𝑗𝑡 = 𝑉 𝑛𝑗𝑡 + 𝜀 𝑛𝑗𝑡 (1)
We assume individual 𝑛 chooses alternative 𝑗 if and only if that alternative maximises his utility amongst all alternatives in choice set 𝑡. The probability that farmer 𝑛 chooses alternative 𝑗 is:

𝑃 𝑛𝑗𝑡 = 𝑃𝑟𝑜𝑏(𝑉 𝑛𝑗𝑡 + 𝜀 𝑛𝑗𝑡 > 𝑉 𝑛𝑖𝑡 + 𝜀 𝑛𝑖𝑡 ) = 𝑃𝑟𝑜𝑏( 𝜀 𝑛𝑗𝑡 -𝜀 𝑛𝑖𝑡 > 𝑉 𝑛𝑖𝑡 -𝑉 𝑛𝑗𝑡 ) ∀𝑖 ≠ 𝑗 (2)
The error term is assumed to follow the Gumbel Type-1 extreme-value distribution [START_REF] Mcfadden | The measurement of urban travel demand[END_REF], such that a logit model can be applied to estimate the parameters. Under the conditional logit (CL) model, the 𝛽 coefficients representing respondents' preferences for the attribute levels 𝑋 𝑛𝑗𝑡 are assumed homogeneous (3).

𝑃 𝑛𝑗𝑡 = 𝑃𝑟𝑜𝑏( 𝜀 𝑛𝑗𝑡 -𝜀 𝑛𝑖𝑡 > 𝛽(𝑋 𝑛𝑖𝑡 -𝑋 𝑛𝑗𝑡 )) ∀𝑖 ≠ 𝑗 (3)
The Hausman test allows to check the independence of irrelevant alternatives (IIA) and validate the CL model specification [START_REF] Hausman | Specification Tests for the Multinomial Logit Model[END_REF]. To relax the IIA assumption and account for taste heterogeneity across farmers or across groups of farmers, the mixed logit (ML) (4) or latent class (LC) (5) models are applied [START_REF] Greene | A latent class model for discrete choice analysis: Contrasts with mixed logit[END_REF].

𝑃 𝑛𝑗𝑡 = 𝑃𝑟𝑜𝑏( 𝜀 𝑛𝑗𝑡 -𝜀 𝑛𝑖𝑡 > 𝛽 𝑛 (𝑋 𝑛𝑖𝑡 -𝑋 𝑛𝑗𝑡 )) ∀𝑖 ≠ 𝑗 (4) 𝑃 𝑛𝑗𝑡|𝑞 = 𝑃𝑟𝑜𝑏( 𝜀 𝑛𝑗𝑡 -𝜀 𝑛𝑖𝑡 > 𝛽 𝑞 (𝑋 𝑛𝑖𝑡 -𝑋 𝑛𝑗𝑡 )|𝑐𝑙𝑎𝑠𝑠 𝑞) ∀𝑖 ≠ 𝑗 (5)
An estimate of the average willingness to accept (WTA) for each attribute 𝑋 are obtained from the coefficient of the corresponding attribute 𝛽 𝑋 and the contract payment coefficient 𝛽 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 (6) [START_REF] Mariel | Environmental Valuation with Discrete Choice Experiments Guidance on Design, Implementation and Data Analysis[END_REF].

𝑊𝑇𝐴 𝑋 = -𝛽 𝑋 𝛽 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 (6)
𝑊𝑇𝐴 𝑋 is the average annual payment per hectare a farmer requires to accept a contract for which the level of attribute 𝑋 is higher by one unit.

Experimental design

A choice experiment was conducted to measure farmers' preferences for a 5-year contract targeting the improvement of the ecological quality of rivers in 3 regions of northwestern France (Brittany, Normandy and Pays de la Loire), for which participants would enroll all their farmland. Contract were characterized by management requirements defining the environmental services to be delivered by farmers to contribute to the improvement of water quality, a per-hectare payment distributed to farmers individually on an annual basis if they comply with management requirements, and a bonus option (Table 1).

None

Individual sponsor bonus: 450€ each time the farmer convinces a peer into entering the scheme Individual sponsor bonus + collective result bonus: 450€ each time the farmer convinces a peer into entering the scheme + 50€/ha distributed to all participants if the river's ecological status reaches a higher step of the water quality scale

The choice of management and per-hectare payment attributes and levels was based on evidence from a previous study undertaken in a similar environmental context in Brittany [START_REF] Gruau | Projet Interreg CPES: Rapport d'Implantation des PSE -Site pilote du Lac au Duc et du bassin versant de l'Yvel-Hyvet[END_REF]. Evidence shows that hedge networks in agricultural landscapes such as bocage, act as buffer zones and erosion barriers preventing runoffs in water catchments, in synergy with many other ecological side-benefits [START_REF] Burel | Social, aesthetic and ecological aspects of hedgerows in rural landscapes as a framework for greenways[END_REF]Caubel-Forget et al., 2001;[START_REF] Merot | The influence of hedgerow systems on the hydrology of agricultural catchments in a temperate climate[END_REF]. Avoiding long periods of bare soil, in particular in winter, also contributes to limiting soil erosion and runoffs [START_REF] Souchère | Grassland and crop trends: Role of the European Union Common Agricultural Policy and consequences for runoff and soil erosion[END_REF].

The higher levels of per-hectare payment are higher than typical AES schemes, to include the possibility that all or part of the payment could be financed by other types of stakeholders (water catchment agency, private companies, municipalities…). The degradation of rivers ecological quality does not only contribute to the deterioration of biodiversity, but also induces higher costs of water depollution for securing drinking water quality. Protecting water resources is therefore of interest for many stakeholders (water catchment bodies, local citizens, local companies, municipalities…). Their role as PES scheme financers would allow to better capture society willingness to pay and farmers WTA, beyond foregone profits. WTA includes uncertainty and factors that are not necessarily technical barriers, such as transaction costs or social capital [START_REF] Espinosa-Goded | Identifying additional barriers in the adoption of agri-environmental schemes: The role of fixed costs[END_REF].

