Eliana S Mano

Laurent Caner

Sabine Petit

Arthur P Chaves

Andre Mexias

André S Mexias

Ni-smectitic ore behaviour

Keywords: nickel lateritic ores, Caron process, Niquelândia, mineralogical characterization, mineral processing, clay minerals, smectite

come

Introduction

Nickel is processed mainly from sulphide ores and secondly from lateritic ores [START_REF] Boldt | The winning of nickel, its geology, mining and extractive metallurgy[END_REF][START_REF] Trescases | Nickeliferous laterites of Brazil[END_REF][START_REF] Bunjaku | The effect of mineralogy, sulphur, and reducing gases on the reducibility of saprolitic nickel ores[END_REF]. However, in Brazil, the latter represents the most common source of nickel. Lateritic deposits are composed of oxidized (limonite) and/or silicate ores [START_REF] Boldt | The winning of nickel, its geology, mining and extractive metallurgy[END_REF][START_REF] Oliveira | Lateritic nickel deposits of Brazil[END_REF], both formed from the weathering of basic and/or ultramafic rocks (e.g., dunites). In the oxidized type, nickel is mainly associated with goethite, spinels and asbolane. By contrast, in the silicate ore, nickel is present in the structures of clay minerals such as smectite, serpentine, vermiculite, talc, and chlorite.

The Niquelândia deposit was composed by both oxidized and silicate ores [START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF]. In this deposit, the formation of the lateritic ore is related to intense weathering processes under a seasonally humid tropical climate from peridotites, dunites and pyroxenites which have been altered into clay minerals and goethite.

During weathering Ni-Mg-rich trioctahedral smectites ((Mg, Ni)x Si4 [Mg,Ni] 3-x •x O10

[OH]2) were formed due to the low contents of aluminium of the ultramafic rocks [START_REF] Colin | Lateritic weathering of pyroxenites at Niquelândia, Goias, Brazil: The supergene behavior of nickel[END_REF][START_REF] Petit | Characterization and crystal chemistry of an Fe-rich montmorillonite from Ölberg, Germany[END_REF][START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF]; and with the increase of the weathering, nickel and magnesium were leached, forming Al-Fe-dioctahedral rich smectites ((Mg, Ni)x Si4 [Fe, Al, Mg,Ni] 2-x O10 [OH]2) with lower nickel grades [START_REF] Gaudin | Accurate crystal chemistry of ferric smectites from the lateritic nickel ore of Murrin Murrin (Western Australia). I. XRD and multi-scale chemical approaches[END_REF][START_REF] Christidis | A new Ni-rich stevensite from the ophiolite complex of Othrys, Central Greece[END_REF]. The formula above exhibits a square as vacancy, due to the chemical substitutions (divalent cations) in the octahedral layers achieve electrical neutrality [START_REF] Moore | X-ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF].

Either pyrometallurgical or hydrometallurgical methods can be used to extract nickel from the lateritic ores, depending on their mineralogical characteristics. [START_REF] Canterford | The treatment of nickeliferous laterites[END_REF]; [START_REF] Dalvi | The past and the future of nickel laterites[END_REF] and [START_REF] Rice | A hydrochloric acid process for nickeliferous laterites[END_REF] noticed that magnesiumrich ores are not suited to acid hydrometallurgical routes due to the high consumption of sulphuric acid by magnesium. Conversely, lateritic ores with a low SiO2/MgO ratio and low iron content are better suited to pyrometallurgical routes, to produce ferronickel phases [START_REF] Canterford | The treatment of nickeliferous laterites[END_REF][START_REF] De Graaf | The treatment of lateritic nickel ores -a further study of the Caron process and other possible improvements: Part II. Leaching studies[END_REF][START_REF] Diaz | A review of nickel pyrometallurgical operations[END_REF][START_REF] Dalvi | The past and the future of nickel laterites[END_REF]. Even though [START_REF] Diaz | A review of nickel pyrometallurgical operations[END_REF] stated that magnesium-rich ores are suited to Caron processing, De [START_REF] De Graaf | The treatment of lateritic nickel ores -a further study of the Caron process and other possible improvements: Part I. effect of reduction conditions[END_REF][START_REF] De Graaf | The treatment of lateritic nickel ores -a further study of the Caron process and other possible improvements: Part II. Leaching studies[END_REF] and Rhamdhani, et al. (2009a) did not obtain over 65% nickel recovery for the silicate ores processed by the Caron process, even in a reducing environment, using different gases (hydrogen, CO2/CO ratio, H2O/H2, and others). However, for the limonitic ores, the Caron process works well, with nickel extractions over 90% [START_REF] De Graaf | The treatment of lateritic nickel ores -a further study of the Caron process and other possible improvements: Part I. effect of reduction conditions[END_REF].

Despite this, the Caron process was applied at Niquelândia in 1980; the initial run of mine (feed) was altered through the years, increasing the silicate proportion and decreasing the nickel yields. The Niquelândia run of mine was established with 4% of MgO, 26% of SiO2, 8% of Al2O3, 25% of Fe and 1.5% of Ni; however, nickel extraction did never exceed 75%. Thereby, in order to understand the lower nickel yields, specially assigned to silicate ore, X-ray diffraction, scanning electron microscopy, coupled to X-ray dispersion energy analysis, medium infrared spectroscopy and thermogravimetric and differential thermal analyses were performed, from the silicate ore residues obtained by the Caron process (roasting+leaching residues) applied to Niquelândia processing.

Five silicate samples, with different nickel, iron and magnesium amounts, previously studied by [START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF], were selected.

Table 1 shows all the minerals mentioned in this study. In turn, in sample ASL-I5, with a low nickel content, Fe 3+ was the dominant octahedral trivalent cation (iron-nickel montmorillonite end-member) [START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF]. The samples VSL1A, ASL-AN3, AS-BNi2, CSL-G8 and VSL-R2 were mixtures of these two end-members and exhibited intermediate properties, as shown in Figure 1.

Materials and Methods

At Niquelândia, the nickel was extracted by the Caron process, which combines a reduction roasting step at 770ºC, conducted in a Nichols Herreshoff multiple hearth furnace, followed by an ammoniacal leaching step. Thereby, this study was conducted on the residues obtained by the Caron process from silicate ore to investigate mineralogical transformations occurring during the processing. Five samples studied by [START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF] were selected based on their chemical compositions and nickel extractions: AS-ANi3, ASL-I5, VSL1A, ASL-AN3 and VSL-R2 (Table 1 and Figure 1).

Reduction roasting and leaching simulations were carried out at the Niquelândia laboratory using the mining company protocol based on the procedure applied by

De [START_REF] De Graaf | The treatment of lateritic nickel ores -a further study of the Caron process and other possible improvements: Part I. effect of reduction conditions[END_REF]; [START_REF] Valix | Study of phase transformation of laterite ores at high temperature[END_REF] and Rhamdhani et al. (2009b). The reduction roasting process was performed in a small tube furnace, the dimensions of which are 573 mm (width), 663 mm (height) and 455 mm (depth).

A reducing atmosphere was used in the furnace all throughout the experiment by injecting a mixture of 10.5% of CO, 8% of CO2, 10% of H2 and 71.5% of N2. This atmosphere is similar to that of the Nichols Herreshoff multiple hearth furnace used in the processing of ores.

Three reduction temperatures were tested: 550C, which corresponds to the dehydroxylation temperature of different dioctahedral clay minerals; 770C, which corresponds to the Caron process temperature; and, finally, 900C, the supposed temperature at which new mineral phases start to form [START_REF] De Graaf | The treatment of lateritic nickel ores -a further study of the Caron process and other possible improvements: Part II. Leaching studies[END_REF].

A mixture of 0.756 g of petroleum coke and 1.47 g of fuel oil was added to 100 g of the bulk sample (the silicate ore <10 m size fraction) and introduced into the furnace at a temperature of 450 º C under a N2 atmosphere. Afterwards, the reducing gas mixture was connected, the N2 flux was interrupted and the temperature of the furnace was increased to 550 º C, at which the sample remained for 40 min. Finally, the reductant gas mixture was unplugged, and the N2 flow was reconnected.

The sample temperature decreased naturally to 450 º C, and then, the temperature was forced to decrease to 60 º C with a ventilator; there was no interruption of the N2 flux during cooling, used to prevent the re-oxidation of the samples. At 60 º C, the sample was removed from the furnace and introduced into a container with water to prevent the oxidation of the metals. All of the above procedure was repeated for the experiments at reduction temperatures of 770 º C and 900 º C.

