Ioannis Bakas

Michael Z Hauschild

Thomas F Astrup

Ralph K Rosenbaum

Preparing the ground for an operational handling of long-term emissions in LCA

Keywords: LCA, landfill, heavy metals, long-term, toxicity

Purpose. Currently, there is no meaningful methodology for the estimation of environmental impacts from longterm heavy metal emissions in a Life Cycle Assessment (LCA) context, when an assessment of landfill and mining technologies is performed. In this paper, the aim is to investigate the main issues hindering the standardization of a methodology to account for potential impacts from long-term metal emissions, and to describe the characteristics of a robust framework for an operational impact assessment methodology.

Methods. In order to demonstrate the issues around potential impacts from long-term emissions in LCA and derive a scientific basis for developing an adequate LCA methodology to address these impacts, a two-part review on metal long-term emissions is performed that a) identifies a suitable time-dependent Life Cycle Inventory (LCI) while underlining the problems in existing emission prediction attempts and b) describes the existing LCA approaches for accounting for toxic potential impacts from these emissions, while explaining the reasons that the identified proposals have not been adopted from the LCA community. These approaches are then compared upon the basis of a common LCI and their differences are highlighted.

INTRODUCTION

Life Cycle Assessment (LCA) is a decision-support tool aiming at assessing the environmental impacts associated with products or systems (ISO 2006a;ISO 2006b). An important element of LCA is the quantification of emissions, representing an environmental exchange between the product or system and the ecosphere, and the subsequent characterization of the emissions into potential environmental impacts by applying characterization factors (CFs) to the emissions. LCA is widely used in decision-making processes in waste management by assessing integrated waste management systems or comparing different alternatives for treatment of waste (Laurent et al. 2013a;Laurent et al. 2013b). Contrary to product LCA, waste LCA focuses only on the end-of-life stage of products' life cycles. In waste LCA, the technologies involved are relatively limited (corresponding to a chain of waste treatment facilities).

The main direct emissions are thus typically caused by a few installations, the location of which is easier to identify as well as the conditions of the receiving environment. This implies that a more site-specific approach is possible, taking into account the local conditions in contrast to the typical situation for product LCAs. A site-specific assessment is also highly relevant in the case of landfills, where the most important leachate impacts are expected to be on a local scale (i.e. within a few km 2 ).

Landfilling of waste (from e.g. households, industrial sites, institutions, construction and demolition sites, etc.) constitutes a predominant waste treatment technology globally. However, landfill leachate poses an important environmental concern. The leachate composition has been well investigated for many types of landfills and its heavy metal content comprises one of the major environmental pollutants in waste management (Christensen et al. Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 2001). Besides toxicity, a problematic property of metals is their environmental persistence, which is practically infinite and thus far superior to any organic chemical. In an LCA context, the toxicity potentials of heavy metal emissions have hence been estimated as relatively high compared to other compounds [START_REF] Huijbregts | Priority assessment of toxic substances in life cycle assessment. Part I: Calculation of toxicity potentials for 181 substances with the nested multi-media fate, exposure and effects model USES -LCA[END_REF].

Given the high toxic potential, an accurate representation of potential impacts from landfill metal leaching in LCA is essential to ensure the credibility of the tool in assisting informed decision-making, neither ignoring nor overestimating their importance.

When trying to estimate the impacts from landfilling in an LCA context, an important characteristic of landfill metal emissions is the very long time horizon of thousands or even hundred thousands of years over which their release takes place in contrast to the other processes in the system which typically emit within minutes to days.

The widely used Ecoinvent inventory database defines long-term metal emissions as occurring after 100 years until 60000 years from now ("until the next plateau-covering glacial period [in Switzerland] is estimated") [START_REF] Hischier | Implementation of Life Cycle Impact Assessment Methods[END_REF]. During this period small amounts of leachate or run-off containing pollutants (especially heavy metals) are emitted from the landfill to the surrounding soil, aquifer, and eventually the surface water.

Apart from leachate from landfills of municipal, inert or hazardous waste, long-term heavy metal emissions can be found in the tailings from mining operations leading to significant environmental burdens [START_REF] Stüben | Environmental monitoring of heavy metals and arsenic from Ag-Pb-Zn mining: a case study over two millennia[END_REF]) that are not properly addressed in LCA mainly due to the lack of reliable data [START_REF] Althaus | Life Cycle Inventories of Metals and Methodological Aspects of Inventorying Material Resources in ecoinvent[END_REF] and an appropriate impact assessment methodology. This problem has been underlined and investigated through a sensitivity study that showed the strong dependence of LCA results from mine tailing management on the choice of time frame [START_REF] Reid | Life cycle assessment of mine tailings management in Canada[END_REF]. Also the management of radioactive waste can cause long-term leaching of metals [START_REF] Singh | Solid-Phase Distribution and Leaching Behaviour of Nickel and Uranium in a Uranium Waste-Rock Piles[END_REF], but due to the special properties of radioactive waste, this source of heavy metal emissions is not investigated in this paper, although some of the considerations described below could be relevant.

Out of the leachate pollutants from landfills, long-term metal emissions constitute a particularity in the LCA context. Inventory modelling in LCA applies a time-integration principle, according to which all emissions should be treated as a pulse emission occurring at one point in time, whether they in reality occur in different parts of a life cycle or extended over long-time periods [START_REF] Guinée | A proposal for the classification of toxic substances within the framework of life cycle assessment of products[END_REF]. The latter case poses problems when emissions occur in relatively low concentrations over very long time periods leading to large cumulated pulse flows.

Their impacts are potentially overestimated when the resulting impact scores from emissions in low concentrations integrated over tens of thousands of years, are interpreted in the same way as impact scores for emissions occurring

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 in significantly shorter periods and thus integrated over shorter periods of time which is the case for transportation processes and many industrial processes. There is a "dilution in time" which is important for the observable impacts from the long-term emissions but not represented in the calculated potential impacts in life cycle impact assessment (LCIA).

In LCIA toxic impacts are modelled using steady-state conditions, applying integration over a defined time horizon. Integrating the potential impacts of long-term emissions over a relatively short time horizon like 100 or 500 years (as done for e.g. Global Warming Potentials), and thus neglecting impacts from emissions occurring later, potentially leads to an underestimation of their impacts. On the other hand, including them fully through integration over very long or even infinite time horizons would lead to a strong overestimation, as the (perhaps negligible if from very low emission concentrations) potential impacts occurring over a long period of time would be fully attributed to the product as if they were occurring right now (as one large emission) in the same way as an emission from e.g. a waste incinerator. While the latter approach does not account for the "dilution in time" of the impact, the first approach completely neglects the long-term potential impacts. These two extremes present a dilemma for which an operational and accurate solution is needed in LCIA. Some LCIA approaches specifically deal with long-term emissions [START_REF] Pettersen | Critical Review: Life-Cycle Inventory Procedures for Long-Term Release of Metals[END_REF][START_REF] Hauschild | Gone…but not away-addressing the problem of long-term impacts from landfills in LCA[END_REF]). However, currently there is no consensus among researchers on a common methodology, which is illustrated by the differences in this perspective of the various LCIA methodologies [START_REF] Hischier | Implementation of Life Cycle Impact Assessment Methods[END_REF]. Moreover, there are no characterization factors available for long-term emissions of metals, which thus have to be represented by the generic characterisation factor for the metal. Further research is called for so that a more accurate representation of long-term emissions is achieved [START_REF] Hischier | Implementation of Life Cycle Impact Assessment Methods[END_REF].

In summary, when attempting to integrate this kind of emissions and their potential impacts into an LCA, two main hurdles need to be overcome: 1) estimating/predicting the future emissions in the inventory phase, and 2) characterising the emissions in a meaningful way that puts them into perspective relative to the impacts caused by emissions that occur over a much shorter time. In order to better understand the perspectives for an adequate representation of long-term emissions, a consistent overview of past experience and current practice within the LCA field is needed. This is done through (i) reviewing the status, reliability and common ground of emission prediction methodologies from an LCA perspective, (ii) reviewing the current proposals for characterization of long-term emissions in LCIA, comparing them in terms of the results they provide, and based on that (iii) derive main

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 principles for a scientifically robust framework for an operational impact assessment for potential impacts of longterm emissions in the LCA context.

METHODOLOGY

For addressing the aforementioned objectives, a literature review is conducted. Central studies are presented which have been published in peer reviewed journals and that address the issue of long-term emissions from landfills.

The first part of the review aims at identifying studies mainly within the waste management field, which can provide a time-dependent life cycle inventory (LCI) for long-term metal emissions from landfills. A scientifically sound study that provides metal emission profiles for Ni, Cd, Zn, and Pb, suitable as an input to an LCI, is selected. The emission profiles correspond to the leaching of these metals from an air pollution control residues (APCR) landfill of a total capacity of 1,000,000 tonnes.

The second part maps research within the LCA field to identify the various approaches that have been developed to address the challenges is assessing potential impacts from heavy metals emitted in low quantities but over long periods of time. The review illustrates the current state of the art and analyzes the existing approaches in terms of the perspectives they adopt on future emissions.