The bonus option levels were defined together with stakeholders involved in the development of experimental PES in the study area. A sponsor bonus, suggested by farmers involved in an experimental PES in Brittany, is introduced and takes the form of an individual reward for convincing a peer farmer from the water catchment area to enter the PES scheme. A farmer would receive a one-time 450€ per new peer sponsored. Each farmer can be sponsored only once. For the parties financing the PES scheme, the sponsor bonus offers the opportunity to increase participation at the water catchment scale while benefiting from the peer effect (communication on the scheme, knowledge spillover…). For the farmers, sponsoring peers induces new transaction costs (social commitments, time consuming). Therefore, a second level of bonus option introduces an additional reward of 50€/ha, distributed to all participants if a collective result is obtained. The environmental result considered is a higher step of the water quality scale for the river's ecological status. This option is introduced to encourage collaborative effort to reach a common objective and increase even further the environmental effectiveness of the scheme. The underlying hypothesis is that the consideration of sponsored peers' environmental outcome externality would lower farmers' individual adoption cost for the sponsor bonus.

Choice sets including two contract alternatives and the status-quo (option to opt-out and choose none of the contracts) were designed by combining the different attribute levels (see Figure 1 for an example of choice card). A d-efficient design of 36 choice sets to be divided into 4 blocks of 9 choice cards was constructed. For the econometric analyses, management attributes (COVER, HEDGEROWS) and the basic payment attribute (PAYMENT) are coded as continuous variables and the bonus levels (BONUSsponsor, BONUSsponsor/collective result) as dummy variables. All the attribute levels are set at 0 for the status-quo alternative. We also define an alternative specific constant controlling for the status-quo alternative (ASCsq).

Survey structure

The CE was included as a section of a pan-EU survey on the acceptability of agrienvironmental-climate contract solutions, conducted in spring 2021 among farmers located in Brittany, Normandy and Pays de La Loire. Voluntary farmers were contacted to organise a face-to-face interview after being recommended by intermediaries (farmers union, organisations of milk producers, farmers associations…). The first section of the survey includes general information on farmer and farm characteristics, and the second section on the impact of contract characteristics on the willingness to adopt contractual solutions. In particular, farmers were asked to state from a scale from 1 to 5 how much would the possibility to collectively agree on environmental targets and measures at landscape-level together with other land managers (ATTITUDEcollective agreement), and to receive a common payment to be distributed among participants (ATTITUDEcollective payment), increase or decrease their willingness to enroll? In this third section dedicated to the CE, respondents were introduced to the context, objective and rules of the game of the CE, and to the contract parameters (those fixed and those varying from one alternative to another). Preliminary questions were included to help the respondents estimating their current levels of management requirements (individual status-quo). The current soil cover duration was calculated from the stated hectares of permanent grasslands, arable crops, permanent crops and total utilised agricultural area (UAA), as well as the average number of days with bare soil on arable lands and proportion of grass cover on the permanent crops surfaces. The current hedgerows density was calculated from the total UAA and total meters of multispecies multilayer hedgerows currently present on the farmland. Farmers were then asked 9 times to choose the preferred option among 2 contract alternatives and the status-quo.

Data

130 farmers' responses were collected. 97 farmers are located in Brittany (74.6% of the sample), 23 in Pays de la Loire (17.7% of the sample), and 10 in Normandy (7.7% of the sample) (Figure 2). Descriptive statistics of the sample are provided in Table 2. A comparison of the sample characteristics with the 2010 agricultural census data for the study area (Brittany, Pays de la Loire, Normandy) shows that the sample is representative of farmers' age and UAA, but over represents male farmers with higher education, organic, dairy and mixed cattle farms [START_REF] Ssp | DATA] 2010 Agricultural census, Agreste[END_REF]. This bias is explained by the non-random sampling procedure respecting the data protection policy, with a preliminary selection of volunteers by intermediaries. The initial levels of anti-erosion multispecies multilayer hedgerows density and soil cover duration estimated for the sample are also particularly high for the surveyed area, with many farms already fulfilling the highest levels of the hypothetical contracts requirements. Farmers stated few days of bare soil for their arable land (25 days on average). Moreover, the farms of our sample stated having on average 88 m/ha of multispecies multilayer hedgerows, while all types of hedgerows considered (including monospecies or monolayer), the observed average density is 49 m/ha in Normandy, 48 m/ha in Brittany, and 55 m/ha in Pays de la Loire (Mission Bocage, 2011;[START_REF] Simon | Evaluation de la biomasse bocagère en Normandie[END_REF][START_REF] Simon | Evaluation de la biomasse bocagère en Bretagne[END_REF]. Regarding farmers perception of collective elements in PES, more than 50% of the sample stated the possibility to collectively agree on environmental targets and measures at landscapelevel with other land managers would increase their willingness to enroll in a contract, while only a bit more than 30% stated receiving a common payment to be distributed among participants would (Figure 3).

Results and discussion

As a baseline, we estimate a CL model with attribute levels and ASCsq as explanatory variables.

The CL specification with effects coding for management attributes was compared with continuous coding [START_REF] Bech | Effects coding in discrete choice experiments[END_REF]. Models did not significantly vary, and it was decided to keep the continuous coding. The Hausman-McFadden test reveals the IIA assumption is violated and preference heterogeneities across respondents, suggesting the need to rely on ML or LC models to analyse the data.

