Nicolas Fil

Mohamed Belhaj

Julien Hillairet

Jérôme Puech

Renaud Mathevet

Electron emission under uniform magnetic field of conductor materials used for spatial and fusion applications

INTRODUCTION

The multipactor effect can decrease the performance of Radio-Frequency (RF) systems functioning under vacuum. Multipactor is a resonance effect between the RF electric field and the motion of the electrons [START_REF] Vaughan | Multipactor[END_REF]. It highly depends on the electron emission properties of the RF component materials. Applications using these kind of components are telecommunication satellite [START_REF] Lara | Multipactor prediction for on-board spacecraft RF equipment with the MEST software tool[END_REF], fusion experimental reactors with Tokamak [START_REF] Goniche | Modelling of power limit in RF antenna waveguides operated in the lower hybrid range of frequency[END_REF] or particle accelerators [START_REF] Rumolo | Simulation of the electron-cloud build up and its consequences on heat load, beam stability, and diagnostics[END_REF] among others. Many experimental [START_REF] Udiljak | New method for detection of multipaction[END_REF] and theoretical [START_REF] Al-Mudhafar | Investigation of Multipactor Effect in Satellite Components Using CST Particle in Cell Solver[END_REF]- [START_REF] Anza | Recent Developments on FEST3D / SPARK3D simulation tools[END_REF] works have been conducted to study this undesirable phenomenon. The aim of these approaches is to determine the multipactor power threshold. Above this threshold, multipactor can appears and damage RF systems. In some applications concerned by the multipactor effect, RF components are submitted to DC magnetic fields. For instance, in telecommunication satellite, magnetic fields of a few tenths of Tesla produced with permanent magnets are used in circulators and isolators. In fusion reactors, rectangular copper waveguides are located under intense magnetic fields of few Tesla generated by toroidal and poloidal coils. Multipactor simulations codes are used to calculate the threshold that would trigger the electron density growth by following the electrons under the RF wave electromagnetic field [START_REF] Romanov | Update on multipactoring in coaxial waveguides using {CST} Particle Studio[END_REF], [START_REF] Semenov | Multipactor in rectangular waveguides[END_REF]. Multipactor modeling can also take into account an external magnetic field. It induces gyratory motions of electrons within the simulated RF structure. Studies have been made on the effect of external magnetic field on multipactor discharge [START_REF] Valfells | Effects of an external magnetic field, and of oblique radio-frequency electric fields on multipactor discharge on a dielectric[END_REF]. However, to our knowledge, there are no multipactor simulation codes which take into account the influence of DC magnetic field on the electron emission process. In this paper we will often speak about incident, primary, secondary and backscattered electrons. Here we specify the definitions and nomenclature. Incident electron (IE) is electron which impacts a material surface. At this impact, IE can penetrate the material and then transfer a part of its energy through inelastic interactions. The IE can excite inner material electron which could escape the material surface [START_REF] Rosler | Theory of Electron Emission from Solids by Proton and Electron Bombardment[END_REF]: in this case the electron emitted is called secondary electron (SE). The IE can also escape the surface material due to several inelastic and elastic interactions: in this case the electron emitted is called backscattered electrons (BSE). Primary electron (PE) term is used to define all the electrons generated by an electron gun. Experimentally, an electron gun is used to provide a quasi mono-energetic primary electron beam. We commonly define the Total Electron Emission Yield (TEEY, σ) which is the number of the whole electrons emitted by the surface material divided by the number of IE.

To study the effect of the magnetic field on the Total Electron Emission Yield (TEEY), a new experimental setup has been developed. The measurement of the TEEY under magnetic field is challenging since the magnetic field affects the trajectory of the electrons. A special attention to the design of the experimental setup and to the choice of the measurement methodology has been taken to circumvent the possible artefacts that are related to the high sensitivity of incoming and emitted electrons trajectories to the DC magnetic field. In this paper, the new developed experimental setup and the measurement methods are described in details. Thereafter, the validation procedure of the TEEY measurement methodology based on both experiments and modeling with SPIS code [START_REF] Roussel | Spacecraft Plasma Interaction Software (SPIS): Numerical Solvers Methods and Architecture[END_REF] is given. TEEY measurements on copper under a normal DC magnetic field are also presented. In the last section we give the works under investigation which continue our study of the influence of the DC magnetic field on electron emission properties.

A NEWLY EXPERIMENTAL SETUP

The experimental setup presented hereafter aims to measure TEEY with magnetic field. First we introduce the setup and its operation. Then we explain the validation procedure that has been made with the help of both measurements and modeling. We use an available vacuum chamber of 34 mm 3 . Working with magnetic field implies to deal with a certain amount of magnetic energy. To obtain the higher magnetic field amplitude as possible while using the lowest coil current, we need to work with the smallest coil as possible. We also need to avoid outgassing in vacuum, so the coil has been placed outside the vacuum vessel, as close as possible to the sample (see the two reducers on Fig. 1). A 41 mm-diameter copper coil has then been directly built on the reducer CF100CF40 tube. A cooling system can be added to prevent overheating of the coil if higher fields are required. The 10 mm-disc sample is located in a 110 mm high cylinder composed of eight pieces with a cylindrical collector. Both are isolated from each other and from the ground. We measure the sample current (I S ) and the collector current (I C ) independently. By connecting the sample and the collector together, the system becomes a Faraday cup, which is used to measure the incident current (I F ). The sample surface was placed in the plane at the center of the solenoid in the plane perpendicular to its axis in such way that the field was normal to the surface and nearly uniform around the sample (we calculated magnetic field nonuniformity well below 1% across the whole sample). The magnetic field amplitude has been measured along the coil axis thanks to a Gaussmeter and a hall-effect sensor longitudinal probe. A 1 A current on the coil generates an 11.3 mT magnetic field at the sample surface. The vacuum vessel can reach a pressure of 10 -8 mbar thanks to turbomolecular pump. A 1eV-2keV ELG 2 Kimball Physics electron gun was used to provide a quasi mono-energetic primary electron beam. The output electron gun diaphragm was placed as close as possible to the sample surface to minimize the influence of the magnetic field on the primary electrons trajectories. The electron gun can operate in continuous or pulsed mode. In this paper, all measurements presented have been made in continuous mode. The sample as well as the collector can be independently biased to positive or negative voltage.

Description

Validation with measurements on copper samples

Before studying the influence of the magnetic field on TEEY, the chosen measurement method was validated by measuring the TEEY on copper without DC magnetic field. First, the primary electron current (I F ) was measured by biasing the electrical connected sample and collector at +18V (faraday cup configuration). Then the sample was disconnected from the collector and biased to -9V (the collector remains at +18V) and both the sample current (I S ) and the collector current (I C ) were measured. The sample was negatively biased with respect to the collector in order to avoid recollection of secondary or backscattered electrons [START_REF] Belhaj | Analysis of two methods of measurement of surface potential of insulators in SEM: electron spectroscopy and X-ray spectroscopy methods[END_REF]. This is crucial to get coherent TEEY results: the sample current (I S ) is only due to primary electrons impacts. From I F , I S and Ic measurements the yield can be deduced thanks to one of the expressions (1), ( 2) or (3) below [START_REF] Tondu | Methods for measurement of electron emission yield under low energy electron-irradiation by collector method and Kelvin probe method[END_REF].

