Marielle Collombet
email: marielle.collombet@univ-smb.fr

Alain Burgisser

Mathieu Colombier

Elizabeth Gaunt

Evidence for deep gas loss in open volcanic systems

Keywords: Silicic volcanoes, outgassing, crystal content, channelling, porosity

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Introduction

The eruption of viscous magma at the Earth's surface often gives rise to abrupt regime changes, such as the transition from the gentle effusion of a lava dome to brief but powerful Vulcanian explosions. These eruptive regimes are controlled by outgassing, a process by which the gas contained in bubbles formed during ascent can escape from the magma. In the case of highly viscous magmas (viscosity >10 6 Pa.s), individual bubbles are trapped within the melt and cannot migrate individually through the magmatic column, hindering the bubbly flow outgassing mechanism that is generally at play for low viscosity magmas [START_REF] Parmigiani | Bubble accumulation and its role in the evolution of magma reservoirs in the upper crust[END_REF][START_REF] Cardosso | On convection in a volatile-saturated magma[END_REF]. Gas loss within highly viscous magmas is mainly related to bubble connectivity and to percolation, which controls the ability for the gas to travel through these bubble connections, making the magma permeable under specific physical conditions. Pavourable physical conditions for percolation to occur depend on the amount, size, and shape of the bubbles, deformation, which promotes bubble connectivity (e.g., [START_REF] Blower | Factors controlling permeability-porosity relationships in magma[END_REF][START_REF] Rust | Permeability of vesicular silicic magma: inertial and hysteresis effects[END_REF][START_REF] Burgisser | The percolation threshold and permeability evolution of ascending magmas[END_REF][START_REF] Kushnir | In situ confirmation of permeability development in shearing bubble-bearing melts and implications for volcanic outgassing[END_REF], and the presence of crystals [START_REF] Lindoo | Crystal controls on permeability development and degassing in basaltic andesite magma[END_REF][START_REF] Degraffenried | The influence of phenocrysts on degassing in crystalbearing magmas with rhyolitic groundmass melts[END_REF][START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF][START_REF] Colombier | In situ observation of the percolation threshold in multiphase magma analogues[END_REF]. In some cases, brittle failure and cracks can also appear [START_REF] Shields | Strain-induced outgassing of three-phase magmas during simple shear[END_REF]. When quantified, permeabilities deduced from the combination of these parameters range between 10 -15 and 10 -12 m 2 (e.g., [START_REF] Klug | Permeability development in vesiculating magmas: implications for fragmentation[END_REF][START_REF] Farquharson | Permeability and porosity relationships of edificeforming andesites: A combined field and laboratory study[END_REF][START_REF] Kushnir | Probing permeability and microstructure: Unravelling the role of a low-permeability dome on the explosivity of Merapi (Indonesia)[END_REF][START_REF] Burgisser | The percolation threshold and permeability evolution of ascending magmas[END_REF]).

When integrated into numerical models, they contribute to reproduce effusive regimes that are compatible with field observations like bubble density distribution described on an eroded conduit, or extrusion rate during dome-forming activity (e.g., [START_REF] Melnik | Dynamics of magma ascent and lava extrusion at Soufrière Hills Volcano[END_REF][START_REF] Collombet | Two-dimensional gas loss for silicic magma flows: toward more realistic numerical models[END_REF][START_REF] Degruyter | The effects of outgassing on the transition between effusive and explosive silicic eruptions[END_REF][START_REF] Cassidy | Controls on explosive-effusive volcanic eruption styles[END_REF]).

However, these numerical models fail to reproduce the very low porosity values inferred to occur in the conduit prior to Vulcanian eruptions. Figure 1 shows the porosity distribution prior to the Vulcanian explosion on February 10, 2010 at Soufrière Hills volcano, Montserrat [START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF]. Samples collected in the field provide porosity data down to approx. 70 MPa (~3 km depth) that are significantly below the theoretical porosities suggested for a closed system. The outgassing mechanisms, which are based on bubble connection relationships implemented in various numerical models, could explain low porosity values near the surface but fail to reproduce porosity values at depth (beyond a corresponding pressure of 10 MPa). This implies that another outgassing mechanism is at play and/or that a large amount of gas has been evacuated from the deepest parts of the magma column (most likely above 70 MPa) during and/or before the ascent from the reservoir.

We test the hypothesis that this mismatch is due to a missing physical mechanism that greatly enhances outgassing efficiency within the conduit, even at very low porosity values (<10 vol%). This mechanism, channelling, which involves a rigid crystal framework, was first described for the case of magma chambers by [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF] and [START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF]. Channelling relies on the capacity of crystal-rich magmas to build sustainable channels for gas percolation independently from magma movements. For crystal volume fractions between 40 and 70 vol%, this mechanism allows gas permeability to reach the order of 10 -10 m 2 , which is two to five orders of magnitude higher than permeability calculated for bubbles alone at an equivalent porosity [START_REF] Klug | Permeability development in vesiculating magmas: implications for fragmentation[END_REF][START_REF] Burgisser | The percolation threshold and permeability evolution of ascending magmas[END_REF]. Under such permeable conditions, it is much more plausible that magma succeeds to extensively degas and outgas, even at the high pressures and low gas volume fractions typical of the deepest parts of a volcanic conduit. In addition, the formation of such channel-like porous pathways reduces significantly the percolation threshold, which is the critical vesicularity at which system-spanning bubble connectivity and permeability occur (e.g., [START_REF] Lindoo | Crystal controls on permeability development and degassing in basaltic andesite magma[END_REF][START_REF] Colombier | In situ observation of the percolation threshold in multiphase magma analogues[END_REF]). As a consequence, provided that crystallinity is high enough, outgassing can occur before or early during ascent, resulting in a magma column severely depleted in gas.

We revisited three data sets of the porosity distribution within volcanic conduits filled by andesitic magmas.

They are from a Vulcanian explosion on February 11, 2010 at Soufrière Hills volcano, Montserrat [START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF]), an explosive event on October 26, 2010 at Merapi volcano, Indonesia [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF], and a large Vulcanian event that occurred on July 14, 2013 at Tungurahua volcano, Ecuador [START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF]. We show that the magmas feeding these Vulcanian events were crystal-rich enough to promote highly efficient outgassing by channelling.

Geological Context

The on-going eruption of Soufrière Hills is dominated by lava dome effusion with intermittent collapse. The magma emitted is andesitic in bulk composition with a rhyolitic melt. The fifth phase of lava extrusion since the beginning of the eruption was marked by a succession of dome growth as lava lobes and spines followed by partial dome collapse (Wadge et al. 2014b;Cole et al. 2014). The February 11, 2010 explosion was preceded by two small Vulcanian events on February 5 and 8 (Stinton et al. 2014b;Cole et al. 2015). The February 11 event was mostly likely triggered by a dome collapse that started 1 hour and 27 minutes prior to the onset of the Vulcanian explosion. [START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF] analyzed twenty-three samples of the resulting pumice-rich, pyroclastic density current deposits and pumice fallout deposits. Phenocrysts are mostly plagioclases that are up to 5 mm across [START_REF] Higgins | Crystal size distribution of plagioclase and amphibole from Soufrière Hills Volcano, Montserrat: Evidence for dynamic crystallization-textural coarsening cycles[END_REF]. Large plagioclases have irregular shapes and smaller plagioclases are euhedral. Euhedral amphiboles up to 12 mm across are also present with a low number density. Microlites are mostly plagioclases with a concave up distribution in the 20-1000 µm 2 range [START_REF] Couch | The kinetics of degassing-induced crystallization at Soufrière Hills volcano, Montserrat[END_REF]) and short/long axis ratios of ~0.5 [START_REF] Murch | Using microlites to gain insights into ascent conditions of differing styles of volcanism at Soufrière Hills Volcano[END_REF].