The leaching process (Yabulu procedure) was performed using a solution of ammonium carbonate and free ammonia with an approximate molar ratio of about 1:2 ((NH4)2CO3) + 2NH3); prepared from 90 to 100 g/L of NH3 and 80 to 85 g/L of CO2. In the steel reactor, approximately 100 mL of the roasted material was added to 3000 mL of ammoniacal solution. The reactor was closed and the mixture was stirred with air injection of 120 L/min. The pH of the experiment was controlled between 9.5 and 10.5 and the shaker was set to 280 rpm (vertical shaker rod) for 2 hours; the temperature was not higher than 50C. At this time, the shaker and the compressed air were turned off and the solution was left quiescent for 1 hour. Finally, the leached residue was filtered and washed in an ammonia solution and then with demineralized water. The residue and the leached solution were analysed by ICP-AES. X-ray diffraction (XRD) and scanning electron microscopy, coupled with an energy dispersion X-ray spectroscopy microanalysis (SEM/EDX) and Fourier Transform Infrared Spectroscopy (FTIR) were used to determine the mineral phase transformations that occurred during the reduction roasting and the leaching steps.

The XRD patterns were recorded on a Bruker D8 Advance instrument with the following parameters: Cu Kα radiation -40 kV and 40 mA -Lynxeye detector, from 3 to 65° 2θ, with steps of 0.02° 2θ and a counting time per step of 115 s.

The mid-infrared spectra (MIR) from the residual material were obtained from pressed KBr pellets using a Nicolet Magna-IR 760 spectrometer in the range 400-4000 cm -1 with a 4 cm -1 resolution. The pellets were prepared following the procedure described by Baron and Petit (2016). Thermogravimetric and differential thermal analyses (TG and DTA) were conducted to check the minerals behaviour during the heating process. These analyses were performed using a Du Pont SDT2960 model at the Universidade Federal de Ouro Preto (Minas Gerais -Brazil). The data were obtained from the bulk samples from 25ºC to 1,000ºC with a heating rate of 10ºC/min under air flow of 100 mL/min.

Results

XRD results

The reduction roasting step is the most important part of the Caron process, being responsible for transforming nickel bearing minerals (i.e. clay minerals, spinels and goethite) to phases more suitable for the ammoniacal leaching, such as ironnickel metallic phases.

The increase of the temperature above 550C, during the reduction roasting stage, transformed clay minerals (mainly smectites) and goethite into talc, olivines, pyroxenes, amphiboles, spinels and hematite (Figures 3 and4); however, samples ASL-I5, AS-ANi3, ASL-AN3 and VSL-R2, already contained spinels and pyroxenes before the reduction roasting step. For sample ASL-I5, the incremental increase of the temperature (>550C) transformed smectites into talcs, which, in turn, formed pyroxene and olivine at 900C. In this sample, new spinel phases and Fe-Ni alloy had already formed at 770C. Sample AS-ANi3, which was initially composed of smectites, talc, pyroxene and spinels, continued to exhibit talc peaks at 770C, as explained by [START_REF] Ptáček | Preparation of dehydroxylated and delaminated talc: Meta-talc[END_REF], which showed that talc dehydroxylation occurs at temperatures close to 900C to form pyroxenes. A minor content of spinels was observed at 770C; however, no Fe-Ni alloy was noted; actually, in this sample, no metallic phases were detected, even at high temperatures (Figure 3).

DTA and TGA analyses

Thermal gravimetric (TGA) and differential thermal analyses (DTA) were conducted to determine the dehydroxylation temperature for samples AS-ANi3 and ASL-I5 (Figures 6 and7) and to confirm the main mineral changes observed by X-ray diffraction.

The peak of the DTA curves at 74-82C is related to the water absorbed by the smectites. For sample ASL-I5 (Fe-rich dioctahedral smectite), the dehydroxylation reaction occurred at 442C (Figure 6), which is in agreement with clay mineral changes observed in the XRD patterns (Figure 3) at low temperatures (<550C). Low temperatures of dehydroxylation for Fe-rich smectites were also observed by [START_REF] Frost | The Garfield and Uley nontronites -an infrared spectroscopic comparison[END_REF] for nontronites from Garfield (USA) and Uley (Australia). Indeed, [START_REF] Brigatti | Relationships between composition and structure in Fe-rich smectites[END_REF] showed that the temperature of dehydroxylation of smectite depends on the iron content; and it is well known that a higher iron content induces lower dehydroxylation temperatures [START_REF] Arab | Identification of clay minerals in mixtures subjected to differential thermal and thermogravimetry analyses and methylene blue adsorption tests[END_REF]. Sample AS-ANi3 (Fe-poor smectite), in turn, revealed a dehydroxylation peak at 648C (Figure 7) attributed to the dehydroxylation of Fepoor smectites. [START_REF] Christidis | A new Ni-rich stevensite from the ophiolite complex of Othrys, Central Greece[END_REF] and [START_REF] Ptáček | Preparation of dehydroxylated and delaminated talc: Meta-talc[END_REF] reported that talc transformed to pyroxene at approximately 850C. The peak at 882C is then attributed into the formation of pyroxenes for sample AS-ANi3, in agreement with the presence of this phase on the XRD patterns (Figure 3).

The dehydroxylation temperature of goethite occurs at 300C, as observed for the TGA curve for sample ASL-I5 (Figure 6) and as described by several authors [START_REF] Chander | Reduction roasting/ammonia leaching of nickeliferous laterites[END_REF][START_REF] Cornell | The iron oxides Structure, Properties, Reactions, Occurrence and Uses[END_REF][START_REF] O'connor | Reduction roasting of limonite ores: effect of dehydroxylation[END_REF][START_REF] Elliott | Thermodynamics of the reduction roasting of nickeliferous laterite ores[END_REF].

Scanning electron microscopy and EDX analyses

Textural aspects were observed by SEM (Figure 8). Clay mineral structures were preserved (Figure 8A) even after roasting at high temperatures; features arising from dehydroxylation were also observed (Figure 8C and D). Figure 8C exhibits a thin iron crust covering an aluminium silicate particle. Figures 8B and8D show acicular crystals and nickel-cobalt alloy droplets trapped within the silicate particles. The EDX analyses coupled to the SEM from the leach residues revealed that iron and nickel are hosted within the silicate or spinel grains. [START_REF] Valix | Study of phase transformation of laterite ores at high temperature[END_REF] suggested that nickel incorporated into the magnesium silicate phase is transformed during reduction roasting into forsterite, which is unsuitable for ammoniacal leaching.

FTIR spectroscopy

Table 3 summarizes the results from FTIR, and Figure 9 exhibits the medium infra-red spectra (MIR) for the bulk samples. The Figure 10 presents the MIR for AS-ANi3 sample after reduction step. Baron et al., 2016;[START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF][START_REF] Christidis | A new Ni-rich stevensite from the ophiolite complex of Othrys, Central Greece[END_REF][START_REF] Petit | Crystal-chemistry of talcs: a NIR and MIR spectroscopic approach[END_REF][START_REF] Gerard | Infrared studies of Ni-bearing clay minerals of the kerolite-pimelite series[END_REF][START_REF] Wilkins | Infrared spectra of some synthetic talcs[END_REF]Madejová et al., 2011 3420 OH stretching vibrations of adsorbed water [START_REF] Madejová | Application of vibrational spectrocopy to the characterization of phyllosilicates and other industrial minerals[END_REF]710 OH bending Madejová et al., 2011 ;[START_REF] Petit | Transformation of synthetic Zn-stevensite to Zntalc induced by the Hofmann-Klemen effect[END_REF]Baron et al., 2016;[START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF][START_REF] Christidis | A new Ni-rich stevensite from the ophiolite complex of Othrys, Central Greece[END_REF][START_REF] Petit | Crystal-chemistry of talcs: a NIR and MIR spectroscopic approach[END_REF][START_REF] Gerard | Infrared studies of Ni-bearing clay minerals of the kerolite-pimelite series[END_REF]Wilkins and Ito, 1967 660 OH bending and Si-O [START_REF] Madejová | Application of vibrational spectrocopy to the characterization of phyllosilicates and other industrial minerals[END_REF]Petit et al., 2008 870 and820 OH bending vibrations Farmer, 1974;[START_REF] Petit | Characterization and crystal chemistry of an Fe-rich montmorillonite from Ölberg, Germany[END_REF][START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF]1020, 950 and 790 Si-O stretching vibration before reduction at 770C [START_REF] Liu | Investigation of the thermal decomposition of talc[END_REF][START_REF] Madejová | Comparative FT-IR study of the structural modifications during acid treatment of dioctahedral smectites and hectorite[END_REF][START_REF] Ptáček | Preparation of dehydroxylated and delaminated talc: Meta-talc[END_REF]Ptáček et al., 1090 Si-O stretching vibration after reduction at 770C For the bulk samples (Figure 9), the trioctahedral character is revealed by absorption bands at 3650, 3624 and 710 cm -1 , assigned to Mg3OH, Ni3OH and Ni3OH modes, respectively [START_REF] Wilkins | Infrared spectra of some synthetic talcs[END_REF][START_REF] Gerard | Infrared studies of Ni-bearing clay minerals of the kerolite-pimelite series[END_REF][START_REF] Petit | Crystal-chemistry of talcs: a NIR and MIR spectroscopic approach[END_REF][START_REF] Christidis | A new Ni-rich stevensite from the ophiolite complex of Othrys, Central Greece[END_REF][START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF]Baron et al., 2016).

