Marie Perrin
email: marie.perrin@univ-avignon.fr

Nicolas Borowiec

Marcel Thaon

Myriam Siegwart

Thomas Delattre

Joffrey Moiroux

Differential influence of temperature on the toxicity of three insecticides against the codling moth Cydia pomonella (L.) and two natural enemies

Keywords: Integrated pest management, climate change, biocontrol agents, chlorantraniliprole, spinosad, emamectin

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

Introduction

Since the second half of the 19th century, with the rst industrial revolution, climatic variations accelerated considerably, increasing greenhouse gas emissions, which are responsible for the warming of Earth's climate. All these climate changes induced by human activities are causing substantial changes in the balance of ecosystems, including agroecosystems, that are of great concern as they are essential for human existence.

Most studies agree that there will be an overall increase in crop losses with accelerated development of resistance to certain control methods, such as the use of insecticides in some species and thus increased damages. This possibility raises major questions about the sustainability of certain pest control methods. Moreover, frequent applications of insecticides to control agricultural pests induce side effects on human health, the environment, and bene cial organisms [START_REF] Pajač | Codling Moth, Cydia pomonella (Lepidoptera: Tortricidae) -Major Pest in Apple Production: an Overview of its Biology, Resistance, Genetic Structure and Control Strategies[END_REF]; [START_REF] Koureas | Systematic review of biomonitoring studies to determine the association between exposure to organophosphorus and pyrethroid insecticides and human health outcomes[END_REF]; [START_REF] Stehle | Agricultural insecticides threaten surface waters at the global scale[END_REF]. Due to climate change, their use is expected to increase signi cantly in the future, aggravating their impact and economic costs [START_REF] Chen | An Investigation of the Relationship between Pesticide Usage and Climate Change[END_REF][START_REF] Koleva | The impact of climate change on the external cost of pesticide applications in US agriculture[END_REF]. Several solutions have been developed to ensure a more sustainable agricultural transition. One of them is Integrated Pest Management (IPM) strategy which is a science-based, decision-making process that combines biological, cultural, physical, and chemical tools to identify, manage and reduce risk from pests in a way that minimises economic, health and environmental risks [START_REF] Sauphanor | Incorporating Ecologically Relevant Measures of Pesticide Effect for Estimating the Compatibility of Pesticides and Biocontrol Agents[END_REF][START_REF] Dara | The new integrated pest management paradigm for the modern age[END_REF].

In IPM strategy, natural enemies, whether they are imported, conserved, or supplemented in agroecosystems [START_REF] Boivin | Parasitoïdes et lutte biologique: paradigme ou panacée? VertigO[END_REF][START_REF] Winkler | Assessing the risks and bene ts of owering eld edges. Strategic use of nectar sources to boost biological control[END_REF], play a key role as biological control agents [START_REF] Lacey | Biological control of codling moth (Cydia pomonella, Lepidoptera: Tortricidae) and its role in integrated pest management, with emphasis on entomopathogens[END_REF]. Despite their prominent role, natural enemies commonly provide incomplete pest control, and insecticides must be used sparingly as a complement [START_REF] Sauphanor | Incorporating Ecologically Relevant Measures of Pesticide Effect for Estimating the Compatibility of Pesticides and Biocontrol Agents[END_REF]). Nevertheless, most insecticides cause lethal and sublethal effects on natural enemies, thus indirectly reducing pest control [START_REF] Desneux | The sublethal effects of pesticides on bene cial arthropods[END_REF][START_REF] Rajak | Effect of acute exposure of acephate on hemocyte abundance in a non-target victim Drosophila melanogaster[END_REF]. It is then important in IPM strategy to assess the impact of insecticides on natural enemies and to select active substances with a low impact on biocontrol agents. Such ecotoxicological studies have been commonly performed, but very few attempted to assess the insecticides' impact on natural enemies in a climate change context, even though temperature in uences their toxicity on several pests [START_REF] Glunt | Chemicals, climate, and control: increasing the effectiveness of malaria vector control tools by considering relevant temperatures[END_REF], predators [START_REF] Mansoor | Post-exposure temperature in uence on the toxicity of conventional and new chemistry insecticides to green lacewing Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae)[END_REF] or parasitoid species [START_REF] Abbes | Combined Non-Target Effects of Insecticide and High Temperature on the Parasitoid Bracon nigricans[END_REF]. Contrasting results have been reported, depending on the insecticide class [START_REF] Musser | The in uence of post-exposure temperature on the toxicity of insecticides to Ostrinia nubilalis (Lepidoptera: Crambidae)[END_REF][START_REF] Boina | In uence of Posttreatment Temperature on the Toxicity of Insecticides Against Diaphorina citri (Hemiptera: Psyllidae)[END_REF]), the active substance itself and the insect species. For example, the toxicity of acetamiprid and chlorpyrifos increases with increasing temperature but decreases for λcyhalothrin and spinosad [START_REF] Mansoor | Post-exposure temperature in uence on the toxicity of conventional and new chemistry insecticides to green lacewing Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae)[END_REF] in the predator Chrysoperla carnea Stephens (Neuroptera, Chrysopidae). Conversely, λ-cyhalothrin toxicity increases at high temperatures, while temperature does not in uence spinosad toxicity in Philodromus spiders [START_REF] Michalko | Temperature-dependent effect of two neurotoxic insecticides on predatory potential of Philodromus spiders[END_REF]. This speciesdependency of temperature-mediated toxicity of insecticides may be especially problematic with global warming in IPM strategy if toxicity decreases with temperature for the pest but increases for natural enemies. We may thus expect pest outbreaks because of both a reduced e ciency of insecticides and a drop in predator and parasitoids populations. To our knowledge, and despite the potential in uence of global warming, no study investigated the impact of temperature and insecticides on a pest species and its natural enemies.

The codling moth Cydia pomonella (L.) (Lepidoptera: Tortricidae) is one of the most important insect pests in apple orchards worldwide, causing serious yield losses [START_REF] Barnes | Codling moth occurrence, host race formation, and damage[END_REF][START_REF] Lacey | Biological control of codling moth (Cydia pomonella, Lepidoptera: Tortricidae) and its role in integrated pest management, with emphasis on entomopathogens[END_REF]. Species from several insect orders have been reported to be its natural enemies, including predatory Dermaptera, Neuroptera, Coleoptera and Heteroptera [START_REF] Nikolic | The in uence of the anthropogenic factor on the biodiversity of codling moth natural enemies[END_REF]) and a diverse assemblage of Hymenopteran parasitoids [START_REF] Athanassov | Les parasitoïdes des larves et des chrysalides du carpocapse" Cydia pomonella[END_REF][START_REF] Cross | Biocontrol of pests of apples and pears in northern and central Europe: 2. Parasitoids[END_REF][START_REF] Mills | Selecting effective parasitoids for biological control introductions: Codling moth as a case study[END_REF] In this paper, we investigated the effect of temperature on the e cacy of three commonly used insecticides against C. pomonella and two natural enemies of this pest occurring in southern France, the predatory European earwig For cula auricularia (L.) (Dermaptera: For culidae) and the parasitoid Mastrus ridens Horstmann (Hymenoptera: Ichneumonidae). For cula auricularia is an abundant native predator known to feed on codling moth eggs in apple orchards [START_REF] Glen | The effects of predators on the eggs of codling moth Cydia pomonella, in a ciderapple orchard in south-west England[END_REF][START_REF] Unruh | Gut content analysis of arthropod predators of codling moth in Washington apple orchards[END_REF]. It thus plays a key role in conservation biological control (CBC). Mastrus ridens have been introduced in several countries to control C. pomonella [START_REF] Sandanayaka | Mass rearing and release of Mastrus ridens (Hym: Ichneumonidae) a parasitoid for the biological control of codling moth Cydia pomonella[END_REF][START_REF] Charles | Establishment and seasonal activity in New Zealand of Mastrus ridens, a gregarious ectoparasitoid of codling moth Cydia pomonella[END_REF]. It was introduced in France between 2018 and 2021 in the frame of a classical biological control (ClBC) programme against the codling moth aiming at the permanent establishment of this parasitoid to provide sustainable pest control [START_REF] Borowiec | Un parasitoïde exotique contre le carpocapse des pommes[END_REF]). To optimise eld practices, we tested insecticides that are commonly used against codling moth and are promising for use in conjunction with biological control strategies: two reduced-risk insecticides used in conventional apple orchards, emamectin and chlorantraniliprole (European Food Safety Authority 2012; Redmond and Potter 2017), and one insecticide approved in organic apple orchards, spinosad.