𝑌𝑖𝑒𝑙𝑑 1: 𝜎 = 𝐼 𝑐 𝐼 𝑓 (1)
𝑌𝑖𝑒𝑙𝑑 2: 𝜎 = 𝐼 𝑓 -𝐼 𝑠 𝐼 𝑓 (2)
𝑌𝑖𝑒𝑙𝑑 3: 𝜎 = 𝐼 𝑐 𝐼 𝑐 + 𝐼 𝑠 (3)
According to the current conservation law (I F = I S + I C ), the quantities defined by the expressions (1), ( 2) and ( 3) should be strictly equal. Any difference reflects an error in the measurement of I c , I F or I S [START_REF] Tondu | Methods for measurement of electron emission yield under low energy electron-irradiation by collector method and Kelvin probe method[END_REF]. Fig. 2 compares the yields deduced by using the three expressions. Theses TEEY were measured twice to check the result reproducibility. For both set of measures we see similar yields which validate the chosen measurement methodology as well as the experimental setup. The very good agreement observed between measurement 1 and measurement 2 confirms the good reproducibility of the measurements on our experimental test-bed.

When measuring the three currents, the oscilloscope gives us respective absolute uncertainties from which we calculate the statistical error on the yields to be less than 1% for all measurements. The main source of experimental uncertainties comes from the stability of the electron gun power supply, especially from grid and focus tensions. Moreover, the cathode's resistance temperature and the chamber's pressure vary with time. The primary electrons have 0.5eV dispersion in energy set while the conical electron beam has an aperture angle up to 8°. Other experimental errors are coming from evaporation and contamination from both the electron gun and the sample. When we work with a magnetic field, the heat from the coil leads to outgassing from inner materials. Taking all these contributions into account makes the determination of the electron emission measurements uncertainty difficult. It also explains the small discrepancy between Measures 1 and 2 on Fig. 2.

Fig. 2. TEEY measurements on laminate copper sample. Measures 1 and 2 have both three yields calculated from three formulas (1), ( 2) and (3).

First TEEY measurements under magnetic field

Thanks to the validation presented in the previous section, we can now make TEEY measurements under magnetic field. First we study the current conservation law (I F = I S + I C ) when a magnetic field is generated. We work with 1Acurrent on the coil which generates an 11.3 mT magnetic field at the sample surface. We measured the primary electron current (I F ) in faraday cup configuration. Then the sample was disconnected from the collector and biased to -9V (the collector remains at +18V) and both the sample current (I S ) and the collector current (I C ) were measured. Fig. 3 compares the yields deduced by using the three expressions (1), ( 2) and (3). We see different yield which means that the current conservation law is not verified with an 11.3 mT magnetic field at the sample surface. The main difficulty in measuring electron emission under a magnetic field comes from electron motions. The effect of a DC magnetic field is to bend the trajectories of charged particles which influences not only the motion of the primary electrons but also secondary and backscattered electrons. We observe during measurements a variation of the primary electron current (I F ) in faraday cup configuration in function of the intensity of the magnetic field while all the others parameters stay constants (voltages of our system, electron gun parameters, oscilloscope settings). We also see variations of the collector current (I C ) when only the magnetic field intensity varies.

To interpret and understand our TEEY measurements under magnetic field, we have thus created a model of our system with SPIS software. In SPIS simulations, we can control the potentials of our system as well as the primary electron beam (angle and energy) and study the trajectories of the three types of electrons (primary, secondary and backscattered) under a homogenous magnetic field.

Test-bed modeling with SPIS software SPIS (Spacecraft Plasma Interaction System) is a software toolkit for spacecraft-plasma interactions and spacecraft charging modelling [START_REF] Roussel | Spacecraft Plasma Interaction Software (SPIS): Numerical Solvers Methods and Architecture[END_REF]. It allows users to model the plasma dynamics (kinetic or fluid, electrostatic or electromagnetic) and its coupling with the spacecraft (equivalent circuit approach). All kinds of environments and systems are supported. SPIS allows us to make simulations with a uniform and a homogenous magnetic field.

We have created a model of our system represented on Fig. 1. The goal is to determine where the primary, secondary and backscattered electrons are collected in function of experimental measurement configuration. Our model is made to get these information for the sample, the collector, the inner flanges (Reducer CF200/CF100+Reducer CF100/CF40+Flange CF40), the sample support, the vacuum vessel and the emission surface of the electron gun. The primary electrons are generated by a surface of π mm² representing the emission surface of the electron gun used in our experimental test-bed. SPIS simulations follow each charged particle. When an electron impacts a surface, SPIS calculates the response thanks to secondary electron emission models [START_REF] Katz | A three dimensional dynamic study of electrostatic charging in materials[END_REF]. The emitted electrons (secondary and backscattered) are also followed by the simulation until the next impact. It is important to notice that SE and BSE can also generate SE and BSE from their impacts with materials; these electrons are commonly called tertiary electrons which can also generate SE and BSE and so on. SPIS software follows all the electrons generated and the outputs give the contributions of all SE and BSE. We study on which surface the primary, secondary and backscattered electrons are collected. We made simulations to study the influence of the magnetic field strength on the electrons trajectories. We also investigate the impact of potential and primary electron energy variations. The magnetic field strength has been varied from 0 to 1.132 T while the primary electron energy from 5 to 2000 eV. We have tested many collector potentials (from +9 to +2000 V) while the sample is maintained at -9 V.

The applied DC magnetic field induces a primary electron beam narrowing or widening depending on the magnetic field strength and the primary electron energy. When the magnetic field is under 39.2mT, all primary electrons (from 0 to 2000 eV) are collected by the sample surface. But if we increase the magnetic field strength up to 113.2 mT, primary electrons below than 100eV goes on both sample and collector surfaces while primary electrons of more than 250eV are collected by the sample surface only. At 1.132 T all primary electrons (from 5 to 2000 eV) are collected by the collector, no one reaches the sample. In this last configuration, we cannot measure the sample current (I S ), the experimental setup should be modified to do so. The emitted electrons (secondary and backscattered) trajectories are also modified: without magnetic field, nearly all the emitted electrons impact the collector but with a magnetic field they escape the system and impact the wall of the vacuum vessel instead impacting the collector. With this SPIS simulation results we find the behavior experimentally observed on Fig. 3; electron escapements explain why the current conservation law is not verify when TEEY is measured under magnetic field. As the consequence, the expressions ( 1) and ( 3) lead to lower yields values and we get measurements like those represented on the Fig. 3. We cannot use these two expressions to calculate the TEEY under magnetic field, but the expression ( 2) is still useful as it is independent of the collector current. There is one necessary condition to use the expression (2): the measure of the sample current (I S ) must be free of electron recollection phenomenon on the sample surface. It means that secondary and backscattered electrons should not be collected by the sample surface. This is verified with SPIS simulation. This last point is illustrated in Fig. 4 which shows the electrical potential map surrounding the sample: no potential barrier is seen which could make SE or BSE recollected by the sample surface. A clipping plane representing the surface where SE and BSE electrons are collected is also given. The sample is not collecting the SE or BSE electrons.