The results from the two parts of the literature search are combined to form a case study where the different LCA approaches are applied on a selected emission profile of a metal leaching out of an APCR landfill over a long time period. The same CF (or comparative toxicity potential) is used for both short-and long-term emissions, adopted from recent literature which estimates CFs for Ni and Cu with respect to terrestrial ecotoxicity [START_REF] Owsianiak | Addressing geographic variability in the comparative toxicity potential of copper and nickel in soils[END_REF]. The CF for Ni is chosen as an emission profile for Ni can be found in literature [START_REF] Astrup | Assessment of long-term leaching from waste incineration airpollution-control residues[END_REF]. The available CF is relevant for terrestrial ecotoxicity impacts, but from a nickel emission to air. Thus this CF is corrected for emissions directly to soil using USEtox [START_REF] Rosenbaum | USEtox-the UNEP-SETAC toxicity model: recommended characterisation factors for human toxicity and freshwater ecotoxicity in life cycle impact assessment[END_REF]) and the resulting CF is 4.86 x 10 3 m 3 /kg emitted to soil x day.

Based on a common emission profile and an identical CF, the existing LCIA approaches can be compared on the same basis. The time dependent emission profile for Ni provides emission quantities per 200 years time steps. This quantity is integrated over 100 years (the first time step is divided in two) and over an infinite time horizon, and the potential impacts in each case are then estimated by multiplying with the CF. The difference between the impacts from the 100 years integration and the infinite time horizon is the impact allocated to a separate impact Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 category, named stored toxicity.

The impact is then estimated per time step and discount rates of ± 0.01 % are applied to future potential impacts. The magnitude of the rates is set to 0.01% as this is shown to correspond to time horizons of up to 100,000 years [START_REF] Hellweg | Discounting and the Environment; Should Current Impacts be Weighted Differently than Impacts Harming Future Generations ?[END_REF]. One positive and one negative discount rate are modelled, in order to account for uncertainties regarding future economic development which determines the level of the compensation required for future damage.

Lastly, the emission concentrations in the landfill leachate, provided also by the Ni profile per time step, are compared to the European median background concentration of Ni in soils. The median situation is chosen for demonstrative reasons, but it is not recommended as the background concentrations for metals vary greatly geographically and according to soil types [START_REF] Zhao | Estimates of ambient background concentrations of trace metals in soils for risk assessment[END_REF]). The median Ni extractable concentration in European soils is estimated at 16 mg/kg [START_REF] Lado | Heavy metals in European soils: A geostatistical analysis of the FOREGS Geochemical database[END_REF]. This is used to estimate the background Ni dissolved concentration by using the equations below and the K dNi (280 l/kg) default values found in the USEtox TM multimedia toxicity model [START_REF] Rosenbaum | USEtox-the UNEP-SETAC toxicity model: recommended characterisation factors for human toxicity and freshwater ecotoxicity in life cycle impact assessment[END_REF]:

It is also assumed that:

where C sorbed (mg/kg soil ) is the sorbed metal concentration, C dissolved is the dissolved metal concentration (mg/kg soil ) and C total is the extractable metal concentration (mg/kg soil ). C dissolved is converted into mg/l by using the soil bulk density ρ bulk (mg/l) and the soil water content w (% v/v): The median global bulk density for soils, based on more than 15,000 samples is estimated at 1.4 t/m 3 [START_REF] Batjes | ISRIC-WISE Harmonized Global Soil Profile Dataset (Ver. 3.1)[END_REF] and it is assumed to apply for Europe. The water content value is adopted from the USEtox default value, which is 0.2. Therefore, the dissolved median Ni concentration in European soils is estimated at 0.038 mg/l.

Only the Ni concentration that is above the background level is transformed into mass and integrated over time, then multiplied with the CF for Ni in order to provide the total actual potential impact.

A comparative analysis of the results of the application of the various LCA approaches helps identify the effect that the specific assumptions and perspectives of each approach have on LCA results, thus directly affecting decisions supported by waste LCA. Based on the analysis, a listing is made of the requirements for developing a robust, common framework for addressing long-term emissions in LCA, by combining different characteristics of the existing approaches.

MODELLING LONG-TERM EMISSIONS OF HEAVY METALS

Different types of landfills have been investigated in terms of pollutant release from the leachate. Inert landfills such as an APCR landfills tend to be investigated more regarding metal emissions (e.g. [START_REF] Hellweg | Time-dependent life-cycle assessment of slag landfills with the help of scenario analysis: the example of Cd and Cu[END_REF], while landfills richer in organic matter are normally investigated in terms of organic pollutants (e.g [START_REF] Kjeldsen | Present and Long-Term Composition of MSW Landfill Leachate: A Review[END_REF].

Long-term metal emissions are present in all types of landfills but the primary focus for toxicity might change with landfill type. Also the waste composition in the landfill influences the pattern of metal emissions [START_REF] Bolton | Elemental composition and speciation of some landfill leachates with particular reference to Cadmium[END_REF]. The literature review conducted here is not confined to a specific landfill type in order to be comprehensive and with the overall aim at identifying a time-dependent leachate inventory.

Heavy metal concentrations in landfill leachate have been extensively monitored and simulated in batch tests for a surveyable time period, usually capped at 100 years (Finnveden et al. 1995;[START_REF] Flyhammar | Heavy metals in a municipal solid waste deposition cell[END_REF][START_REF] Kjeldsen | Composition of leachate from old landfills in Denmark[END_REF]. A review of published monitoring and testing results concludes that the leachate metal concentrations within such a short time frame do not pose a great environmental risk [START_REF] Kjeldsen | Present and Long-Term Composition of MSW Landfill Leachate: A Review[END_REF].

This observation fits well with the generally accepted assumption that typically the vast majority of the landfilled waste content of heavy metals remains in the landfill 100 years after the waste deposition [START_REF] Hauschild | Gone…but not away-addressing the problem of long-term impacts from landfills in LCA[END_REF].

The heavy metal retention in landfills can be explained by mechanisms such as sorption and precipitation [START_REF] Kjeldsen | Present and Long-Term Composition of MSW Landfill Leachate: A Review[END_REF].

On the other hand, the long-term heavy metal concentration in leachate is difficult to predict in a solid way

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 as laboratory simulation is not possible and mathematical models hence cannot be validated for time frames as long as 100,000 to 250,000 years and should, therefore, not be over-interpreted (Finnveden et al. 1995). Theoretically, after the stable methanogenic phase of a landfill rich in organic matter, the oxygen intrusion facilitates metal mobility due to decreasing pH and oxidation to more soluble metal species [START_REF] Christensen | Passive soil vapor extraction of chlorinated solvents using boreholes[END_REF][START_REF] Bozkurt | Long-term processes in waste deposits[END_REF]. However, existing experimental work leads to contradictory results even for the medium time frame [START_REF] Kjeldsen | Present and Long-Term Composition of MSW Landfill Leachate: A Review[END_REF].

Given the importance of oxygen intrusion on the landfill chemistry, a modelling approach has been developed based on the oxygen effect [START_REF] Bozkurt | Long-term processes in waste deposits[END_REF]. In order to predict future heavy metal concentrations in the leachate, this model is based on the fact that, after the methanogenic phase of an organic landfill is completed, the subsequent humic phase is characterized by much slower organic carbon degradation which means that oxygen diffuses into the landfilled waste [START_REF] Bozkurt | Long-term processes in waste deposits[END_REF]. The conceptual model is based on an analysis of the main processes governing each landfill phase after the methanogenic phase, with the presence of oxygen considered as the determining factor for metal mobility [START_REF] Bozkurt | Long-term fate of organics in waste deposits and its effect on metal release[END_REF]).

Bozkurt et al. modelled several scenarios in order to determine the total depletion time for organics and metals in the waste mass and the influence of factors such as the type and characteristics of the top cover [START_REF] Bozkurt | The long-term evolution of and transport processes in a selfsustained final cover on waste deposits[END_REF]). However, no results are presented regarding the quantity of heavy metals leaching out of the landfill as a function of time. Therefore, this work is not suitable for compiling an LCI.

Finnveden attempted to produce emission rates for metals contained in a municipal waste landfill based on a collection of mass balance approaches from literature [START_REF] Finnveden | Solid Waste Treatment Within the Framework of Life Cycle Assessment -Metals in Municipal Solid Waste Landfills[END_REF]. The author produced best estimates of emission rates for a surveyable time period (about one century from waste deposition), which may constitute a dynamic LCI. However, the mass balance approach for an infinite time frame, which is in line with the scope of this paper, claims that all metals will eventually leave the landfill. Therefore, this study does not provide a suitable timedependent LCI.