Our experiment was thus performed to investigate changes in insecticide toxicity on the codling moth and its natural enemies as temperature increases and discuss the relevance of these substances in IPM strategy relying on both methods to control C pomonella in a warming world.

Material And Methods 1. Insects

Mastrus ridens Horstmann

Mastrus ridens were reared at INRAE ISA (Sophia Antipolis, France) in insect-proof cages. The rearing temperature was 23°C with a photoperiod of 16:8 h L:D. This strain results from a mix of several strains: laboratory stock from New Zealand (2015) and Chile (2016) and individuals collected in Kazakhstan (2018). Each cage contained 50 females and 35 males and was provided fresh honey and water daily. For reproduction, 50 to 60 overwintering codling moth cocoons were placed in cages every 3-4 days.

For cula auricularia L.

For cula auricularia insects were sampled between March and June 2021 using traps cardboard sheets in peach and apple experimental orchards of INRAE PSH Avignon, southern France, where very few insecticides have been applied for the last 10 years. Fifty F. auricularia adults were placed in ventilated boxes with an arti cial diet (the same as C. pomonella) and cardboard sheets as shelters. The rearing temperature was 25°C with a photoperiod of 16:8 h L:D until experiments.

Insecticides and bioassays 2.1 Insecticides

The commercial formulations of emamectin benzoate (A rm® 0.95%), spinosad (SUCCESS® 4 480 g/L) and chlorantraniliprole (CORAGEN® 200 g/L) were purchased respectively from Syngenta (France), Dow AgroSciences Distribution (France) and FMC Agricultural solutions (France). These products were used diluted in water for all the bioassays by ingestion. The dilutions were made separately according to the species (Tables 1, 2 and3). The pure active substances of insecticides (chlorantraniliprole PESTANAL®, standard analytical purity ≥ 95.0%; emamectine benzoate PESTANAL®, standard analytical purity ≥ 85.0%; spinosad PESTANAL®, standard analytical purity ≥ 95.0%) were purchased and used dissolved in acetone to perform all the bioassay by contact. For these bioassays by contact, one unique dose corresponding to the one used in the eld (X dose) was used for each insecticide: 2 mg/L for emamectin, 0.096 mg/L for spinosad and 0.035 mg/L for chlorantraniliprole.

Exposure methods

The application method differs for each species depending on the targeted stage in the eld. Codling moths are targeted at the larval stage and are more likely to be exposed through ingestion. The two natural enemy species used will be present in the eld at the end of their development as larvae and adults for F. auricularia and only as adults for M. ridens. These two species can then be exposed in natura by ingesting contaminated food (fruits, nectar, eggs, larvae and others) or by contact with the surface of contaminated leaves and fruits.

Temperature ranges

The temperature range evaluated is based on (i) the IPCC warming forecasts projected for the 2005-2010 average summer temperatures in Avignon and (ii) the thermal optima of the different species. These combined data allowed us to set the maximum temperature tested in this study at 35°C, which is consistent with the warming predictions in the Southern France region.

Cydia pomonella toxicity bioassay by ingestion

After a few days of mating, eggs were collected, washed with a water-based solution of dishwashing liquid and bleach, and dried. Neonatal larvae were used for bioassays since it is the target of insecticide treatments. We assessed the in uence of both temperature and insecticides on the mortality of C. pomonella larvae.

To perform these tests, 96 microwell plates containing approximately 150 µL of arti cial diet (Stone y diet Industries Ltd, Rochester, NY) per microwell were treated with different insecticide concentrations diluted in osmosed water (Table 1). Six µL of insecticide solution, or water for control, was deposited in each microwell on the diet surface. After 20 minutes of drying, newborn larvae were individually deposited, and microwells were closed with para lm strips. Plates were then placed in climatic chambers at four different temperatures: 20°C, 25°C, 30°C and 35°C. The mortality rate was assessed at 105-degreedays, i.e., 10 days at 20°C, 7 days at 25°C, 5 days at 30°C and 4 days at 35°C, to homogenise the larval stages at the time of observation. A larva was considered dead when not responding to a probe with dissecting forceps. Missing larvae were removed from the data (< 1%). The corrected mortality was calculated using the Abbott formula [START_REF] Abbott | A method of computing the effectiveness of an insecticide[END_REF]. Each test consisted of 24 individuals per concentration, insecticide, and temperature and was replicated three times. To ensure that potential differences in toxicity with temperature were physiologically explained and not the consequences of recording mortality at different times according to temperature (i.e., 105-degree-days), we also performed three replicates with mortality observations at 5 days for all temperatures.

By contact

In this experiment, we assessed the in uence of temperature and insecticide exposure by contact on the mortality of males. Little pieces of paper (1 cm 2 ) were soaked with 15 µL of an untreated honey/water solution (3/1) and placed in 10 mL glass vial caps. Glass vials were previously treated with 500 µL of acetone for control or with 500 µL of insecticide-polluted acetone (see insecticides section). Control and treated vials were gently laid down and rolled until complete evaporation of the solvent to homogenise the distribution of the solution throughout the vial's surface. After 2 hours of drying, ve males were placed per vial. Caps were partially screwed on the vials, so air would always pass through. Bioassays vials were placed in climatic chambers at 23°C, 28°C or 33°C. The mortality rate was assessed as in the previous experiment. Each test consisted of ve individuals per dose, insecticide and temperature and was repeated four times.

2.6 For cula auricularia toxicity bioassay 2.6.1. By ingestion Since F. auricularia adults are more active than larvae and the most likely to be exposed to insecticides, we tested the in uence of both temperature and ingestion of insecticides on their mortality. To perform this experiment, individual ventilated Petri dishes were lled with humidi ed sand, and Eppendorf tube caps were lled with the arti cial diet [START_REF] Guennelon | Progrès réalisés dans l'élevage permanent du Carpocapse (Laspeyresia pomonella L.) sur milieu arti ciel[END_REF] without formaldehyde). For each cap, a 6 µL volume of insecticide solution with different concentrations or no solution for control was deposited on the diet surface (Table 3). After 20 minutes of drying, one cap was placed on a single petri dish, and one individual of F. auricularia was introduced. Petri dishes were placed in climatic chambers at 23°C, 28°C or 33°C. The mortality was assessed each day at the same hour for ve days. Individuals were considered dead when not responding to a probe with dissecting forceps. Missing individuals were removed from the data. The corrected mortality was calculated using the Abbott formula (Abbott 1925), represented in section 2.4. Each test consisted of one individual per dose, insecticide and temperature and was repeated 15 times per sex.