To disentangle preference heterogeneities, we apply a ML model with all attributes and statusquo coefficients as random parameters, expect for the basic payment coefficient we keep fixed (Table 3). The first ML specification (1), without individual specific variables, shows that the density of hedgerows and the level of the individual payment significantly affects respondents' choice, with the expected signs (negative effect for the level of hedgerows requirements and positive effect of the level of payment). The requirement of soil cover is however not significant. Farmers exhibit positive preferences for the bonus attribute, but only the sponsor bonus by itself is significant. The status-quo was chosen in 16% of the choice situations but results suggest farmers had no significant preferences for this option. The significance of standard deviation coefficients shows strong preference heterogeneities for both management attributes and the bonus option offering both the possibility of a sponsor bonus and a collective result bonus. In a second ML specification (2), we investigate preference heterogeneities for management requirements and the combined bonuses option by adding interaction terms with individual specific variables collected in the survey. The covariates included were farms' current management attribute levels (COVERcurrent and HEDGEROWScurrent), and organic status (ORGANIC), plan to stop managing farm activities in 5 years or less (SHORT-TERM), and attitude towards collective payments as contract design characteristic (ATTITUDEcollective payment). Results suggest that, when controlling for the perceived current density of eligible hedgerows and duration of soil cover, coefficients for both the management attributes become significantly negative. In addition, interaction terms show that the higher the initial management requirement levels, the higher the preferences for higher levels of the corresponding attributes. Maintaining high density of hedgerows and a long period of soil cover is costly and farmers might see an opportunity to be compensated for it with a PES scheme. In particular, many farmers of the sample are located in a nitrate vulnerable zone and must already comply with strict rules of soil coverage during winter. Controlling for organic status shows that organic farmers prefer lower levels of cover duration, which can be explained by their higher need to use tillage for weed control. However, they tend to prefer higher density of antierosion hedgerows. We can assume they also value the multiple ecosystem services delivered by hedgerows that support organic practices (habitats for natural predators of pests, reducing exposure to pesticide spray drift from neighbouring farms…). Moreover, respondents who plan to stop farming activities in 5 years or less have stronger negative preferences for hedgerows, which require long-term engagement of maintenance. Finally, farmers who scored high in terms of impact of a common payment on the willingness to join a contract exhibit positive preferences for the combined sponsor and collective result bonuses, while on average, sample preferences are negative for this bonus level. It suggests that some farmers are "pro-collective" while others are opposed to collective payments.

Farmers' average marginal WTA and 95% confidence intervals for the attributes for both ML specifications are reported in Table 4. Ceteris paribus, a farmer accepts a contract with on average 67€ (specification (2)) less of individual payment per hectare if there is a sponsor bonus of 450€/peer. For a farm of 100ha (average farm size of the sample), it represents a decrease of 6,700€ of basic payment per year. A farmer would need to convince at least 15 new farmers each year to receive the same amount of sponsor bonuses, what confirms the result by [START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: The role of a collective bonus[END_REF] that introducing a bonus option can improve the cost-effectiveness of a scheme. However, the WTA a contract increases on average by 165€/ha if a collective result bonus of 50€/ha is also included in the scheme, in addition to the sponsor bonus. We further characterise preference heterogeneities by estimating a LC model (Table 5). The first class (25.6% of respondents) describes preferences for low hedgerows density requirements and non-significant effects of bonuses. Farmers stopping their activity within 5 years are more likely to be in this "hedgerows averse" class. The second class (11.8% of respondents) depicts farms preferring the status-quo or contracts with high management requirements and no bonuses. Organic farmers are more likely to be in this "pro-environment individualists" class. The third class (62.6% of respondents) describes farmers with positive preferences for both types of bonuses, who also require higher levels of per-hectare payment.

The level of financial incentives seems to drive their choice, more than technical constraints. This "pro-incentive" class more receptive to bonuses includes younger (not short-termoriented) and conventional farmers. [START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: The role of a collective bonus[END_REF] also found that younger farmers are more likely to prefer bonuses while asking for higher compensation levels. Since our sample over-represents organic farmers (39% instead of 10% locally), it would suggest that the combined bonuses can be cost-effective insofar as the overall payment is high enough to reach an environmentally effective participation level.

Concluding remarks

The effectiveness of payment schemes for delivering AECPGs with provision thresholds (biodiversity, water quality) depends on reaching enough farmland enrolment at the landscape scale. The objective of the present study was to elicit farmers' preferences for a mixed-payment mechanism made of a bonus on top of a basic payment incentivizing farmers to adopt a collaborative behavior favoring the delivery of public goods with landscape thresholds effects.

Findings suggest that overall, farmers prefer contracts with a bonus for sponsoring a peer to no bonus, but prefer contracts with no bonus to a combined sponsor/collective bonus for environmental achievement. Designing bonuses distributed according to an individual effort for attracting more farmers could be a promising way to increase participation, while collective bonuses distributed equally to all might be counterproductive. We characterized respondents' heterogeneity with a latent class model and identify 3 groups of farmers with a different attitude towards the bonus options: (i) "pro-environment individualists" with negative preferences for both, (ii) "hedgerows averse" farmers who seem indifferent to both, and (iii) "pro-incentive" farmers with positive preferences for both. The later class of farms, most likely to be receptive to the introduction of bonuses for collective actions in environmental contracts, tend to include younger and more conventional farmers. This is a particularly interesting result in the prospect of developing those incentive mechanisms in the future.

A limit to the generalization of our findings is that due to our sampling procedure, our data are slightly biased. Asking and controlling for individual status-quo levels allowed us to control part of the bias regarding the already high levels of management requirements implemented by respondents. In addition, there is an over-representation of organic farms (39% of the respondents while the actual share is closer to 10%). Since organic farms are more likely to have a "pro-environment individualist" preference pattern, our results likely overestimate the negative attitude towards the combined sponsor/collective result bonuses, which, according to the two other behaviour patterns identified, might actually be cost-effective as long as the total amount of financial incentive is attractive enough to effectively boost participation.