Other attempts to predict the evolution of metal concentrations out of a landfill involve geochemical models. One study attempted a prediction of the evolution of Cu and Cd concentrations in a municipal incineration residues landfill, based on soil infiltration rate, share of macropore flow, and sorption capacity of the waste [START_REF] Hellweg | Time-dependent life-cycle assessment of slag landfills with the help of scenario analysis: the example of Cd and Cu[END_REF]. With the help of scenarios that determine the presence of these two heavy metals in waste and the use of the geochemical model PHREEQC [START_REF] Parkhurst | User's Guide to PHREEQC (Version 2)--A Computer Program for Speciation, Batch-Reaction, One Dimensional Transport, and Inverse Geochemical Calculations[END_REF], the authors tried to predict the Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 development of emission concentrations over the next 20,000 years for Cd and over 100,000 years for Cu. The results of this work could be used in an LCA context, as illustrated in the same study which also presents results of an LCIA. On the other hand, only information for two metals is given and the time frames for the emission development are different for both metals. A different geochemical landfill model, LandSim, has also been employed to predict the depletion of heavy metals (among others) from a typical municipal solid waste landfill over a 20,000-years period, based on a variety of landfill parameters [START_REF] Slack | Household hazardous waste disposal to landfill: using LandSim to model leachate migration[END_REF]. Results of the simulation show that heavy metals leach at very low concentrations over a long period of time and that only chromium and mercury at any point in time exceed current drinking water standards proposed by health organizations. Moreover, the results indicated that the heavy metal content remaining inside the waste mass is negligible after 4,000 years. This conclusion contradicts other evidence of literature suggesting long attenuation of heavy metals in landfills but also findings of laboratory tests [START_REF] Flyhammar | Heavy metals in a municipal solid waste deposition cell[END_REF][START_REF] Hyks | Long-term leaching from MSWI air-pollution-control residues: leaching characterization and modeling[END_REF]. Therefore, the reliability of these results for compiling an LCI is questionable.

A laboratory test aiming at simulating the landfill leaching process can also be found in literature [START_REF] Hyks | Long-term leaching from MSWI air-pollution-control residues: leaching characterization and modeling[END_REF]). The test used a column percolation set-up, which applied forced infiltration of eluent in the column, filled with samples from an inert landfill, in order to simulate leaching until high liquid-to solid (L/S) ratios were reached, corresponding to a leaching duration of thousands of years [START_REF] Hyks | Long-term leaching from MSWI air-pollution-control residues: leaching characterization and modeling[END_REF]. The test was performed on samples from a landfill for municipal solid waste incineration air pollution control residues, up until the L/S ratio reached 200-250 l/kg, in order to determine the leaching behaviour of a large variety of heavy metals. The L/S ratio could then be translated into time based on site-specific landfill characteristics [START_REF] Hjelmar | Leachate from land disposal of coal fly ash[END_REF]) and in this case, the total simulated duration corresponds to more than 10,000 years. Results of the test showed that less than 3% of the initial heavy metal mass had leached during the simulated time period of 10,000 years. This test cannot, however, be used in the context of LCI as it does not cover the entire leaching time period of a landfill.

If a relationship between pH and the liquid-to-solid (L/S) ratio is established for fly ash landfills, it is possible to predict Al, Ca, Cd, Ba, Mg, Ni, Pb, S, Pb, V, and Zn concentrations in the leachate, using pH as a determining factor, as shown in another study [START_REF] Astrup | Assessment of long-term leaching from waste incineration airpollution-control residues[END_REF]. Two types of incineration residues (semi-dry and fly ash) were treated in batches while they were either carbonated before or they were in an uncarbonated form. The pH was measured in the batches and for each measurement, the leaching of metals and the liquid-to-solid (L/S) ratio was calculated. In this way, leaching concentrations were able to be connected with the level of pH. The L/S ratio Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 was translated into time based on average Danish environmental conditions. Based on these assumptions, the authors produced emission profiles for the selected heavy metals until an L/S ratio of 5,000 which corresponds to 100,000 to 250,000 years. The results show different behaviour for different metals, but also according to the type of residue investigated and the presence of carbonation. Therefore, it is difficult to group metals according to their leaching patterns.

The graphs in Figure 1 present the leaching concentration profile over time modelled using the results of Astrup and co-workers for four selected metals and averaged over the two waste streams modelled (non-carbonated fly ash and semi-dry residue). The model has a temporal resolution of 200 years, and therefore this study could easily be used to provide a time dependent LCI for this type of landfills. The total time frame is chosen at the lower end of the range, set at 100,000 years.

The extrapolation of information obtained through leaching tests into considerations regarding metal leaching behaviours in real landfills is hindered by restriction posed in the leaching simulations in the laboratory [START_REF] Van Der Sloot | Similarities in the leaching behaviour of trace contaminants from waste, stabilised waste, construction materials and soils[END_REF]. However, for the scope of long-term emissions where actual measurements are impossible to obtain, laboratory tests are the only source of information available regarding metal leaching development patterns in the distant future.

It is important to notice that for a very long initial stage, the concentrations of leaching metals remain at a low level, but then start to rise, with Ni and Zn reaching their maximum predicted concentrations at the end of the modelling period. This observation has important consequences when assessing potential impacts and monitoring of pollution around landfill sites.

STATE OF THE ART IN LCA

The life cycle impact assessment of long-term heavy metal emissions is currently problematic. The uncertainty of including heavy metal long-term emissions in toxicity assessments within LCA has been identified as a problem for quite some time, from both a methodological and case-study perspective [START_REF] Finnveden | Long-Term Emissions from Landfills Should Not be Disregarded[END_REF]Hauschild et al. 2008;[START_REF] Hischier | Implementation of Life Cycle Impact Assessment Methods[END_REF]. Many LCA studies of solid waste management systems underline the uncertainty in their results stemming from the inability to accurately account for these potential impacts, while others choose to ignore toxicity impacts altogether (Laurent et al. 2013a;Laurent et al. 2013b). The uncertainty discussed relates mainly to modelling uncertainty (both inventory and impact modelling). However, there is also a methodological

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 uncertainty present which is based on the choice of time aggregation principle for the emissions [START_REF] Finnveden | Long-Term Emissions from Landfills Should Not be Disregarded[END_REF][START_REF] De Haes | Best Available Practice Regarding Impact Categories and Category Indicators in Life Cycle Impact Assessment[END_REF]).

Long-term emissions are currently treated in LCA either by modifications in the inventory modelling or by hybrid methods adopted from other fields such as risk assessment [START_REF] Hischier | Implementation of Life Cycle Impact Assessment Methods[END_REF]. The state of the art in the inventory registration of long-term emissions is represented by Ecoinvent, which is one of the most widely used LCA databases, providing inventories for many processes, including waste management [START_REF] Frischknecht | The ecoinvent database system: a comprehensive web-based LCA database[END_REF].

The Ecoinvent background report for landfills provides a comprehensive set of arguments for and against inclusion of long-term emissions in the inventories and consequently in impact assessment [START_REF] Doka | Life Cycle Inventories of Waste Treatment Services[END_REF]), but no consensus is reached by the authors [START_REF] Hischier | Implementation of Life Cycle Impact Assessment Methods[END_REF].

Therefore, Ecoinvent inventories report both short-and long-term emissions from landfills, but their inclusion or not in the impact assessment depends on whether or not the chosen impact assessment methodology allows for it. Impact assessment methodologies such as CML2001, EDIP 97/2003, as well as IMPACT 2002+ [START_REF] Hauschild | Environmental Assessment of Products[END_REF]Guinée et al. 2001a;[START_REF] Guinée | Life cycle assessment; An operational guide to the ISO standards -Part 3: Scientific Background[END_REF][START_REF] Jolliet | IMPACT 2002+: A New Life Cycle Impact Assessment Methodology[END_REF][START_REF] Hauschild | Background for spatial differentiation in LCA impact assessment: The EDIP03 methodology[END_REF] can produce differentiated impact assessment results by including or excluding long-term (beyond 100 years) emissions. Other methodologies, such as Ecoindicator 99 and ReCiPe apply social perspectives reflecting the social and environmental values of current generations towards future generations (Goedkoop and Spriensma 2001a;[START_REF] Goedkoop | The Eco-indicator 99; A damage oriented method for Life Cycle Impact Assessment -Methodology Report[END_REF][START_REF] Goedkoop | ReCiPe 2008; A life cycle impact assessment method which comprises harmonised category indicators at the midpoint and the endpoint level -Report I: Characterisation[END_REF]). Some of these perspectives include both short-and longterm emissions and apply the same characterization factor for the two emission durations in the impact assessment.

A similar approach of differentiated time periods has been developed previously, by distinguishing between two time periods, namely the surveyable time period (set to 100 years corresponding to the end of the methanogenic phase of a typical municipal waste landfill) and the infinite time period (set to the time necessary for all emissions to occur) [START_REF] Finnveden | Methodological aspects of life cycle assessment of integrated solid waste management systems[END_REF]. The author recommends assessing potential impacts over both time periods in a full LCA, since it should consider impacts from all relevant emissions, instead of the common practice of cutting off emissions occurring after 100 years.

Several approaches have been developed beyond the LCI phase in order to tackle the issue of long-term emissions' potential impacts. These approaches aim at developing specific LCIA methodologies that estimate impacts from emissions beyond a point in time (stored toxicity) [START_REF] Hauschild | Gone…but not away-addressing the problem of long-term impacts from landfills in LCA[END_REF]), or at weighing differently Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 impacts from future emissions compared to current impacts (environmental discounting) [START_REF] Hellweg | Discounting and the Environment; Should Current Impacts be Weighted Differently than Impacts Harming Future Generations ?[END_REF]. The last methodology presented here functions as an intercept between LCI and LCIA by eliminating emissions beyond a certain threshold. Dynamic LCIA methods that have been developed but do not address specifically emissions during very long time frames are not examined here as the long-term perspective requires a special framework compared to simple time differentiated approaches [START_REF] Levasseur | Considering time in LCA: dynamic LCA and its application to global warming impact assessments[END_REF].