Merapi volcano produced in 2010 the largest explosive eruption since 1872 (Surono et al. 2012). This unusual event, which emitted basaltic andesites with a rhyolitic melt [START_REF] Costa | Petrological insights into the storage conditions, and magmatic processes that yielded the centennial 2010 Merapi explosive eruption[END_REF], occurred in several stages between October 26 and November 23 (Komorowski et al. 2013;Jenkins et al. 2013). The first large explosion lasted for 2h on October 26, producing an ash plume and pyroclastic density currents. This explosion had a phreatomagmatic component and was interpreted as a laterally directed explosion from a newly formed cryptodome. [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF] analyzed forty-one samples from a pumice levee of the valley-filling pyroclastic deposits produced by the October 26 event. Phenocrysts populations vary little between the recent eruptions (van der [START_REF] Van Der Zwan | Textural history of recent basaltic-andesites and plutonic inclusions from Merapi volcano[END_REF]. Crystals that are 1.6-4 mm across make up one population with a size distribution that is approximately a straight line. The most common phenocrysts are plagioclases and pyroxenes that both have subhedral morphologies with evidences of resorption (Erdmann et al. 2016). Microlites are mostly plagioclases with a rectangular prism habit, areas of 10-15 µm 2 , and short/long axis ratios ranging from 0.35 to 0.67 [START_REF] Costa | Petrological insights into the storage conditions, and magmatic processes that yielded the centennial 2010 Merapi explosive eruption[END_REF].

The latest activity (1999 -2016) at Tungurahua volcano varied from small-scale gas and ash venting and Strombolian outbursts to rare sub-Plinian events [START_REF] Eychenne | Causes and consequences of bimodal grain-size distribution of tephra fall deposited during the August 2006 Tungurahua eruption (Ecuador)[END_REF][START_REF] Hall | Sequential plug formation, disintegration by Vulcanian explosions, and the generation of granular Pyroclastic Density Currents at Tungurahua volcano (2013-2014), Ecuador[END_REF][START_REF] Battaglia | Autopsy of an eruptive phase of Tungurahua volcano (Ecuador) through coupling of seismo-acoustic and SO2 recordings with ash characteristics[END_REF]. The magma emitted is a low silica andesite with a high silica andesitic melt. The last six years of this eruptive phase was marked by two to three months of relative quiescence followed by Vulcanian events and ending with several weeks of low-explosivity Strombolian activity and ash venting [START_REF] Hidalgo | SO2 degassing at Tungurahua volcano (Ecuador) between 2007 and 2013: Transition from continuous to episodic activity[END_REF]. On July 14, 2013, an unusually large Vulcanian event occurred at 06h46 (local time), producing a large ash column and pyroclastic density currents that travelled up to 7.5 km away from the vent. [START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF] analyzed twenty-seven samples from three lithological groups (pyroclastic current deposits, fallout pumice, and ballistic ejecta) present in the ejecta. Plagioclase is the most abundant phenocryst phase, followed by pyroxene [START_REF] Samaniego | Petrological analysis of the pre-eruptive magmatic process prior to the 2006 explosive eruptions at Tungurahua volcano (Ecuador)[END_REF]. Both exhibit mostly euhedral habits. Microlites are mostly plagioclase with habits ranging from rectangular prisms to acicular crystals [START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF]. Dense plug rocks have mean microlite areas of 4.2-26 µm 2 with mostly tabular morphologies. Juvenile vesicular clasts of the pyroclastic current deposits have mean microlite areas of 10-66 µm 2 with occasional swallow-tail and hopper morphologies.

Methods

We modified data treatment of the recompression model of Burgisser al. (2010) used by [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF], [START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF][START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF]. We briefly outline the data acquisition and the data treatment done in these three studies before describing our modification. The petrological and textural analysis of the samples was carried out in the three studies according to the procedures outlined in Burgisser al. (2010) and [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF]. Polished sections were imaged by Scanning Electron Microscopy (SEM) or by element mapping based on Energy Dispersive Spectroscopy (EDS). Images were taken at several magnifications depending on the average size of the vesicles and crystals. Images were used to quantify the amounts of vesicles, glass, phenocrysts, and microlites in the samples by manually tracing each of the elements (SEM) or by automatic thresholding and by successive subtractions of Boolean combinations of the binary images of the analyzed elements (EDS). The segmented images were then used to measure the proportions of phenocrysts, microlites, and vesicles. In this study, we use "vesicles" and "vesicularity" to characterize voids regardless of genesis. We use "bubbles" and "porosity" to characterize voids resulting from the exsolution of magmatic volatiles.

Imaged vesicles were subdivided in four types (Fig. 2, [START_REF] Burgisser | Pre-explosive conduit conditions of the 1997 Vulcanian explosions at Soufrière Hills Volcano, Montserrat: I. Pressure and vesicularity distributions[END_REF][START_REF] Giachetti | Bubble nucleation, growth and coalescence during the 1997 Vulcanian explosions of Soufrière Hills Volcano, Montserrat[END_REF]). The first type was composed of large, deformed vesicles of equivalent diameter >300 m and circularity <0.2.

The second type was composed of small, rounded vesicles of equivalent diameter <40 m and circularity >0.65. The third type was composed of large angular voids between crystal fragments and of irregular voids delimited by crystal faces that are found in dense, diktytaxitic samples. The last type was composed of the remaining vesicles, which are of intermediate sizes and often composed of coalesced bubbles. Type 1 vesicles were caused by degassing during magma ascent from the reservoir. The sudden decompression linked to the explosion nucleated new, syn-explosive bubbles. The first syn-explosive bubbles are of Type 4 because they had enough time to grow and coalesce before quenching. The latest syn-explosive bubbles are of Type 2 because they were quenched as small, isolated vesicles. Finally, Type 3 vesicles that are gaps between crystal fragments result from crystal failure caused by the decompression accompanying conduit evacuation. The remaining Type 3 vesicles found in diktytaxitic samples are likely due to reorganization of voids under shear [START_REF] Laumonier | Porosity redistribution enhanced by strain localization in crystal-rich magmas[END_REF]).

The recompression model of Burgisser al. (2010) assumes that, prior to explosion, the piece of magma to be ejected is at a pressure Pi and porosity, ϕ, with water weight fraction distributed as exsolved, xi, and dissolved, si. The clast is quenched at pressure Pq, porosity ϕq, and dissolved water content, sq. Quench porosity, ϕq, is the sum of volume fractions of the four vesicle types. Only Type 1 vesicles were present in the conduit prior to the explosion. Type 2 vesicle nucleate during the explosion but were not affected by outgassing. Type 3 and 4 vesicles both appeared during the explosion and could participate to outgassing because they feature various degrees of interconnection. The weight fraction of the exsolved water content at quench time is thus composed of an outgassed part, xout, and a part remaining within the clast that is divided into three weight fractions: xq1 (Type 1 vesicles), xd1 (Type 2 vesicles), and xq2 (Type 3 and 4 vesicles).

Similarly, quench pressures differ from pre-explosive pressures. The conversion from quench to preexplosive conditions (Fig. 2) was done by a mass balance linking the state of the magma just before the explosive event (pre-explosive state characterized by Pi, ϕ, si and xi) to that once the magma has quenched (quench state characterized by Pq,ϕq,sq,xq1,xd1,and xq2).

Model input data are the magma temperature, the densities of melt and crystals at that temperature, ϕq, and, to obtain Pi, one of plagioclase microlite content, or glass water content. In [START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF], Pi was obtained by converting the glass-referenced volume proportions of plagioclase microlites of each sample into pressure. In [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF] and [START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF], Pi was calculated by using the glass water content determined by elemental analyzer and converting successively glass water content into dissolved water content and into pressure with a solubility relationship. The original recompression model has four free parameters [START_REF] Burgisser | Pre-explosive conduit conditions of the 1997 Vulcanian explosions at Soufrière Hills Volcano, Montserrat: I. Pressure and vesicularity distributions[END_REF]). The first one, O = xout/(xq1 + xq2 + xd1 + xout), quantifies the gas fraction outgassed during the explosion to propel the ejecta. This poorly constrained parameter, which has a modest effect on pre-explosive values [START_REF] Burgisser | Pre-explosive conduit conditions of the 1997 Vulcanian explosions at Soufrière Hills Volcano, Montserrat: I. Pressure and vesicularity distributions[END_REF], is assumed to lie between 10% and 70-82% with a reference value of 50%. The second parameter, H, estimates the maximum, near-instant pressure drop that clasts can sustain before breaking [START_REF] Mueller | Permeability control on magma fragmentation[END_REF]) as a proxy for quench pressure. In other words, Pq is the smallest of Pi and Patm + H PMueller, where Patm is the atmospheric pressure, PMueller is the value of the pressure drop, and H is a multiplicative factor that was assumed to lie between 0.5 and 2 with a typical value of 1. The upper limits of O and H were chosen so that the maximum total water content of every clast lies below that inferred in the reservoir and that all clasts undergo syn-explosive inflation so as to match textural observations. The upper values of O were 70, 76, and 82% for Tungurahua, Soufrière Hills, and Merapi, respectively. The two last parameters of the model quantify the proportions of vesicles: E=(xd1+xq2)/xq1 and F=xd1/xq1. As vesicle types occur in similar proportions in the products of a given explosion, [START_REF] Burgisser | Pre-explosive conduit conditions of the 1997 Vulcanian explosions at Soufrière Hills Volcano, Montserrat: I. Pressure and vesicularity distributions[END_REF] and the authors of the three data set studied herein [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF][START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF][START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF]) used a lumped approach; they averaged vesicle proportions in all samples of a given explosion.