Further work is needed to see if conditional bonuses are successful in improving public good provision in practice. An agri-environment-climate measure to protect the European Hamster in France recently introduced an individual bonus payment when a burrow is detected on a plot. This case study might provide useful empirical evidence.

Figure 1 :

 1 Figure 1: Example of choice set of the CE.

Figure 2 :

 2 Figure 2: Distribution of the sampled farms in the surveyed regions (%)

Figure 3 :

 3 Figure 3: Stated effect of collective components in contract design on willingness to adopt

Table 1 : Attributes and attribute levels in the CE.

 1

	Attribute	Description	Levels
	Soil cover	Average agricultural soil	85%
		coverage throughout the	90%
		year at the farm level	95%
	Hedgerows	Average density of anti-	20m/ha
		erosion	multi-species	60m/ha
		multilayer hedgerows at	100m/ha
		the farm level
	Basic	Per-hectare individual	150€/ha
	payment	annual payment	300€/ha
				450€/ha
				600€/ha
	Bonus	Whether the contract
		includes the option of
		receiving	a	bonus
		conditioned	to	a
		collective action

Table 2 : Descriptive statistics of the sample Variable Sample mean Standard deviation

 2

	Farms' characteristics
	UAA (ha)	100.3	64.3
	Share of rented area (%)	72.1	28.5
	Share of permanent grasslands (%)	35.7 (4 n.a)	31.6
	Share of arable land (%)	62.3 (4 n.a)	31.9
	Share of land under permanent crops (%)	2.0 (4 n.a)	10.2
	Specialised in dairy (%)	50.8	50.2
	Specialised in crops (%)	14.6	35.5
	Specialised in granivores (%)	8.5	27.9
	Organic farming (%)	39.2	49.0
	Enrolled surfaces in AES in 2020 (%)	40.8	49.3
	Number of full time workers	2.1	1.2
	Farmers' characteristics
	Female (%)	13.1	33.8
	Older than 50 years old (%)	44.6	49.9
	Plan to stop managing farm activities in 5 years or less (%)	20.0	40.2
	Higher education (%)	63.1	48.4
	Current levels of management requirements
	Soil cover (%)	94.9 (4 n.a)	7.1
	Hedgerows (m/ha)	87.8 (10 n.a)	73.7
	n.a: not answered.

Table 3 : Mixed Logit estimations (normal distribution of random parameters

 3

	)

Table 4 : Average marginal willingness to accept PES contract design characteristics (delta method)

 4

	ML specification	(1)				(2)
	Attributes		Confidence		Confidence
		WTA	interval	WTA	interval
		(€/ha/year)			(€/ha/year)
			2.5% 97.5%		2.5% 97.5%
	COVER	-2.7	-8.1	2.6	32.1 *	7.7	56.4
	HEDGEROWS	2.2 **	0.8	3.7	5.8 ***	3.4	8.1
	BONUSsponsor	-56.9 *	-108.2 -5.6	-66.9 *	-120.9 -12.9
	BONUSsponsor/collective result	-52.4	-111.9	7.0	165.3 *	28.2	302.4
	ASCsq	20.1	-457.3 497.4	-333.6	-842.3 175.2

Table 5 : Latent Class estimation

 5

		Class 1	Class 2	Class 3
		Estimate	Estimate	Estimate
	PAYMENT	0.002 (0.001)	0.003 *** (0.001)	0.007 *** (0.001)
	COVER	0.105 ** (0.035)	-0.027 (0.032)	0.025 (0.016)
	HEDGEROWS	0.022 *** (0.005)	-0.059 *** (0.006)	0.004 (0.002)
	BONUSsponsor	-0.681 * (0.324)	0.461 (0.298)	0.701 *** (0.180)
	BONUSsponsor/collectiv	-1.117 **	0.122	0.795 ***
	e result	(0.355)	(0.353)	(0.167)
	ASCsq	11.882 *** (3.197)	-4.579 (2.900)	1.575 (1.589)
	Log likelihood		-825.03
	Pseudo-R 2		0.313
	AIC		1698.06
	BIC		1819.615
	Observations		1170
	Number of farms		130
	Probability of class	0.118	0.256	0.626
	Significance levels: *** p-value <0.001, ** p-value <0.01, * p-value<0.05.
	Standard errors in parentheses.

This research is funded by the Horizon 2020 programme of the European Union (EU) under Grant Agreement No. 817949 (CONSOLE project, https://consoleproject.eu/). The authors would like to thank the students from Institut Agro who participated in the data collection.


M Becoulet
email: marina.becoulet@cea.fr

G T A Huijsmans

C Passeron

Y Q Liu

T E Evans

L L Lao

L Li

A Loarte

S Pinches

A Polevoi

M Hosokawa

S K Kim

S J P Pamela

S Futatani

Non-linear MHD modelling of Edge Localized Modes suppression by Resonant Magnetic Perturbations in ITER

Edge Localized Modes (ELMs) suppression by Resonant Magnetic Perturbations (RMPs) was studied with the multi-harmonic non-linear MHD code JOREK for ITER H-mode scenarios 15MA,12.5MA,10MA/5.3T, obtained by the ASTRA code. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N=2, N=3, N=4 used as boundary conditions of the computational domain of JOREK including realistic RMP coils, plasma, divertor and wall geometry. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. The threshold for ELM suppression was found at a maximum RMP coils current of 45kAt-60kAt compared to the coils maximum capability of 90kAt. With RMPs, the main harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing continuous MHD turbulent transport and suppressing ELMs in all scenarios. In the high beta poloidal steady-state 10MA/5.3T scenario a rotating QH-mode without ELMs was observed even without RMPs. N=3 RMPs induced a static QH-like mode, locked to the RMP fields in this scenario. The 3D divertor heat and particle fluxes in the stationary RMP phase show the characteristic splitting with the main RMP toroidal symmetry. The radial extension of the footprints typically was ~20 cm in inner divertor and ~40 cm in outer divertor with heat fluxes decreasing further out from the initial strike point from ~5MW/m 2 to ~1MW/m 2 in the stationary regime with RMPs and total power in the divertor ~50MW. The footprints remain within the divertor target and baffle areas, however with rather small margin in the outer divertor which could be an issue for the first wall especially in transient regimes when part of the plasma thermal energy is released due to switching on the RMP coils.