By contact

We evaluated the in uence of temperature and insecticide exposure by contact on the mortality of F. auricularia adults. Insecticides were used in the form of pure active substances dissolved in acetone. Petri dishes were treated with 115 µL of acetone for control or with 115 µL of insecticide-polluted acetone (see insecticides section). Following application, the solvent was spread over the entire surface of the Petri dish, including the sides. After 30 minutes, ve individuals of F. auricularia were placed in a single Petri dish, and the arti cial diet [START_REF] Guennelon | Progrès réalisés dans l'élevage permanent du Carpocapse (Laspeyresia pomonella L.) sur milieu arti ciel[END_REF] without formaldehyde) was provided. The Petri dishes were placed in climatic chambers at 23°C, 28°C or 33°C. The mortality rate was assessed as in the previous experiment. Each test consisted of ve individuals per dose, insecticide and temperature and was repeated three times per sex. For contact bioassays, corrected mortality was calculated using the Abbott regression (Abbott 1925), and differences in mortality between treatments, sexes (for F. auricularia) and temperatures were analysed using a Chi-square test.

Data analyses

Results

Cydia pomonella

Based on observations at 105-degree-days, the temperature decreased the toxicity of emamectin by 1.5, two and three times the dose of chemicals required to kill 50% of the larvae at 25°C (p = 0.01), 30°C (p = 0.008) and 35°C (p = 0.009) respectively, compared to 20°C (Fig. 1A).Temperature also decreased the toxicity of Spinosad with fourth the dose of chemicals required to kill 50% of the larvae at 25°C, 30°C and 35°C compared to 20°C (p = 0.04) (Fig. 1B). However, no signi cant difference was observed between the three higher temperatures (p > 0.3) (Fig. 1B). Temperature did not signi cantly in uence the mortality of codling moth larvae exposed to chlorantraniliprole (p > 0.6) (Fig. 1C).

We observed similar results for mortality assessment at constant time, i.e., 5 days (Online Resource 1, Table 1). Thus, our results are due to differences in the in uence of temperature on insecticides' toxicity and not by differences in reading time.

Mastrus ridens

Toxicity by ingestion

Spinosad toxicity increased with increasing temperatures when M. ridens ingested the insecticide. Four times less product was needed to kill 50% of the individuals at 28°C (p = 0.008) and six times less at 33°C (p = 0.009) compared to 23°C (Fig. 2B). Similarly, chlorantraniliprole toxicity increased with increasing temperatures with eight and 15 times less product needed to kill 50% of the individuals at 28°C and 33°C respectively compared to 23°C (p = 0.04) (Fig. 2C). For emamectin, a similar trend as for the other insecticides was observed. However, differences between temperatures were not signi cant (p > 0.8), probably because of a high variability occurring at 23°C (Fig. 2A).

Toxicity by contact

For cula auricularia

Toxicity by ingestion

Emamectin increased at 28°C (p = 0.008) and 33°C (p = 0.009) but did not at 23°C (Fig. 3A) when earwigs ingested the insecticide. A similar trend was observed for spinosad, but differences between temperatures were not signi cant (p > 0.8), probably because of a high variability occurring at 23°C (Fig. 3B). For chlorantraniliprole, no mortality occurred at the single dose tested (3.5 mg/L, corresponding to 100× the approved eld rate), regardless of temperature.

Toxicity by contact

We tested a single dose corresponding to the approved eld dose of each insecticide substance. No mortality was observed for F. auricularia adults regardless of the insecticide or the temperature evaluated.

Discussion

Climate change may differentially affect the e ciency of insecticide treatments against pests and bene cial insects through a wide range of factors in the eld. This study rst wants to assess the effect of temperature on three insecticide toxicity in the controlled condition in the laboratory to avoid the complex interactions between factors, including the behaviour or ecology of arthropods in natura. It provides a rst step of whether the e cacy of these insecticides may change with the climate using the example of a pest and two of its natural enemies used in IPM programmes. Indeed, the consequences of climate change on biological control caused by a differential in uence of temperature on insecticide toxicity between pests and their natural enemies have never been considered, although such an in uence is known to be species-speci c. This topic is especially relevant for organic farming and IPM strategy, which rely on both natural enemies and insecticides. The worst scenario is that insecticide toxicity decreases with global warming for a pest but increases for its natural enemies.

In this study, we observed that higher temperature (i) decreased the toxicity of emamectin and spinosad but did not in uence the toxicity of chlorantraniliprole against the pest C. pomonella, while it (ii) increased the of these three insecticides on the parasitoid, M. ridens, and (iii) increased the toxicity of emamectin on the predator, F. auricularia. Our results suggest a possible problem in future C. pomonella population control in the eld because of a decreased e ciency of insecticides on the pest coupled with the opposite effect on natural enemies' populations.

Our results on C. pomonella agree with those reported for spinosad on another pest species, the cotton mealybug Phenacoccus solenopsis Tinsley [START_REF] Mansoor | Temperature-toxicity association of organophosphates, pyrethroids and Neonicotinoids: selection and scheduling chemical control of cotton mealybug Phenacoccus solenopsis tinsley (Homoptera: pseudococcidae)[END_REF]). However, our results on C. pomonella contrast with those obtained on P. solenopsis [START_REF] Mansoor | Temperature-toxicity association of organophosphates, pyrethroids and Neonicotinoids: selection and scheduling chemical control of cotton mealybug Phenacoccus solenopsis tinsley (Homoptera: pseudococcidae)[END_REF]) and Plutella xylostella L., on which toxicity of emamectin increased with temperature as for chlorantraniliprole on P. xylostella [START_REF] Li | Toxicity of emamectin to the diamondback moth, Plutella xylostella, and the effects on survivors of parent generation treated with sub--lethal dosage[END_REF][START_REF] Teja | Effect of variable temperature on the toxicity of novel insecticides against diamondback moth, Plutella xylostella (Linn.)[END_REF]). Indeed, interspeci c differences in temperature-mediated insecticides' toxicity between pests have been frequently reported [START_REF] Boina | In uence of Posttreatment Temperature on the Toxicity of Insecticides Against Diaphorina citri (Hemiptera: Psyllidae)[END_REF]), although underlying mechanisms still have to be investigated.

Compared to pests, few studies have been conducted on natural enemies. Still, increased toxicity at high temperatures was reported for chlorantraniliprole on the parasitoid Bracon nigricans Szépligeti (Abbes et al. 2015), as we observed for M. ridens when the substance was ingested. However, in our study, spinosad toxicity increased with temperature for M. ridens. At the same time, it was not in uenced by temperature in B. nigricans [START_REF] Abbes | Combined Non-Target Effects of Insecticide and High Temperature on the Parasitoid Bracon nigricans[END_REF] and decreased with increasing temperature in the lacewing Chrysoperla carnea Stephens [START_REF] Mansoor | Post-exposure temperature in uence on the toxicity of conventional and new chemistry insecticides to green lacewing Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae)[END_REF]. The same interspeci c differences for pests were also observed for natural enemies.

The positive relationship between toxicity and temperature observed for the three substances in M. ridens and emamectin ingested by F. auricularia may result from several mechanisms that should be investigated in further studies. First, high temperature may in uence detoxi cation enzymes (Yan et [START_REF] Boina | In uence of Posttreatment Temperature on the Toxicity of Insecticides Against Diaphorina citri (Hemiptera: Psyllidae)[END_REF]).

This study was conducted in a simpli ed system where insects are "forced" into contamination. In natura, other complex behavioural or ecological parameters might limit contact between insects and insecticide. For example, F. XXXuricularia is a nocturnal species that hunt at dusk, which could allow them to avoid diurnal substances spraying [START_REF] Vancassel | La n du cycle parental de Labidura riparia (Dermaptere, Lariduridae)[END_REF]. Moreover, some parasitoid species also avoid hosts resistant to some insecticides to minimise contamination (Alfaro-Tapia et al. 2021).