Fig. 4. SPIS modelling of the setup. The whole system is showed on the left while the electrical potential map is represented in the middle. On the right, a clipping plane of the system represents the surface where SE and BSE are collected.

TEEY UNDER MAGNETIC FIELD

After the validation and calibration procedures, TEEY measurements under magnetic field were performed. Each configuration is verified with SPIS simulations. Some results are shown in Fig. 5. For the first two series (measure 1 & 2), no magnetic field has been used while a 4.53 mT and 11.3 mT magnetic field was applied normal to the surface in measures 3 and 4. For all primary electron energies we observe a decrease of the TEEY when the magnetic field was applied. The effect of the field increases with its amplitude. These first results still need further investigations before drawing any final conclusion. We know, thanks to simulations on SPIS, that there no artefact due to the experimental setup. We also observe that 4.53 mT and 11.3 mT magnetic fields induce a primary electron beam narrowing which decreases the sample surface impacted. We then need to study the relation between the magnetic field intensity and the conditionning effect [START_REF] Kirby | Secondary electron emission yields from PEP-II accelerator materials[END_REF] as well as the Dose effect [START_REF] Kumar | The Dose Effect in Secondary Electron Emission[END_REF].

Fig. 5. TEEY measurements on laminate copper sample with and without magnetic field perpendicular to the surface sample

FUTURE WORKS

We are working on making new measurements and modeling with different magnetic field amplitudes as well as different morphology surface samples. We are investigating the correlations between surface morphology and magnetic field amplitude on electron emission intensity. The magnetic field bends electron's trajectories which could make recollections of secondary and backscattered electrons or in contrary help them to escape from sample surface. We can also have conditionning and dose effects due to the magnetic field. These effects are under investigations and depend on the electrons energies, the magnetic field amplitude and the sample morphology surface.

We are making studies which involve both experiments and SPIS modeling. First we want to measure TEEY on polished copper. Many ways to obtain low roughness copper sample is under investigation such as mechanical polishing and electro-polishing. Simulations on SPIS already show no SE and BSE recollections by the sample with and without magnetic field. This kind of samples will give us new information on our experimental setup as well as on conditionning and dose effects.

In a second time, we study specific surface morphologies. We are working on three dimensions periodic morphology surfaces made with rectangular or pyramidal blocks (Fig. 6) [START_REF] Wang | SUPPRESSION OF SECONDARY EMISSION IN A MAGNETIC FIELD USING A SAWTOOTH AND ISOSCELES TRIANGLE SURFACE[END_REF], [START_REF] Chang | Review of recent theories and experiments for improving high-power microwave window breakdown thresholds[END_REF]. This figure shows SPIS modeling and we want to create some of these surfaces on real samples in order to make TEEY measurements under magnetic field. Fig. 6. SPIS modeling of four samples in order to the correlations between surface morphology and magnetic field amplitude on electron emission properties.

First SPIS simulation results show that the plane sample has no recollection of SE and BSE for magnetic field amplitude of 0, 0.0001, 0.001, 0.01, 0.1 and 1 T. For the other three samples, we observe recollection of SE and BSE from the samples. We discern if the electrons are collected by the top surfaces of the blocks, by the lateral surfaces of the blocks or by the surfaces between the blocks. We determine the percentages of PE, SE and BSE collected by each of these surfaces as well as by the sample support surface or by the surrounding surface.

For example if we study the Fig. 6 -sample 4 at PE energy of 250eV, we can make the Table 1. We first see a narrowing of the primary electron beam due to the magnetic field: the percentage of PE collected by the blocks top surfaces increase with the magnetic field amplitude. We also observe an increase of the SE and BSE collection by the blocks lateral surfaces with an increase of the magnetic field intensity. Then the vacuum vessel collected current decreases with the magnetic field intensity which means that the number of electrons emitted by the sample decreases with the magnetic field intensity. This leads to a decrease of the TEEY. SPIS simulations are being made for each samples presented on Fig. 6 and for other samples. Results depend on the primary electron energy and the magnetic field amplitude.

CONCLUSION

As a step toward understanding the effect of the magnetic field on the electron emission proprieties under electron impact, a new experimental setup has been developed. This setup is dedicated to measure the Total Electron Emission Yield under a magnetic field perpendicular to the sample surface. Thanks to measurements and PIC modeling we have validated the measurement methodology. First results show a decrease of the TEEY when the magnetic field is applied but we still need further investigations before drawing any final conclusion. We are working on making new measurements and modeling with different magnetic field amplitudes as well as different morphology surface samples. We are investigating the correlations between surface morphology and magnetic field amplitude on electron emission properties.

Fig. 1 .

 1 Fig. 1. Illustrations of the experimental setup. I S is the sample current while I C is the collector current.

Fig. 3 .

 3 Fig.3. TEEY measurements under magnetic field perpendicular to the surface laminate copper sample. Measure 4 has been made with an 11.3mT magnetic field at the coil center. The yields are calculated from the three formulas (1),[START_REF] Lara | Multipactor prediction for on-board spacecraft RF equipment with the MEST software tool[END_REF] and (3).

Table 1 .

 1 Percentages of collected currents from PE, Se and BSE on surfaces of the sample 4 in function of the magnetic field amplitude. SPIS simulations made with primary electron energy of 250eV.

	Electron type	Surface definition	B = 0 T	Percentage of collected current on surfaces B = 0.16 T	B = 1.6 T
		Blocks top surfaces	0.4	1.5	1.4
		Blocks lateral surfaces	1.5	9.4	18.2
	Primary Electrons (PE)	Surfaces between blocks	98.1	89.1	80.4
		Sample support surfaces	0	0	0
		Vacuum vessel	0	0	0
		Blocks top surfaces	0	0	0
		Blocks lateral surfaces	3.5	19.7	86.9
	Secondary Electrons (SE)	Surfaces between blocks	0.4	0.4	0
		Sample support surfaces	0	0	0
		Vacuum vessel	96.1	79.9	13.1
		Blocks top surfaces	0	0	0
	BackScattered Electrons (BSE)	Blocks lateral surfaces Surfaces between blocks Sample support surfaces	7.9 1.3 0	13.6 7.0 0	29.2 1.5 0
		Vacuum vessel	90.8	79.4	69.3


PhD, MSc Catherine Potard
email: catherine.potard@univ-angers.fr

MSc Cle ´mence Landais

Relationships between frustration intolerance beliefs, cognitive emotion regulation strategies and burnout among geriatric nurses and care assistants

Keywords:

The purpose of this study was to address cognitive emotional factors (frustration intolerance beliefs, cognitive emotion regulation strategies) related to burnout among professionals caring for older persons. A sample of 202 nurses and care assistants for older people completed online questionnaires about their cognitive emotion regulation strategies, frustration intolerance beliefs, and burnout. Use of maladaptive strategies, especially self-blame and catastrophizing, predicted greater emotional exhaustion and depersonalization. Adaptive strategy use, such as refocusing on planning and positive reappraisal, was found to be linked to both lower emotional exhaustion and higher personal accomplishment. Frustration intolerance beliefs appeared to be closely associated with the emotional exhaustion and depersonalization dimensions of burnout, with higher frustration intolerance beliefs indicating a high risk of depersonalization. The present findings have several practical implications for reducing nurses' burnout based on cognitive behavioral therapy approaches, such as rational emotive behavior or mindfulness therapies.