INTRODUCTION

The intensive experimental and theoretical study of ELMs and methods of their control is of great importance for ITER [1,3]. The application of small external RMPs has been demonstrated to be efficient in the suppression/mitigation of ELMs in present day tokamaks [2]. RMPs are foreseen as the main method of ELMs control in ITER [3]. However, significant progress in understanding of physics of the interaction of ELMs with RMPs is still required to make reliable predictions for next step machines such as ITER and DEMO. The nonlinear MHD code JOREK [4] is successfully used to model ELMs mitigation and suppression in present day tokamaks. Recent modelling results of RMP experiments in ASDEX-Upgrade [5] and KSTAR [6] validated in many aspects the RMPs and ELMs physics models implemented in JOREK code [5][6][7]. It was demonstrated, in particular, that the non-linear multi-harmonics approach, including a realistic tokamak geometry with the X-point and the Scrape-Off-Layer (SOL), realistic geometry and spectrum of RMP coils, toroidal rotation, the bi-fluid diamagnetic effects and neoclassical poloidal friction represent a minimum model which permits to reproduce experimental results. In particular, it was found that the external kink-peeling plasma response is an important factor for ELM suppression [5] and that the RMP spectrum should be adjusted in this respect. This provides additional support to the new (compared to vacuum [2]) criterion for ELM suppression proposed in [9] where the RMP spectrum is optimized to obtain a maximum displacement near the X-point (kink response) with the linear resistive MHD plasma response provided by the MARS-F code. In the non-linear modelling [6][7], RMPs drive non-linearly coupled side harmonics locked to the static RMP in the ELM suppression stage while strongly mitigating the medium N-harmonics responsible for ELM crash. In the present work, the non-linear MHD modelling results of the interaction of ELMs with RMPs in ITER are presented for the first time. Realistic ITER scenarios and geometry including wall, divertor, SOL and RMP coils with the optimum [9,10] phasing, according to linear MHD MARS-F criterion, were used.

INITIAL CONDITIONS

The parameters of ITER H-mode scenarios with the magnetic field B tor =5.3T and plasma currents of 15MA, 12.5MA and 10MA as modelled by the ASTRA code [8] with toroidal flow profiles self-consistently calculated with NBI heating and momentum input, documented in ITER IMAS database (Tab.1), were used as initial conditions. Note that here the two fluid version of JOREK was used but with equal temperatures: T i = T e . The initial profiles for each ITER scenario studied here are presented in Fig. 1. The non-linear MHD code JOREK with relevant flows and RMP model is described in detail in [5][6][7]. The numerical domain includes closed flux surfaces, X-point and SOL up to the ITER wall. On the divertor targets, Bohm sheath boundary conditions were used for the fluid velocity and the heat flux normal to the target plates [5][6][7]. The vacuum RMPs generated by external coils were calculated by the vacuum code ERGOS [11] and are imposed at the computational boundary (ITER wall), progressively increasing on a time scale of a few ms. The progressive switch on of the RMPs at the boundary was implemented for numerical reasons to avoid transient unphysical currents at the edge in the vacuum region. In the vacuum code ERGOS the horizontal parts of the RMP coils are approximated with curves and vertically with straight lines. In the ERGOS code, the upper (1) and low (2) corners of the coils were taken as follows: upper row: R 1 = 7.73m, Z 1 =3.38m, R 2 =8.26m, Z 2 =2.62m; middle: R 1 =8.62m, Z 1 =1.79m, R 2 =8.66m, Z 2 =-0.55m; low: R 1 =8.23m, Z 1 =-1.55m, R 2 =7.77m, Z 2 =-2.38m. The toroidal coordinates of the corners (the same for 1 and 2) of the 9 coils in each row are calculated as following:

(1) ,

;

coil corner coil i width shift i         (2) (2)
;  is taken from the linear MHD response of code MARS-F optimization studies, which maximized the magnetic displacement near the Xpoint [9,10]. Because of the different definition of the starting toroidal angle in MARS-F and ERGOS codes for the phase shift between coils we used the formula: kg/m/s in SI). However, the Spitzer expression is valid only for high collisionality plasmas, so it was corrected for the central plasma by a kinetic flux limit (here we used //,max 10 K  ) similar to [12]. In the current source, the bootstrap current was evolved selfconsistently in time depending on profile evolution as described in [13]. All dissipation parameters are rather close to realistic experimental values except the normalized resistivity

coil i i width       ,, 0
,, ( 180 )
7 0 10   
, which was about of two orders higher (because of state-of-art numerical limitations for ITER-sized machine) if calculated for central ITER values in the 15MA scenario.