They then calculated E and F using the median proportions and standard deviations of each vesicle type.

In this study, we attempted to gain precision in the pre-explosive porosities by considering for each clast the respective proportions of the vesicle types. These proportions were published in the original studies. Using individual vesicle proportions means that E and F were no longer considered as free parameters with a median value and a standard deviation. Instead, they were considered as input parameters with an assumed negligible uncertainty, which reduced the number of degrees of freedom of the recompression procedure from four to two. In the [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF] study of the October 26 event at Merapi, for instance, the vesicles of Types 1, 2, and 3-4 were present in respective median proportions of 28.4:2.5:70, which yields E=2.7 and F=0.14. We replaced these median proportions by the individual values of each sample (AME 10 A1: 33.5:3.1:63.4,etc.) to obtain E and F values for each sample. Beyond reducing the number of sources of uncertainties, this modification evidenced a shortcoming of the vesicle size distribution analysis, which led us to discard data from [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF] (Supplementary Text S1).

The recompression model has two types of uncertainty. Analytical uncertainties result from error propagation of the uncertainties on quench vesicularities, glass water contents, and plagioclase microlite proportions.

Analytical uncertainties for each sample were calculated with four sets of model outputs that used the reference values of H and O and the respective minimum and maximum values of ϕ, microlite content and/or glass water content. Analytical errors on pre-explosive porosity are small in absolute value (<1 vol%). Our new procedure with fewer free parameters does not significantly affect these absolute errors (<15%).

Similarly, errors on pre-explosive pressure are modified by <10% and typically by <2%. These changes will not be discussed further as they are smaller than those stemming from model uncertainties. This second type of uncertainty results from propagation of the uncertainties on H and O. The reference values and bounds of these two parameters were combined to yield five sets of pre-explosive pressures and porosities. The set with the reference values was kept as the average set and the two sets with the largest and smallest porosity values at any pressure were kept as extrema to characterize model uncertainty. Only these three sets are reported in the Results section.

In the case of a rigid crystal network with crystal volume fraction ϕx between 0.4 and 0.7, the minimum porosity required to make percolation possible (i.e. the percolation threshold), ϕcr (Fig. 2), follows a thirddegree polynomial equation :

= - + + (1)
where the constants are a=0. 7495, b=0.4268, c=-0.16267495, b=0.4268, c=-0. , and d=0.14787495, b=0.4268, c=-0. for Degruyter et al. (2019) ) or a=2.75, b=2.79, c=0.6345, and d=0.0997 for [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF]. The difference between these two sets of constants is due to the initial conditions chosen for the bubbles. In the case of [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF], the initial positions of the bubbles and their respective size was set randomly, whereas these parameters followed a spinodal distribution in the case of [START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF]. A spinodal distribution means that the size and the position of bubbles satisfy the principle of mass conservation and capillary stresses, which leads to more consistent and more accurate initial conditions. This higher level of physical verisimilitude led us to use the set of parameters of [START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF].

The vesicle-free crystal content, ϕxvf, is related to ϕx by (Fig. 2):

= (1 -) (2)
Drignon et al. ( 2016) reported bulk volume fractions of vesicles, phenocrysts and microlite, from which ϕxvf (Table 1) was calculated using Eq (2). [START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF] reported ϕq and ϕxvf. We used their original unpublished quantifications of microlites to obtain vesicle-free volume fractions of phenocrysts. Gaunt et al.

(2020) reported bulk volume fractions of vesicles, of plagioclase and pyroxene phenocrysts, and of plagioclase and pyroxene microlite. We used their original unpublished quantifications of oxide phenocrysts and microlites to calculate ϕxvf.

For a given vesicle-free crystal content, there is one critical porosity such that ϕ=ϕcr:

(1 -) -(1 -) + (1 -) + -= 0 (3)
For each ϕxvf within the 40-70% interval, we solve equation ( 3) to obtain a solution ϕcr=f(ϕxvf). The associated uncertainties, dϕxvf, were obtained by error propagation and mostly reflect natural variability. Uncertainties on the critical porosity, dϕcr, were calculated using the variation of the f function: dϕcr= d f(dϕxvf).

Results

Considering the vesicle proportions of each sample instead of an average value does not change much (<17%) the final values of pre-explosive pressures (Fig. S1). When using microlites [START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF], no pressure change occurs because the power-law relationship linking microlite proportion to pressure does not depend on vesicle content. Pre-explosive porosities are more influenced by this reduction of free parameters.

Samples located at pressures >10 MPa change by <10% from the original value. Shallower samples undergo porosity changes of up to 25% with one outlier at 40% (Fig. S2), but the general trend with pressure remains (Fig. S1). Changes in model uncertainties compared to the ones from the original studies are small but uneven between data points, varying by <15% from the original value except for a couple of samples with vanishing porosity. As a result, the overall respective envelopes of model uncertainties are similar for each volcano.

Two conditions need to be met for outgassing to occur by channelling [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF][START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF]. The first condition is that total crystal content must be between 40 and 70 vol%. Provided the germane amount of crystals, the second condition is that a critical porosity is reached. Channelling allows gas escape at very low gas volume fraction with a percolation threshold below 10 vol%. We used the critical values given by the empirical relationship of [START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF] because they correspond to more realistic initial conditions, but similar results are found when using the [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF] values. To take the empirical nature of these fits into account, we also considered the maximum and minimum percolation values they yield within the validity bounds of crystal content (5 and 12 vol% porosity, respectively). Once channelling is established, outgassing rate is controlled by a balance between magma permeability, driving pressure, and the collapse rate of the medium. As a result, outgassing could evacuate more gas than the critical porosity. Such hysteresis has been proposed to occur at low [START_REF] Rust | Permeability of vesicular silicic magma: inertial and hysteresis effects[END_REF][START_REF] Michaut | Ascent and compaction of gas rich magma and the effects of hysteretic permeability[END_REF][START_REF] Gonnermann | Permeability During Magma Expansion and Compaction[END_REF]) and high crystal contents [START_REF] Colombier | In situ observation of the percolation threshold in multiphase magma analogues[END_REF], albeit not by channelling. In the absence of more specific evidence, we considered that non-vanishing porosities lower than the percolation threshold could result from channel collapse.

To test if channelling could explain low porosity distributions within volcanic conduits before explosion, we assessed to which extent these two conditions of crystallinity and porosity were met in three sets of data on andesitic products from different volcanoes. These datasets are composed of the pressures associated with the corresponding pre-eruptive porosities and of the amounts of phenocrysts (which are generally already present in the magmatic chamber) and microlites (which develop during magma ascent). It is important to consider these two populations of crystals since they could, depending on how their amounts change during ascent, prevent or enhance channelling.

Montserrat

The amounts of "phenocrysts" and "phenocrysts plus microlites" in the Soufrière Hills samples from 2010 are plotted in Fig. 3a. Microlite crystallization during ascent increased the total amount of crystals from 30 vol% to approximatively 55 vol% on average, thereby helping channelling to develop. Figure 3b shows pre-explosive porosities of the samples, of closed-system degassing, and of the channelling threshold. All threshold porosities are within a narrow range smaller than 5 vol%. Considering that all samples have a porosity well below that of closed-system degassing, it means that most of the gas present in the conduit has been lost. Physical conditions propitious to channelling were thus probably met during ascent. However, it appears that most measured porosities are slightly below the threshold values, except two points among the shallowest samples and one point around 57 MPa that are slightly above threshold. This situation indicates that, if channelling occurred, a little more than the gas in excess of the threshold value has been lost, deflating the magma back below the critical porosity.