The adsorbed water is assigned to the absorption band at 3420 cm -1 [START_REF] Madejová | Application of vibrational spectrocopy to the characterization of phyllosilicates and other industrial minerals[END_REF]. For the dioctahedral smectites, in the OH-bending region, the absorption band at 870 cm -1 is assigned to the AlFe 3+ OH mode and the band of 820 cm -1 , to the Fe 3+ Fe 3+ OH mode [START_REF] Farmer | Infrared Spectra of Minerals[END_REF][START_REF] Petit | Characterization and crystal chemistry of an Fe-rich montmorillonite from Ölberg, Germany[END_REF][START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF]. The band at 660 cm -1 is also characteristic of trioctahedral smectites and assigned to the Mg3OH mode [START_REF] Petit | Transformation of synthetic Zn-stevensite to Zntalc induced by the Hofmann-Klemen effect[END_REF][START_REF] Madejová | Application of vibrational spectrocopy to the characterization of phyllosilicates and other industrial minerals[END_REF].

Minor clay mineral structural modifications can be noted by FTIR spectroscopy [START_REF] Madejová | Review: FTIR techniques in clay mineral studies[END_REF][START_REF] Pálková | Acid dissolution of reduced-charge Li-and Ni-montmorillonites[END_REF]. Mid-infrared (MIR) spectra of sample AS-ANi3, performed before and after the roasting step, are shown in Figure 10. After the reduction step at 770C, the absorption bands attributed to OH-stretching modes disappeared. The absorption band at 1020 cm -1 , attributed to Si-O stretching vibrations in tetrahedral sheets of layer silicates, shifted to 1090 cm -1 after the reduction step. This band, together with new bands at 950 cm -1 and 790 cm -1 (Figure 10) suggest the presence of amorphous silica [START_REF] Madejová | Comparative FT-IR study of the structural modifications during acid treatment of dioctahedral smectites and hectorite[END_REF][START_REF] Liu | Investigation of the thermal decomposition of talc[END_REF] that can be formed during the roasting step.

Nickel extraction

The nickel extractions, expressed as the percentage of the nickel extracted over the total nickel in each sample, after roasting at the different temperatures and leaching steps are presented in Figure 11.

Figure 11 -Nickel extraction after different temperatures. The leaching conditions were the same for all the samples: pH between 9.5 to 10.5, temperature <50C, 120 min of leaching time.

higher temperatures (>800C), nickel can be trapped into the neoformed phases, decreasing nickel extractions values. [START_REF] Apostolidis | The kinetics of the sulphuric acid leaching of nickel and magnesium from reduction roasted serpentine[END_REF] showed that nickel is properly leached from the Fe-Ni alloy, whereas the extraction is slow and incomplete from the olivines.

The Fe-rich dioctahedral smectite from Niquelândia gave nearly 90% of nickel extraction; in turn, for the trioctahedral smectite, the nickel extraction did not exceed 10%, despite the higher nickel content. Iron-rich phases, such as spinels and Fe-Ni alloy, were formed from the Fe-rich dioctahedral smectite, during the roasting reduction step, according to XRD analysis. In turn, pyroxene, talc and olivine were formed from the trioctahedral smectite.

De Graaf (1979) described a graph, which although considered a gross simplification of Fe-O and Ni-O systems, is useful to predict nickel extraction behaviour, based on the newly formed phases. For example, De Graaf explained that for limonitic ore, the optimum nickel extraction is obtained in the "wustite" zone; however, for silicate ore, the maximum extraction can be reached in the "magnetite/wustite" zone. To account for the formation of these phases, [START_REF] Elliott | Thermodynamics of the reduction roasting of nickeliferous laterite ores[END_REF], presented the reactions:

2FeOOH (goethite) → Fe2O3 (hematite) + H2O 6(Fe, Ni)OOH (goethite) → 2(Ni, Fe)3O4 (spinel) + 3H2O + ½ O2 3Fe2O3 (hematite) + CO → 2Fe3O4 (magnetite) + CO2 Fe3O4 (magnetite) + CO → 3 FeO (wustite) + CO2 FeO (wustite) + CO → Fe + CO2
Some of the reactions above were also described by [START_REF] Wang | Preparing ferro-nickel alloy from low-grade laterite nickel ore based on metallized reduction-magnetic separation[END_REF] as intermediates in the formation of Fe-Ni alloys. They also presented the standard Gibbs free energy for some of these reactions. [START_REF] Wang | Preparing ferro-nickel alloy from low-grade laterite nickel ore based on metallized reduction-magnetic separation[END_REF] explained that it is easy to transform Fe3O4 to FeO at temperatures higher than 973 K (700C).

Based on the XRD results from samples ASL-I5 and AS-ANi3, the following reactions were indicated: The XRD results suggest that, if a Fe-rich mineral (e.g. goethite) was added to the Ni-rich smectite ore, perhaps the nickel may combine with reduced iron to form Fe-Ni alloys, resulting in better nickel extractions. Indeed, [START_REF] Canterford | The treatment of nickeliferous laterites[END_REF] reported that Davidson (1972) added ferric oxide to high-magnesia silicate ores, improving the nickel extraction by 20%. However, Canterford also mentioned another research conducted by Scott and Dyson in which ferric oxide was added to their sample, but did not give any improvement.

Conclusions

In the Caron process, the composition of the mineralogical assemblage and the reducing atmosphere, carried out during the roasting reduction step, are essential parameters to induce the formation of new Fe-Ni phases. In samples, in which there was no Fe-Ni alloy or low Fe/Ni ratio (<1.5), the nickel extraction was poor (<10% at 770C). Thereby, only the nickel from the Ni-Fe alloys were solubilized by ammoniacal leaching. In addition, the nickel losses were also due to drops of Fe-Ni alloys, being trapped within silicate phases, which were not leached by the ammoniacal solutions.

The nickel extraction data showed that the optimal reduction roasting temperature to obtain the best nickel extractions was 770ºC. Temperatures higher than 800ºC caused a decrease in nickel extraction as new silicate minerals, such as pyroxenes and olivines, not solubilized by ammoniacal solutions, were formed. These neoformed minerals which are more resistant to leaching can trap Ni-Fe alloys within their particle structure and/or host nickel within their crystal structures.

In spite of all the studies previously conducted, the mechanisms for the formation of neoformed minerals are not fully understood, and further studies varying chemical compositions on the feed and redox atmosphere should be performed.

Figure 1 -

 1 Figure 1 -EDX analyses showing smectite compositions varying from di to trioctahedral group members. Modified from Mano et al. (2014). Data points represent compositions in Table 2.

Figure 2 -

 2 Figure 2 -(A) Tri and (B) Dioctahedral structures of the smectites from Niquelândia (see Mano et al., 2014).

  Two scanning electron microscopes (SEM) coupled with EDX microanalysis systems were used to investigate the association of nickel with the different minerals in the reduction and leaching products: a LEO-Stereoscan 440/INCA -Oxford instrument operating at 20 kV and 20 mA, with a silicon drift detector (SDD) at the Universidade de São Paulo and a JEOL JSM-5600 LV instrument coupled with a BRUKER X-Flash 4010 EDS spectrometer at the Université de Poitiers.

For

  samples VSL1A, ASL-AN3 and VSL-R2, with different proportions of di and trioctahedral smectites, different behaviours were noted, based on the initial mineral phases. Sample VSL1A, which was composed essentially of smectites and a minor amount of spinel, formed a talc, pyroxene and an Fe-Ni alloy at 770C. At 900C, talc disappeared and only pyroxene, spinels and Fe-Ni alloy were noted. Sample ASL-AN3, revealed smectites, talc, pyroxenes, spinels and hematite in the bulk sample, formed a small amphibole content at 770C. Talc and pyroxene remained at this temperature; olivine and Fe-Ni alloy had been formed. Finally, sample VSL-R2, consisted essentially of pyroxenes and secondarily of smectites and spinels; after the reduction roasting stage (770C), in addition to pyroxenes and spinels, small quantities of amphibole and Fe-Ni alloy were formed.