Introduction

Geriatric care is an inherent occupational stressor for healthcare professionals, potentially contributing to the development of occupational burnout syndrome. [START_REF] Mantzorou | Professional burnout of geriatric nurses caring for elderly people with dementia[END_REF] According to Maslach and Leiter, 2 burnout is a "syndrome of emotional exhaustion, depersonalization, and reduced personal accomplishment that can occur among individuals who do 'people work' of some kind" (p. 3). The burnout syndrome is classically described on three interrelated dimensions. [START_REF] Maslach | Understanding the burnout experience: recent research and its implications for psychiatry[END_REF][START_REF] Maslach | What have we learned about burnout and health?[END_REF] (1) Emotional exhaustion (EE) refers to feeling overextended, and physically and emotionally depleted at work (Maslach et al., 2001). Individuals experience a loss of energy, fatigue and weakness. (2) Depersonalization (DP; or cynicism) occurs when a worker shows emotional detachment or distance from patients and work colleagues. This can manifest itself in impersonal, detached and negative attitudes toward patients. Cynicism and lack of empathy can occur. (3) Low personal accomplishment (PA) describes a negative self-evaluation of professional competence, efficacy, and personal achievement at work. A combination of higher EE and DP with lower PA is considered to be symptomatic of burnout. [START_REF] Maslach | What have we learned about burnout and health?[END_REF] As burnout mainly occurs in a helping relationship, it is primarily found in healthcare professionals. A recent review reported a burnout risk score of 25-75% among healthcare professionals in geriatric settings. [START_REF] Sanchez | Burnout in the field of geriatric medicine: review of the literature[END_REF] Despite this broad range, an international consensus has been built around the figure of 25-30%. Burnout is particularly prevalent among nurses working in a geriatric setting [START_REF] Cocco | How Much is geriatric caregivers burnout caring-specific? Questions from a questionnaire survey[END_REF] and with residents with dementia. [START_REF] Costello | Burnout in UK care home staff and its effect on staff turnover: MARQUE English national care home longitudinal survey[END_REF] A European study showed that caregivers working in longstay geriatric services or nursing homes were the most exhausted in their work, which is often physically difficult, especially in France. For example, in France, they are off work for twice as long as their colleagues in other European countries, and mean exit rates are 61% for nurses and 68% for nursing auxiliaries in nursing homes for dependent elderly people (EHPADs). [START_REF] Mccain | A study of the relationship between resilience, burnout and coping strategies in doctors[END_REF] In one study among French nurses and care assistants in geriatric settings, [START_REF] Estryn-Behard | La souffrance au travail en ge ´riatrie. Comprendre et agir[END_REF] 50.1% of participants exhibited signs of burnout. Another recent survey showed that 8.5% of staff in French assisted living facilities belonging to one private company had burnout. [START_REF] Zawieja | Burnout des soignants en ge ´riatrie : Pre ´valence et de ´terminants dans 185 e ´tablissements franc ¸ ais[END_REF] Burnout has been shown to have an impact on both mental (e.g., anxiety, depression) and physical (e.g., headaches, digestive disorders, insomnia, cardiovascular diseases) health, [START_REF] Harrad | Factors associated with and impact of burnout in nursing and residential home care workers for the elderly[END_REF] and affects individuals' professional (e.g., job satisfaction, sick leave, turnover, absenteeism [START_REF] Leiter | Nurse turnover: The mediating role of burnout[END_REF] ) and older person's well-being (e.g., mistreatment, lower perceived quality of care [START_REF] Neuberg | Is the burnout syndrome associated with elder mistreatment in nursing homes: results of a cross-sectional study among nurses[END_REF][START_REF] Schmidt | The satisfaction with the quality of dementia care and the health, burnout and work ability of nurses: a longitudinal analysis of 50 German nursing homes[END_REF] ).

Factors that can lead to burnout among health professionals caring for the older persons may be either organizational, such as time pressure to perform monotonous tasks, lack of control, unrealistic expectations or unreasonable demands [START_REF] Harrad | Factors associated with and impact of burnout in nursing and residential home care workers for the elderly[END_REF] or individual, such as personality traits or coping strategies. [START_REF] Narumoto | Relationships among burnout, coping style and personality: study of Japanese professional caregivers for elderly[END_REF] In particular, studies have suggested that emotion and problem-focused coping strategies play a crucial role in predicting burnout level. [START_REF] Montero-Marin | Coping with stress and types of burnout: explanatory power of different coping strategies[END_REF] Research indicates that active problem-focused strategies such as planful problem solving (i.e., deliberate problem-focused efforts to alter a situation, such as making and then following a plan of action), positive reappraisal, and seeking social support, are negatively associated with burnout symptoms (especially high DP and low PA [START_REF] Garrosa | The relationship between job stressors, hardy personality, coping resources and burnout in a sample of nurses: a correlational study at two time points[END_REF] ) among nurses. [START_REF] Duquette | Psychosocial determinants of burnout in geriatric nursing[END_REF] By the same token, burnout, especially EE and DP, may partly stem from the use of ineffectual emotion-focused coping strategies such as avoidance and distraction [START_REF] Duquette | Psychosocial determinants of burnout in geriatric nursing[END_REF] among nurses and care assistants. [START_REF] Narumoto | Relationships among burnout, coping style and personality: study of Japanese professional caregivers for elderly[END_REF] Thus, emotional responses to a stressful job can also be controlled or regulated through the use of cognitive emotion regulation strategies, [START_REF] Garnefski | The cognitive emotion regulation questionnaire[END_REF] describing conscious cognitive strategies for monitoring and regulating responses to stressful life events. [START_REF] Aldao | Emotion-regulation strategies across psychopathology: a meta-analytic review[END_REF][START_REF] Garnefski | Cognitive emotion regulation strategies and psychological adjustment in adolescents with a chronic disease[END_REF] Nine such strategies have been identified: (1) self-blame (blaming oneself for what has happened); (2) blaming others; (3) acceptance (accepting that the event has happened and resigning oneself); (4) refocus on planning (thinking about the next steps and how to manage the negative event); ( 5) positive refocusing (focusing on positive experiences); ( 6) rumination (being preoccupied by thinking about the feelings and thoughts generated by the negative situation); ( 7) positive reappraisal (assigning a positive meaning to the negative situation); (8) putting into perspective (minimizing the importance of the negative event); and ( 9) catastrophizing (having recurrent thoughts about the severity of the event and how it is the worst experience that could happen to someone). Garnefski and Kraaij [START_REF] Garnefski | The cognitive emotion regulation questionnaire[END_REF] suggested making a distinction between adaptive (acceptance, refocus on planning, positive refocusing, positive reappraisal, and putting into perspective) and maladaptive strategies (self-blame, rumination, blaming others, and catastrophizing). Research indicates that maladaptive strategies are associated with the burnout of professional caregivers working with older people, [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF][START_REF] Castellano | Cognitive processes of emotional regulation, burnout and work engagement[END_REF][START_REF] Bamonti | Cognitive emotion regulation strategies predict burnout in geriatric nursing staff[END_REF] especially EE symptoms. [START_REF] Bassal | Relationship between emotions, emotion regulation, and well-being of professional caregivers of people with dementia[END_REF] Higher acceptance and rumination are associated with higher levels of EE among care assistants employed in long-term care [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF] . Positive reappraisal is negatively related to DP. [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF] Refocus on planning and positive reappraisal are related to PA. [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF][START_REF] Castellano | Cognitive processes of emotional regulation, burnout and work engagement[END_REF] These promising findings underline the specific role of cognitive emotion regulation strategies in healthcare burnout, [START_REF] Jackson-Koku | Emotion regulation and burnout in doctors: a systematic review[END_REF] but need to be replicated with larger samples, focusing on geriatric settings (i.e. hospitals, nursing home, and home care institutions). Moreover, several cognitive coping processes, such as catastrophizing, blaming others, and rumination, are associated with negative emotions, [START_REF] Martin | Cognitive emotion regulation in the prediction of depression, anxiety, stress, and anger[END_REF] and are often employed to deal with the daily frustration [START_REF] Garnefski | Negative life events, cognitive emotion regulation and emotional problems[END_REF] and emotions reported by professional caregivers. [START_REF] Rae | Managing feelings: caregiving as emotion work[END_REF] It may be particularly important to examine caregivers' frustration, as it has been characterized as the stage prior to burnout. [START_REF] Maslach | What have we learned about burnout and health?[END_REF][START_REF] Bridgeman | Burnout syndrome among healthcare professionals[END_REF] Frustration intolerance is another emotional cognitive process (evaluative cognition), based on a refusal to accept the difference between desire and reality, that has unhealthy emotional and behavioral consequences. [START_REF] David | Rational and irrational beliefs[END_REF] Frustration intolerance is essentially an "attempt to shoehorn reality to fit our desires, whilst tolerance is the acceptance of the undesirable in order to achieve longer-term goals" 31 (p. 193). Frustration intolerance beliefs refer to irrational beliefs regarding the tolerance of discomfort and frustration, and the demand for comfortable and easy conditions [START_REF] Harrington | It's too difficult! Frustration intolerance beliefs and procrastination[END_REF] . It refers to unreasonable, rigid and inconsistent with reality cognitions related to the demand for comfort, gratification and that reality should be how we want it to be. [START_REF] Jibeen | Frustration intolerance beliefs as predictors of emotional problems in University undergraduates[END_REF] It may play an important role in specific emotional dysfunctions and disorders, such as anxiety, depression, and anger. [START_REF] Filippello | The relationship between frustration intolerance, unhealthy emotions, and assertive behaviour in Italian students[END_REF] Relatively little is known about frustration intolerance beliefs among professional caregivers.