Merapi

Data from the October 26, 2010 Merapi eruption are particularly interesting because they provide information down to ~10 km (270 MPa), which is close to the pure water exsolution level for that eruption [START_REF] Erdmann | Constraints from Phase Equilibrium Experiments on Pre-eruptive Storage Conditions in Mixed Magma Systems: a Case Study on Crystal-rich Basaltic Andesites from Mount Merapi, Indonesia[END_REF][START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF]. Estimating the exsolution level at Merapi is a complex task because 1) a significant amount of CO2 coexisted with H2O in the gas phase and 2) the magmas feeding the 2010 eruption were stored at multiple levels and mixed prior to their final ascent towards the surface [START_REF] Costa | Petrological insights into the storage conditions, and magmatic processes that yielded the centennial 2010 Merapi explosive eruption[END_REF][START_REF] Nadeau | Magmatic-hydrothermal evolution and devolatilization beneath Merapi volcano, Indonesia[END_REF]Preece et al. 2014;[START_REF] Erdmann | Constraints from Phase Equilibrium Experiments on Pre-eruptive Storage Conditions in Mixed Magma Systems: a Case Study on Crystal-rich Basaltic Andesites from Mount Merapi, Indonesia[END_REF][START_REF] Widiyantoro | Seismic imaging and petrology explain highly explosive eruptions of Merapi Volcano[END_REF]). The mixing process started by magma assembly at depth and continued during ascent. This induced complexities in the crystal cargo that hinders straightforward interpretations of porosity and crystal contents (Supplementary Text S2). Here, we framed the likely conduit conditions according to the experimental results of [START_REF] Erdmann | Constraints from Phase Equilibrium Experiments on Pre-eruptive Storage Conditions in Mixed Magma Systems: a Case Study on Crystal-rich Basaltic Andesites from Mount Merapi, Indonesia[END_REF] by performing two closed-system, multicomponent decompressions.

Following [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF], we used the model D-Compress [START_REF] Burgisser | Simulating the behavior of volatiles belonging to the C-O-H-S system in silicate melts under magmatic conditions with the software D-Compress[END_REF] to simulate the porosity evolution of rhyolitic melts undergoing isothermal, equilibrium decompression at NNO+1. The first decompression represents the hotter recharge magma at 975 °C. It starts from 250 MPa with 5 wt% melt H2O content and 400 ppm melt CO2 content, which yields a CO2/H2O molar ratio of 0.2. The second represents the colder resident magma at 925 °C. It starts from 175 MPa with 3 wt% melt H2O content and 500 ppm melt CO2 content, which yields a CO2/H2O molar ratio of 0.66. The resident and recharge magmas were mixed in a way that we expect to fall within these two end members. The initial porosity is mostly unconstrained, so we considered a small (<< 1 vol%) and a large (10 vol%) value for each magma. MPa, samples suggest that the conduit was filled with nearly gas-free magma, well below percolation threshold. This observation makes the two scenarios starting with high initial porosities unlikely, so they were not given further consideration. Assuming that the porosity evolution was controlled by an initially gaspoor recharge magma, no bubbles are expected at pressures higher than 250 MPa, which is consistent with the very small values (<1 vol%) of the samples located around that pressure. At ~150 MPa, the gas available by closed-system degassing matches that needed for channelling (black line on Fig. 4b) although measured porosities are well below percolation. Assuming instead that the eruptive products sampled the resident magma brings the pressure at which closed-system porosities are within the threshold range from 150 to 70 MPa (green line on Fig. 4b). This situation is compatible with the vanishing measured porosities at higher pressure and the fact that porosities increase below 70 MPa while remaining below the threshold porosities.

The combined data of Figs. 4a and 4b suggest that deeper than 3 km (70 MPa), there was not enough gas available in the reservoir to be outgassed despite the favourable phenocryst content for channelling. Between 3 km and the surface, however, gas contents stemming from closed-system degassing would have been high

enough for outgassing to occur. Shallower than 3 km, crystal contents vary from 40-50 vol% before microlite crystallization, to more than 70 vol % post-crystallization. If the shallow magma column stagnated while (or before) microlite crystallization occurred, channelling could have started before microlite crystallization and continued until 70 vol% of crystals was reached. If the magma still contained substantial gas volume fraction once this high limit of crystallinity reached, other mechanisms, such as cracks due to brittle failure of the melt, should be evoked to explain further outgassing. In any case, the degassing trends suggest that the analysed clasts sampled the colder resident magma. As in the case of Soufrière Hills, preeruptive shallow samples display porosities below the critical threshold, possibly suggesting outgassing accompanied by deflating.

Tungurahua

Storage conditions at Tungurahua were more H2O-rich than at Merapi, with a molar fraction of H2O in the gas phase of 0.8 [START_REF] Andújar | Structure of the Plumbing System at Tungurahua Volcano, Ecuador: Insights from Phase Equilibrium Experiments on July-August 2006 Eruption Products[END_REF]). As a result, D-Compress runs with mixed H2O-CO2 fluids do not differ much from pure H2O ones, and closed-system decompressions with pure water were assumed instead for simplicity. Porosities and crystal contents from Tungurahua give information from the surface down to ~7 km depth (170 MPa), which, like at Merapi, is deep enough to constrain the point at which gas loss starts.

Similarly to Soufrière Hills, phenocrysts in the Tungurahua magma cannot trigger channelling alone (Fig. 5a). The total amount of crystals, however, approaches the lower limit of 40% around 100 MPa, and exceeds it for pressures lower than 50 MPa. This implies that microlites were required for channelling to occur possibly around 100 MPa, and more certainly around 50 MPa. Near the surface, the upper limit of 70% is overcome, stopping channelling and potentially fostering a shallow gas-rich area that appears clearly on the porosity data with values spanning from 25% to 50 vol% (Fig. 5b). Closed-system porosities suggest that gas was available for channelling at ~150 MPa, although the amount of crystals was not sufficient at this depth to foster channelling (Fig. 5a). The first calculated pre-eruptive porosity approaching the channelling threshold is located around 110 MPa and the first pre-eruptive porosity which effectively coincides with that threshold appears at ~50 MPa (Fig. 5b). As a result, gas loss by channelling may have started between 110 and 50 MPa and was no longer possible below 10 MPa.

Discussion

Our data show that, to first order, channelling is a process that is consistent with the low porosities inferred in volcanic conduits prior to Vulcanian explosions. That channelling can occur during ascent due to an increase in crystal content brings a partial answer to the long-standing issue of gas transfer across the entire depth of magmatic systems (e.g., [START_REF] Oppenheimer | Pulsatory magma supply to a phonolite lava lake[END_REF]) despite sometimes very high magma viscosity and no obvious physical mechanism of transfer [START_REF] Edmonds | Excess volatiles supplied by mingling of mafic magma at an andesite arc volcano[END_REF]. Gas percolation in magmas has long been studied in decompression experiments, which have notably shown that the presence of >20 vol% crystals lowers percolation thresholds compared to crystal-poor melts [START_REF] Lindoo | Crystal controls on permeability development and degassing in basaltic andesite magma[END_REF][START_REF] Degraffenried | The influence of phenocrysts on degassing in crystalbearing magmas with rhyolitic groundmass melts[END_REF]. Such type of viscous percolation occurs when bubbles can expand spherically while pushing crystals apart [START_REF] Colombier | In situ observation of the percolation threshold in multiphase magma analogues[END_REF]).