Stored toxicity

In order to distinguish between potential toxic impacts from short-and long-term emissions, a new impact category has been proposed, which builds upon current Ecoinvent practice: the emissions occurring during the first 100 years of a landfill are treated together with the emissions released from all other processes in the life cycle (Hauschild et al. 2008). The emissions beyond that point in time are classified as belonging to a new impact category, named stored toxicity (or stored human toxicity and stored ecotoxicity), following the EDIP 2003 method [START_REF] Hauschild | Background for spatial differentiation in LCA impact assessment: The EDIP03 methodology[END_REF]. In order to estimate the potential toxic impacts, emissions inventoried in the stored toxicity categories are characterised in the same way (and based on the same factors) as in the traditional toxicity categories. The characterised results are then normalised based on an area's total annual stored toxicity, which is determined from the mass flow of heavy metals within all waste streams in the year 1994, divided by the area's population. The normalization is performed in order to assess the relative magnitude of the examined system's impact.

The proposed stored toxicity approach was applied in an LCA study on landfilled bottom ash and the results showed that stored toxicity impacts are 325 times greater than the highest result in the traditional impact categories spectrum (namely Ecotoxicity water ) [START_REF] Birgisdóttir | Life cycle assessment model for road construction and use of residues from waste incineration[END_REF]. This approach, although in line with current practice, is still problematic since the introduced impact category lacks interpretation and weighting factors needed in the comparison with potential impacts in the other categories. However, it provides a first step in separating between (i) emissions occurring within a time period where landfill chemistry, and therefore heavy metal emissions, is well known and monitoring or testing is possible, and (ii) emissions occurring in a distant future where uncertainty in their development is high and no monitoring or testing is possible.

Environmental discounting

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4

Hellweg and co-workers attempted an application of economic discounting in environmental assessment under the context of LCA [START_REF] Hellweg | Discounting and the Environment; Should Current Impacts be Weighted Differently than Impacts Harming Future Generations ?[END_REF]. The authors based their analysis on four main arguments for environmental discounting (changes in magnitude of damage, pure time preference, productivity of capital, uncertainties). These arguments, based on the economic theory, can be quantified in order to produce discount rates, applied on potential impacts from future emissions, so that the weight of future impacts is differentiated compared with impacts from emissions occurring instantly.

The choice, however, of a discount rate is subjective and very decisive, and in order for it to be meaningful, it needs to be close to 0 (-1% ≤ r ≤ + 1%). Under a higher positive discount rate, even potential impacts from relatively short-term emissions (below 100 years) would practically disappear. Even in the case of low discount rates the value of the discount rate is the sole most determining factor for the resulting potential impacts, because of the exponential nature of discounting. The choice of a discount rate presupposes the monetization of environmental impacts and depends on assumptions on the development of the future global economy, as well as value choices of the LCA practitioner.

The adoption of moral archetypes from Cultural Theory for LCA modelling purposes [START_REF] Hofstetter | Modelling the Valuesphere and the Ecosphere : Integrating the Decision Makers ' Perspectives into LCA[END_REF])could be a guide for selecting an appropriate discount rate according to the selected cultural perspective [START_REF] Hellweg | Discounting and the Environment; Should Current Impacts be Weighted Differently than Impacts Harming Future Generations ?[END_REF]. However, even within each cultural perspective the subjectivity of the choice is still not eradicated which endangers the objectiveness of decisions supported by an LCA, while it has been shown that the influence of an archetype choice is significant for the overall LCA results [START_REF] Schryver | The influence of value choices in life cycle impact assessment of stressors causing human health damage[END_REF].

Background concentrations

Another approach for tackling the issue of long-term emissions has been inspired by the field of risk assessment.

According to this, emissions occurring at leachate concentrations that are below the background concentration levels for each heavy metal can be discarded as they cause no effect [START_REF] Finnveden | Methodological aspects of life cycle assessment of integrated solid waste management systems[END_REF]). Therefore, it has been proposed to cut off emissions of heavy metals that occur after the point in time when their concentrations fall below the background concentrations [START_REF] Finnveden | Life Cycle Assessment and Treatment of Solid Waste[END_REF]. This approach has inspired studies related to landfill aftercare period and technologies related to an effort for a fast reduction of metal leaching concentrations [START_REF] Brand | Development of emission testing values to assess sustainable landfill management on pilot landfills[END_REF].

This approach neglects that heavy metal emissions do not necessarily follow a decreasing trend, as

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 illustrated in Figure 1, and that background concentrations might not stay at the same level during the long time frame considered. For some heavy metals, emissions have been shown to decrease steadily and then to increase again in the future [START_REF] Astrup | Assessment of long-term leaching from waste incineration airpollution-control residues[END_REF]). On the other hand, heavy metal background concentrations could increase substantially in the future because of accumulation in specific environmental compartments (van der Voet et al.

2000).

Moreover, this approach could be considered as conflicting with the general LCA principles according to which all emissions should be taken into account whether above or below thresholds (Udo de [START_REF] De Haes | Best Available Practice Regarding Impact Categories and Category Indicators in Life Cycle Impact Assessment[END_REF], although attempts to include background levels in LCIA can be found in literature [START_REF] Hellweg | Time-dependent life-cycle assessment of slag landfills with the help of scenario analysis: the example of Cd and Cu[END_REF]. This holds in particular in the extreme case of landfill leaching in contaminated soil where landfill emissions could potentially dilute the soil pore water, thus reducing its toxicity to some extent, depending on the affected organisms and the dose-response curves for the leached metal. It could, however be argued that a cut-off determined by the natural background pore water concentration gives a more relevant representation of actual potential toxic impacts resulting from long-term heavy metal emissions than a cut-off at an arbitrarily set time limit or an infinite time horizon, as concentrations of metals below the background level have no toxic effect on the local ecosystems. Due to the natural variation in soil water concentrations of metals, a high degree of site-specificity would be relevant in the modelling [START_REF] Lado | Heavy metals in European soils: A geostatistical analysis of the FOREGS Geochemical database[END_REF].

COMPARISON OF DIFFERENT METHODS DEALING WITH LONG-TERM EMISSIONS

The LCA methods described above differ in many aspects: (i) the approaches to handling the short-and long-term emissions; (ii) the respect of the time equity principle; (iii) the inclusion of subjective (value) choices in the accounting of potential impacts. To investigate the importance of these differences, the different LCA approaches are applied on the same emission profile of Ni leaching out of an air pollution control (APC) residues landfill. Based on the assumptions on the initial content of the landfill, Ni will have leached out in about 73,000 years. The cut-off of emissions after 100 years, the adoption of an infinite time horizon, the handling of emissions in a separate "stored toxicity" impact category, the concept of environmental discounting and the estimation of potential impacts only from emissions above the background concentrations, are all applied on the Ni profile.

The CF used for the analysis is estimated at 4.86 x 10 3 m 3 /kg emitted to soil x day and it represents the impact on terrestrial ecotoxicity from an emission of Ni to soil.

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4

The results of the application are shown in Figure 2. The lowest impact given by the cut-off of emissions at 100 years, and the highest impact from the negative discount rate differ by approximately eight orders of magnitude.

The stored ecotoxicity approach (which is practically the difference between the cut-off and the infinite time horizon approaches) gives an impact around five orders of magnitude higher than the results of the cut-off approach, demonstrating the significance of long-term emissions against short-term. The use of a negative discount rate, which gives a higher importance to impacts occurring in the future, provides the highest results. The difference between impacts with a small positive and a small negative discount rate is about five orders of magnitude, highlighting the importance of the choice of discount rate, which relies on subjective criteria. The second lowest overall impact is produced by the inclusion of emissions only above the background concentrations. This is because the pattern of the emission profile for Ni shows a sharp increase in the leached metal only after 35,000 years and exceeding the background Ni concentration after 55,000 years approximately.

A similar pattern would result from the comparison of the methods for emissions of other metals, as only the magnitude would change (based on different emission levels, CFs, and background concentrations). Therefore, it is safe to say that the cumulative effect of the choice of LCIA approach towards long-term emissions from all metals leaching out of the landfill would be much higher.

If the results from this comparison are put in the context of a full LCIA, the selection of method becomes critical as it would potentially lead to very different decisions supported by the corresponding LCA study. For example, the infinite time horizon method would lead to a dominance of toxicity impact categories over the full LCIA profile [START_REF] Hauschild | Gone…but not away-addressing the problem of long-term impacts from landfills in LCA[END_REF].

DISCUSSION

The prediction of the development of emissions over time for heavy metals in landfills is shown to be difficult due to hindering factors such as (i) the complexity and dynamics of landfill chemistry where many processes and the waste characteristics (waste composition) influence heavy metal mobility, (ii) many different parameters (e.g. pH, organic matter in the deposit) that govern metal kinetics and (iii) the inherent uncertainty when attempting to predict future conditions in landfills determining the chemicals behaviour for very long time periods. Due to this complexity, there is little common ground among the different methods reviewed. No study has been identified that has made comprehensive use of all information available regarding the governing mechanisms of metal mobility -Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 instead the studies tend to focus on a selected few of these mechanisms and adopt them in the construction of a prediction model.