Whether the two natural enemies ingested the insecticides or were exposed by contact, M. ridens was more sensitive to substances than F. auricularia. The three insecticides caused 100% mortality in M. ridens above 28°C at the authorised eld dose, while no mortality was detected in F. auricularia. This interspeci c difference may be due to differences in the composition or thickness of their cuticle [START_REF] Fernandes | Impact and Selectivity of Insecticides to Predators and Parasitoids[END_REF]) and/or insecticide penetration, depending on the a nity between the cuticle and the substance [START_REF] Leite | Selectivity of insecticides with and without mineral oil to Brachygastra lecheguana (Hymenoptera: Vespidae), a predator of Tuta absoluta (Lepidoptera: Gelechiidae)[END_REF]). The smaller size of M. ridens compared to F. auricularia may also account for this difference, as the speci c target area of the insecticides decreases with increasing body size, resulting in reduced insecticide exposure (Picanco et al. 1997;[START_REF] Bacci | Toxicity of insecticides to the sweetpotato white y (Hemiptera: Aleyrodidae) and its natural enemies[END_REF]).

Such differences may also explain that toxicity was mediated by temperature for the three insecticides for M. ridens, while it was only true for emamectin in F. auricularia. These interspeci c differences in the relationship between temperature and insecticides' toxicity underline the need to study speci cally each pest-natural enemy's system. This approach would allow for selecting insecticides that will be the most reliable with global warming. Ideally, insecticides used in IPM programmes and organic agriculture should be less toxic to natural enemies than to target insect pests [START_REF] Zhao | Assessment of toxicity risk of insecticides used in rice ecosystem on Trichogramma japonicum, an egg parasitoid of rice lepidopterans[END_REF]) and remain harmless as temperature increases.

From our results, spinosad was as toxic to the codling moth as it was to the European earwig and was even more toxic to M. ridens, regardless of the temperature. It was also more toxic to natural enemies than emamectin and chlorantraniliprole, considering the tiny dose needed to kill 50% of parasitoids compared to the two other insecticides. Lethal and sublethal effects of spinosad and other spinosyns on bene cial arthropods have been previously reported in several studies [START_REF] Biondi | The non-target impact of spinosyns on bene cial arthropods[END_REF][START_REF] Abbes | Combined Non-Target Effects of Insecticide and High Temperature on the Parasitoid Bracon nigricans[END_REF], and yet, this product is authorised and widely used in organic farming while emamectin and chlorantraniliprole are not [START_REF] Biondi | The non-target impact of spinosyns on bene cial arthropods[END_REF]). Moreover, our results indicate that higher temperatures emphasise differences in spinosad toxicity between the two trophic levels. Among the insecticides evaluated, it is likely to cause problems managing codling moth populations under high-temperature conditions. The combination of spinosad with strategies of regulation based on natural enemies should be avoided. Its approval for organic production may raise questions in the future considering its increased toxicity on some bene cial organisms as temperature increases.

Surprisingly, chlorantraniliprole may be the most promising insecticide in a warming world for strategies relying partly on biological control by conservation. The toxicity of this substance indeed remained very effective at high temperatures against C. pomonella while it did not cause any mortality on F. auricularia, regardless of temperature or exposure method. Moreover, it was relatively safe against M. ridens when parasitoids ingested the substance. Despite the product's increased toxicity at high temperatures, the lethal doses for 50% of individuals remained high (equivalent to 10-50× the recommended eld dose). However, the substance caused 100% mortality during contact for M. ridens. Thus, this substance may be appropriate for classical biological control relying on the introduction of parasitic wasps, although eld experiments should con rm our laboratory observations.

For both natural enemies, the LD ). However, we observed that its toxicity increased rapidly with temperature for F. auricularia and M. ridens and decreased for the codling moth. In this sense, its e cacy may decrease with global warming despite being the most effective insecticide against C. pomonella among the three tested in terms of effective doses at high temperatures.

Contrary to chlorantraniliprole, emamectin toxicity on F. auricularia increased strongly with temperature.

Alternating the use of these insecticides in conservation biological control, with preferential use of emamectin during the colder periods (e.g., early spring) and the use of chlorantraniliprole (e.g., during the summer) could limit the risks of resistance appearance in pest's populations while limiting the impact of chemical substances on the European earwig. However, its use in CBC programmes involving the introduction of M. ridens should be avoided considering its toxicity at high temperatures.

The present study highlights opposite cross effects of temperature and insecticides (spinosad, emamectin, chlorantraniliprole) on C. pomonella and two of its natural enemies, one exotic (M. ridens) and one native (F. auricularia) in southern France. According to the future climate change predictions, we recommend using these insecticides to preserve natural enemies associated with C. pomonella. The use of spinosad should be avoided, while emamectin can be used in conjunction with the conservation of F. auricularia. Only chlorantraniliprole appears suitable for controlling C. pomonella, conserving F. auricularia and establishing M. ridens. The present study remains a simpli ed but essential tool to understand the cross effects of temperature and three insecticides on the target pest and two of its natural enemies, allowing us to propose an adaptation of strategies relying on insecticides in apple orchards in a changing climate. We focused on the mortality of natural enemies, but the effects of sublethal exposures, which affect insects' behaviour and life history traits, should also be investigated since they may be critical to the long-term conservation and/or establishment of natural enemies [START_REF] Saber | Acute and population level toxicity of imidacloprid and fenpyroximate on an important egg parasitoid, Trichogramma cacoeciae (Hymenoptera: Trichogrammatidae)[END_REF][START_REF] Poorjavad | Effect of Ferula assafoetida essential oil on some biological and behavioral traits of Trichogramma embryophagum and T. evanescens[END_REF]).

Declarations

Ethical Approval Not applicable.

The authors have no relevant nancial or non-nancial interests to disclose.

Authors' Contributions

Perrin M participated in the design of the study, performed the bioassays, performed the statistical analysis and drafted the manuscript. Borowiec N participated in the design and coordination of the study and helped to draft the manuscript. Moiroux J and Siegwart M conceived of the study, and participated in its design and coordination and helped to daft the manuscript. Delattre T helped to draft the manuscript.

Thaon M helped to performed the bioassays. All authors read and approved the nal manuscript. (EDcomp, α = 0.05).

Figure 3

  . However, their effectiveness in orchards is quite limited (Maalouy et al. 2013; Thorpe et al. 2016) and insecticides are commonly used to manage C. pomonella and mating disruption (Witzgall et al. 2008; Grigg-McGu n et al. 2015; Ioriatti and Lucchi 2016). The intensive use of insecticides, associated with the multivoltinism and high fertility of the codling moth, has, however, led to the development of resistance toward several chemical groups of insecticides in wild populations (Sauphanor et al. 2000; Boivin et al. 2001; Bouvier et al. 2001; Brun-Barale et al. 2005). There is thus a need to improve alternative or complementary methods to chemical products for the management of this pest.

1. 1

 1 Cydia pomonella L. The laboratory strain of C. pomonella used for this study (later called C. pomonella strain NPP) originates from northern France and has been mass-reared in the laboratory since 1995. It is used on an industrial scale to produce Carpovirusine™ by Natural Plant Protection Firme, Pau, France. In our study, C. pomonella strain NPP was reared on an arti cial diet (prepared according to Guennelon et al. 1981 recipe without formaldehyde) at INRAE PSH Avignon (France). The rearing temperature was of 23°C with a photoperiod of 16:8 h Light:Dark (L:D).

  (i) According to the 5-year data (2005-2010) of the meteorological station of Avignon (Station METAR/SYNOP 07563, 48 m.a.s.l., 43.95°N 4.82°E), the average maximum summer temperature was 30.13°C. According to the IPCC 2021, climatologists predict an average warming of 1.8°C (best scenario) to 4.4°C (worst case) by 2100 (IPCC 2021).

(

  ii) For natural enemies more sensitive to temperature changes, temperature selection was based on two publications (Kharboutli & Mack, 1993; Devotto et al. 2010) and unpublished experimental data. For codling moths, unpublished experimental data on larval development at different temperatures allowed the selection of the four most suitable temperatures.