The percolation associated with channelling, on the other hand, is fostered by buoyancy-driven deformation of the bubbles in the constricted space between crystals and subsequent coalescence at moderate to low Bond numbers. Additional processes can also form similar channel-like interconnected porous pathways at low critical porosity in crystal-rich magmas. For instance, [START_REF] Colombier | In situ observation of the percolation threshold in multiphase magma analogues[END_REF] showed that brittle-viscous coalescence is favoured at melt viscosities higher than 10 6 Pa.s and relatively high gas overpressure. Because of such alternatives, conditions adverse to channelling do not imply the absence of outgassing. Figure 7 shows a literature compilation of vesiculation experiments on crystal-free to crystal-rich magmas and magma analogues [START_REF] Gardner | Bubble growth in highly viscous silicate melts during continuous decompression from high pressure[END_REF][START_REF] Larsen | Experimental constraints on bubble interactions in rhyolite melts: implications for vesicle size distribution[END_REF][START_REF] Mangan | Delayed, disequilibrium degassing in rhyolite magma: decompression experiments and implications for explosive volcanism[END_REF][START_REF] Gardner | Bubble coalescence in rhyolitic melts during decompression from high pressure[END_REF][START_REF] Takeuchi | Degassing conditions for permeable silicic magmas: Implications from decompression experiments with constant rates[END_REF][START_REF] Shea | Linking experimental and natural vesicle textures in Vesuvius 79 AD white pumice[END_REF][START_REF] Okumura | Experimental constraints on permeable gas transport in crystalline silicic magmas[END_REF][START_REF] Martel | Timescales of bubble coalescence, outgassing, and foam collapse in decompressed rhyolitic melts[END_REF][START_REF] Oppenheimer | Gas migration regimes and outgassing in particle-rich suspensions[END_REF][START_REF] Preuss | Special Collection: Rates and Depths of Magma Ascent on Earth: Degassing of Hydrous Trachytic Campi Flegrei and Phonolitic Vesuvius Melts: Experimental Limitations and Chances to Study Homogeneous Bubble Nucleation[END_REF][START_REF] Colombier | In situ observation of the percolation threshold in multiphase magma analogues[END_REF]. Data is tallied in crystal-poor (<10 vol%), moderately crystal-rich (10-40 vol%), and crystal-rich (>50 vol%) categories, as well as whether samples underwent closed-system degassing, or bore connected bubbles networks able to outgas. Figure 7 suggests that experimental magma outgassing has only been explored in low-pressure, shallow conditions, which contrasts with our deep-seated determination of channelling during magma ascent. This compilation also confirms that high crystal contents promote outgassing at low percolation thresholds.

The conditions leading to channelling are based on several key assumptions [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF][START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF], the validity of which must be assessed in the case of conduit flow. One is that capillary forces dominates buoyancy forces so that the Bond number is 0.1-1. The Bond number depends on gravity, the density difference between melt and gas, the surface tension, and the radius of the gas bubbles. A reasonable estimate for the melt density of the three studied volcanoes is 2300 kg/m 3 . According to [START_REF] Lyakhovsky | Bubble growth in rhyolitic melts: experimental and numerical investigation[END_REF], surface tension can be taken as 0.05 N/m. The most variable quantity is bubble size because it depends highly on the pressure and bubble number density. A Bond number between 0.1 and 1 implies a bubble radius between 0.2 and 0.8 mm. At depth, bubbles that size and smaller were likely, and the assumption of dominating capillary forces holds. The possibility that bubbles adhere to crystal surfaces was also left aside. This is a reasonable assumption in conduit conditions because microlites are mostly composed of non-wetting phases like plagioclase in arc magmas. We note, however, that wetting phases like Fe-Mg silicates or Fe-Ti oxides are also present, which suggests that investigating how crystal adherence affects bubble channelling is a worthy pursuit.

Two other assumptions of [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF] and [START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF] are that the ambient pressure is hydrostatic and that the crystal framework remains static during the onset of channelling. The lower crystallinity limit of 40 vol% stems from the assumption that crystalline matrix resists frictional sliding, which corresponds to a random loose packing. Their synthetic crystal size and shape distributions aim to represent a scaled version of phenocrysts prevailing in storage conditions. Microlite crystallization during ascent yielded in our three studied cases linear to concave-up crystal size distributions with a significant proportion of highly elongated microlites. Random loose packing and frictional effects in such distributions occur at volume fraction lower than 40 vol%, possibility as low as 8 vol% [START_REF] Saar | Numerical models of the onset of yield strength in crystal-melt suspensions[END_REF][START_REF] Guo | Granular shear flows of flat disks and elongated rods without and with friction[END_REF].

The bubble coalescence leading to channelling, however, is controlled by how much interstitial space occurs between crystals, which is inversely proportional to the cubic root of crystal volume fraction. It is thus unlikely that the onset of channelling occurs at crystallinities much lower than that proposed by [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF], depending on crystal shapes and sizes. Similarly, the transition from channelling to bubble trapping could also occur at a different (yet probably close to) volume fraction than the 70 vol% determined numerically.

Bubble trapping assumes a static solid matrix. It is no longer static when either local overpressure occurs, or a far-field stress is applied to the medium, which are two likely processes in ascending magmas. Different regimes of matrix deformation by local gas overpressure exist. Analogue experiments [START_REF] Holtzman | Capillary Fracturing in Granular Media[END_REF][START_REF] Oppenheimer | Gas migration regimes and outgassing in particle-rich suspensions[END_REF] show that a regime of slow solid matrix rearrangement occurs at the random loose packing, when gas bubbles begin to deform. This change is insensitive to liquid viscosity in the range 10-1000 Pa s. Another regime of rapid deformation of the immersed granular medium by gas-induced overpressure has been described as "venting" [START_REF] Varas | Flow and fracture in water-saturated, unconstrained granular beds[END_REF] or "capillary fracturing" [START_REF] Holtzman | Capillary Fracturing in Granular Media[END_REF]. It occurs near the random close packing [START_REF] Oppenheimer | Gas migration regimes and outgassing in particle-rich suspensions[END_REF], and it is characterized by gas migration in a fracture-like manner. These regimes have recently been proposed to play a role in Strombolian dynamics when gas proportions are large and melt viscosities low (<5 Pa s; [START_REF] Barth | Valve-like dynamics of gas flow through a packed crystal mush and cyclic strombolian explosions[END_REF][START_REF] Oppenheimer | Analogue experiments on the rise of large bubbles through a solids-rich suspension: A "weak plug" model for Strombolian eruptions[END_REF]. It is unclear yet probable that outgassing by channelling leads to limited grain displacement in melts of much higher viscosity. The two values of crystal content framing channelling are thus reasonable estimates that will be refined when reproduced experimentally with the assumption of static solid matrix relaxed. As the same reasoning holds for the critical porosity (Eq. ( 3)), the shaded regions in Fig. 3b, 4b, and 5b indicate the two extreme values ever reached by numerical simulations of channelling [START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF]. Considering only these extreme values does not change the conclusion that conditions for channelling were met in the three studied cases.

Once channelling is established, gas evacuation can proceed to the point of fracture healing if large-scale stresses are applied [START_REF] Caricchi | Strain-induced magma degassing: insights from simple-shear experiments on bubble bearing melts[END_REF][START_REF] Laumonier | Porosity redistribution enhanced by strain localization in crystal-rich magmas[END_REF][START_REF] Heap | Fracture and compaction of andesite in a volcanic edifice[END_REF]. Such gas expulsion is thus expected in a crystal-rich magma sheared along a volcanic conduit (e.g., [START_REF] Thomas | Crystals, Bubbles and Melt: Critical Conduit Processes Revealed by Numerical Models[END_REF]. Provided that Eq. ( 3) is accurate, this is the most probable explanation of the porosities close to but lower than the critical porosity at Soufrière Hills and Merapi (Figs. 3b and4b). We reiterate that channelling in deforming suspension remains to be quantified to add weight to our inferences.

At Tungurahua, conditions for channelling were met between 110 MPa and a gas-rich region located at 1-10

MPa. Outgassing, however, could have happened through other mechanisms such as viscous percolation in the main part of the conduit owing to the low melt viscosity (10 3.7 Pa s at the reservoir level, [START_REF] Chevrel | Viscosity measurements of crystallizing andesite from Tungurahua volcano (Ecuador)[END_REF], or brittle-viscous coalescence shallowly, where much higher melt viscosities are expected. Figure 6 shows closed-system degassing paths for three starting points: at 200 MPa (reservoir level, [START_REF] Andújar | Structure of the Plumbing System at Tungurahua Volcano, Ecuador: Insights from Phase Equilibrium Experiments on July-August 2006 Eruption Products[END_REF], at 108 MPa, and at 34 MPa. These intermediate pressures correspond to the samples closest to the points where total crystal contents reach and exceed the lower bound for channelling, respectively. The decompression starting at 108 MPa overestimates shallower porosities, whereas that starting at 34 MPa closely follows the trend of the most porous samples. That the measured shallow porosities can be explained by decompressing the residual porosity around 40 MPa suggests that gas loss by channelling was enabled by microlite crystallization between 100 and 40 MPa (1.6-2.9 km depth). The gas-rich region at 1-10 MPa (40-400 m depth) could be due to the ascent of material immediately below that was fast enough to minimize outgassing, or to gas accumulation. Accumulation implies that outgassing was inefficient close to the surface.