Figure 5

 5 Figure5shows the XRD patterns for the reduced and leached products (VSL1A,

Figure 3 -

 3 Figure 3 -XRD patterns for samples: a) ASL-I5 and b) AS-ANi3, before and after the reduction roasting step.

Figure 4 -

 4 Figure 4 -XRD patterns for samples: a) VSL-1A, b) ASL-AN3 and c) VSL-R2, before and after the reduction roasting step.

Figure 5 -

 5 Figure 5 -XRD patterns for samples: a) VSL-1A, b) ASL-AN3 and c) VSL-R2, heated and leached products. Iron phases were leached.

Figure 6 -

 6 Figure 6 -DTA and TGA curves for sample ASL-I5.

Figure 7 -

 7 Figure 7 -DTA and TGA curves for sample AS-ANi3.

Figure 8 -

 8 Figure 8 -SEM/BSE images, sample ASL-AN3, after the reduction roasting step. A-pyroxene particle which retains a clay mineral structure. B-Iron oxide was observed in the residue product of the reduction step. C-Iron migrates toward the particle surface after the reduction step. D-metals, such as iron and nickel, trapped inside particles.

Figure 9 -

 9 Figure 9 -MIR spectra of the bulk samples, showing the effect of changing cations replacements (Fe, Al, Ni and Mg) on the absorption bands

Fe2Si4O10(

  OH)2 (dioctahedral smectite) + 2Fe2O3(hem) + (Fe,Mg) Al2O4 (spinel) + 2(Mg,Ni)3 Si4O10(OH)2 (talc) → 2Mg2SiO4 (oliv) + (Fe,Mg)2Si2O6 (pyrox) + MgAl2O4 (spinel) + Fe 3+ 2Fe 2+ O4 (magn) + 2FeNi3 + 8SiO2 + 3H2O + 5 /2 O2 and (Ni,Mg)3 Si4O10(OH)2 (trioctahedral smectite) + (Mg,Ni)3 Si4O10(OH)2 (talc) + (Ni,Mg)2Si2O6 (pyrox) + (Fe, Al)2O4 (spinel) → 2(Mg,Ni)3 Si4O10(OH)2 (talc) + (Fe,Al)2O4 (spinel) + (Ni,Mg)2 Si2O6 (pyrox) Due to the low iron content in the AS-ANi3 sample, nickel did not report to ironbearing phases but was rather trapped in the structure of neoformed silicates. De Graaf (1980), deduced that nickel was trapped in the silicates phases by attacking the silicate ore residue with a strong acid HCl+(NH4F), increasing the nickel extraction from 70% to 100%. The iron/nickel ratio can explain the nickel extraction results for the others samples. Iron-nickel alloys formed during the reduction roasting step are attacked by ammoniacal solutions. Sample VSL1A (Figures 11 and 5), despite forming Fe-Ni alloy at 770C, exhibited a poor nickel extraction (nearly 10% of Ni); due to the lower Fe/Ni ratio (1.5). Conversely, sample VSL-R2 (Fe/Ni ratio2) showed nickel extractions close to 55%; compared with samples VSL1A and ASL-AN3. The leached Fe-Ni alloy was higher in this sample than the two others (Figure 5). Finally, sample ASL-AN3 exhibited an intermediate nickel extraction, of nearly 25%; and also, an intermediate Fe/Ni ratio. The reaction concerning these newly formed phases as suggested from the XRD results is: (Ni,Fe)3 Si4O10(OH)2 (trioctahedral smectite) + Fe2Si4O10(OH)2 (dioctahedral smectite) + (Ni,Mg)2Si2O6 (pyrox) + (Fe,Al)2O4 (spinel) → (Ni,Mg)2Si2O6 (pyrox) + 2Fe2O3(hem) + FeNi3 + (Fe,Al)2O4 (spinel) + 8SiO2 + 2H2O

Table 1 -

 1 Minerals relevant in this study

	minerals	formulae	minerals	formulae
		(Mg, Ni)x Si4 [Mg,Ni] 3-x •x O10
	smectite	[OH]2	amphibole	Ca2(Mg,Fe ++ )5Si8O22(OH)2
		(Mg, Ni)x Si4 [Fe, Al, Mg,Ni] 2-x
		O10 [OH]2		Ca2[Mg4(Al,Fe +++ )]Si7AlO22(OH)2
	talc	(Ni,Mg)3Si4O10(OH)2		[ ]Ca2Mg5Si8O22(OH)2
	pyroxene	Mg2Si2O6	Olivine	Mg2SiO4
		CaMgSi2O6		Fe ++	2SiO4
	serpentine	Mg3Si2O5(OH)4	magnetite	Fe ++ Fe +++	2O4
		(Ni,Mg,Fe ++ )2Al(SiAl)O5(OH)4	spinel	MgAl2O4
		(Mg,Fe ++ )3Si2O5(OH)4	hematite	Fe2O3
	vermiculite Mg1.8Fe 2+ 0.9Al4.3SiO10(OH)2•4(H2O)	goethite	FeO(OH)
				Ni0.3Co0.1Ca0.1Mn 2+	1.5O1.5
	chlorite	Mg3.75Fe 2+ 1.25Si3Al2O10(OH)8	asbolane	(OH)2•0.6(H2O)
			Fe-Ni
	quartz	SiO2	phase	FeNi3
	Previous results of the characterized samples
	Mano et al. (2014) showed that the silicate ores from the Niquelândia deposit
	contained Ni-bearing clay minerals, quartz, iron and/or manganese
	oxides/hydroxides, pyroxene and olivine in minor quantities. The chemical
	compositions of the bulk samples measured by inductively coupled plasma (ICP-
	AES) are given in Table 2, and energy dispersion X-ray spectroscopy

Table 2 -

 2 Chemical analyses results from ICP-AES for all samples[START_REF] Mano | Mineralogical characterization of Ni-bearing smectites from Niquelândia, Brazil[END_REF].

	Samples				Chemical results (wt%)
		NiO	Fe2O3 CoO CuO MnO Cr2O3 Al2O3 MgO SiO2	LOI
	AS-ANi3	23.4	5.23	0.45	0.8	0.12	1.30	2.45	7.44	39.9 6.82
	ASL-I5	1.16	32.4	0.05 0.19	0.56	1.96	4.76	5.07	44.6 6.68
	VSL1A	9.43	14.3	0.05 0.21	0.3	2.39	8.52	7.55	44.1 7.91
	ASL-AN3	7.75	13.4	0.02 0.23	0.3	1.33	5.07	12.4	40.1 5.53
	CSL-G8	2.08	15.3	0.03 0.13	0.23	1.39	5.07	10.5	50.7	-
	AS-BNi2	2.11	17.7	0.08 0.24	0.52	ND	3.95	4.87	51.0 8.45
	VSL-R2	4.74	10.1	0.02 0.04	0.22	1.08	3.93	19.1	35.1 3.71

Table 3

 3

		-FTIR bands observed and their attribution for Ni-Fe smectites
	wavenumber	vibrations	references
	(cm -1 )
	3650, 3624	OH stretching vibrations

Acknowledgments

This study has been supported by CAPES -Coordenação de Aperfeiçoamento de Pessoal de Nível Superior/ Brazilian Coordination for the Improvement of Higher Education Personnel [Project CAPES/COFECUB: 9075/12-7 -Te 761/12] and FAPESP -Fundação de Apoio à Pesquisa do Estado de São Paulo/ the State of São Paulo Research Foundation [Project: 10/50849-4]. The authors also thank Eng. Marco Antonio Angora, Héctor Nelson E. Troncoso and Bianca Foggiatto; Votorantim Metais Níquel Company for all the contributions and Professor Danilo Rheinheimer dos Santos from the Universidade Federal de Santa Maria. The authors are very grateful to the reviewers and to the editor in chief of the Hydrometallurgical Journal who greatly helped us to improve this article.

A remarkable nickel recovery, with greater than 90% of the total nickel extracted, was observed for sample ASL-I5 (dioctahedral smectite) after reduction roasting at 770ºC (Figure 11). By contrast, less than 10% of the total nickel was extracted from sample AS-ANi3 (trioctahedral smectite), which exhibited low and near constant nickel extraction, regardless of the roasting temperature. Sample VSL-R2 exhibited over 50% nickel extraction after reduction roasting at 770ºC. The nickel extraction for samples VSL1A and ASL-AN3 did not reach 30% after reduction roasting at 770ºC.

The best nickel extractions were obtained for the samples reduced at approximately 700-800C. A substantial drop in nickel extractions was observed especially for samples ASL-I5 and VSL-R2 at temperatures higher than 770-800C.