Dose-response curves

  were tted with the package drc using R software (Ritz et al. 2015; R Core Team 2020 version 4.0.2) to calculate the different LD 50 for each temperature and each insecticide. The drm function was used to calculate the different LD 50 , and the EDcomp function was used to compare each concentration and temperature evaluated.

Figures Figure 1

 1 Figures

Figure 2 Effects

 2 Figure 2

Table 1

 1 Concentrations of active insecticide substance used for bioassays on Cydia pomonella neonate larvae (for information, only doses in mg/L were converted in X dose corresponding to the eld dose used in French orchards)In this experiment, we evaluated the in uence of both temperature and ingestion of insecticides on the mortality of M. ridens. Since only adults are exposed to insecticides in orchards (larvae are ectoparasitoids of cocoons), we used freshly (< 48 h old) emerged males of M. ridens for bioassays. To perform this experiment, little pieces of paper (1 cm 2 ) were soaked with 15 µL of a honey/water solution (3/1) untreated for control or polluted with different insecticides concentration (Table2). Soaked papers were placed in 10 mL glass vial caps. After the preparation of control and treated vials, ve males were placed per vial, and the caps were only partially screwed to allow the air to pass through. Bioassays vials were placed in climatic chambers at 23°C, 28°C or 33°C. The mortality rate was assessed each day for 72 hours. Individuals were considered dead when not responding to a probe with dissecting forceps. Missing individuals were removed from the dataset. The corrected mortality was calculated using the Abbott formula (Abbott 1925), represented in section 2.4. Each test consisted of ve individuals per dose, insecticide and temperature and was repeated four times.

				deadtreatedindividuals
			(1 -(		))
				totaltreatedindividuals
	C orrectedmortality = 100 × (1 -			)
				deadcontrolindividuals
			(1 -(		))
				totalcontrolindividuals
	Insecticides	Concentrations (mg/L)
	A rm® (emamectin)	0.02	0.03	0.05	0.08	0.14	0.22
		(X/100)	(X/67)	(X/40)	(X/25)	(X/14)	(X/9)
	CORAGEN® (chlorantraniliprole)	0.3	0.53	0.95	1.69	3
		(8.5X)	(15X)	(27X)	(48X)	(86X)
	SUCCESS 4® (spinosad)	0.05	0.15	0.45	1.34	4.01	12
		(X/2)	(1.5X)	(4.7X)	(14X)	(42X)	(125X)

Table 2

 2 Concentrations of active insecticide substance used for ingestion bioassays on Mastrus ridens. Concentrations are given in mg/L and converted in X dose corresponding to the eld dose used in French orchards.

	Insecticides	Concentrations (mg/L and X dose)
	A rm® (emamectin)	0.4	1	2	4	10	20
		(X/5)	(X/2)	(X)	(2X)	(5X)	(10X)
	CORAGEN® (chlorantraniliprole)	0.018	0.035	0.07	0.175	0.35	1.75	3.5
		(X/2)	(X)	(2X)	(5X)	(10X)	(50X)	(100X)
	SUCCESS 4® (spinosad)	0.02	0.05	0.096	0.2	0.48	0.96
		(X/5)	(X/2)	(X)	(2X)	(5X)	(10X)

Table 3

 3 Concentrations of active insecticide substance used for ingestion bioassays on For cula auricularia. Concentrations are given in mg/L and converted in X dose corresponding to the eld dose used in French orchards.

	Insecticides	Concentrations (mg/L and X dose)
	A rm® (emamectin)	4	10	20	40	100
		(2X)	(5X)	(10X)	(20X)	(50X)
	CORAGEN® (chlorantraniliprole)	3.5
		(100X)
	SUCCESS 4® (spinosad)	0.096	0.2	0.48	0.96	2
		(X)	(2X)	(5X)	(10X)	(20X)

Table 4

 4 Effects of temperature and insecticides at eld dose (X dose) on the mortality of Mastrus ridens adults. Different letters indicate signi cant differences between treatments. (Chi-square χ² test).

	Insecticide	Corrected mortality (%)
	(X dose)	23°C	28°C	33°C
		64.74 a (χ² = 0)	100 b (χ² = 8.17)	100 b (χ² = 8.17)
	spinosad	68.27 a (χ² = 0)	100 b (χ² = 6.97)	100 b (χ² = 6.97)
	chlorantraniliprole 100 (χ² = 0.40)	100 (χ² = 0.15)	100 (χ² = 0.15)

Toxicity bycontact of emamectin and spinosad increased signi cantly with temperature as it rose from less than 70% at 23°C to 100% mortality at 28°C and 33°C for both insecticides. The mortality reached 100% when chlorantraniliprole was applied, regardless of the temperature.

  [START_REF] Pajač | Codling Moth, Cydia pomonella (Lepidoptera: Tortricidae) -Major Pest in Apple Production: an Overview of its Biology, Resistance, Genetic Structure and Control Strategies[END_REF] remained very high at low temperatures for emamectin, indicating that a high quantity of this insecticide should be applied to kill 50% of the individuals. These results are consistent with the literature on other natural enemies for this substance[START_REF] Argentine | Potency, spectrum and residual activity of four new insecticides under glasshouse conditions[END_REF][START_REF] Khan | Lethal effects of λ-cyhalothrin and Emamectin benzoate in Plexippus paykulli (Araneae: Salticidae)[END_REF]. Emamectin has been recommended in IPM strategies for a long time because of its low toxicity on bene cial organisms, high selectivity for pests and rapid environmental degradation (Argentine et al.

	2002; López et al. 2010

Acknowledgements

This study was supported by FranceAgriMer ('BIOCCYD-Mastrus' 2019-2022). We are grateful to the PACA region, France, and the experimental station "la Pugère" for the nancial support of M. Perrin doctoral fellowship.

Funding

This work was supported by FranceAgriMer ('BIOCCYD-Mastrus' 2019-2022), the PACA region, France, and the experimental station "la Pugère". The author N. Borowiec has received research support from FranceAgriMer ('BIOCCYD-Mastrus' 2019-2022) and the author M. Perrin has received research support from the PACA region, France, and the experimental station "la Pugère" for doctoral fellowship.

Availability of data and materials

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests

Effects of temperature on doses of emamectin (A) and spinosad (B) needed to kill 50% (LD 50 ) of For cula auricularia adults. Results for males and females were pooled since there were no signi cant differences between the sexes. Different letters indicate signi cant differences between treatments. (EDcomp, a = 0.05).

Supplementary Files

This is a list of supplementary les associated with this preprint. Click to download.

ESM1.docx


J Zs

Mezei

F Colboc

N Pop

S Ilie

K Chakrabarti

S Niyonzima

M Lepers

A Bultel

O Dulieu

O Motapon

J Tennyson

K Hassouni

I F Schneider

Dissociative recombination and vibrational excitation of BF + in low energy electron collisions

HAL is

Introduction

Boron fluoride (BF 3 ) containing plasmas are important for applications in the field of material processing. BF 3 and Ar/BF 3 plasmas are for instance used for p-type doping in the semi-conductor industry (Torregrosa et al 2004, Matsui et al 2004). Moreover, electrical discharges generated in complex mixture of BF 3 with nitrogen containing compounds have been proposed and investigated for the deposition of boron nitride coatings (Yu & Matsumoto 2003, Yamamoto et al 2006). All these processes make use of low pressure high density plasma sources where BF 3 interacts with the free electrons of the plasma through elastic and inelastic collisions. These collisions are not only the driver for the generation of the active key-species of the process, e.g., the positive ions for the plasma immersion ion implantation (PIII) doping processes or active radicals for the deposition processes, but they also contribute and govern the discharge equilibrium and stability through ionisation, attachment and recombination processes (Agarwal &Kushner 2007, Farber & Srivastava 1984[START_REF] Kim | AIP Conf. Proc[END_REF]. In particular, for high density magnetised inductively coupled radio-frequency sources used in many of these processes, the surface losses are limited due to the magnetic confinement, which makes the contribution of ion recombination and mutual recombination processes to the discharge equilibrium very significant. In this context, the BF + ion can represent a significant fraction of the ions produced when working at high power density discharge conditions for which BF 3 dissociation and dissociative ionisation are strongly enhanced and the plasma is dominated by BF 2 and BF fragments [START_REF] Maury | To be submitted to Plasma Chemistry and Plasma Processing[END_REF]. These species can therefore significantly contribute either as an active species in the processes or in the discharge ionisation-recombination equilibrium. The investigation of the dissociative recombination of BF + is therefore of importance for understanding BF 3 plasma processes.