This could be caused by a combination of hindered channelling at high crystal content, hindered brittleviscous coalescence because of insufficient gas overpressure, and impermeable plug and conduit walls. Gas accumulation is supported by the near-surface observation that measured porosities decrease to very low values (<1 vol%), revealing the presence of a low permeability, rigid plug [START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF]. Since the amount of crystals is very high in this plug, cracks or bubble connections (e.g., [START_REF] Heap | Microstructural controls on the physical and mechanical properties of edifice-forming andesites at Volcán de Colima, Mexico[END_REF] were not efficient enough to evacuate the residual gas, thereby allowing the gas-rich region to form.

Our results suggest that outgassing by channelling could have occurred down to (and probably deeper than) 2.7 km at Soufrière Hills, shallower than 3 km depth at Merapi, and between 1.5 and 3 km at Tungurahua.

One implication of such widespread channelling depths is that, besides rapidly changing magma rheology to possibly trigger more explosive eruptions [START_REF] Arzilli | Magma fragmentation in highly explosive basaltic eruptions induced by rapid crystallization[END_REF], microlite could also spur gas escape. Another implication is that outgassing by channelling could occur regardless of near-surface conditions such as the presence of a dome, a plug, or a permeable wallrock. Finally, the permeabilities reached by channelling are high for magmas in general, and several orders of magnitude higher than commonly admitted permeabilities at low porosity (e.g., [START_REF] Farquharson | Permeability and porosity relationships of edificeforming andesites: A combined field and laboratory study[END_REF][START_REF] Kushnir | Probing permeability and microstructure: Unravelling the role of a low-permeability dome on the explosivity of Merapi (Indonesia)[END_REF]. Such high permeabilities would affect transitions in eruptive style [START_REF] Cassidy | Controls on explosive-effusive volcanic eruption styles[END_REF], and the corresponding permeability relationships given by [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF] and [START_REF] Degruyter | How do volatiles escape their shallow magmatic hearth?[END_REF] can readily be tested in conduit flow models.

Conclusions

We revisited three reconstructions of porosity and crystal distributions prior to Vulcanian events that occurred respectively on February 10, 2010 at Soufrière Hills volcano, Montserrat [START_REF] Burgisser | Conduit processes during the February 11, 2010 Vulcanian eruption of Soufrière Hills, Montserrat[END_REF], on October 26, 2010 at Merapi volcano, Indonesia [START_REF] Drignon | Preexplosive conduit conditions during the 2010 eruption of Merapi volcano (Java, Indonesia)[END_REF]) and on July 14, 2013 at Tungurahua volcano, Ecuador [START_REF] Gaunt | Triggering of the powerful 14 July 2013 Vulcanian explosion at Tungurahua Volcano, Ecuador[END_REF]. They all feature porosities too low to be explained by common shallow processes such as connected bubble pathways or cracks. Our data show that these magmas have high enough crystal contents for outgassing to occur by a process named channelling. When the amount of crystals in a three-phase magma lies within the 40-70 vol% range, the interstitial space is narrow enough to force bubbles to form channels in which the gas buoyantly moves upwards but not so constricted that channel connections are ruptured [START_REF] Parmigiani | The mechanics of shallow magma reservoir outgassing[END_REF]. Channelling creates gas permeability of the order of 10 -10 m 2 , which is two to five orders of magnitude higher than the other permeability processes at the equivalent bubble content.

At Soufrière Hills, microlite crystallization during ascent yielded conditions propitious to channelling from near surface down to a depth greater than 2.7 km. If confidence is given in the critical porosity quantification, outgassing deflated the magma slightly below the critical porosity, which suggests that largescale stresses such as those related to conduit wall shearing were also at play in controlling the evolution of porosity during ascent.

At Merapi, the phenocrysts in the reservoirs could have fostered outgassing at depth without magma ascent.

Closed-system degassing in response to ascent, however, only yielded enough gas for channelling at midconduit depths. The part of the conduit where both gas contents were large enough and calculated porosities fall within the percolation range is located around 3 km depth. In this region and in the shallower parts of the conduit, outgassing by channelling could have taken place during (and possibly before) microlite crystallization but before the 70% crystal content was reached. This suggests that the strong gas depletion in the magma column could have resulted from weak exsolution at the beginning of the ascent followed by channelling at depths shallower than 3 km. Of the two end-member magmas involved in the eruption that we 20 considered in our analysis, this degassing behaviour is best explained if the conduit was filled by the colder resident magma.

At Tungurahua, outgassing by channelling was enabled by microlite crystallization at 1.6-2.9 km depth.

Near the surface, a low permeability plug trapped a gas-rich region between 40 and 400 m depth. Inefficient outgassing between 1.6 km and the gas accumulation region was probably caused by a combination of hindered channelling at high crystal content, hindered brittle-viscous coalescence because of insufficient gas overpressure, and impermeable plug and conduit walls. This suggests that the triggering of the paroxysmal explosion was controlled by near-surface gas trapping.

We presented lines of evidence for deep gas loss prior to sudden explosive emissions of three basaltic andesitic to andesitic magmas. They suggest that channelling is a viable mechanism for gas to be removed from the magma column at various levels during ascent, yielding mostly gas-depleted magma columns prior to eruption. Such outgassing by channelling could thus influence eruptive style. Depending on the phenocryst content, microlite growth during ascent can either foster, or impede gas escape by channelling.

Considering the pervasive occurrence of microlites and ensuing high crystal contents in volcanic conduits, the high likelihood of outgassing by channelling implies that other outgassing mechanisms might not be as dominant as previously envisioned.

Tables 530 (2000), [START_REF] Larsen | Experimental constraints on bubble interactions in rhyolite melts: implications for vesicle size distribution[END_REF], [START_REF] Mangan | Delayed, disequilibrium degassing in rhyolite magma: decompression experiments and implications for explosive volcanism[END_REF], [START_REF] Gardner | Bubble coalescence in rhyolitic melts during decompression from high pressure[END_REF]; a Values at 0 are <0.1 vol% and errors at 0 are <1%.

b Values at 0 are <0.001 ppm per weight.

Figure

  Figure4ashows the phenocrysts and total crystal content for Merapi conduit prior to the October 26

Fig. 1 :Fig. 2 :Fig. 6 :Fig. 7 :

 1267 Fig.1: Porosity as a function of pre-explosive pressure for the February 10, 2010 Vulcanian explosion at

  Figure

Figure

  Figure

Table 1 :

 1 Pre-explosive volatile proportions, vesicle-free crystal proportions, and pressures. Values in 531 parenthesis are relative uncertainties in % except for the pressure, where they indicate lower and upper