Different forms of frustration intolerance have been described. [START_REF] Harrington | It's too difficult! Frustration intolerance beliefs and procrastination[END_REF] including discomfort intolerance, entitlement, emotional intolerance, and achievement frustration. Discomfort intolerance is the belief that life should be easy, comfortable and free of hassle, effort or inconvenience. Entitlement is the belief that wishes should be met (immediate gratification), and other people should indulge and not frustrate these desires. Emotional intolerance is the belief that emotional distress is unbearable and must be quickly relieved or avoided. Achievement frustration is a perfectionist belief and reflects intolerance of obstacles to achieving high standards. The contents of frustration intolerance beliefs may play a central role in determining the type of emotional disturbance. For example, emotional intolerance is related to high anxiety, depression, and low assertiveness, while entitlement is significantly related to anger. [START_REF] Stanković | The relationship of a measure of frustration intolerance with emotional dysfunction in a student sample[END_REF] Until now, no study has investigated the relationships between burnout and frustration intolerance.

There is evidence in the literature that nurses and care assistants for older adults experience a higher burnout level that is linked in some ways to emotional disturbance. Considering the role of cognitive emotion regulation strategies in the development of burnout could lead to improvements in treatment and prevention. However, empirical data collected from healthcare professionals working in geriatric settings are still scant and fragmented. The present study therefore had two objectives. First, we set out to investigate the relationships between the use of specific cognitive emotion regulation strategies and burnout syndrome in a sample of French nurses and care staff working with older persons. Based on previous empirical findings, [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF][START_REF] Bamonti | Cognitive emotion regulation strategies predict burnout in geriatric nursing staff[END_REF] we hypothesized that maladaptive strategies such as rumination, catastrophizing, and blaming others are more consistently associated with a higher level of burnout, while adaptive strategies such as refocus on planning, positive refocusing, and putting into perspective are more consistently associated with a lower level of burnout. Second, we examined the extent to which frustration intolerance beliefs are related to burnout syndrome. We hypothesized that greater frustration intolerance is associated with higher levels of burnout. Concerning the relationships between specific domains of frustration intolerance (e.g., emotional intolerance, entitlement) and burnout, given the lack of previous research on this relationship, analyses were purely exploratory, with no specific more hypotheses.

Method

Design and participants

The present cross-sectional study was carried out in France. We administered an online self-report survey to nurses and care assistants (or equivalent) working in a geriatric setting (i.e., rehabilitation, palliative geriatric and long-term geriatric care units, geriatric psychiatry units, or nursing homes). Inclusion criteria were (1) caring for older persons, (2) age at least 18 years, and (3) French speaking. Participants were recruited through institutional listserv emails, community health forums, and support groups dedicated to geriatric caregivers, but not specifically to problems at work or burnout. These contained a description of the study and a weblink to the online survey. All participants completed the questionnaires in the same order, and none received any remuneration. Multiple responses were not authorized. A respondent could only answer once (activation of cookies to avoid repeated participation). Data were collected from 252 questionnaires, of which 41 (16.3%) were incomplete and nine (3.6%) were invalid, leaving 202 usable questionnaires. The overall response rate was 81.1%. The number of people who accessed but did not respond to the survey was 152 (40.2%). This study was performed in line with the principles of the Declaration of Helsinki, and recruitment and consent procedures were approved by an ethics committee. Participants read the information letter and provided their informed consent before accessing the survey.

-Table 1 Characteristics of the 202 professional caregivers.

Sociodemographic characteristics

N (%) M (SD)[Range]
accordance with the cut-offs for French health professionals detailed in the MBI study [START_REF] Dion | Validation de la traduction de l'inventaire d'e ´puisement professionnel de Maslach et Jackson[END_REF] Participants were 202 French nurses (28.7%, n = 58), care assistants (56.4%, n = 114) and care auxiliaries (14.9%, n = 30) 1 with a mean age of 36 years (SD = 10.47, range = 19-60, median = 35.50). The majority of participants were female (98%, n = 198). They worked either part time (i.e., more than 12.5 h per week; 46%, n = 93) or full time (29.7%, n = 60) in either an assisted living facility (98.1%, n = 198). The majority had a high school diploma or lower (57.4%, n = 116), were living with a partner (76.2%, n = 147), and had children (60.9%, n = 123). The length of work experience with older persons ranged from 6 months to 36 years (M = 9.98, SD = 8.65), and participants reported working an average of 7.36 years in their current job (SD = 7.46, range = 0.1-36, median = 5.00). Socio-demographic and socio-professional characteristics of the 202 nursing home caregivers are presented in Table 1.