In the LCA domain, the use of predictions of long-term emissions is limited, as the current state-of-the-art either uses emissions from robust models or laboratory findings that extend to the first 100 years after deposition or uses mass balance calculations to estimate the aggregated emissions over infinite time horizons. The proposed approaches to account for potential impacts from long-term emissions present some interesting insights but carry individual, inherent problems. An overall conclusion is that a distinction in the way potential impacts are calculated for short-and long-term emissions is required.

None of the approaches considers the changes in environmental conditions or ecosystem equilibrium when estimating future potential impacts. The CF used is the same for short-and long-term emissions, although the environmental compartments receiving long-term emissions are bound to change if such long time perspectives are investigated. Currently, the predominant approaches for integrating emissions over time does not allow for a timedifferentiated CF, although that would increase accuracy. For example, fluctuations in the soil pH would change drastically the metal mobility [START_REF] Richards | Effect of sludge-processing mode , soil texture and soil pH on metal mobility in undisturbed soil columns under accelerated loading[END_REF], increasing or decreasing their toxic potential. The presented dynamic inventory allows for investigating impacts in every future point in time and paves the way for investigations regarding changing over time soil properties that influence the calculations of metal toxicity.

The comparison of existing LCIA approaches on the same metal emission profile shows that the resulting predicted potential toxic impacts differ quite substantially, thus leading to very different assessments of the toxicity potential of landfill leachate. The common practice in LCA, of cutting off emissions after 100 years, is problematic as it ignores the vast majority of potential impacts, regardless of the selected approach towards long-term emissions as shown in Figure 2 and supported by other studies [START_REF] Huijbregts M A | Priority assessment of toxic substances in life cycle assessment. III: Export of potential impact over time and space[END_REF]. However, given the importance of heavy metal emissions in the total toxicity-related impacts, it is essential that a robust, accurate, and realistic approach is developed so that properly informed decisions can be made based on the LCA results. A robust approach needs to include an accompanying module on uncertainty in both the prediction of emissions (LCI) and the subsequent toxicity modelling (LCIA), which, although very complex, is essential for putting the impact assessment results into context and avoiding their over-interpretation.

In order to produce an accurate representation of potential impacts from long-term emissions, the changes in the receiving environment need to be investigated and possibly reflected in a time-dependent toxicity CF for each

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 metal being emitted. This should be based on a modelling of the temporal changes in landscape properties over longterm time frames of the environmental compartments receiving the emissions (mainly soil) and the response of the exposed ecosystems, which would result in time dependent fate, exposure, and effect calculations. Site-specificity is also crucial, as soil properties that affect metal toxicity, such as pH or soil organic matter, vary across the globe.

On the other hand, the handling of long-term emissions should be realistic, so that only real potential toxic impacts are taken into account. The inclusion of background concentrations [START_REF] Birgisdóttir | Life cycle assessment model for road construction and use of residues from waste incineration[END_REF]) in a comparison with the emission concentrations would disregard emissions that actually dilute existing background levels in the environment. These considerations should reflect the fact that metal emissions from landfills occur over long time frames but in relatively low concentrations. These low concentrations are not currently considered, due to the predominant practices of integrating emissions over time. The evolution of background levels with time can be addressed by modelling different scenarios [START_REF] Hellweg | Time-dependent life-cycle assessment of slag landfills with the help of scenario analysis: the example of Cd and Cu[END_REF]. As the background levels have a significant effect on the amount of emissions contributing to toxicity, a spatially differentiated approach is required in order to capture the natural variations in soil concentrations of metals in different regions (e.g. [START_REF] Shacklette | Element Concentrations in Soils and Other Surficial Materials of the Conterminous United States. US Geological Survey Professional Paper[END_REF][START_REF] Herselman | Baseline concentration of Cd, Co, Cr, Cu, Pb, Ni and Zn in surface soils of South Africa[END_REF][START_REF] Lado | Heavy metals in European soils: A geostatistical analysis of the FOREGS Geochemical database[END_REF] Some of these method elements may challenge traditional axioms of LCA specifically and sustainability in general. The time equity principle, essential to the sustainability concept aiming to preserve equal development chances for current and future generations, according to which all emissions from a system should be treated equally regardless of the point in time at which they occur, is one of them. This principle functions well in relatively short time frames (one day, one year or even a decade) since the internal and external conditions that determine the potential impacts from an emission do not change substantially. However, in extreme conditions, when emissions occur over a very long time frame, the time equity principle cannot hold, since the conditions determining the estimation of the impacts are bound to change. Therefore, emissions occurring in different time periods should be treated differently in an LCA context, by modifying accordingly the associated CFs. Some existing approaches in LCIA already challenge the equity principle by explicitly applying discounting in future impacts, or differentiating between impacts within a surveyable time period and future impacts [START_REF] Hellweg | Discounting and the Environment; Should Current Impacts be Weighted Differently than Impacts Harming Future Generations ?[END_REF][START_REF] Hauschild | Gone…but not away-addressing the problem of long-term impacts from landfills in LCA[END_REF].

Likewise, the common practice in LCA to ignore impacts from emissions occurring after a specific time frame, without adequate scientific argumentation, clearly violates the time equity principle.

On the other hand, the involvement of background concentrations is not consistent with the general rule in LCA of treating emissions in the same way whether above or below thresholds (Udo de [START_REF] De Haes | Best Available Practice Regarding Impact Categories and Category Indicators in Life Cycle Impact Assessment[END_REF]. However, such an approach is necessary for producing more realistic future estimates for potential toxic impacts, but also for addressing the fact that long-term emissions typically emit in low concentrations but over very long time periods.

Overall, it is time a consensus was reached for the issue of long-term emissions in LCA. The complexity of emissions prediction, the diversity of approaches, and the inherent uncertainty lead most practitioners to ignore longterm emissions altogether. On the other hand, policy makers tend to undervalue or ignore future potential impacts due to pure time preference [START_REF] Harvey | The reasonableness of non-constant discounting[END_REF], which is not supported by environmental ethics [START_REF] Hellweg | Discounting and the Environment; Should Current Impacts be Weighted Differently than Impacts Harming Future Generations ?[END_REF].

These two factors cause a significant misrepresentation of potential toxic impacts in LCA studies involving long term emissions of metals.

COMPLIANCE WITH ETHICAL STANDARDS

Our research does not involve any human or animal participants.

  above equations, C dissolved can be calculated as: 1000 Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4

Figure 2

 2 Figure 2 Assessment of the terrestrial ecotoxicity impact for a given emission pattern of Ni leaching out of an APC residues landfill, applying five different approaches towards handling of long-term emissions

  Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(10), p. 1444-1455. The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4 Figure 1. Development in average leaching concentrations for four heavy metals over 100,000 years (based on[START_REF] Astrup | Assessment of long-term leaching from waste incineration airpollution-control residues[END_REF]. Note: The proposed patterns do not fully cover the time frame of 100,000 years, as the metal content in the waste is depleted earlier, except for Pb.

															Zn
		140 000																													500 000
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	μg/l	60 000 80 000																													200 000 250 000 300 000
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The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0941-4


Olivier Emile

Ronan Niemiec

Christian Brousseau

Janine Emile

Kouroch Mahdjoubi

Wenlong Wei

Bo Thide

Mechanism of angular momentum transfer from microwaves to a copper ring

Keywords: 41, 20, Jb Electromagnetic wave propagation; radiowave propagation -45, 20, da Forces and torques -84, 40, Ba Antennas: theory, components and accessories -42, 50, Tx Optical angular momentum and its quantum aspects

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Since Beth pioneering experiments [1,2] on the transfer of Angular Momentum (AM) between electromagnetic waves and macroscopic objects, there have been several studies reporting mechanical torques on various objects. Whereas some works manipulate the radiation pressure on specifically designed complex objects [3][4][5], most of the experiments use the AM of light. It can either be the Spin Angular Momentum (SAM) in the microwave domain [6,7] and in the optical domain with macroscopic [8] and microscopic objects [9][10][11], or the Orbital Angular Momentum (OAM). The latter has only been evidenced in the optical domain, with micro particles [12][13][14] and Bose-Einstein condensates [15]. The objects to be rotated could be birefringent particles or absorbing particles in the case of SAM exchange, and mostly absorbing particles in the case of OAM. Indeed, purely transparent particles do not change the helical phase front and hence do not interact with OAM, except when they induce astigmatism or when light is scattered [16]. The origin of the transfer mechanism, in terms of torque, was difficult to interpret for birefringent particles for SAM [START_REF] Jauch | the theory of photons and electrons[END_REF], but it has now been elucidated [START_REF] Simmons | States, Waves and Photons[END_REF][START_REF] Allen | [END_REF][20]. It is also clear for absorption, for SAM and/or OAM. Recently, we have reported the transfer of AM to a copper ring in the centimeter range [21] at 870 MHz.

Since the copper ring only little absorbs radiations at this wavelength, one may then wonder what the transfer mechanism is. The aim of this article is thus to investigate the Electro-Magnetic field (EM) and the current in the copper ring, to try to elucidate the AM transfer to the object and then to estimate the torque exerted on the ring. After describing the experimental set-up (see Sect. 2), and recalling few theoretical results (see Sect. 3), we present the experimental results in Sect. 4. We then discuss them and focus on the transfer mechanism. We finally compare it with other transfer mechanisms (see Sect. 5) before reaching the conclusion.