MODELING OF NATURAL ELMs WITHOUT RMPs

For each ITER scenario considered, the stationary equilibrium with flows was obtained first on few ms time scale including only the N=0 harmonic [7], then natural ELMs were modelled by adding the N=1:9 harmonics initially at the noise level. The magnetic energy of natural ELMs for 15MA(Vtor2) 12.5MA, 10MA scenarios are presented in Fig. 2. Note that in the 15MA scenarios the low N harmonics (N=2,3,4) are the most unstable (Fig. 2a). In the 12.5MA scenario the precursor N=5 is followed by triggering of the most unstable N=7,9 harmonics (Fig. 2b). In the high beta 10MA scenario the N=3 harmonic remains the most unstable at the edge with QH-mode like behavior without ELM crashes (Fig. 2c). The density and the maximum divertor heat flux during a natural ELM for 15MA 12.5MA scenarios are presented in Fig. 3. The total thermal energy loss in ELMs was 4MJ and 2MJ respectively (Fig. 3-a,b). The two fluid diamagnetic effects and toroidal rotations included in the model were found to be the most important factors in explaining the experimentally observed rotation of the ballooning modes before the ELM crash and in the inter-ELM phase [6,14]. In the 10MA scenario the main N=3 QH-mode like structure also rotates in the electron diamagnetic (or ExB) direction (Fig. 4). The RMP current threshold studies were done for the 15MA/5.3T scenario. The magnetic energies of the modes N=1:9 during application of N=3 RMPs with different maximum RMP coils currents (from 0kAt to 60kAt) are shown in Fig. 5. Here the initial time without RMP was the same, but the harmonics energies are plotted here artificially shifted in time just for a better visual representation. One can see that for an RMP coil current larger than 45kAt, the magnetic energy of RMPs (N=3 harmonic) and the non-linearly most strongly coupled harmonics (N=6,9) are dominant. The other harmonics remain at a low noise level. This corresponds to ELM suppression picture similar to one found in [5,6]. For lower RMP currents (<45kAt) the growth rates are usually decreased by RMPs, however the ELMs harmonics remain unstable, growing continuously and eventually produce an ELM crash. In the 15MA/5.3T scenario with increased toroidal rotation (Fig. 1 left) very similar results of ELM suppression were obtained (Fig. 6). Here only the initial stage of an ELM without RMP is shown (with increased rotation the most unstable modes were N=6,7,8). For the case with RMPs we used two harmonics N=3,6 in the RMP spectrum at 60kAt and N=1:9 modes were initialized when RMPs were established (Fig. 6). The results of application of RMPs separately with N=2, N=3, N=4 at maximum RMP current 60kAt in 15MA scenario are presented in Fig. 7. Note that ELMs are strongly mitigated and crashes are avoided in all cases. The side harmonics N*k, where N is the main RMP harmonic number and k is integer are more strongly coupled to RMPs, are developing with RMPs but at lower level (Fig. 7). Other side harmonics also are triggered via nonlinear coupling and saturate, providing edge MHD turbulence instead of ELM crashes. Note that saturation level is higher for N=2 and N=4 RMPs compared to the N=3 case. The corresponding Poincare plots of plasma edge magnetic topology for N=2,3,4 at the last time of the modelling are presented in Fig. 8.As expected the magnetic energy (and edge ergodisation) of the main RMP harmonic at fixed current (here 60kAt) decreases with toroidal number N, since harmonics with higher poloidal numbers (M) are resonant at the edge (q res =M/N) and the RMP perturbation decreases with a distance from the RMP coils approximately as ~1/r M . Note characteristic lobes near X-point and narrow edge ergodic region typical for RMPs application pulses [5,6]. The plasma profiles in mid- The high beta 10MA scenario is rather specific, since even without RMPs it exhibits features of a QHmode without ELMs (Fig. 2c), unlike the 12.5 MA scenario which resembles the 15 MA one. The application of RMPs at different RMP current amplitudes (20kAt, 40kAt) also lead to QH-mode like behavior (Fig. 11). However the main N=3 harmonic locks to the static RMP after few ms and the time of locking is larger for smaller RMP amplitude. (Fig. 12 compared to Fig. 4). The plasma profiles with RMPs are presented in Fig. 13 showing strong density transport and almost no changes in temperature profile, which is typical for QH-modes. The magnetic energies of harmonics N=1:9 with RMP N=3 at 60kAt in 12.5MA/5.3T scenario are presented in Fig. 14, where ELM suppression is also obtained. The plasma profiles in the mid-plane without/with RMPs are presented in Fig. 15. Note the larger density transport compared to energy transport, which is observed also in many RMP experiments (Fig. 16). In linear MHD studies with MARS-F code it was found that the external kink-peeling plasma response is an important factor for ELM suppression by RMPs [9]. At present, the maximum perpendicular magnetic surface displacement near X-point with linear MHD plasma response gives better predictions for ELM suppression in experiment [9] compared to the initial vacuum criterion of edge islands overlapping [2]. The non-linear modelling [5] also pointed out on the role of the external kink plasma response in ELM suppression. Since the RMP coils phasing was optimised according to MARS-F criterion [10], it is interesting to compare displacements in linear and non-linear MHD codes. Note however that properly speaking the magnetic displacement is difficult to define in non-linear MHD especially when edge magnetic field is ergodic. Here we define the displacement in non-linear MHD as: / ( / ) ee TT        also used in [15], where e T  is electron temperature perturbation,  is poloidal magnetic flux For the scenario 12.5MA/5.3T with optimum phasing according to MARS-F, the displacement near the X-point at the last closed flux surface  n ~0.99 was about ~7mm at 60kAt (Fig. 17 is done for 30kAt RMP current). With non-optimum phasing (Tab.1) the same displacement can be obtained by MARS-F simply by increasing the RMP current amplitude up to ~80kAt , since MARS-F is a linear code (Fig. 17). These values were very similar in JOREK modelling at early time (<6.2ms) when the single RMP harmonic N=3 is established: ~6mm for optimum phasing at 60kAt and ~8mm for the non-optimum phasing at 80kAt (Fig. 18). However, usually in the later non-linear stage (here >17ms) with multi-harmonics and self-consistently changing plasma profiles the displacement in non-linear MHD is much larger (~60mm, not shown here) than in the linear MARS-F code.