	532
	533	bounds of uncertainties in MPa. Uncertainties on phenocryst content are sometimes very low (<1%), which
	534	reflects that few SEM images were imaged to characterize phenocrysts. Uncertainties on the total crystal
	535	fraction include those due to microlite, which are obtained from a larger number of images. They thus reflect
	536	more accurately the natural spatial variability.
			Pressure	Porosity a	Gas b	Phenocrysts	Crystals
			(MPa)	(vol%)	(ppmw)	(vol%)	(vol%)
		Soufrière Hills
		AMO 210 A	40 (-9,+10)	1.9 (1)	0.6	34 (2)	54 (10)
		AMO 210 C	51 (-25,+31)	2.3 (2)	0.92	34 (12)	55 (22)
		AMO 210 D	14 (-3,+3)	1.9 (1)	0.2	31 (6)	39 (11)
		AMO 210 E	54 (-19,+22)	3.5 (0)	1.54	48 (0.3)	69 (9)
		AMO 210 F	33 (-8,+9)	1.6 (1)	0.41	50 (2)	66 (13)
		AMO 210 G	42 (-13,+15)	1.2 (3)	0.39	40 (12)	63 (11)
		AMO 210 H	12 (-5,+6)	8.5 (1)	0.89	39 (8)	65 (12)
		AMO 210 L	46 (-13,+14)	1.4 (2)	0.52	59 (3)	77 (6)
		AMO 210 Q	41 (-7,+7)	3.4 (1)	1.14	32 (1.3)	40 (14)
		WP1.095A	24 (-5,+5)	4.3 (0)	0.86	24 (0.4)	52 (3)
		WP1.095B	16 (-6,+7)	7.2 (0)	0.95	32 (0.2)	59 (9)
		WP1.108A	31 (-5,+5)	2.8 (0)	0.72	32 (0.3)	52 (10)
		WP1.108B	56 (-5,+5)	7.8 (1)	3.68	36 (1.1)	48 (3)
		WP2.200A	36 (-8,+9)	2.8 (0)	0.81	42 (0.3)	63 (19)
		WP2.200B	31 (-2,+2)	3 (0)	0.76	31 (0.7)	42 (3)
		WP2.201A	35 (-8,+9)	4.6 (0)	1.33	45 (0.2)	59 (10)
		WP2.201B	69 (-14,+15)	2.4 (0)	1.36	31 (0.2)	51 (8)
		WP2.329A	7 (-1,+1)	23.6 (0)	1.62	11 (1.2)	27 (15)
		WP2.329B	41 (-4,+4)	2.7 (1)	0.89	51 (2)	65 (3)
		Merapi Oct. 26
		AME 10 A1	75 (-22,+25)	2.3 (4)	1.27	33 (7)	70 (11)
		AME 10 A2	100 (-34,+38)	1.5 (4)	1.12	44 (8)	79 (8)
		AME 10 A3	150 (-123,+174) 1.2 (3)	1.32	40 (3)	82 (11)
		AME 10 A4	100 (-22,+24)	1.6 (5)	1.16	45 (8)	80 (8)
		AME 10 A5	73 (-25,+29)	2.4 (3)	1.32	47 (5)	76 (6)
		AME 10 A6	58 (-12,+13)	3.1 (2)	1.32	46 (3)	72 (5)
		AME 10 B1	158 (-48,+53)	0.9 (4)	1.03	41 (9)	80 (10)
		AME 10 B2	63 (-11,+12)	2.3 (3)	1.05	50 (5)	72 (8)
		AME 10 B4	268 (-106,+118) 0.6 (4)	1.14	36 (6)	87 (6)

Acknowledgements

We thank Nicolas Gillet for the time spent to help with proper uncertainties calculations. We also thank the thoughtful and detailed comments of two anonymous reviewers and the constructive editorial handling of K.

Cashman. This work was partially supported by the Agence Nationale pour la Recherche grant ANR-19-CE31-0007.


Anna Volokitina

Pavel Loiko

Anatoly Pavlyuk

Sami Slimi

Rosa Maria Solé

Ezzedine Ben Salem

Esrom Kifle

Josep Maria Serres

Uwe Griebner

Valentin Petrov

Magdalena Aguiló

Francesc Díaz

Xavier Mateos
email: xavier.mateos@urv.cat

Laser operation of cleaved single-crystal plates and films of Tm:KY(MoO 4 ) 2

We report on the crystal growth, spectroscopy and first laser operation of a novel double molybdate compound -Tm:KY(MoO 4 ) 2 . This orthorhombic (sp. gr. Pbna) crystal exhibits strong anisotropy of the spectroscopic properties due to its layered structure. The maximum stimulated emission cross-section for the 3 F 4 → 3 H 6 transition is 2.70×10 -20 cm 2 at 1856 nm with a bandwidth of >110 nm (for E || b). The lifetime of the 3 F 4 state is 2.29 ms. Crystalline films and plates (thickness down to 70 μm) of high optical quality are obtained by mechanical cleavage along the (100) plane. Continuous-wave diode-pumped laser operation is achieved in such thin films and plates yielding a maximum output power of 0.88 W at ~1.9 μm with a slope efficiency of 65.8% and a linearly polarized laser output. Vibronic lasing is demonstrated at ~2.06 μm. Tm:KY(MoO 4 ) 2 is promising for microchip and thin-disk lasers.

Introduction

Monoclinic (sp. gr. C2/c) double tungstate (DT) crystals, KRE(WO 4 ) 2 (where RE = Gd, Y, Lu), doped with rare-earth ions (RE 3+ ), and, in particular, with trivalent thulium (Tm 3+ ) ions are known for efficient lasing in the eye-safe spectral range of ~2 μm according to the 3 F 4 → 3 H 6 electronic transition [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF][START_REF] Mateos | Efficient 2-μm continuous-wave laser oscillation of Tm 3+ :KLu(WO 4 ) 2[END_REF][START_REF] Troshin | Spectroscopy and laser properties of Tm 3+ :KY(WO 4 ) 2 crystal[END_REF]. This is due to the high achievable Tm doping concentrations, strong cross-relaxation for neighboring Tm 3+ ions, 3 H 4 (Tm 1 ) + 3 H 6 (Tm 2 ) → 3 F 4 (Tm 1 ) + 3 F 4 (Tm 2 ) [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ∼80% slope efficiency[END_REF], even at moderate doping levels, broad and intense emission bands at ~2 μm with polarized light [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF], weak non-radiative relaxation from the upper laser level ( 3 F 4 ) and Raman activity. The host crystals themselves also provide suitable thermo-optical properties enabling microchip laser operation [START_REF] Gaponenko | Thermal lensing and microchip laser performance of N g -cut Tm 3+ :KY(WO 4 ) 2 crystal[END_REF][START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF]. Monoclinic DTs exhibit a polymorphic phase transformation below the melting point. Thus, they are typically grown by the Top-Seeded Solution Growth (TSSG) method (from the flux) [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF].

Such attractive spectroscopic properties are also expected for their double molybdate (DMo) counterparts, KRE(MoO 4 ) 2 . One representative of this crystal family is the potassium yttrium double molybdate, KY(MoO 4 ) 2 [START_REF] Klevtsova | X-ray structural study of the double molybdate KY(MoO 4 ) 2[END_REF]. It belongs to the orthorhombic crystal class (sp. gr. Pbna) and does not exhibit polymorphism [START_REF] Klevtsov | Polymorphism of the double molybdates and tungstates of mono-and trivalent metals with the composition M + R 3+ (EO 4 ) 2[END_REF]. Thus, it can be easily grown by the Czochralski (Cz) method (from the melt). Moreover, KY(MoO 4 ) 2 features a layered structure further enhancing the polarization-anisotropy of vibronic [START_REF] Hanuza | Polarized Raman and infrared spectra of a multilayer KY (MoO 4 ) 2 crystal[END_REF][START_REF] Hanuza | Polarized IR and Raman spectra of orthorhombic KLn(MoO 4 ) 2 crystals (Ln = Y, Dy, Ho, Er, Tm, Yb, Lu)[END_REF] and spectroscopic properties [START_REF] Kaminskii | Ribbon and sheet miniature crystal laser[END_REF][START_REF] Kaminskii | Stimulated emission from KY(MoO 4 ) 2 -Nd 3+ crystal laser[END_REF] and leading to a perfect cleavage feature that can be utilized in microchip or thin-film lasers [START_REF] Kaminskii | Ribbon and sheet miniature crystal laser[END_REF]. The structure of undoped KY(MoO 4 ) 2 is known [START_REF] Klevtsova | X-ray structural study of the double molybdate KY(MoO 4 ) 2[END_REF].

The previous studies of laser properties of RE 3+ -doped KY(MoO 4 ) 2 crystals focused solely on Nd 3+ ions. The first laser operation of Nd:KY(MoO 4 ) 2 at the wavelengths of 1.067 µm and 1.349 µm was obtained in the free-running regime (flashlamp pumping) [START_REF] Kaminskii | Stimulated emission from KY(MoO 4 ) 2 -Nd 3+ crystal laser[END_REF][START_REF] Kaminskii | Investigation of stimulated emission in the 4 F 3/2 → 4 I 13/2 transition of Nd 3+ ions in crystals (III)[END_REF]. Continuouswave (CW) operation with bulk crystals was later achieved in [START_REF] Kaminskii | New high power, high efficient quasi-CW and CW single-mode KY(MoO 4 ) 2 :Nd 3+ laser end-pumped by a GaAlAs laser-diode array[END_REF][START_REF] Loiko | Efficient continuous-wave in-band pumped Nd:KY(MoO 4 ) 2 laser[END_REF]. Kaminski et al. also proposed the concept of a thin-film or a belt-shaped laser using thin crystalline films (thickness: down to 50 μm) of Nd:KY(MoO 4 ) 2 pumped by flash-lamps and Ar + ion laser [START_REF] Kaminskii | Ribbon and sheet miniature crystal laser[END_REF].