Instruments Burnout

Burnout was measured with the French version of the Maslach Burnout Inventory (MBI). [START_REF] Dion | Validation de la traduction de l'inventaire d'e ´puisement professionnel de Maslach et Jackson[END_REF] This self-report measure consists of 22 items related to occupational burnout, divided into three subscales: EE, DP, and PA. Participants were asked to rate the frequency of each statement on a Likert-like scale ranging from 0 (Never) to 6 (Every day). Responses were summed for each subscale, with higher scores on the EE and DP subscales indicating higher burnout, but higher scores on the PA subscale indicating lower burnout. Scores on each of the three subscales were categorized as high, average, or low, in [START_REF] Mantzorou | Professional burnout of geriatric nurses caring for elderly people with dementia[END_REF] Nurses ensures care and coordinate the work of the nursing assistants. Nursing assistants are in charge of hygiene, comfort, and curative care, under the supervision of a nurse. Care auxiliaries include nursing auxiliaries, medical and psychological assistants.

Cognitive emotion regulation strategies

The French version of the Cognitive Emotion Regulation Questionnaire (CERQ) [START_REF] Jermann | Cognitive Emotion Regulation Questionnaire (CERQ)[END_REF] was used to measure cognitive strategies for handling emotionally arousing information. This self-report questionnaire consists of 36 items probing nine cognitive emotion regulation strategies: self-blame, acceptance, focus on thoughts/rumination, positive refocusing, refocus on planning, positive reappraisal, putting into perspective, catastrophizing, and blaming others. Participants responded on a 5-point Likert-like scale ranging from 1 (Almost never) to 5 (Almost always). Scores on these subscales were summed to reflect two general coping styles: adaptive coping or elaborative processes (positive refocusing, refocus on planning, acceptance, positive focusing, and putting into perspective), and maladaptive coping or automatic processes (rumination, catastrophizing, self-blaming, and blaming others), with higher scores indicating greater use of the coping strategy. Internal reliability coefficients in the present study ranged from .84 to .71.

Frustration intolerance

The French version of the Frustration Discomfort Scale (FDS) 39 was used to probe participants' perceived capacity for withstanding frustration. This 23-item self-report questionnaire assesses four subdomains: discomfort intolerance, entitlement (emotional intolerance, and achievement frustration. Respondents estimated the strength with which they held a particular belief when distressed or frustrated on a 5-point Likert-like scale ranging from 1 (Absent) to 5 (Very strong), with higher scores indicating greater frustration intolerance. Four mean subdomain scores and a mean overall score were computed. In the present study, internal consistency for the four FDS subscales was adequate (a = .91-.75).

Data analysis

Both descriptive and correlational (Spearman's r) to examine the correlations among study variables. were performed to examine the correlations among study variables, using SPSS 23.0 ® . Kruskal Wallis analyses of variance (ANOVAs) and Dunn Bonferroni post hoc comparisons were used to compare emotion regulation strategies and frustration intolerance subdomains scores between nurses' level of burnout (low, moderate, and high) for each dimension (EE, DP and PA). We also used ANOVAs, followed by Dunn-Bonferroni post hoc comparisons, to test whether EE, PD, and PA levels differed according to sociodemographic characteristics. A p value of < .05 was considered to be statistically significant.

Results

Prevalence of burnout symptoms and descriptive analysis of variables

Figure 1 shows the percentages of nurses and care assistants who experienced high, medium, or low burnout on each of the three subscales. A majority (80.7%, n = 163) of professional caregivers had a low burnout risk, 13.4% (n = 27) a moderate risk (i.e. high scores on two burnout dimensions) and 5.9% (n = 12) a high risk of burnout (i.e. high scores on all three burnout dimensions). Overall, 38.1% (n = 77) of nurses and care assistants had at least one symptom of burnout (high EE or DP, or low PA). Furthermore, the means and standard deviations of burnout of professional caregivers are shown in Table 1. No differences were found regarding working hours (fulltime or parttime), type of job, (nurse, assistant nurse, etc.), type of institution (e.g., EHPAD), or length of time in the profession. Nevertheless, it should be emphasized that there was a significant age difference between the three PA subgroups, U(2, 200) = 6.34, p < .002. The lower-risk PA subgroup had a higher mean age than the other two subgroups.

Relationships between burnout, cognitive emotion regulation strategies, and frustration intolerance subdomains

Relations between burnout and CERQ, FDS and socio-economic variables are depicted in Table 2. An examination of the association patterns among the burnout variables showed the expected correlations with adaptive (r = 0.14 0.24, p < .05 to .01) and maladaptive (r = 0.13 31, p < .05 to .01) cognitive emotion regulation strategies. EE was moderately positively associated with rumination, self-blame, and catastrophizing (r = 0.12 0.30, p < .05 to .01), and negatively correlated with positive reappraisal (r = 0.22, p < .01). DP was significantly positively correlated with self-blame, acceptance, catastrophizing, and blaming others (r = 0.12 0.29, p < .05 to .001), but negatively correlated with refocus on planning (r = 0.12, p < .05). PA was positively correlated with positive refocusing, refocus on planning and positive reappraisal (r = 0.20 0.33, p < .001). Self-blame was negatively related to PA (r = 0.22, p < .001). These correlations are summarized in Table 2. Concerning frustration intolerance, EE, DP and the overall burnout score were all positively related to all the FDS subdomains (r = 0.19 0.32, p < .05 to .001). Finally, PA was negatively associated with discomfort intolerance (r = .16, p < .05), and positively associated with achievement frustration (r = 0.12, p < .05).

Comparison between emotional exhaustion level groups on emotion regulation variables

As observed in Table 3, the EE risk groups differed significantly on maladaptive coping, especially self-blame, rumination, and catastrophizing. The high-risk subgroup had the highest mean score. Participants in this subgroup also made less use of adaptive cognitive emotion regulation strategies, particularly refocus in planning and positive reappraisal. The high-risk and moderate-risk subgroups both had higher mean scores on discomfort intolerance and emotional intolerance than the lower-risk subgroup did.

Comparison between depersonalization level groups on emotion regulation variables

Concerning the DP subgroups, we found statistically significant differences on maladaptive coping, such as self-blame, catastrophizing, and blaming others. Participants in the high-risk subgroup made significantly a greater use of maladaptive strategies (Table 4). They also scored significantly higher on each frustration intolerance subdomain.

Comparison between personal accomplishment level groups on emotion regulation variables

Finally, ANOVAs indicated that the mean self-blame score of the high-risk PA subgroup was significantly higher than that of the lowrisk subgroup. Similarly, the mean adaptive coping score (especially refocus on planning) of the high-risk subgroup was significantly lower than that of the low-risk subgroup. Furthermore, the moderate-risk PA subgroup had a lower positive reappraisal score and a higher discomfort intolerance score than the low-risk subgroup. All details are provided in Table 5. No other significant differences were found (see Tables 5).