DIVERTOR FOOTPRINTS

One important consequence of RMP application is the complex magnetic topology and splitting of the separatrix into a set of manifolds, seen in experiment as helical "lobes" at the X-point [2,3]. Crossing the divertor plates they form non-axisymmetric heat and particle fluxes which potentially can represent an issue for ITER, leading to local "hot spots" and material erosion. Rotation of the RMP field thus was considered as an option to smear out heat and particle fluxes, but as a drawback it could lead to significant mechanical stresses in RMP coils.

Here we access the heat and particle fluxes without rotation of the RMP fields. Note also that in the present model many essential divertor physics such as kinetic neutrals, recycling, pumping, etc., are missing. However the localization of divertor heat and particle fluxes with self consistently modelled RMPs with plasma response can be estimated here. The modeling time for all scenarios (~few tens of ms) is short compared to ITER confinement time (>3s), which is not presently accessible due to the computer time requirements for the small Alfven-like time steps needed in the non-linear multi-harmonics MHD modelling with JOREK code, even with a fully implicit scheme [4]. The extrapolation of heat fluxes to the stationary situation is done here using a normalization of the divertor heat fluxes with P div,st =50MW power going to the divertor and walls based on the assumption that approximately 66% of the total heating power (including fusion power) will be radiated in the core plasma and SOL+divertor in high Q ITER scenarios [8]. The extrapolation to the stationary situation when the time derivative of thermal energy is zero : dW th /dt=0 is done by multiplying actual non-stationary perpendicular to the divertor target-baffle and first wall heat flux , () div nst e P T n V n     by a factor P div,st /P div,nst ( n is a normal to the surface vector, T=T e +T i ). The normalized heat fluxes versus toroidal angle along the divertor length for the 15MA scenario without RMPs and with RMPs N=2,3,4 at 60kAt are presented in Fig. 19. Here the uppermost point at the inner divertor baffle is taken as zero length along divertor L div =0 and the lowest point of the outer divertor is at L div =0.411m. The non-normalized particle fluxes at the last time of modelling are presented in Fig. 20. Note increased particle fluxes with RMPs, however not-stationary here. One can see that the splitting of the footprints in the 15MA/5.3T scenario exhibits the N-symmetry of the main RMP harmonic (Fig. 19,20). A footprint radial extension of ~20cm was observed in the inner divertor and of ~40 m in the outer divertor. At the LFS the peak heat fluxes with RMPs decrease from the initial strike point value remain in the divertor target/baffle areas. Note, however, that at the outer divertor baffle/first wall boundary the heat flux can remain as high as ~1MW/m 2 in stationary conditions (Fig. 10). This could be a potential concern for first wall loads at the start of ELM suppression, since the switch-on of the RMP coils leads to a partial loss of confinement (up to 20% in experiments [2]), so that heat fluxes to plasma facing components will transiently increase before a new stationary situation with RMPs is reached. This fact should be considered when RMPs are applied with more favorable application before or soon after the L-H transition, although optimization is required to avoid increasing the L-H power threshold with RMPs. Modelling of such conditions is out of scope of the present paper. The stationary normalized (P div,st =50MW ) heat fluxes in 12.5MA and 10MA scenarios are presented in Fig. 21-22. Note that in the 10MA scenario no clear splitting in inner divertor was observed (Fig. 22). Similar to the 15MA scenario (Fig. 10

CONCLUSIONS

The interaction of ELMs with RMPs was studied in multi-harmonic non-linear MHD simulations for ITER scenarios 15MA,12.5MA,10MA/5.3T. The RMP spectrum, optimized by the linear resistive MHD MARS-F code, with the main toroidal harmonics N=3 and N=4 were used (Tab.1). In the 15MA scenario, the threshold for ELM suppression was found to be at an RMP coil current of ~45kAt-60kAt, compared with a maximum coil capacity of 90kAt. RMPs non-linearly generate a continuous MHD turbulent transport stabilizing ELMs in all scenarios. In the high beta poloidal 10MA/5.3T steady-state scenario without RMPs an N=3 rotating QH-mode was observed. With N=3 RMPs (at 20kAt, 40kAt), the mode is locking to the static RMPs in this scenario. The 3D divertor heat and particle fluxes demonstrate typical splitting with the main toroidal symmetry of the RMP spectrum. The radial extension of the 3D heat fluxes at maximum RMP coils current 60kAt is about ~20 cm at the inner divertor and ~40cm at the outer divertor with the heat fluxes decreasing further out from the strike point from ~5-6MW/m 2 reaching ~1MW/m 2 at the outer divertor baffle/first wall interface in the stationary RMP regime (assuming a total power to the divertor/first wall of ~50MW). Note that at the LFS heat fluxes with RMPs mainly remains within the divertor target/baffle area and within the design limits for divertor target (<10MW/m 2 ), baffle (< 5 MW/m 2 ) and first wall (~1MW/m 2 ). However in transient regimes when RMPs are switched on, part of plasma thermal energy is lost and these heat fluxes can be much larger; optimization of RMP switch-on needs to be studied further with respect to the ensuing power fluxes and L-H access.

Fig. 1 .

 1 Fig.1. From left to right: initial electron density, electron temperature and rotation profiles used in modelling for different ITER scenarios. Note that for 15MA scenario two rotation profiles were used.

4 .

 4 MODELLING OF ELMs WITH RMPs N=2,3,4 IN 15MA/5.3T SCENARIO.

Fig. 2 .

 2 Fig3 The density and divertor maximum heat flux during a natural ELM N=1:9 for 15MA (left) 12.5MA (right) scenarios.

Fig. 4 .

 4 Fig.4. Rotation of the N=3 QH-mode like structure in the electron diamagnetic direction in 10MA scenario.

Fig. 5 .