Experimental set-up

The experimental set-up, which has already been described in [21], is sketched in figure 1. This is an adaptation of the proposal made several years ago by Vulf'son [22]. The EM field carrying OAM is generated by a so-called turnstile antenna [23] made of two 17-cm-long, 2-mm-diameter copper dipole antennas. According to the Voltage Standing Wave Ratio (VSWR), which describes the adaptation of the antenna impedances to the transmission lines they are connected to, we decided to perform the experiment at a frequency ν = 870 MHz (see insert of fig. 1). A -3dB coupler splits the signal generated from a sinusoidal frequency synthesizer in two, and induces a φ 1φ 2 = π/2 phase between the outputs. The two signals are amplified by two 40 dB gain amplifiers and then sent to the antennas. The maximum total output for each dipole is 25 W. This turnstile antenna is usually used to radiate a circularly polarized field in the axis of the antenna. However, it also radiates an electric field carrying OAM in the plane of the antenna. We are here interested in this last case.

The rotating object is a copper ring (radius R = 150 mm, height H = 50 mm, thickness T = 0.165 mm). Its polar moment of inertia is J = 8.4 10 -4 kgm 2 . The suspension is a 2-m-long, 0.5-mm-diameter cotton thread, fixed to the ceiling. Its torsion constant is measured from the 12-min-period of the free oscillations of the pendulum. It equals C = 5.6 10 -8 N.m/ • . To avoid any spurious EM effect, the experiment is confined in an anechoic chamber dedicated to this frequency range. Special care is taken to isolate the set-up from any mechanical vibration. An angular graduation is glued on the copper ring, and the rotation is recorded on a computer via a webcam.

3 Theoretical considerations

Expression of the EM field

We have calculated the electric field radiated in the plane of the antenna using CST simulation software [24], taking into account the near and the far field components of the field. The results of these simulations are shown on figure 2. Figure 2a presents the amplitude of the electric field and figure 2b corresponds to its phase. Whereas the amplitude decreases according to a 1/r law in the far field, as for the usual field radiated by a dipole [START_REF] Thidé | Electromagnetic Field Theory 2d ed[END_REF], the phase variation is very differently from a single dipole antenna. On concentric circles aligned on the center of the antenna (dotted lines in figure 2b), the phase has a 2π variation in one turn. It thus seems that the EM field indeed carries OAM and that the topological charge is equal to 1. On the other hand, the electric field could be analytically calculated. This has already been done in [21], and can be also found in the literature, see for example [START_REF] Thidé | [END_REF] and references therein. We have recalled the main results of the calculations in order to express the AM and we have fixed a few inaccuracies. However, in the following, the formula expressing the infinitesimal orbital (Eq.5), spin (Eq.7) and total AM for the ring (Eq.8) were not derived previously, neither the torque in the following paragraph (Eq.9). We use the cylindrical coordinates (ρ, θ, z), the origin O being at the center of the turnstile antenna, e z being perpendicular to it. The complex vector potential, in the plane of the turnstile antenna, writes at a point M A(M, t) = -µ 0 4π jω r p 0 e j(kr-ωt) e jθ (e ρ + je θ ),

where r = OM , ω is the pulsation of the current, p 0 is the dipole moment, µ 0 is the magnetic permeability and k is the wave vector modulus. The complex magnetic field then writes

B(M, t) = - µ 0 4π jω r 2 p 0 (1 -jkr)e j(kr-ωt) e j(θ-π/2) e z . ( 2
)
The complex electric field writes

E(M, t) = e jθ 4π 0 p 0 r 3 e j(kr-ωt) 2(1 -jkr)e ρ - j(1 -jkr -k 2 r 2 )e θ , (3)
0 being the electric permittivity. These analytical expressions also correspond to the simulations of figure 2 that have been performed with CST. One can note in equation 3 that, for a given distance r from the turnstile antenna, the modulus of the electric field is constant, its direction rotates around z, and its phase varies as a function of θ, from 0 to 2π in one turn. This is in agreement with simulations and experiments that have been performed on radial slot antennas [START_REF] Sudo | Proc. 33rd Eur. Microwave Conf[END_REF], in a different configuration.

Expression of the angular momenta

Let us calculate the AM density and the associated torque. This last point has not been completely elucidated previously in [21]. From equations 2 and 3, one evaluates the total AM density w T taking the real part of the EM fields, w T = 0 r×(E×B), [START_REF] Thidé | Electromagnetic Field Theory 2d ed[END_REF][START_REF] Thidé | [END_REF][START_REF] Van Enk | [END_REF], in the plane of the antenna at a point M . This is nothing but the vectorial product of the Poynting vector by r. Since B is along e z and r is along e ρ , one has only to consider the component of the electric field along e ρ , which indeed corresponds to a near field component. One gets

w T (M, t) = 2µ 0 ω (4π) 2 p 2 0 r 4    cos 2 (kr -wt + θ)+ k 2 r 2 sin 2 (kr -wt + θ)+ 2kr cos(kr -wt + θ)× sin(kr -wt + θ)    e z , (4)
In order to calculate the torque exerted on the ring, one has to evaluate the infinitesimal AM dJ r passing through the ring during dt. Then one has to integrate equation 4 over the whole ring and estimate the AM crossing the ring during dt. This corresponds to a multiplication by cdt. As one integrates over θ, rdθ being the elementary length, the cos 2 term averages to π, as well as the sin 2 , whereas the sin × cos averages to zero. Assuming that the EM field keeps the same expression on the whole height H of the ring as the one in the plane of the antenna (we have indeed checked numerically, that the variations in amplitude and in phase are less than 5%), this leads to a total AM on the ring that equals to

dJ r = 2µ 0 ω (4π) 2 p 2 0 r 3 πHcdt 1 + k 2 r 2 e z , (5)
Similarly, one can calculate the SAM. To avoid any gauge choice dilemma [START_REF] Thidé | Electromagnetic Field Theory 2d ed[END_REF][START_REF] Van Enk | [END_REF], one has to evaluate the SAM density w S = 0 r × (E × A) considering the transverse component of the vector potential only. Then, from equations 1 and 3, one gets

w S (M, t) = µ 0 ω (4π) 2 p 2 0 r 4   2 cos 2 (kr -wt + θ) +kr cos(kr -wt + θ)× sin(kr -wt + θ)   e z , (6)
One also estimates the infinitesimal SAM dS r exerted on the ring following the same procedure as above. This leads to

dS r = 2µ 0 ω (4π) 2 p 2 0 r 3 πHcdte z , (7)
From equations 5 and 7, one deduces the infinitesimal OAM exerted on the ring. It is simply

dL r = dJ r -dS r = 2µ 0 ω (4π) 2 p 2 0 r k 2 πHcdte z , (8)
It has to be noted that the OAM has the same expression in the near field and in the far field, assuming that the height of the ring increases linearly with r as one moves further up.

Estimation of the topological charge

Although equation 4 clearly shows that the phase of the electric field has a 2π variation in one turn, one may wonder whether the value = 1 of the topological charge could be confirmed using equation 8.

Let us imagine that OAM would have kept the same expression as the one found in the plane of the turnstile antenna. We now evaluate the torque over an infinite cylinder. Let us call φ the angle between the plane of the antenna and the radial vector (H is replaced by r sin φdφ in the OAM density). Since one considers the projection of the AM over the z axis, one should add a cos φ. Finally, for a given φ, the OAM passing through the cylinder corresponds to thickness c cos φdt. Then one would have to integrate cos 2 φsinφdφ between 0 and π/2 corresponding to a half infinite cylinder and to multiply by a factor of 2 to get the whole cylinder. This would lead to a factor 2/3. Then, the available torque would be

dL r dt = 4 3 µ 0 ω (4π) 2 p 2 0 ck 2 πe z . (9)
From a general point of view, an EM field with a power P and a topological charge exerts a torque that is

Γ th = P/ω. ( 10
)
Such power is related to the dipole moment [23] by the relation

P = 1 12π 0 c 3 p 2 0 ω 4 , (11)
then comparing this expression with equation 9, this would lead to

dL r dt = P/ω, (12)
which indeed corresponds to a topological charge equal to = 1. This confirms that the OAM associated to the EM field in the plane of the antenna has a topological charge equal to = 1. It has been here estimated by the available torque in a manner similar to what has been done in acoustics [29]. This torque is a multiple integer of the radiated power. Then, the measurement of the OAM carried per photon leads to an integer number times , being the reduced Plank constant.

Paradox

However, the expression of the electric field could be viewed as a kind of a paradox. Indeed, if one considers the far field only in equation 3, or if one moves in the far field region, the electric field writes

E(M, t) = 1 4π 0 p 0 r e j(kr-ωt) e jθ jk 2 e θ . ( 13
)
The electric field is tangential. From equation 2 the magnetic field is vertical. The Poynting vector is thus radial. This erroneous back-of-an-envelope calculation would lead to an OAM equal to zero, since the OAM is the vectorial product of the radial vector and the Poynting vector. Indeed, the radial component of the electric field (which is usually said to be the near field component) only contributes to the OAM, even in the far field.