Discussion

The present study explored the associations between cognitive emotion regulation strategies, frustration intolerance, and burnout among nurses and care assistants for older adults. First, our sample is consistent with the national data (France) on gerontological caregivers. In France, it is estimated that care assistants represent 67.2% of the paramedical/social staff in geriatric setting, nurses 18.5%, and care auxiliaries 14.3%, with an average age between 37 and 39 years old, and an over-representation of women (about 94%). Average job tenure was 9.3 years for care assistants and 7.7 for nurses and care auxiliaries in 2007. [START_REF] Bazin | Le personnel et les difficulte ´s de recrutement dans les Ehpad[END_REF] Burnout was present in our sample, with 19% of participants being categorized with a moderate-to-high risk of burnout. A substantial number of participants reported high levels of EE (27%) and DP (24%), and low levels of PA (16%). Consistent with previous research, [START_REF] Narumoto | Relationships among burnout, coping style and personality: study of Japanese professional caregivers for elderly[END_REF] older caregivers reported significantly higher PA than their younger counterparts. They probably had better stress management strategies. These results are also consistent with international [START_REF] Cocco | How Much is geriatric caregivers burnout caring-specific? Questions from a questionnaire survey[END_REF] and national [START_REF] Estryn-Behard | La souffrance au travail en ge ´riatrie. Comprendre et agir[END_REF][START_REF] Zawieja | Burnout des soignants en ge ´riatrie : Pre ´valence et de ´terminants dans 185 e ´tablissements franc ¸ ais[END_REF] findings on the prevalence of burnout in professional caregivers for the older persons.

First, across the diverse types of cognitive emotion regulation strategies, maladaptive strategies predicted higher levels of EE and DP, consistent with recent findings. [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF][START_REF] Castellano | Cognitive processes of emotional regulation, burnout and work engagement[END_REF][START_REF] Bamonti | Cognitive emotion regulation strategies predict burnout in geriatric nursing staff[END_REF][START_REF] Bassal | Relationship between emotions, emotion regulation, and well-being of professional caregivers of people with dementia[END_REF] More specifically, greater use of self-blame significantly contributed to all three dimensions of burnout (EE, DP and PA). Harmful strategies, such self-blame (blaming oneself for what has happened), may be seen as variations in disengagement and objectification in care, [START_REF] Doolittle | Burnout, coping, and spirituality among internal medicine resident physicians[END_REF] and have been related to burnout in other medical settings. [START_REF] Mccain | A study of the relationship between resilience, burnout and coping strategies in doctors[END_REF] Focus of self-perceived errors or insufficient (higher self-blame) can be related to catastrophizing (repetitive thoughts about a negative event) and rumination (emphasis on the negative aspect of an experience) patterns, as potential markers of an EE risk. This hypothesis is supported by the literature indicating that female physicians have a stronger tendency to focus attention on their own negative thoughts and feelings. [START_REF] Spataro | The toxicity of self-blame: sex differences in burnout and coping in internal medicine trainees[END_REF] Rumination or catastrophizing increase anxiety and alert responses, as they hinder more rational and profitable interpretations of problems. [START_REF] Castellano | Cognitive processes of emotional regulation, burnout and work engagement[END_REF] Higher level of catastrophizing and other-blame were also found to be associated with elevated DP scores. These findings also suggest that nurses using avoidance strategies such as blaming others are more prone to DP. [START_REF] Duquette | Psychosocial determinants of burnout in geriatric nursing[END_REF] Blaming others may be seen as a psychological defense to temper or manage disturbing emotions through reappraisal, in that it reconstructs the cognitions from which threatening emotions arise. An association between blaming another person and poor adjustment has previously been identified, [START_REF] Tennen | Blaming others for threatening events[END_REF] and is seen as an important determinant of negative attitudes toward patients (higher DP), such as anger. [START_REF] Quigley | Mediating effects of blame attributions on feelings of anger[END_REF] More attention should be paid to reducing healthcare professionals' use of maladaptive strategies, especially since a meta-analysis suggested that their use is more damaging than the nonuse of adaptive strategies. [START_REF] Aldao | Emotion-regulation strategies across psychopathology: a meta-analytic review[END_REF] Adaptive strategies were associated with lower EE and higher PA. No significant results were found for the DP dimension. As hypothesized, two strategies seemed protective in terms of high EE and low PA: refocus on planning and positive reappraisal. These same two strategies were also associated with higher PA in two previous studies of burnout among nursing staff working with older persons. [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF][START_REF] Castellano | Cognitive processes of emotional regulation, burnout and work engagement[END_REF] However, the current study found no association between use of positive reappraisal and lower DP, in contrast to Bamonti et al. [START_REF] Bamonti | Coping, cognitive emotion regulation, and burnout in long-term care nursing staff: a preliminary study[END_REF] Using these proactive strategies allows for the positive reinterpretation of stressful situations and acceptance of stressors, thereby increasing the sense of PA and decreasing EE. [START_REF] Rowe | Skills training in the long-term management of stress and occupational burnout[END_REF] Planning and identifying the positive aspects of a stressful situation (an optimistic appraisal pattern [START_REF] Lowe | Exploring coping reactions to work-stress: application of an appraisal theory[END_REF] ) maintain positive evaluations and positive expectations about self and work, thus reducing EE and supporting PA. Frequent use of refocus on planning and positive reappraisal strategies is reported to be strongly associated with fewer psychopathological symptoms than the use of other adaptive strategies. [START_REF] Garnefski | Cognitive emotion regulation strategies and psychological adjustment in adolescents with a chronic disease[END_REF][START_REF] Garnefski | Negative life events, cognitive emotion regulation and emotional problems[END_REF] Second, the current study investigated the role of frustration intolerance in burnout symptomatology. More specifically, higher EE and DP levels were related to difficulty regulating frustration. Discomfort intolerance and emotional intolerance were higher in the high-risk EE subgroup than in the other subgroups. DP was also the domain closest to each frustration intolerance dimension. These exploratory findings suggest that low frustration tolerance helps to explain burnout syndrome. This is in line with previous research underlining that frustration intolerance beliefs may contribute to a larger construct of negative affectivity encompassing stress, anxiety, and depression. [START_REF] Harrington | Frustration intolerance beliefs: their relationship with depression, anxiety, and anger, in a clinical population[END_REF] In particular, the higher levels of discomfort intolerance and emotional intolerance within the high-risk EE subgroup were consistent with the idea that specific areas of frustration intolerance are related to psychological problems. [START_REF] Harrington | Frustration intolerance beliefs: their relationship with depression, anxiety, and anger, in a clinical population[END_REF] Frustration intolerance beliefs may make professional caregivers unwilling to tolerate negative emotional events or daily work stress, such that they become vulnerable to burnout. In particular, relationships have been found between emotional intolerance and anxiety, and between discomfort intolerance and depressed mood. [START_REF] Stanković | The relationship of a measure of frustration intolerance with emotional dysfunction in a student sample[END_REF] These disorders can partially overlap EE symptoms (e.g., fatigue, inability to concentrate). Finally, closer relationships between DP and frustration intolerance were identified in our study. Negative affective states (e.g., anger, cynicism, frustration) arising from DP can be triggered or maintained by dysfunctional frustration beliefs. Professional caregivers with high achievement frustration were also more likely to have higher PA. Achievement-related irrational beliefs intersect with the desirable level of achievement related outcomes or perfectionism. [START_REF] Hall | Risky adolescent sexual behavior: a psychological perspective for primary care clinicians[END_REF] Striving for perfection has been found to be negatively related to burnout (including low PA) and active coping (e.g., positive refocusing) among school teachers. [START_REF] Stoeber | Perfectionism in school teachers: relations with stress appraisals, coping styles, and burnout[END_REF] The present study had several limitations that need to be taken in account. First, as the data came from self-reports collected via the Internet, there may have been a response bias. Online questionnaires generate less social desirability, but have a higher nonresponse rate than face-to-face surveys (Heerwegh & Loosveldt, 2008). Future research should consider other measurement methods, such as interviews or observations, and replicate these findings with a more representative sample. Second, the fact that all participants were recruited online limits the generalizability of results. Third, the cross-sectional design of the present study meant that we could not confirm causal relationships between variables. A longitustudy with a larger, more diverse sample of older nurses is needed to fully test both the intercorrelations and causal ordering of the constructs in this study. Moreover, it would be useful to investigate the relative importance of self-worth beliefs in burnout and frustration intolerance. It is important to extend this research by including other potential factors of likely importance, such as mood (e.g., depression and anxiety), critical stressful life events, and perceived social support.