Discussion

Nickel laterites, depending upon their mineralogical composition, are processed by either hydrometallurgical or pyrometallurgical process. [START_REF] Canterford | The treatment of nickeliferous laterites[END_REF][START_REF] De Graaf | The treatment of lateritic nickel ores -a further study of the Caron process and other possible improvements: Part II. Leaching studies[END_REF], [START_REF] Dalvi | The past and the future of nickel laterites[END_REF], suggested that nickel silicate ores are better suitable for pyrometallurgical processing, and limonitic ores for hydrometallurgical processing. [START_REF] Apostolidis | The kinetics of the sulphuric acid leaching of nickel and magnesium from reduction roasted serpentine[END_REF]Distin (1978), De Graaf (1979) and [START_REF] Chander | Reduction roasting/ammonia leaching of nickeliferous laterites[END_REF] pointed out that nickel extractions are intrinsically related to the iron and nickel metallic phases formed during the roasting and leaching steps. Nickel extraction reaches a maximum when it combines with iron as (Ni-Fe)O [START_REF] Chander | Reduction roasting/ammonia leaching of nickeliferous laterites[END_REF]. This phase is probably formed nearly 700C (for limonitic ore) in which iron is partially reduced and most of the nickel is reduced. [START_REF] Chander | Reduction roasting/ammonia leaching of nickeliferous laterites[END_REF] explained that at


Kazem Ardaneh
email: kazem.arrdaneh@gmail.com

Dongsheng Cai

Ken-Ichi Nishikawa

Bertrand Lembége

Collisionless Weibel shocks and electron acceleration in gamma-ray bursts

Keywords: acceleration of particles -galaxies, jets -gamma rays, burstsmagnetic fields -plasmas -shock waves

A study of collisionless external shocks in gamma-ray bursts is presented. The shock structure, electromagnetic fields, and process of electron acceleration are assessed by performing a self-consistent 3D particle-in-cell (PIC) simulation. In accordance with hydrodynamic shock systems, the shock consists of a reverse shock (RS) and forward shock (FS) separated by a contact discontinuity (CD). The development and structure are controlled by the ion Weibel instability. The ion filaments are sources of strong transverse electromagnetic fields at both sides of the double shock structure over a length of 30 -100 ion skin depths. Electrons are heated up to a maximum energy ǫ ele ≈ √ ǫ b , where ǫ is the energy normalized to the total incoming energy. Jet electrons are trapped in the RS transition region due to the presence of an ambipolar electric field and reflection by the strong transverse magnetic fields in the shocked region. In a process similar to shock surfing acceleration (SSA) for ions, electrons experience drift motion and acceleration by ion filament transverse electric fields in the plane perpendicular to the shock propagation direction. Ultimately accelerated jet electrons are convected back into the upstream.

Introduction

Relativistic jets are present in a variety of high-energy astrophysical systems, e.g., pulsar wind nebulae (PWNe), gamma-ray bursts (GRBs), and active galactic nuclei (AGNs). The jets propagate through an external medium and create a double shock structure at the leading edge (Bromberg et al. 2011). The most extreme relativistic jets are known to be associated with GRBs (Ramirez et al. 2002). GRBs are often seen when massive stars culminate their lives producing powerful internal jets and supernovae explosions. Non-thermal emission associated with the relativistic jets is believed to be generated by the accelerated electrons via synchrotron or inverse Compton mechanisms. Diffusive shock acceleration (DSA) is the most applicable theory for the acceleration of particles in shock systems (Blandford & Eichler 1987). In this process, particle acceleration takes place as the result of particle trapping and oscillating at the shock front. Even though DSA is successful for elucidating ion acceleration, acceleration of the electrons cannot be directly related to this mechanism. To experience DSA a thermal electron requires crossing the shock front multiple times. However, a thermal electron is closely tied to the magnetic field lines because of its small Larmor radius. Thus with no strong pre-acceleration process, a thermal electron is convected downstream without feeling any serious DSA. The lack of DSA for thermal electrons is often referred to as the electron injection problem (Hoshino & Shimada 2002;Amano & Hoshino 2009;Guo et al. 2014).

PIC simulations can shed light on the mechanism of electron acceleration in collisionless shocks. In the high Mach number (the ratio of the upstream bulk flow speed to the sound speed in the ambient medium) regime, many authors have reported that the SSA process can inject highenergy electrons into the DSA (Dieckmann et al. 2000;Hoshino 2001;McClements et al. 2001;Hoshino & Shimada 2002;Schmitz et al. 2002;Amano & Hoshino 2009;Matsumoto et al. 2012). In the SSA process predominantly electrostatic fluctuations are excited at the leading edge of the shock via the Buneman instability (Buneman 1958), due to the interaction between incoming electrons and reflected ions. The incoming electrons are then trapped in the electrostatic potential and efficiently accelerated by the shock convective electric field (i.e., the electric field resulting from the motion of the magnetized upstream region toward the shock,

E 0 = -β 0 × B 0 ).
To date, electron acceleration in unmagnetized (B 0 = 0) electron-ion shocks has been poorly investigated. The injection process is anticipated to be different from magnetized shocks because there is no convective electric field to accelerate the electrons. In the present work, a 3D PIC simulation is used to study the shock structure, and the process of electron acceleration associated with a relativistic jet propagating into an unmagnetized plasma. This setup is the most applicable model for external GRBs shocks. The spatial and temporal scales of the present simulation are much larger than those used in previous studies (Nishikawa et al. 2003;Ardaneh et al. 2014;Choi et al. 2014) in order to allow us to observe efficient particle acceleration. The present paper aims to address the following questions related to an unmagnetized double shock system: (i) What are the field structures responsible for the processes of electron heating, and acceleration?, (ii) Where do these processes mainly take place?, (iii) What is the resulting associated electron energy spectrum?, and (iv) What are the principal mechanisms responsible for electron heating, and acceleration?

In this paper the simulation method and parameters setup are summarized in § 2. The main simulation results are discussed in § 3. Finally, we conclude in § 4.

Simulation method and parameter setup

In recent works, in order to generate a shock, a relativistic plasma stream is injected from one end of the computational grid and reflected from a rigid wall at the opposite end (for instance, a 1D simulation by Hoshino & Shimada (2002), 2D simulations by Spitkovsky (2008a,b); Amano & Hoshino (2009); Martins et al. (2009), and a 3D simulation by Guo et al. (2014)). This method resembles the collision of two identical counter-streaming beams and reduces by one-half the number of calculations. This approach simulates only a moving FS. In the present work we inject a particle jet into an ambient plasma, so that a double shock structure is fully captured. With this setup the jet-to-ambient density ratio can be changed and by assuming a density ratio greater than one, the shock formation process can be properly handled by smaller scale (temporal and spatial) simulations. Deceleration of the jet flow by the ambient plasma results in a CD (the CD is the location where the electromagnetic field and the velocity of jet and ambient plasmas are similar and the density changes). Two shocks propagate away from the CD into the jet and ambient upstreams (in the CD frame). Hence, two shocks and one CD split up the jet and ambient plasma into four regions: (1) unshocked ambient, (2) shocked ambient, (3) shocked jet, and (4) unshocked jet. Hereafter, subscripts 1, 2, 3, and 4 refer to the unshocked ambient, shocked ambient, shocked jet, and unshocked jet, respectively. Quantities with a single index Q i denote the value of quantities Q in region i in frame i and quantities with double indices Q ij denote the value of quantities Q in region i as seen in frame j.

The present simulation is performed using an adopted version of the TRISTAN code [START_REF] Buneman | Tristan[END_REF]Niemiec et al. 2008), a massively parallel, fully relativistic, PIC code that can be used for many applications in astrophysical plasmas (Nishikawa et al. 2003(Nishikawa et al. , 2005(Nishikawa et al. , 2009;;Ardaneh et al. 2014;Choi et al. 2014). The simulation is carried out in the ambient frame with a box including 8005 nodes in the x-direction, and 245 nodes in the y and z-directions. There are 6 particles per cell per species for the ambient plasma (≈ 3 billion particles per species) and the jet-to-ambient density ratio used is 1.7. The ion-to-electron mass ratio used is 16. The system is numerically resolved with 5∆x per electron skin depth in each direction and ∆tω pe = 0.01, where ∆x and ∆t are the grid size and the time step, respectively. The thermal speed of ambient electrons and ions is 0.05c and 0.01c, respectively. In the simulation, the jet fills the whole computational box in the yz-plane and is injected at x = 25∆x in the positive x-direction. The injected jet bulk speed is β 41 = 0.9950, γ 41 = (1 -β 2 41 ) -1/2 = 10, the Mach number M ≡ β 41 /β s1 = 60, and the jet electrons and ions have a thermal speed of 0.014c and 0.003c, respectively. The surfaces at x = x min and x max are rigid reflecting boundaries for the ambient particles, while they are open boundaries for the jet particles. These surfaces are radiating boundaries for the fields based on Lindman's method as explained in [START_REF] Buneman | Tristan[END_REF]. Periodic boundary conditions are applied at all other boundaries for both particles and fields. In the following, time is normalized to ω -1 pe , space to the electron skin depth, λ ce = c/ω pe , particle momentum for species i to the corresponding m i c (e: electron and i: ion), and density to the upstream ambient density, n 1 . The dimensionless form of a variable, such as x, is shown by x * . The energy is normalized to the total incoming energy density, n n γ n m n c 2 , and is denoted by ǫ, according to the notation of Medvedev & Loeb (1999).