The kinetic description of all the above mentioned environments is based on the knowledge of the rate coefficients of the dominant reactions, including those between electrons and molecular ions. As for the BF + ions, their abundance and their vibrational distribution are strongly affected by the dissociative recombination (DR),

BF + (v + i ) + e -→ B + F, (1)
and also by other competitive processes, such as inelastic collisions (v + f > v + i ) and super-elastic collsions (v + f < v + i ) which are also known as collisions of the second kind:

BF + (v + i ) + e -→ BF + (v + f ) + e -, (2)
where v + i and v + f stand for the initial and final vibrational quantum number of the target ion, and rotational structure is neglected. In the present work, we compute the DR and vibrational transition (VT) -vibrational excitation/de-excitation (VE/VdE) -cross sections and rate coefficients for the lowest three vibrational levels of the BF + in its ground electronic state using the multichannel quantum defect theory (MQDT). The paper is structured as follows: Section 2 outlines the main ideas and steps of our MQDT approach. Section 3 presents the molecular data used in the calculation. The main results are given in section 4 and the paper ends by conclusions.

The MQDT-type approach to DR

The MQDT approach (Seaton 1983, Greene and Jungen 1985[START_REF] Jungen | Molecular Applications of Quantum Defect Theory[END_REF], Giusti-Suzor 1980) has been shown to be a powerful method for the evaluation of the cross sections in collisions of electrons/photons with molecular cation/neutral systems. It was applied with great success in calculating DR cross sections to several diatomic systems like H + 2 and its isotopologues (Giusti-Suzor et al 1983, Schneider et al 1991, Takagi 1993, Tanabe et al 1995, Schneider et al 1997, Amitay et al 1999), O + 2 [START_REF] Guberman | Dissociative Recombination: Theory, Experiment and Applications IV[END_REF]Giusti-Suzor 1991, Guberman 2000) In the present paper, we use an MQDT-type method to study the electron-impact collision processes given by eqs.

(1) and (2) which result from the quantum interference of the direct mechanism -the capture takes place into a dissociative state of the neutral system (BF * * ) -and the indirect one -the capture occurs via a Rydberg state of the molecule BF * which is predissociated by the BF * * state. In both mechanisms the autoionization is in competition with the predissociation and leads, through the reaction (2), to super-elastic collision (SEC) (v

+ i > v + f in eq. (2)), elastic collision (EC) (v + i = v + f ) and inelastic collision (IC) (v + i < v + f ).
A detailed description of our theoretical approach is given in previous studies (Little et al 2014, Mezei et al. 2015). The major steps of the method only can be briefly outlined as follows:

(i) Defining the interaction matrix V:

Within a quasi-diabatic representation of the BF states, the interaction matrix is based on the computed (Chakrabarti andTennyson 2009, Chakrabarti et al 2011) couplings between ionisation channels -associated to the vibrational levels v + of the cation and to the orbital quantum number l of the incident/Rydberg electron -and dissociation channels d j .

(ii) Computation of the reaction matrix K: Given H 0 the Hamiltonian of the molecular system under study in which the Rydberg-valence interaction is neglected, we adopt the second-order perturbative solution for the Lippman-Schwinger integral equation (Ngassam et al 2003a, Florescu et al 2003, Motapon et al 2006), written in operatorial form as:

K = V + V 1 E -H 0 V. (3)
(iii) Diagonalization of the reaction matrix, yields the corresponding eigenvectors and eigenvalues which are used to build the eigenchannel wavefunctions.

(iv) Frame transformation from the Born-Oppenheimer (short-range) to the close-coupling (long-range) representation, relying, for a given electronic total angular momentum quantum number Λ and a given orbital quantum number of the incident/Rydberg electron l, on the quantum defect µ Λ l (R) and on the eigenvectors and eigenvalues of the K-matrix. (v) Construction of the generalised scattering matrix X, based on the frame-transformation coefficients, this matrix being organised in blocks associated to open and/or closed (o and/or c respectively) channels:

X = X oo X oc X co X cc . (4)
(vi) Construction of the generalised scattering matrix S,

S = X oo -X oc 1 X cc -exp(-i2πν) X co . (5)
based on the open channels, the first term in eq. ( 5), but also on their mixing with the closed ones, given by the second term, the denominator being responsible for the resonant patterns in the shape of the cross section (Seaton 1983). Here the matrix exp(-i2πν) is diagonal and contains the effective quantum numbers ν v + associated to the vibrational thresholds of the closed ionisation channels.

(vii) Computation of the cross-sections:

For each of the relevant BF states, which are grouped by symmetry properties: electronic total angular momentum quantum number Λ, electronic spin singlet/triplet, and for a given target cation vibrational level v + i and energy of the incident electron ε, the dissociative recombination and the vibrational excitation/de-excitation cross sections are computed using, respectively:

σ sym diss←v + i = π 4ε ρ sym l,j | S dj ,lv + i | 2 , (6)
σ sym v + f ←v + i = π 4ε ρ sym l,l | S l v + f ,lv + i -δ l l δ v + i v + f | 2 , ( 7
)
where ρ sym stands for the ratio between the multiplicity of the involved electronic states of BF and that of the target, BF + .

Molecular data

The molecular data necessary to model the DR are the potential energy curve (PEC) of the ground state of the ion, the PECs of the neutral valence dissociative states interacting with the ionization continua, those of the Rydberg states associated to these continua below the threshold, and all the relevant Rydberg-valence couplings. These molecular data are mostly obtained from ab initio R-Matrix calculations. In order to extend the PECs to small and large values of the internuclear distance R, we used the quantum chemistry molecular data of Magoulas et al (2013).

Ab initio R-Matrix calculations for the molecular states

Ab initio R-matrix calculations of electron collision with the BF + ion yielding the relevant molecular data were performed by three of us (Chakrabarti andTennyson 2009, Chakrabarti et al 2011). The R-matrix method is a state-of-the-art quantum scattering technique which can be used to calculate the properties of bound and resonant electronic states of a molecule (Tennyson 2010). The BF + target states were first obtained by performing a configuration interaction (CI) calculation. Subsequently this CI target wave function was used in an R-matrix calculation. The bound states of the BF molecule were obtained by searching for negative energy solutions using the BOUND program available within the R-Matrix code suite (Sarpal et al. 1991, Carr et al 2012). This also produces quantum defects of the bound states. Resonances were detected and fitted to a Briet-Wigner profile (Tennyson & Noble 1984) to obtain their energies and widths. Subsequently the electronic couplings V dj ,l were obtained from the resonance widths Γ dj ,l using the relation

V dj ,l = Γ dj ,l 2π . (8)
The calculations were repeated for 11 internuclear distances in the range 1.5 a 0 -3.5 a 0 . While the R-matrix calculations used several partial waves l to represent the scattering, one single generic partial wave for each symmetry was considered to take in charge the total strength of the Rydberg-valence interaction in the current calculations. Dissociative curves were constructed using the resonance data above the ion PEC and their continuation as bound states below the ion PEC.