 5 Fig.5. Magnetic energy of N=1:9 harmonics without and with RMPs in log scale (left) and linear scale (right) at 0-60kAt maximum currents in RMP coils.

Fig. 6 .

 6 Fig.6. Magnetic energy without/with RMPs N=3&6 at 60kAt in 15MA scenario with increased rotation Vtor(1)

Fig. 7 .

 7 Fig.7. Magnetic energy of N=1:9 harmonics with RMPs N=2,3,4 (from left to right) at 60kAt.

Fig. 8 .

 8 Fig.8. Magnetic topology for 15MA, with RMPs N=2,3,4 ( left to right), 60kAt. Fig.9.Plasma profiles for 15MA scenario with RMPs N=2,3,4, 60kAt. N=1:9.

Fig. 10 .

 10 Fig.10. 15MA/5.3T scenario. Edge density, magnetic topology and normalized (considering power in divertor P div,st =50MW, see Sec.7) stationary divertor heat flux with RMP N=3,60kAt (left) and normalized divertor and wall heat fluxes scaled to max 1MW/m 2 (right).

Fig. 11 .

 11 Fig.11. Magnetic energy without RMPs (N=1:9) and RMP N=3 at 20kAt,40kAt in 10MA/5.3T scenario.

Fig. 12 .

 12 Fig.12. Transotion from rotation to locking to static RMPs N=3,40kAt in 10MA scenario

Fig. 16 .

 16 Fig.16. Plasma profiles for 12.5MA scenario with RMPs N=3, 60kAt, N=1:9.

Fig. 17 .

 17 Fig.17. 12.5MA. MARS-F displacement,  n ~0.99, RMP N=3,30kAt, 12.5MA

Fig. 19 .

 19 Fig.19. Normalized heat fluxes in 15MA scenario without and with (from left to right) RMPs N=2,3,4 at 60kAt.

  Fig.21. Divertor normalized heat flux and edge magnetic topology (left), heat flux on the diveror-wall (right) scaled to max 1MW/m 2 , 12.5MA, RMP N=3,60kAt.

Fig. 22 .

 22 Fig.22. Divertor normalized heat flux and edge magnetic topology (left), heat flux on the divertorwall (right), 10MA , RMP N=3,40kAt.

  .5

										 	corner coil shift	  	center coil shift	  	coil width	and the
	toroidal width and shifts for the corresponding coils are:	 	coil width	=29.4°(upper), 20.9°(middle), 30.5°(low);
	 	, center coil shift	=30°(upper), 26.7°(middle), 30°(low), i=1:9. The currents in the coils are calculated as:
	I	i		I	C	cos[ ( N  ) / 180] coil coil i    	, where C I is the peak current,	coil i   	, center coil shift	40 ( 1); i    , N -is the
	main toroidal number of the RMP spectrum needed and the phasing between coils	coil

  / The optimum phasing for each scenario (except for the 12.5MA "non-optimum" case which was done for comparison with linear and non-linear MHD codes, see Sec.6) are presented in Tab. 1. Both codes ERGOS and MARS-F were successfully benchmarked for vacuum modelling to ensure that the same RMP coils geometry and vacuum fields (not presented here) were used.

	the middle coil is taken to be zero both in MARS-F and ERGOS codes, so that the relative phasing can be calculated
	using formula: k=1. Scenario , , , , 360 / ; ; mid new mid temp coil coil temp mid new ERGOS ERGOS ERGOS ERGOS ERGOS kN            IMAS MARS MARS MARS ERGOS Reference N up  mid  low  up 		ERGOS mid		ERGOS low
	15MA,Vtor(2)	131025_24	N=2		145°				0°		195°	110.8°	0°	85.8°
			N=3		200°				0°		140°	56.63°	0°	76.63°
			N=4		250°				0°		95°	30.8°	0°	69.55°
	15MA,Vtor(1)	131025_23	N=3		200°				0°		140°	56.63°	0°	76.63°
	12.5MA	131039_0	N=3		215°				0°		120°	51.63°	0°	83.3°
	optimum
	12.5MA non-	131039_0	N=3		135°				0°		25°	78.3°	0°	114.97°
	optimum
	10MA	131036_21	N=3		240°				0°		110°	43.3°	0°	86.63°
		Tab.1 RMP coils phasing for different ITER scenarios used in modelling.
	The resistivity, poloidal viscosity 5/2 || ||,0 ,0 ( / )	,  	0   ,  	0	( / ee TT	,0	)	3/2 	and parallel Spitzer heat conductivity
												||	10	5
					K	||,0 ~8 10 	5	(~4x10 5
						coil temp ERGOS	  	center coil shift	 	coil MARS			N	. The phase in

ee

K K T T 

are temperature dependent in JOREK

[7,14]

. In the present modelling the central perpendicular heat and particle diffusion were take ~10 -6 in normalized JOREK units [see for normalization 13-14], which corresponds to ~1.3m 2 /s in SI units. The diffusion is decreased in the pedestal region to keep the Hmode profiles without ELMs and RMPs [4-7]. The normalized parallel diffusivity is   (~13m 2 /s in SI), the normalized parallel heat conductivity was taken

ACKNOWLEDGEMENTS. The authors would like to thank the whole JOREK Team for collaborations and fruitful discussions. Part of this work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research program 2019-2020 under grant agreement No 633053 and the ITER IO Contract No. IO/19/CT/ 4300001845. The views and opinions expressed herein do not necessarily reflect those of the European Commission. ITER is the Nuclear Facility, INB No. 174. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. This publication is provided for scientific purposes only. Its content should not be considered as commitments from the ITER Organization as a nuclear operator in the frame of the licensing process. This work was carried out the Marconi-Fusion supercomputer operated by CINECA