Simulation Results

The present simulation includes growth of the Weibel instability, and the generation of electromagnetic fields which decelerate the jet flow and consequently form a double shock structure. At late times the particles are effectively heated, and accelerated. In the following this scenario is clarified in more detail.

Shock structure

When the jet with density ratio of n 41 /n 1 = 1.7 and γ 41 = 10 interacts with the ambient plasma, the total density initially increases to 2.7n 1 near the jet front. In this interaction, the distribution of particles is extremely anisotropic and this distribution is unstable to several plasma instabilities, such as the electrostatic Buneman instability (Buneman 1958) and the electromagnetic Weibel instability (Weibel 1959). In relativistic shocks, the Weibel instability has the largest growth rate and will dominate the interaction (Medvedev & Loeb 1999;[START_REF] Califano | [END_REF]Hededal & Nishikawa 2005). Time evolution of the Weibel instability was analyzed in Ardaneh et al. (2014) and we summarize the results here. Jet electrons are deflected when interacting with ambient particles to form electron current filaments. Subsequently magnetic fields are amplified principally as a result of mutual attraction between the electron filaments and their merging to larger scale filaments. When the magnetic fields become strong enough to deflect the heavier ions, the ions begin to participate in the instability. The ion current filaments then grow with a smaller growth rate related to the electron-ion mass ratio and to transverse heating. As time evolves, the Weibel instability induced electromagnetic fields facilitate momentum transfer between the jet and ambient plasma. A double shock structure forms when the relative velocity between the jet and ambient plasmas exceeds the sound speed in the ambient plasma and the magneto-sonic speed in the jet, and the pressure in the shocked region exceeds the pressure in the unshocked region (Zhang & Kobayashi 2005). A first density compression appears due to the deflection of jet electrons and ambient ions which we define as the RS. This density compression grows due to amplification of the Weibel instability at the expense of the streaming ions. Time stacked plots of the transversely averaged (in the yz-plane) total ion density as a function of axial distance are shown in Fig. 1a. The time range is t * = 20 -540 with an interval of ∆t * = 20. One can readily identify a RS propagating in the positive x-direction with β RS1 ≈ 0.70. The shape and peak value of the total density corresponding to the RS are almost constant in time (n 31 /n 41 ≈ 2.35, Fig. 1b), and the RS is fully developed. On the other hand, a density compression appears mainly in the ambient plasma at late times (t * ≈ 300) that we identify as the FS. The compression ratio rises with time until reaches about n 21 /n 1 ≈ 6 at the end of the simulation (Fig. 1b). The FS structure moves at a speed β FS1 ≈ 0.89 in the positive x-direction. The CD moves in the positive x-direction at a speed β CD1 ≈ 0.80. The shocked region (340 ≤ x * ≤ 430 at t * = 500) between the RS and FS separates the jet and ambient upstreams (Fig. 1b). The results of present simulation are quantitatively validated by the theoretical calculations described in the Appendix. The speed of the CD in the ambient frame from Eq. (A7)) is β CD1 = 0.8. Combining Eq. ( A3a) and (A3b), the FS speed can be determined. For a shocked ambient adiabatic index between 4/3 ≤ Γ ≤ 5/3 and γ CD1 = 1.67 (corresponding to β CD1 = 0.8) the FS speed will lie between 0.85 ≤ β FS1 ≤ 0.90 (1.91 ≤ γ FS1 ≤ 2.23) where upper and lower limits correspond to the upper and lower limits of Γ, respectively. From Eq. (A8), the jump condition at the FS lies between 5.66n 1 ≤ n 2 ≤ 9.66n 1 , where n 2 is the shocked ambient density in the CD frame and the lower and upper limits correspond to the upper and lower limits of Γ, respectively. Measured in the ambient frame the density compression would lie between 9.4n 1 ≤ n 21 ≤ 16.0n 1 . In the jet frame the CD moves with speed β CD4 = -β 4CD = -0.96 (Eq. ( A5a)) and the corresponding Lorentz factor is γ CD4 = 3.41. By 1 → 4, 2 → 3 and γ 34 → γ CD4 transformations in Eqs. (A3), we can calculate the speed and the corresponding Lorentz factor of the RS in the jet frame. In this frame we have 0.97 ≤ -β RS4 ≤ 0.98 and 4.35 ≤ γ RS4 ≤ 5.77, where upper and lower limits correspond to upper Γ = 5/3 and lower Γ = 4/3 limits for the shocked jet adiabatic index, respectively. The RS speed in the ambient frame (Eq. ( A10)) lies between 0.51 ≤ β RS1 ≤ 0.70. The density jump at the RS region can be obtained from Eq. (A9) where n 4 = n 41 /γ 41 . Hence the density compression of shocked jet is between 1.0n 41 ≤ n 3 ≤ 1.66n 41 according to the upper and lower limits of Γ. In the ambient frame the shocked jet density lies between 1.7n 41 ≤ n 31 ≤ 2.7n 41 . Although the density jump for the shocked ambient is about a factor of ∼ 1.5 smaller than theoretically predicted for a fully developed FS, the simulation results for the RS, CD, and FS speed and also for the density jump at the RS are in the ranges provided by the theoretical analysis for a fully developed shock system.

Shown in Fig. 2a and 2b are the z-component of the electric field, E z , and y-component of the magnetic field, B y , respectively. Panels 2c-2e show the transversally averaged (in the yzplane) electric and magnetic field components, [E x (B x ), E y (B z ), E z (B y )]. The energy distribution (total of jet+ambient) and average energy along the x-direction for electron and ion species are shown in Figs. 2f-2i. All panels are at t * = 500. Where high-speed jet particles interact with the ambient medium (behind the RS at x * ≤ 340) or scattered ambient particles blend with the upstream ambient (in front of the FS at 430 ≤ x * ), particles distribution becomes strongly anisotropic. Anisotropies result in the Weibel instability which generates current filaments in these regions with currents in the x-direction. According to Ampere's law, these current filaments are encircled by transverse magnetic fields, and we see that B x = 0 in Fig. 2c. The transverse electric fields are related to the magnetic fields via β e:i × E = B where β e:i is the velocity of the electron (ion) carrier. The carriers move roughly at the speed of light in the x-direction, β e:i ≃ β e:ix ≃ 1. Therefore, the transverse electric field components are E y = B z , and E z = -B y , as are observed in the simulation results for [E y (B z ), E z (B y )] (Figs. 2a-2e). Additionally, there is a longitudinal ambipolar electric field within the RS transition region, 140 ≤ x * ≤ 340 for t * = 500 (Fig. 2c). This electric field is generated by the density gradient and different mobilities of electrons and ions (Forslund & Shonk 1970;Forslund & Freidberg 1971;Hoshino 2001;Choi et al. 2014). The magnetic fields act to isotropize the momentum distribution, while the electric fields function to thermalize, and accelerate the particles afterwards. In Figs. 2f-2i, the shocked region lies between x * = 340 and x * = 430. Within the RS transition region (140 ≤ x * ≤ 340) jet electrons are trapped by the ambipolar electric field and effectively accelerated up to γ e = 200 by the transverse electric fields (Figs. 2f and2g). A tenuous population of these electrons convect upstream due to reflection by the magnetic fields in the shocked region (ellipse in Fig. 2f). On the other hand, jet ions are slowed in the RS transition region (140 ≤ x * ≤ 340) by 40% from the initial Lorentz factor γ i = 10, due to the effect of the ambipolar electric field. In the shocked region, jet electrons have been fully thermalized and are well merged with the thermalized ambient electrons. Thus, only a single electron population is present in the hot shocked region (Fig. 2f). On the other hand, the kinetic energy of jet ions is transferred to the heating of ambient particles by means of the electromagnetic fields generated by the ion Weibel instability (Fig. 2h). Full thermalization of the two ion populations (jet and ambient) has not yet occured (demands a longer simulation time), i.e., the two populations are distinguishable in Fig. 2h. Electrons located in the FS transition region (430 ≤ x * ≤ 500), predominantly ambient electrons, also undergo the Weibel instability and are thermalized by the jet upstream kinetic energy. In this region, penetrating jet ions interact with ambient particles and are slowed down gradually by 50% from the jet front Lorentz factor γ i = 10 to a minimum value of γ i = 5 (Figs. 2h and2i). + ambient (red) particle energy distribution, and average energy along x-direction are presented in panels (f) and (g) for electrons, and (h) and (i) for ions. The shocked region is identified by orange coloring or between vertical orange lines (as shown in Fig. 1). The ellipse in panel (f) shows the high-energy electrons reflected into the upstream. In (f) and (h), 1.2 × 10 6 particles are randomly selected. Due to the very large number of particles in the simulation, only a part of them is represented. Particles of each population are selected randomly so that the respective distribution function is not affected.