The same kind of paradox also holds for Beth experiment [2] for SAM. In that case, a plane wave crosses a half wave plate. Rapidly estimating the SAM, one would say that the Poynting vector is along the propagation direction. This cannot induce any torque on the plate which is perpendicular to the propagation direction. This paradox has been solved in [START_REF] Simmons | States, Waves and Photons[END_REF]. The light beam could be Gaussian thus having components not parallel to the propagation direction, or the plate could have finite dimensions thus creating diffraction and components non parallel to the propagation direction. As a result, the components of the Poynting vector which are not parallel to the propagation direction, only contribute to the torque.

Experimental results

The experimental results have already been presented in [21]. We have evidenced a uniformly accelerated rotation of the pendulum, as can be seen from figure 3. In figure 3a we have plotted the rotation versus time for three different powers. The rotation depends on the power, as expected. As the phase between the two dipole antennas is reversed from +π/2 to -π/2, the sign of the OAM switches from = 1 to = -1. The sign of the torque then also changes. We find experimentally a change of the rotation direction of the pendulum. Besides, the two plots of the rotation are nearly perfectly symmetric. When the two dipole antennas are in phase, no rotation is observed.

Figure 3b shows the angular acceleration induced by the EM field versus the transmitted power to each dipole. The experimental results evidence a linear dependence versus the power, as expected, that holds over one order of magnitude. Note also that the linear coefficient is exactly reverse for the other rotation direction. From Fig. 3b, for a 25 W power, we find an acceleration of 7.8 10 -4 • /s 2 which corresponds to an OAM torque of Γ ex = 1.1 10 -8 Nm.

Discussion

Comparison between experiment and theory

According to the theoretical section (Eq. 10), assuming that the total radiated power P t is twice the power emitted by each dipole (which is of course an over estimation), the maximum torque available would be

Γ th = N = (P t /hν) = P t /ω = 9.2 10 -9 Nm, ( 14
)
where N is the number of photons emitted per second, assuming that all photon are used and that they have the same AM. At first glance, there is a very good agreement between this theoretical value Γ th and the experimental one Γ ex . However, the height of the ring is only 50 mm, at a distance of 150 mm, which leads to a solid angle that equals π/3, whereas Γ th is estimated for an isotropic radiation with a solid angle that equals 4π. Then, the theoretical value seems to be more than one order of magnitude under estimated.

Fabry-Perot effect

First, the ring is made of copper which is a nearly perfectly reflecting material at this frequency. It is usually assumed that for a perfectly electrical conductor, no AM transfer by reflection could be performed [30][31][32]. Indeed, following the arguments given in these references, to ensure continuity of the fields, the tangential component of the electric changes sign upon reflection, thus excluding any inversion of the AM. Because of AM conservation, no transfer can then be performed. Nevertheless, in our case, the OAM is due to the longitudinal component of the electric field which does not change its sign upon reflection, enabling for OAM change and AM transfer. This is the same argument as the one used in [32] for SAM transfer at oblique incidence. This leads to a transfer of 2 . This can be evidenced on figure 4, where we have plotted the equi-phase of the electric field for different times. Second, the ring is at a distance R = 150 mm from the source, that is of the order of λ/2, i.e. still in the near field. The copper ring thus interacts with the totality of the field. One has to consider the antenna and the field as a whole. In order to check this hypothesis, we have carried out calculations still using CST software taking into account the antenna and the ring. The results can be seen in figure 5. Actually, one can notice that in the plane of the antenna, there is hardly any field radiated outside the strip location. All the field is concentrated inside the strip.

Third, since the diameter of the ring equals λ, the copper ring behaves as a Fabry-Perot. As already discussed, the topological charge of the AOM is reversed upon reflection. It is again reversed when crossing the center of the turnstile antenna which is at the focus of the reflecting ring. Indeed, when crossing this focus, the longitudinal component of the electric field remains unchanged. Due to the so-called Gouy phase [START_REF] Born | Principles of optics[END_REF], the magnetic field experiences a π/2 phase shift for a = 0 Gaussian beam. This is exactly the same experimental situation as the one encountered with acoustical waves [START_REF] Kolomenskii | [END_REF] where they evidenced also a π/2 phase shift for a spherical wave in two dimensions. For a = 1 topological charged beam, there is an extra π/2 phase shift [START_REF] Siegman | Lasers[END_REF]. Thus the magnetic field changes its sign crossing the focus, leading to a change of the topological charge, in a manner similar to what can be found in optics for cylindrical lenses [START_REF] Molina-Terriza | [END_REF]. This can be evidenced also on figure 4. After the focus, the topological charge is the same as for the incoming beam. Since the tangential component of the electric field also changes it sign due to the Gouy phase, the reflected field interferes constructively with the incoming beam, leading to a Fabry-Perot effect.

Yet, because the same EM wave serves several times to rotate the ring, one may wonder whether energy conservation might be violated. Indeed, the reflected wave, due to the rotational Doppler effect [37], has a slightly lower frequency. The increase of the energy of the ring due to rotation is compensated by a lowering of the photon energy that enables energy conservation. Could this variation be detected? For a 1 Hz rotation frequency of the ring, which is far above the rotation frequency our pendulum could experience, the rotational Doppler shift would be of 1 Hz. Compared with the 1 GHz microwave frequency we used in our experiment, it is a 10 -9 relative variation. This is much lower than the natural width of our frequency synthesizer which is of the order of 100 Hz. The frequency change is hardly noticeable in our case and must be difficult to unambiguously isolate and to determine.

Since the strip lies in the near field, it is quite difficult to estimate the finesse of this radio frequency Fabry-Perot. We have tried to determine it experimentally. Due to high losses, the photons are only bouncing a few times. The finesse should be lower than ten, that is a very low finesse. Then the width of the transmission resonance frequency must be very broad, of the order of few tens of megaHertz. Performing experiments, the only resonance we evidenced when we changed the excitation frequency was the width of the frequency response of the antennas which is of the order of 10 MHz (see insert of Fig. 1).

As for a usual Fabry-Perot in optics, and according to figure 5, the ring position corresponds to a node of the interfering waves. The electrons within the metal react so as to ensure EM field continuity. Since the field is equal to zero at the strip location the transfer mechanism could not be via absorption as supposed in [22]. It must be by reflection. However, the argument given above doesn't explain the transfer mechanism at a microscopic scale, neither the discrepancy between the expected torque values and the experimental observations. The EM waves must anyhow interact with the copper ring. Since EM waves cannot penetrate below the surface of the ring, the Lorentz force of the light can only act on the charges and the currents at the surface of the ring [32]. The next paragraph is dedicated to discuss the transfer mechanism in terms of currents, taking all these effects into account.

Transfer mechanism

At the strip location, the tangential component of the EM field induces an alternative current I running at the surface of the strip with a cos(θ -ωt) variation (see Eq.3). This current experiences a resistance thus generating an electric field that drives the copper atoms. These atoms then radiate an EM field to compensate for the incoming field. Following Newton's second law of mechanics, considering a small portion of the ring, one finds that

d 2 θ dt 2 = ρ q ρI ρ m RHT cos(θ -ωt) = a cos(θ -ωt), (15)
where ρ q is the charge density, ρ m is the mass density, ρ is the copper resistivity. We have plotted the intensity of the current at a given time on the ring still using CST software, taking into account the influence of the ring. The result is displayed in figure 6. One can clearly see that there is an oscillating current running on the inner side of the copper ring only. With these simulations we are able to estimate the amplitude of the current. This current is found to be I = 0.25 A, leading to a = 5.5 10 3 • /s 2 . This value is the amplitude of the oscillating term in equation 15. It is not directly linked to the average acceleration experienced by the ring. One has then to solve the differential equation. Indeed, a temporal variation of the form cos(ωt) would have lead to the collective oscillations of the atoms of the copper ring at the EM field frequency. However, the presence of θ in Eq.15 also leads to a position drift. We have plotted in figure 7 the numerical solution of equation Eq.15 with the experimental values. One can clearly identify two regimes. The first one corresponds to an oscillation of the mobile with the frequency of the radiated field. This oscillation would have been present even with a plane wave. However, at longer time scales, there is a drift of this oscillation. Actually the electrons are drifted due to the existence of the phase variation of the electric field. The angle variation resembles a parabola. From equation 15, there seems to be a self contradiction between paragraph 5.1.1 and the current paragraph 5.1.2. In paragraph 5.1.1, we claim that the transfer mechanism is via reflection whereas in this paragraph we introduce a dissipation mechanism via the copper resistivity in a way that resembles to absorption.

Here, the transfer mechanism is clearly via reflection. It can't be via absorption for the two following reason. First, in a perfectly conducting material, the running currents at the ring surface would tend towards infinity. The currents are proportional to the inverse of the resistivity. There must be a dissipation mechanism within the copper that accounts for the interaction of the "free" electrons of the metal and the periodic structure. This enables AM conservation. However this absorption is far too weak to be the main transfer mechanism. Indeed, since the reflection coefficient in intensity of copper is of the order of 99, 99% [23], the absorption is in the 0.01% range or lower. Then if we considered this absorption from the total available power, which is of course an over estimation, this would lead to a torque of the order of Γ abs = 10 -4 × N = 9.2 10 -13 Nm. This is negligible. Second, as explained in the beginning of subsection 5.1, there is not enough power available even if all the power is absorbed and transformed to AM to explain our observations.