Modeling of the potential energy curves and electronic couplings

Our earlier studies on molecular systems such as H 2 (Epée Epée et al 2015), HD (Motapon et al 2014), NO (Motapon et al 2006), N 2 (Little et al 2014) and CO (Mezei et al. 2015) revealed that accurate and complementary R-matrix and quantum chemistry calculations are needed for a reliable description of the molecular dynamics in electron/molecular cation collisions. In particular, we found that the DR cross section is extremely sensitive to the position of the PECs of the neutral dissociative states with respect to that of the target ion. Indeed, a slight change of the crossing point of the PEC of a neutral dissociative state with that of the ion ground state can lead to a significant change in the predicted DR cross section. In addition, the PECs of the dissociative states must also go to the correct asymptotic limits for large values of the internuclear distance R.

In order to fulfil these accuracy criteria, we smoothly matched the PECs corresponding to R-matrix resonances, situated above the ion PEC, to branches of adiabatic PECs coming from previous quantum chemistry calculations (Magoulas et al 2013). Some of these latter PECs allowed us to complete the relevant diabatic landscape. More specifically, since for the states having 1 Σ + and 1 Π symmetry the avoided crossings involved always two adiabatic states only, the adiabatic PECs can be a transformed into (quasi-)diabatic PECs using a 2 × 2 rotation matrix (Roos et al 2009). Meanwhile, far from the avoided crossing, we assumed that the adiabatic and diabatic potential curves are identical. This assumption forces the rotational angle to be a function DR cross section (cm 2 )

1 ∆ 1 Π 1 Σ total process direct process Figure 2
. DR cross section for the direct (dashed lines) and the total (direct and indirect) processes (continuous lines) for each symmetry, with the ion initially in v + i = 0, that varies steeply from 0 to π/2, chosen in the present case a tangent hyperbolic function. In this way we were able to extract the diabatic PECs for the dissociative states with singlet symmetries relevant for DR. The electronic couplings provided by the R-matrix theory (Chakrabarti et al 2011) for the triplet states are at least one or even two orders of magnitude smaller then those of the singlet ones, so they are omitted in the present calculation.

The data on the PECs are limitted to internuclear distances with R ≤ 8 a 0 . We completed the diabatic PECs by adding a long-range tail of Dn C n /R n type (Stone 1996, Lepers andDulieu 2011) for larger values of R, where D is the dissociation limit as given in the (NIST Atomic Spectra Database 2016). For the ground state of BF + , the leading term C 3 /R 3 of the multipolar expansion comes from the interaction between the charge of B + and the quadrupole moment of fluorine in its ground state 2 P o (M L = 0), with M L the azimuthal quantum number of F with respect to the internuclear axis. The corresponding coefficient C 3 = Q = 0.731 a.u. [START_REF] Medved | [END_REF] gives rise to a repulsive interaction, which is balanced by the next term C 4 /R 4 of the multipolar expansion, due to the polarisation of the electronic cloud of F by the ion B + . The coefficient is given by C 4 = -α zz /2 = -1.72 a.u., where α zz = 3.43 a.u. [START_REF] Medved | [END_REF] is the static dipole polarisability of the ground state 2 P o (M L = 0) of fluorine. As for the states of the BF , the C n coefficients are calculated as fitting parameters to ensure a smooth connection with the existing part of the PECs.

The top panel of Figure 1 shows the PEC of the ion ground state -together with its vibrational structure -and the PECs of the DR-relevant dissociative states obtained using the procedure outlined above and taken into account in the present MQDT calculation. The electronic couplings of these latter states with the ionization continua, computed from the R-Matrix-produced autoionization widths followed by Gaussian-type extrapolations to small and large internuclear distances, are shown in the bottom panel of the same figure.

Results and discussion

Evaluation of the cross section using the MQDT approach

Using the set of molecular data (PECs, electronic couplings and quantum defects) determined as described in the previous section, we performed a series of MQDT calculations of cross sections for DR and competitive processes, assuming BF + to be initially in its electronic ground state X 2 Σ + and on one of its lowest vibrational levels v + i = 0, 1 and 2. We have considered that the reactive processes take place via BF-states of total symmetry of 1 ∆, 1 Π, 1 Σ + -see Figure 1 -and we neglected rotational and spin-orbit effects.

We consider incident electron energies from 0.01 meV up to 5 eV -the dissociation energy of BF + X 2 Σ + electronic state -and all the 30 vibrational levels of the ion are included in the calculations.

At very low energy, all the excited levels are associated with closed ionisation channels, as defined in section 2, responsible for temporary resonant capture into Rydberg states. As the energy increases, more and more ionisation channels open, which results in autoionization, leading to competitive processes, such as IC and SEC, and decreasing the flux of DR.

The direct electronic couplings between ionisation and dissociation channels -mentioned in paragraph (i) of section 2were extracted from the autoionization widths (see eq. ( 8)) of the valence states calculated by Chakrabarti and Tennyson (2009). )

v i + = 0 v i + = 1 v i + = 2 1 ∆ + 1 Σ + + 1 Π Figure 3.
Total DR cross sections for different initial vibrational levels of the ion, for all of the symmetries considered. Black continuous lines are for DR from v + i = 0, while the red dotted and green dashed lines are for DR from v + i = 1 and 2, respectively.

For each dissociation channel available, we considered interaction with the most relevant series of Rydberg states including only one partial wave for each symmetry. By examining the magnitude of the valence-Rydberg couplings (shown in the bottom panel of figure 1) and the positions of the crossing points between the dissociative states correlating to the B(2p 1 ) + F(2p 5 ) atomic limits with the ionic ground state -blue and black curves in the first figure of the upper panel of the same figure -at low collision energies (up to 1 eV) one may predict that the major part of the total cross section comes from the 1 ∆ symmetry (solid black line in figure 2), while the 1 Σ and 1 Π symmetries (solid green and red lines in the same figure) only make a minor contribution to the cross section. The importance of these latter two symmetries is revealed at higher collision energies, when the crossing of the first dissociative state with the molecular ion becomes favorable. At collision energies about 1 eV, the 1 Σ + states give a larger contribution to the DR cross section than the 1 ∆ symmetry, which in turn is exceeded by the 1 Π symmetry at about 2 eV. Moreover, one can notice that at higher collision energies, around 3.5 eV, when all the dissociative states are open, the DR cross section shows a sharp revival and, at 5 eV, the resonance structures disappear since all the ionization channels are open, and consequently the direct process only drives the DR.

Figure 2 shows the importance of the indirect process for the DR of vibrationally relaxed BF + at low energies. Within the 1 ∆ symmetry, the entrance ionization channel associated with the v + i = 0 state is strongly coupled to the dissociation continuum (see Figure 1), allowing the direct process to dominate. The indirect process diminishes the cross section destructive interferences with the direct one -due to stronger coupling between closed channels associated with highly-excited vibrational levels -v + = 12 -16 -and the dissociative ones.

Within the 1 Π symmetry one finds the opposite. The direct process gives only a minor contribution to the DR cross section, due to the poor Franck-Condon overlap between the vibrational wave function of the initial state of the ion and the dissociative neutral states. However, the much stronger couplings between some closed ionisation channels -v + = 8 -10 -and the dissociative states significantly increases the total cross section through the indirect mechanism [START_REF] Pop | AIP Conf. Proc[END_REF], Schneider et al 2012) resulting into constructive quantum interferences.

Finally, for the states with 1 Σ + symmetry, the indirect process plays a relatively minor role, the magnitude of the total cross section being given mainly by the direct process. The indirect process is responsible for resonant structures which are a consequences of both constructive and destructive interference.