Ion current filaments generated by the ion Weibel instability play a crucial role in establishing the shock transition, electron heating, and acceleration in an unmagnetized electron-ion plasma (Frederiksen et al. 2004;Hededal et al. 2004;Spitkovsky 2008a). In Figs. 3, the longitudinal current density, J x = J ix + J ex , through a transverse cross section is shown at x * = 320, in the RS transition region (Fig. 3a and3c) and at x * = 480, in the FS transition region (Fig. 3b and3d) for t * = 500. Positive (red-white colors) and negative (green-blue colors) represent the ion and electron contribution to the total current, respectively. As one can see, longitudinal current filaments are surrounded by approximately azimuthal magnetic fields (illustrated by the arrows in Fig. 3a and3b). Electric fields are perpendicular to the magnetic fields and the associated arrows point in the radial direction (Fig. 3c and3d). In the RS transition region, magnetic fields are predominantly due to the ion filaments (counter-clockwise arrows) and electrons act to Debye shield these filaments (Frederiksen et al. 2004). However, there are some electron filaments (clockwise arrows) within the FS transition region. Furthermore, electromagnetic fields in the RS transition region are stronger than those in the FS transition region. The transverse size of the filamentary structures is on the order of several electron Larmor radii (R * ≈ 3 -5). Perpendicular electric and magnetic fields lead to the E × B drift motion of electrons parallel to the shock propagation direction (x-direction). During this motion, the electrons are effectively heated.

Acceleration mechanism

One of the key factors in generating non-thermal radiation from GRB afterglows is a nonthermal, high-energy electron population. This population can be seen in the electron spectrum, where a pure 3D Maxwell-Jüttner distribution does not account for the high energies. In fact, a more complex spectrum is anticipated as a result of electron acceleration. Shown in Fig. 4 is the electron spectrum from time t * = 420 up to 500 with an interval of ∆t * = 20 taken at 200λ ce in the RS transition region where most of the accelerated electrons are located. The electron spectrum consists of a main thermal peak around p * ≈ 14, and a high-energy tail which extends to p * ≈ 400 at t * = 500. The dashed line shows a 3D Maxwell-Jüttner distribution with f (p * ) = p * 2 /T * K 2 (1/T * ) exp (-1 + p * 2 /T * ) where K 2 is the modified Bessel function of the second kind, and T * = K B T /m e c 2 . We set T * = 5, in accordance with T * = (γ 41 -1)n 41 /3n 1 = 5 which is expected if the upstream jet kinetic energy is completely converted into internal kinetic energy of the jet and ambient particles. The dashed-dotted line shows a power-law fit to the non-thermal, high-energy electron population. The power-law begins around p * = 100 and extends to p * = 360 with index α = 2.2, and is in agreement with theoretical predictions for a γ = 10 relativistic shock (Kirk et al. 2000;Achterberg et al. 2001).

The mechanism responsible for the non-thermal tail is analyzed by tracing the trajectories of some of the electrons located in the RS transition region at t * = 420. At first, the electrons are heated with heating principally associated with the ion current filaments (Hededal et al. 2004;Medvedev 2006;Spitkovsky 2008a). As discussed previously, when a relativistic jet interacts with the ambient medium, current filaments are formed by the Weibel instability. The ion filaments are sources of strong electromagnetic fields in the transition regions of the RS and FS, while the electrons provide Debye shielding of the ion filaments. The electromagnetic fields in the vicinity of the ion current filaments can be seen in Figs. 3. The magnetic fields are predominantly azimuthal while the electrostatic fields are in the radial direction. The presence of perpendicular electric and magnetic fields results in a drift motion of the electrons with v d = |E × B|/B 2 parallel to the shock propagation direction (x-direction). At distances less than a Debye length, an electron initially moves in a direction opposite to the electric field. Due to the velocity v ⊥ thus acquired, the magnetic part of the Lorentz force produces a motion perpendicular to the electric and magnetic fields which instantly bends the electron trajectory. During the first-half gyration, an electron is accelerated at the expense of the potential energy stored in the transversal electric field (A-B in Fig. 5a and Fig. 5b). On the other hand, an electron in its second-half gyration does work on the electric field and its kinetic energy will be transferred to the electric field energy (B-C in Fig. 5a and Fig. 5b). The growth of the ion Weibel instability increases the electric charge of the ion filaments with time, hence in the next gyration (C-D-E in Fig. 5a and Fig. 5b) an electron experiences deeper electric potentials that enhance the amplitude of energy oscillations. The maximum attainable energy for an electron during the heating stage can be estimated analytically. Approximately, an electron moving toward an ion current filament gains energy u ele ≈ eE∆r ≃ eB∆r (β xi ≃ 1). The maximum radial distance that an electron can travel is about half the distance between the filaments (measured from the filaments axes), ∆r ≈ c/ω pi,r , where ω pi,r = (4πn i e 2 /m i γ i ) 1/2 is the relativistic ion skin depth. Hence, the electron energy density is ǫ ele ≈ √ ǫ b (normalized to the total incoming energy). In the present simulation, the maximum of √ ǫ b for 140 ≤ x * ≤ 340, where electrons are found at high energies, is about 0.06 (calculated based on the magnetic field components in Figs. 2c-2e and normalized to the total incoming energy n n γ n m n c 2 = 170). Therefore, the maximum Lorentz factor of electrons during the heating stage is about 102, in agreement with the 3D Maxwell-Jüttner distribution dashed line shown in Fig. 4. Acceleration of electrons within the RS transition region (Fig. 2f) is associated with an ambipolar large-scale electric field induced in the negative x-direction due to the inertia difference between electrons and ions (Hoshino 2001). The basic idea behind the electron acceleration process is illustrated in Fig. 6a. In the figure the yellow region represents a distance in front of the ambipolar electric field and behind the RS (such as 250 ≤ x * ≤ 340 in Fig. 2f) in which electrons can oscillate. Consider an incoming electron that enters this region with a small β ex . The electron moves in the positive x-direction (opposite the ambipolar electric field direction), and will be reflected by the strong magnetic fields (B y , B z ) in the shocked region, and then this process may repeat. During this process, the electron experiences a drift motion in the yz-plane parallel to the RS plane (Figs. 6a and6b). As a result, the electron is efficiently accelerated by the transversal electric fields (Fig. 6c) because for

|E ⊥ | = |B ⊥ | (Figs. 2a-2e) and 0 ≤ β ex ≤ 1, |eE ⊥ | ≥ |eβ ex × B ⊥ |.
After multiple reflections, the magnetic force experienced by the electron, e(β ey B z -β ez B y ) becomes larger than the electric force, eE x . At this point the electron will be convected in the negative x-direction and again be trapped, but now in the region of the ambipolar electric field (like 140 ≤ x * ≤ 250 in Fig. 2f). The electron undergoes the same acceleration process in this region until it is convected into the upstream. The resulting small high-energy electron population is indicated by the ellipse in Fig. 2f. This acceleration process resembles the SSA process for ions (Sagdeev & Shapiro 1974;Zank et al. 1996;Lee et al. 1996). This efficient acceleration process for electrons in the shock transition region is indicated in 1D PIC simulations by Hoshino (2001); Hoshino & Shimada (2002) and in 2D PIC simulations by Amano & Hoshino (2009); Matsumoto et al. (2012)), where a series of large amplitude electrostatic solitary waves (ESWs) were induced by the Buneman instability resulting from the interaction between reflected ions and incoming electrons. Instead of the upstream convective electric field in the SSA, in the present acceleration process there are transverse electric fields generated by the Weibel instability that effectively accelerate the electrons. Although previous work has shown that at late times both electrons and ions are accelerated by the DSA (Sironi et al. 2013), in the present simulation, electrons are accelerated to the highest energies via the SSA process.

Summary and conclusions

In this work, we have studied the physics of electron acceleration in a relativistic collisionless Weibel instability mediated shock by means of a 3D PIC plasma simulation. In our simulation, an unmagnetized jet plasma with a 3D drifting Maxwell-Jüttner distribution and temperature T e = T i is injected into an ambient unmagnetized medium. This process results in a double shock structure

Fig. 1 .