--

Relevance to clinical practice

Adaptive emotion regulation strategies, such as positive reappraisal, seem to be a promising avenue in burnout prevention. Nevertheless, more attention should be paid to reducing healthcare professionals' use of maladaptive strategies. Particular attention should be paid to reducing self-blame, as this may be effective in helping to reduce the experience of worthlessness and higher levels of burnout seen in female nurses. Burnout prevention programs should consider screening the caregiver, even informally, for the use of self-blame. Interventions incorporating perspective-taking components that reduce self-blame and facilitate self-forgiveness could promote better adjustment and thereby avert burnout. This could be done during regular feedback sessions during staff meetings (e.g., briefing and debriefing sessions). The use of a team-based approach in care provides additional support and resources for caregivers, thus helping them feel less exhausted, and less responsible for unmet work goals. Education could focus on helping caregivers form realistic expectations of clinical/nursing practice, by (1) encouraging them to share their experiences, thoughts, and feelings, and (2) enhancing their feelings of competence or achievement when working with older residents. Geriatric caregivers could also benefit from brief stress-reducing interventions, such as mindfulness, that enable them to redirect their attention to the present moment, rather than focus on catastrophizing about past or ongoing negative experiences. [START_REF] Turner | Mindfulness-based stress reduction and cognitive behavioral therapy for chronic low back pain: similar effects on mindfulness, catastrophizing, self-efficacy, and acceptance in a randomized controlled trial[END_REF] Previous studies have underlined that mindfulness-based stress reduction programs (e.g., based on positive reappraisal) are an effective strategy for reducing burnout among nurses and other healthcare providers, especially the emotional exhaustion dimension. [START_REF] Cohen-Katz | The effects of mindful-nessbased stress reduction on nurse stress and burnout, Part II: a quantitative and qualitative study[END_REF][START_REF] Mackenzie | A brief mindfulness-based stress reduction intervention for nurses and nurse aides[END_REF] This approach would also be useful to limit rumination among geriatric caregivers and encourage them to be less critical in their thinking. [START_REF] Andreotti | Rumination and mindlessness processes: trajectories of change in a 42-day mindfulness-based intervention[END_REF] Interventions focusing on dysfunctional frustration intolerance beliefs, such as rational emotive behavior therapy might be useful for reducing burnout among caregivers working with older adults. This type of intervention, targeting a change in caregivers' irrational beliefs (e.g., group therapy to counter irrational beliefs and stay healthy and happy), might improve their resilience and reduce their burnout symptoms. Previous studies have suggested that REBT could be a beneficial approach for combating burnout. [START_REF] Onuigbo | Clinical benefits of rational-emotive stress management therapy for job burnout and dysfunctional distress of special education teachers[END_REF]

Conclusion

This study highlights the risk of burnout among professional caregivers, as well as the importance of understanding the various cognitive emotion regulation styles that predict burnout in geriatric settings. Cognitive emotion regulation strategies may be a pivotal factor for determining how individuals cope with stress in the workplace, and more particularly how they regulate and impede negative emotions, such as frustration. Planning and identifying the positive aspects of a stressful situation maintains positive evaluations and positive expectations about self and work, thus reducing the risk of burnout syndromes. However, more comprehensive research is needed to explain the directionality of causation between the emotion regulation variables and burnout among geriatric caregivers.

Declaration of Competing Interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Fig. 1 .

 1 Fig. 1. Percentages of professional caregivers reporting emotional exhaustion, depersonalization and personal accomplishment, by risk of burnout (n = 202).

  : high EE was defined as a score greater than or equal to 27; high DP a score greater than or equal to 10; and high PA a score lower than or equal to 33. In the present study, reliability coefficients ranged from .87 to .67.

	Gender	Female	198 (98)
		Male	4 (2)
	Age (years)		36.00 (10.47)[19-60]
	Living environment Urban	111 (55)
		Peri urban	48 (23.8)
		Rural	39 (19.3)
	Couple status	In a couple	147 (72.8)
		Single	48 (27.2)
	Children	Yes	123 (60.9)
		No	79 (39.1)
	Natural caregiver	Yes	24 (11.9)
		No	178 (88.1)
	Socio-professional characteristics
	Profession	Nurse	58 (28.7)
		Nursing assistant	114 (56.4)
		Care auxiliaries	30 (14.9)
	Years of experience In the profession	10.40 (8.04)[.5-39]
		With older persons	9.98 (8.65)[.5-36]
		In current work	7.36 (7.46)[.5-36]
	Full time	Yes	60 (29.7)
		No, at half time or more	93 (46.0)
		No, less than half time	49 (24.3)
	Type of structure	Nursing homes for	150 (74.3)
		dependent older persons
		Hospital / clinic	31 (15.4)
		Home care institutions	17 (8.0)
	Workplace	Urban	49 (24.3)
		Peri urban	93 (46.4)
		Rural	60 (29.3)
	Burnout	Emotional exhaustion	22.58 (11.41)[0-50]
		Depersonalization	6.91 (5.90)[0-27]
		Personal accomplishment	39.43 (5.69)[20-48]

Table 2

 2 Spearman correlation coefficients for cognitive emotion regulation strategies, frustration intolerance subdomains and burnout subscales, and covariates (age, professional experience).

	Variables

*p < . 05; **p < .01; ***p < .001.

Table 3

 3 Mean (standard deviation) scores according to emotional exhaustion level, and results of ANOVA and post hoc comparisons.

	Variables

Note. Maslach Burnout Inventory cut-offs: high emotional exhaustion ≥ 30; moderate emotional exhaustion =18-29; low emotional exhaustion ≤ 17.

Table 4

 4 Mean (standard deviation) scores according to depersonalization level, and results of ANOVA and post hoc comparisons.

	Variables

Note. Maslach Burnout Inventory cut-offs: high depersonalization ≥ 12; moderate depersonalization = 6-11; low depersonalization ≤ 5.

Table 5

 5 Mean (standard deviation) scores according to personal accomplishment level, and results of ANOVA and post hoc comparisons.Note. Maslach Burnout Inventory cut-offs: high personal accomplishment ≤ 33; moderate personal accomplishment = 39-34; low personal accomplishment ≥ 40.

	Variables

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.