For a given initial vibrational level of BF + , the total DR cross section is obtained by summing over the partial cross sections of the three symmetries contributing to the process -1 ∆, 1 Π and 1 Σ + -given in eq, ( 6). The results of the calculations performed for the lowest three vibrational levels of the ground electronic state of the ion are shown in Figure 3.

Reaction rate coefficients for DR and its competitive processes

Besides the dissociative recombination cross sections presented in Figure 3, we use eq. ( 7) to calculate the vibrational excitation (VE) and de-excitation (VdE) cross sections for the same vibrational levels of the target. Since many of the features of the VE and VdE cross sections either are similar to, or may be understood with the same reasoning as those of DR, we do not display them here. Instead, we present in this section their Maxwell rate coefficients for a broad range of electronic temperatures, in

= |v + f -v + i |; v + f > v + i for the VE and v + f < v + i
for the VdE global rate coefficients. The final vibrational quantum numbers of the ion are indicated for these processes.

comparison with those of the DR. All these data are relevant for cold non-equilibrium plasmas.

Figure 4 shows the total DR and vibrational transition -VE and VdE -rate coefficients for the three lowest vibrational levels of the ion. The DR rate for v + i = 0 shows different behaviour to those for the v + i = 1 and 2 states. It has a maximum at an electron temperature T e of about 400 K, while the rates for the other two states are monotonically decreasing with T e , reaching nearly the same magnitude at higher temperatures. This behaviour for v + i = 0 comes from the strong resonant peaks just below 0.01 eV, see Figure 2 and black curve in Figure 3.

For other recently studied molecular systems, N 2 (Little et al 2014) and CO (Mezei et al. 2015), the DR clearly dominates the electron-ion collisions. However, for BF the calculated VdE rate coefficients are larger than the DR-ones, and VE rate coefficients exceed the DR-ones at high T e by almost an order of magnitude. Thus, one can conclude that in the case of the BF + containing plasma, the internal vibrational energy is much more important for energy-exchange via VE and VdE, than the kinetic energy release via the exothermic DR.

To facilitate the use of our rate coefficients (Figure 4) in modeling calculations, we fit them using modified Arrhenius-type formulas. The calculated DR rate coefficients for v = 0, 1, 2 are given by :

k DR BF + ,v (T e ) = A v T e αv exp - 7 i=1 B v (i) i • T e i ( 9
)
over the electron temperature range 100 K<T e < 3000 K. The parameters A v , α v , and B v (i) are listed in table 1. The corresponding formula for the vibrational transitions (VE and VdE) has the form:

k DR BF + ,v →v (T e ) = A v →v T e α v →v exp - 7 i=1 B v →v (i) i • T e i ( 10
)
over the electron temperature range T min <T e < 3000 K. The parameters T min , A v →v , α v →v , and B v →v (i) for i = 1, 2, . . . , 7 are given in tables 2-4.

Table 1. Parameters used in equation ( 9) to represent the DR rate coefficient of BF + . Powers of 10 are given in square brackets.

Figure 1 .

 1 Figure1. The dissociative states and electronic couplings relevant for BF + dissociative recombination within the major symmetries, indicated in each figure. Top panel: the potential energy curves of the dissociative BF * * states (colour, cf section 3), the ground state potential energy curve of BF + and its vibrational levels (black). Bottom panel: couplings between the valence BF * * dissociative states and the ionisation continua BF + + e -.

Figure 4 .

 4 Figure 4. DR and state-to-state VE and VdE Maxwell rate coefficients of BF + in its ground electronic state, v + i standing for the initial vibrational quantum number of the target ion. Curves of the same color show the rate coefficients for the vibrational (de-)excitations corresponding to the same |∆v|= |v + f -v + i |; v + f > v + i for the VE and v + f < v + ifor the VdE global rate coefficients. The final vibrational quantum numbers of the ion are indicated for these processes.

  703050632[-5] -0.108298227[1] -0.363984388[2] 0.68522753[6] -0.341534791[9] 0.86262362[11] -0.117919938[14] 0.821543800[15] -0.229194862[17] 1 0.205402433[-11] 0.557133316[0] -0.185580405[4] 0.110399946[7] -0.316387400[9] 0.531242790[11] -0.525109108[13] 0.283203635[15] -0.643843159[16] 2 0.144845145[-5] -0.806777388[0] 0.285629778[4] -0.322036339[7] 0.160926033[10] -0.409338097[12] 0.558087964[14] -0.388815002[16] 0.108682270[18]

  , NO + (Sun and Nakamura 1990, Vâlcu et al 1998, Schneider et al 2000a) and triatomics like H + 3 (Schneider et al 2000b, Kokoouline et al 2001, Kokoouline and Greene 2003), and for its competitive processes like ro-vibrational transitions in case of NO + (Motapon et al 2006), CO + (Mezei et al. 2015) and H + 2 (Ngassam et al 2003a, Epée Epée et al 2015). Recently, a global version of MQDT (Jungen 2011) has been used to describe the photoabsorption, photoionisation and photodissociation of H 2 (Mezei et al 2012, Mezei et al 2014, Sommavilla et al 2016), providing very good agreement with highly accurate experimental results.

Acknowledgments

The authors acknowledge support from the International Atomic Energy Agency (IAEA, Vienna) via the Coordinated Research Project "Light Element Atom, Molecule and Radical Behaviour in the Divertor and Edge Plasma Regions", from the French Agence Nationale de la Recherche via the projects "SUMOSTAI" (No. ANR-09-BLAN-020901) and "HYDRIDES" (No. ANR-12-BS05-0011-01), from the IFRAF-Triangle de la Physique via the project "SpecoRyd", and from the Centre National de la Recherche Scientifique via the programs "Physique et Chimie du Milieu Interstellaire", and the PEPS projects "Physique théorique et ses interfaces", TheMS and TPCECAM. They also acknowledge generous financial support from Région Haute-Normandie via the CPER "THETE" project, and the GRR Electronique, Energie et Matriaux, from the "Fédération de Recherche Energie, Propulsion, Environnement", and from the LabEx EMC 3 , via the project PicoLIBS (No. ANR-12-BS05-0011-01). KC thanks the Institut des Sciences de l'Ingénierie et des Systèmes (INSIS) of CNRS for a research grant in 2013, and the Laboratoire Ondes et Matériaux Complexes (LOMC) of Le Havre University for hospitality. SI, NP and IFS acknowledge EU for financial support via the ERASMUS convention between Le Havre University and Politehnica University of Timisoara.

Table 3. Parameters used in equation ( 10) to represent the VE rate coefficient of BF + (v = 1). Powers of 10 are given in square brackets. Table 4. Parameters used in equation ( 10) to represent the VE rate coefficient of BF + (v = 2). Powers of 10 are given in square brackets.

Conclusion

This paper presents a theoretical study of the dissociative recombination of BF + and of its competitive processes -vibrational excitation and de-excitation -over a broad range of electron energies -up to about 5 eV -and considering all the relevant dissociative states within different symmetries. Our MQDT dynamical approach is relying on molecular data calculated by the ab initio R-matrix method, completed by quantum chemical results. The computed Maxwell rate coefficients are relevant for the kinetic modelling of molecule based cold non-equilibrium plasmas, in the context of complete lack of other theoretical or experimental data on these processes for this cation. The present calculations complete our very recent studies of the DR performed on N + 2 (Little et al 2014) and on CO + (Mezei et al. 2015) based on fully ab initio potential energy curves and couplings computed with the R-matrix method (Tennyson 2010), since BF + is isoelectronic with these two molecular systems. We note that while there is no experimental data available for the processes considered here for BF + , our previous calculation on N + 2 and CO + gave good agreement with the available measurements.