 1 Fig. 1.-Panel (a) shows stacked profiles of the transversely averaged ion density (total jet+ambient) from t * = 20 up to 540 with an interval of ∆t * = 20 and panel (b) represents the ion density profile at t * = 500. Solid, dashed-dot, and dotted black lines in panel (a) indicate the RS, FS, and jet front, respectively. In panel (b) the shocked region is shown as orange, yellow represents the shock transition region (left for the RS and right for the FS), white shows the unshocked regions (jet or ambient), and the dashed blue line shows the CD.

Fig. 2 .

 2 Fig. 2.-Structure of the relativistic double shock at t * = 500. Panels (a) and (b) show the zcomponent of the electric field E z and the y-component of the magnetic field B y at y * = 24. Panels (c)-(e) show the transversally averaged (in the yz-plane) field components. Total of the jet (blue)+ ambient (red) particle energy distribution, and average energy along x-direction are presented in panels (f) and (g) for electrons, and (h) and (i) for ions. The shocked region is identified by orange coloring or between vertical orange lines (as shown in Fig.1). The ellipse in panel (f) shows the high-energy electrons reflected into the upstream. In (f) and (h), 1.2 × 10 6 particles are randomly selected. Due to the very large number of particles in the simulation, only a part of them is represented. Particles of each population are selected randomly so that the respective distribution function is not affected.

Fig. 3 .

 3 Fig. 3.-Longitudinal current density through a transverse cross section at x * = 320 (first column) and x * = 480 (second column) for t * = 500. The arrows represent the transverse magnetic (first row), and electric (second row) fields.

Fig. 4 .

 4 Fig. 4.-The electron spectrum taken at 200λ ce within the RS transition region from t * = 420 (leftmost solid black line) up to 500 (rightmost solid red line) with an interval of ∆t * = 20 (200λ ce is calculated relative to the RS position at each time). The dashed line shows a 3D Maxwell-Jüttner distribution. Dashed-dotted line shows a power-law fit to the non-thermal component in the electron energy spectrum at the latest time.

Fig. 5 .

 5 Fig. 5.-Panel (a) shows the 3D trajectory of an electron (selected at t * 0 = 420) during heating over a time interval ∆t * = 80 and panel (b) shows the electron energy over time. The color of the electron trajectory expresses its energy based on the color in panel (b). The longitudinal electron position is calculated relative to the RS front position (x * e -β RS1 × t * ).

Fig. 6 .

 6 Fig. 6.-Panel (a) represents the schematic diagram of the electron acceleration process, panel (b) is the 3D trajectory of an electron (selected at t * 0 = 420) during acceleration in a time interval ∆t * = 80, and in panel (c) the electron energy over time is illustrated. The colors of the electron trajectory reflect its energy according to the color in panel (c). The longitudinal electron position is calculated relative to the RS front position (x * e -β RS1 × t * ).

which consists of three regions. 1) A pre-shock acceleration region (behind the RS), consisting of the incoming jet and ambient particles and with large particle distribution anisotropy. In this region, strong electromagnetic fields due to the Weibel instability, and an ambipolar electric field due to the density gradient and the different mobilities of electrons and ions are induced. 2) A fore-shock region (in front of the FS) where the magnetic fields are relatively weak but still strong enough to be considered for some GRB afterglow radiation. 3) A hot shocked region where the magnetic field energy density is a few percent of equipartition with the kinetic energy density. This region is clumpy, with large structures that are on the order of 30 ion skin depths in length. In the present simulation, the jet RS forms first. The ambient medium FS forms at later times. In this simulation, the RS is fully developed and the shock structure and jump conditions confirm theoretical predictions obtained from an analytical treatment. The FS still developing at the end of the simulation and has not yet reached the theoretically predicted jump conditions.

Ion current filaments are the origin of deeply penetrating electromagnetic field structures. Heating of electrons is directly tied to the ion filaments. This links electron heating closely with the micro-structure of relativistic collisionless shocks. With no restriction on the stage of shock formation, the maximum electron energy density is ǫ ele ≈ √ ǫ b during the electron heating stage. This is in excellent agreement with values of ǫ ele / √ ǫ b derived from afterglow data from 10 GRBs (Panaitescu 2001;Medvedev 2006). Thus, there are two equipartition parameters in the GRB shock: the magnetic field energy density , ǫ b , and the energy density of the electrons, ǫ ele , normalized to the total energy density of the shock, respectively. In the current simulation, the electrons are heated by the Lorentz factor γ e = 100.

We have shown that non-thermal electrons with a power-law index of 2.2 are generated behind the RS. Concerning a relativistic jet propagating into an unmagnetized plasma, this non-thermal electron population is observed for the first time to the knowledge of the authors. Although the particles are mostly accelerated in the shock-dominated systems via DSA, tracing the electron trajectories reveals that the mechanism responsible for electron acceleration differs significantly from DSA. Acceleration of electrons is due to the presence of a strong ambipolar electric field behind the RS. The incoming jet electrons move opposite to the direction of the ambipolar electric field (x-direction in the present work). The electrons are then reflected back by the strong transverse magnetic fields in the shocked region. This results in an electron drift motion in a plane parallel to the RS plane while they are efficiently accelerated by the transverse electric fields. When the magnetic force becomes large enough to overcome the force of the ambipolar electric field, the electron are convected into the jet upstream of the RS. Therefore, a high-energy tenuous population of electron exists in the jet upstream. The acceleration mechanism is similar to the SSA for ions, where transverse electric fields generated by the Weibel instability play the role of the upstream convective electric field in the SSA.

The authors thank the referees for insightful comments and suggestions that led to correct interpretation of the acceleration observed in the present simulation. The authors thank Philip Hardee for critical reading and improvement of the text. The work of KN is supported by NSF AST-0908040, NNX12AH06G, NNX13AP21G, and NNX13AP14G. The simulation presented here was performed using the supercomputer of ACCMS, Institute for Information Management and Communication, Kyoto University.

A. Jump conditions for a relativistic 90 • shock

We review first the MHD analysis of a relativistic 90 • shock propagating into an unmagnetized plasma, and then extend the analysis to double shock structure. In the following, indices 1, 2, and s refer to the upstream, downstream, and shock frame, respectively. The jump conditions for 90 • shocks are solutions to the following one-dimensional MHD conservation equations (Kennel & Coroniti 1984):

where

) is the magnetization, with B 1s as the transverse magnetic field, µ * 1 as the dimensionless specific enthalpy, and Y as the ratio of shock frame magnetic fields or density (Kennel & Coroniti 1984), where µ * i and Y are defined by

Here P * denotes the dimensionless thermal pressure, P * = P/n 1 mc 2 , and Γ is the adiabatic index.

In our simulations the upstream flow is considered a cold plasma, i.e., P * 1 = 0, so that µ * 1 = 1. Solving Eq. (A1a) for µ * 2 and inserting the resulting expression into Eq. (A1b) leads to the following equations for an unmagnetized plasma (Zhang & Kobayashi 2005):

The corresponding jump condition can then be determined by Eq. (A2b). Now we consider an unmagnetized jet with Lorentz factor γ 41 being decelerated by an ambient medium with density n 1 .

For such system, indices 1, 2, 3, and 4 refer to the unshocked ambient, shocked ambient, shocked jet, and unshocked jet, respectively. Relative to the CD, the above formalism can easily include the shocks associated with jet-ambient interactions. The speed of the CD can be determined by applying Eq. ( A1b) at the interface to the ambient and jet plasmas (Nishikawa et al. 2009). Hence, in the CD frame we have

The jet speed measured in the CD frame and the associated Lorentz factor are given by

In our simulations, the jet and ambient medium are initially cold plasmas. Hence Eq. (A4) reduces to

where µ r is the jet-to-ambient enthalpy ratio. Making use of Eqs. (A5), after some algebra Eq. (A6) gives

which is the speed of ambient medium towards the CD, and thus the speed of the CD through the ambient medium. In the shocked ambient, once β 1CD (γ 1CD ) is determined from Eq. (A7), by γ 21 → γ 1CD Eqs. (A3) can be solved to find the speed of the shocked ambient (FS) in the ambient frame, β FS1 = -β 1s . The jump condition for the FS is

In the shocked jet (RS), making use of Eq. (A5a) allows the speed of CD in the jet frame to be calculated β CD4 = -β 4CD . Under 1 → 4, 2 → 3 and γ 34 → γ 4CD transformations in Eqs. (A3), we can calculate the speed of the RS in the jet frame, β RS4 = -β 4s . In this region the jump condition becomes

Finally, the speed of the RS in the ambient frame is given by )