Torque estimation

From the numerical integration of equation 15, that appears on figure 7, we estimate the angular acceleration of the ring to a m = 8.2 10 -4 • /s 2 . The corresponding torque is of the order of Γ cal = 1. 2 10 -8 Nm. This value is in very good agreement with the experimental value Γ ex = 1. 1 10 -8 Nm. This thus validates the fact that the turnstile antenna and the copper ring should be considered as a whole system as calculated in figure 5. It also validates that the ring behaves like a Fabry-Perot interferometer. This Fabry-Perot effect could not have been taken into account in the calculation carried out in paragraph 3.3.

From Eq.15, since I varies linearly with the frequency, one may think that the torque varies accordingly contrarily to Eq.14. However, the numerical integration of Eq.15 gives a factor proportional to the inverse of the square of the pulsation, leading to a linear dependence of the torque with the wavelength.

Discussion of the transfer mechanism

Comparison with other transfer mechanisms

The rotation of small objects by light sources can be induced either by the linear momentum or by the AM. The first scheme takes advantages of specially shaped threedimensional objects and the scattering of ordinary light [4,[START_REF] Nieminen | Proc. SPIE[END_REF][START_REF] Rubinsztein-Dunlop | Optical Nano and Micro Actuator Technology[END_REF]. The radiation pressure or/and the scattered light exert a force that leads to a torque on such objects. In addition to this mechanism, one can refer to thermocapillary propulsion observed for asymmetric microgears [START_REF] Maggi | [END_REF] where the heat transfer due to the light absorption leads to a torque effect. One can also mention the diffraction of a plane wave on an asymmetric object, [41,42], where the diffracted light carries OAM. Nevertheless, we are interested here in the transfer of momentum from light carrying AM to objects. As for the second scheme, the mechanisms of OAM transfer between light carrying AM and objects can be considered under two different aspects. The first one relies on the determination of the origin of the torque, whereas the second one considers the AM conservation that must be always fulfilled [43]. We are interested here in both aspects.

For SAM, the rotating objects could be birefringent or absorbing objects. In the case of absorbing objects, the torque is applied by the absorbed light and the AM conservation implies that each absorbed photon transfers . In the case of birefringent objects, as discussed in paragraph 3.4, diffraction is responsible for the torque. In the ideal case of λ/2 birefringent objects, each circularly polarized photon flips its polarization leading to a 2 per photon transfer. It could even be increased by a factor of 2 by adding a λ/4 plate and a mirror [1,8]. Birefringent particles could also follow adiabatically (in a quantum mechanical sense, see for example [44]) a rotating polarization [9,45].

For OAM, the transfer mechanism for absorbing or reflecting particles relies in the twisting photons around their propagation direction. Then each photon transfers for absorption and 2 for reflection as in our case. For transparent objects the problem is of a different nature. As already stated in the introduction, for purely transparent particles, the helical phase of the incident beam is not changed while crossing the objects. Hence the objects cannot interact with OAM [16]. However, when these objects introduce astigmatism, the phase front is modified and OAM could be transferred [46]. Besides, in those latter cases, scattering or diffraction of OAM by these objects, could be the transfer mechanism. Nevertheless, scattering and diffraction also modify the helical wavefront and the objects couldn't be considered as purely transparent any more. For example, a "free" cylindrical lens could rotate under the influence of an OAM field [START_REF] Molina-Terriza | [END_REF]. As for birefringent objects, micro-particles can also be trapped in patterns that are rotating. These particles would then follow adiabatically the pattern rotation at a low frequency of the order of few Hertz [47,48]. However such mechanical rotation is not directly linked to the OAM of light.

There is another OAM transfer mechanism based on coherent processes that has been applied to atoms. In particular, the OAM carried by a pump beam could be absorbed by an atom and then probed in a four wave mixing experiment [49]. In the case of Bose Einstein condensates, the absorption of a photon in an incident OAM carrying beam could transfer OAM to the condensate by a resonant two photon process [15]. In such processes, the transfer mechanism relies also on absorption. Nevertheless, in a two photon process, both beam could carry OAM [50]. Then the transfer mechanism is induced both by absorption and stimulated emission. It could also be the same mechanism for ions [51].

In our case, the transfer mechanism is clearly via reflection via a 2 transfer by reflected photon. The reflected beam induces a current inside the rotating strip that causes the mobile to rotate. It is very different from other mechanisms of AM transfer. This transfer mechanism resembles the transfer of AM in the case of the induction motor for magnetic field [52]. Since the detection of a tiny current can be easily carried out, this kind of detection scheme can be an alternative to the determination of an OAM EM field.

Torque estimation as a measure of the topological charge of a twisted beam

In optics, the precise determination of the OAM is still a challenging issue [53,54], for example in highly focused geometry or for large values of [55]. There are mainly three different existing ways to measure the OAM carried by an EM field. The method we have described here could be considered as a fourth method.

The most commonly used method is via interferences either with a plane wave [56][57][START_REF] Lavery | Opical Angular Momentum D[END_REF] or with self interferences [START_REF] Leach | [END_REF][60][61][62][63][64], or even considering the light speckle [65]. An alternative to measure OAM is by optical transformation, operating for example the mode creation optics in reverse [56,[66][67][68][69]. These two techniques could be called classical optical methods. The third method uses the rotational Doppler shift of the beam [70]. It is linked to the EM fieldmatter interaction. The fourth method also relies on EM field-matter interaction. It measures both the torque and the applied power to deduce the topological charge. Such measurement leads to an integer value of the OAM quantity. It has been described in this article in microwaves, although it is coupled here with a Fabry-Perot effect. Besides, in order to measure the topological charge, we can here either measure the torque or the electrical current.

Conclusion

We have investigated the OAM transfer from the EM field radiated by a turnstile antenna in the plane of the antenna to a suspended copper ring. We have shown that the AM transfer mechanism is by reflection of the EM field on the conducting ring. Actually, the EM field induces a small oscillating current with a drift, in the ring. Due to this drift, the ring starts to rotate. The estimated torque is in reasonable agreement with numerical estimations and with the maximum torque available from the antenna. However, each photon must have been used several times like in a Fabry-Perot interferometer. As the sign of the topological charge is reverse, the sign of the torque is also reversed.

Such an experiment could be a new way to detect OAM. Actually, the topological charge can be either detected by the torque exerted on the pendulum like we did here, but it could also be done via the current generated on the detector. Since, in principle, very tiny current could be detected, this could lead to applications in the OAM detection especially in the radio domain where for a given power, the OAM varies linearly with the wavelength, and where the techniques used in optics do not always apply [71,72]. It could even be used to detect OAM in astronomy [73,74]. Conversely, it may also be applied in optics since light beams can generate static electric fields and current via nonlinear effects such as optical rectification [75,[START_REF] Boyd | Nonlinear optics 3d ed[END_REF].

Fig. 1 .

 1 Fig. 1. Experimental set-up. G: radio frequency generator, C: -3 dB coupler, A: 40 dB amplifier. The experiment is performed in an anechoic chamber. Inset VSWR versus frequency for the two dipole antennas. The arrow at a frequency of 870 MHz corresponds to the crossing of the two VSWR signals.

Fig. 2 .

 2 Fig. 2. Plot of the amplitude a) in logarithmic scale (dB(V/m) units), and phase b) of the electric field radiated by the turnstile antenna in the plane of the antenna, without the copper ring. The dotted concentric circles of figure b are guides for the eye to exemplify the 2π phase rotation.

Fig. 3 .

 3 Fig. 3. a) Rotation versus time for a π/2 (circle) and -π/2 (square) phase between the two dipole antennas for different transmitted powers. b) Acceleration versus power for a π/2 (circle) and -π/2 (square) phase between the two dipole antennas.

Fig. 4 .

 4 Fig. 4. Interference effect. Evolution of phase fronts of the electric field in the plane of the antenna, for a phase front φ = 0 (solid line) and φ = π (dotted line) for a) t=0, b) t=T/8, T being the period, c) t=T/2 and d) t=T. Upon reflection (t=T/2), the sense of rotation of the electric field has changed. After a period, the field corresponds to the field at t=0. Thus the field interferes constructively. Bold blue arrows show the direction of the propagation of the wave.

Fig. 5 .

 5 Fig. 5. Amplitude of the electric field in the plane of the antenna, in presence of the ring, in logarithmic scale (dB(V/m) units). The radius of the ring corresponds to the experimental value R = 150 mm.

Fig. 6 .

 6 Fig.6. Simulated distribution of the electric current on the copper ring at a given time for our experimental set-up, for a radiated power of 25 W. Note that the current is running inside the ring. There is hardly any current running outside.

Fig. 7 .

 7 Fig. 7. Integration of the differential equation (Eq. 15) for a radiated power of 25 W. The electrons are submitted to an oscillatory force at the frequency of the EM field and a drift that is due to the OAM.

We would like to thank D. Levalois and R. Legave for technical assistance. This work was supported by the University of Rennes 1 via a "défi émergent" action, the French Ministry of Defense (DGA) and the council of Brittany (Région Bretagne).

Author contribution statement OE, CB and BT conceived the experiment, CB, OE and RN did the experiments, OE and JE carried out the calculations, RN, KM and WL performed the simulations, OE, CB, JE, KM and BT discussed the results, and OE, JE and CB wrote the paper.