Recently, efficient lasers operating at ~1 μm based on single-crystal plates were demonstrated using other cleaving crystals such as Yb:LuPO 4 or Yb:BaGd 2 (MoO 4 ) 4 [START_REF] Liu | Spectroscopic properties and continuouswave laser operation of Yb:LuPO 4 crystal[END_REF][START_REF] Zhu | Growth, spectral properties, and laser demonstration of Yb 3+ :BaGd 2 (MoO 4 ) 4 cleavage crystal[END_REF].

In the present work, we report on the crystal growth by the Czochralski method, structural and spectroscopic characterization as well as the first laser operation of a novel representative of the DMo crystal familythe orthorhombic Tm:KY(MoO 4 ) 2 crystal.

Crystal growth and structure

Crystal growth

The crystal growth was performed by the Low Temperature Gradient (LTG) Cz method [START_REF] Borovlev | Progress in growth of large sized BGO crystals by the low-thermal-gradient Czochralski technique[END_REF]. The Tm:KY(MoO 4 ) 2 crystal melts at ~1243 K. The starting materials for preparing the growth charge were Y 2 O 3 (purity: 5N), Tm 2 O 3 (4N), MoO 3 (4N) and K 2 CO 3 (5N) taken for the composition 100 mol% KY 0.97 Tm 0.03 (MoO 4 ) 2 -5-7 mol% K 2 Mo 3 O 10 . Potassium trimolybdate (K 2 Mo 3 O 10 ) was added to prevent partial dissociation of the melt and to stabilize the growth process. The raw materials were carefully mixed and placed in a Pt crucible with a cylindrical shape (diameter: 70 mm, height: 120 mm). The crucible was first heated until ~1320 K in air and kept at this temperature for 2-3 h to homogenize the melt. Then, the melt was cooled to ~1240 K (the starting growth temperature). The crucible was placed in a three-zone resistive heating furnace having good bottom and top heat insulation [START_REF] Borovlev | Progress in growth of large sized BGO crystals by the low-thermal-gradient Czochralski technique[END_REF]. A seed prepared from an undoped KY(MoO 4 ) 2 crystal was oriented orthogonal to the cleavage plane (i.e., along the [100] crystallographic axis). It was rotated at 20 r.p.m. (revolutions per minute); the pulling rate was 1-2 mm/h; the cooling rate was ~2 K/day. The temperature gradient in the melt was below 3 K/cm as measured by a Pt/Pt-Rh thermocouple along the crystal growth direction. After the growth process was completed, the crystal was removed from the melt and slowly cooled down to room temperature (RT, 293 K). No post-grown annealing was applied. The as-grown 3 at.% Tm:KY(MoO 4 ) 2 crystal boule is shown in Fig. 1(a). The Tm 3+ concentration was calculated to be N Tm = 1.95×10 20 cm -3 (assuming a segregation coefficient K Tm ≈ 1). The crystal boule had a donut shape and contained no cracks and inclusions. The crystal had a slight yellowish coloration due to the Tm 3+ doping. Tm:KY(MoO 4 ) 2 exhibits a perfect natural cleavage along the crystallographic (100) plane (i.e., orthogonal to the growth direction in the present work), as verified by single-crystal X-ray diffraction (XRD). The orientation of the [010] and [001] axes was also determined by single-crystal XRD. It can be also found in a different way. The (100) cleaved thin crystal plates of Tm:KY(MoO 4 ) 2 brake under bending along the [001] axis. Along the orthogonal [010] axis, the plates exhibit an elastic deformation. An anisotropy of thermal properties of Tm:KY(MoO 4 ) 2 in the (100) plane also determines a slight ellipticity of the cross-section of the crystal boule with the principal directions along the [010] and [001] axes.

A Scanning Electron Microscope (SEM) image of the fracture edge of a mechanically cleaved single-crystal plate of Tm:KY(MoO 4 ) 2 is shown in Fig. 1(b). Note that the whole boule of Tm:KY(MoO 4 ) 2 has a single-crystalline nature. The fracture of crystal-plates occurs along the [001] axis. The SEM image reveals the natural cleavage feature as the fracture edge represents multiple "stairs" running parallel to the c-axis in the (100) plane.

Crystal structure and Raman spectra

The structure and phase purity of Tm:KY(MoO 4 ) 2 were confirmed by powder XRD, see Fig. 2 The polarized Raman spectra were measured using a Renishaw inVia confocal Raman microscope with a ×50 objective. The excitation wavelength λ exc was 488 nm (Ar + ion laser line). The spectral resolution was ~1 cm -1 . The Raman spectra of an (100)-oriented plate from the Tm:KY(MoO 4 ) 2 crystal are shown in Fig. 2(b). The spectra contain bands localized in three ranges and having different intensity. The low-frequency range (at <275 cm -1 ) contains weak vibrations related to translational (T′) modes of K, Y|Tm and Mo and rotational (R) lattice modes. Internal modes are observed at higher frequencies. The second intermediate-frequency range at 318-436 cm -1 exhibits bands of medium intensity related to the bending (δ) vibrations of the oxygen bridged [MoO 4 ] tetrahedra. Finally, the high-frequency range, 727-945 cm -1 , contains intense modes due to the stretching (ν) vibrations of [ MoO 4 ]. The most intense and strongly polarized Raman peak appears at 865.6 cm -1 with a full width at half maximum (FWHM) of 10.5 cm -1 . It is assigned to one of the internal (ν) vibrations of [ MoO 4 ]. The maximum phonon energy of Tm:KY(MoO 4 ) 2 is 945 cm -1 . More details can be found elsewhere [START_REF] Hanuza | Polarized Raman and infrared spectra of a multilayer KY (MoO 4 ) 2 crystal[END_REF][START_REF] Hanuza | Polarized IR and Raman spectra of orthorhombic KLn(MoO 4 ) 2 crystals (Ln = Y, Dy, Ho, Er, Tm, Yb, Lu)[END_REF].

Spectroscopic study

Experimental

The KY(MoO 4 ) 2 crystal is orthorhombic and, thus, optically biaxial. The frame of the optical indicatrix axes (X, Y, Z) coincides with the (a, b, c) crystallographic frame (not necessarily respectively). Only a mean value of the refractive index ⟨n⟩ ≈ 2 is known [START_REF] Kaminskii | Stimulated emission from KY(MoO 4 ) 2 -Nd 3+ crystal laser[END_REF]. Thus, the anisotropic absorption and luminescence properties were characterized for the E || a, b, c light polarizations. All the spectroscopic studies were performed at RT (293 K).

For measuring the absorption and luminescence spectra, we used a ~1 mm-thick cleaved crystal plate. The absorption spectra were measured for the available light polarizations E || b and E || c using a Varian CARY 5000 spectrophotometer and a Glan-Taylor polarizer. The spectral resolution was 0.1-0.5 nm. It was complicated to prepare a polished sample oriented orthogonal to the cleavage plane thus accessing the E || a polarization in absorption.

The luminescence spectra at ~2 μm for the polarizations E || a, b, c were measured using an optical spectrum analyzer (AQ6375B, Yokogawa, spectral resolution: 1 nm) and a Glan-Taylor polarizer. The spectral response of the set-up was calibrated employing a quartz iodine lamp. The excitation source was a CW Ti:Sapphire laser tuned to ~802 nm.

The luminescence decay of Tm 3+ ions was studied using a 1/4 m monochromator (Oriel 77200), an InGaAs detector and a 8 GHz digital oscilloscope (DSA70804B, Tektronix). The luminescence was excited by the output of a ns optical parametric oscillator tuned to ~802 nm (Horizon, Continuum).

Optical absorption and luminescence

The absorption spectrum of the Tm:KY(MoO 4 ) 2 crystal for light polarizations E || b and E || c is shown in Fig. 3(a). In the spectrum, the absorption bands are due to transitions of Tm 3+ ions from the ground-state ( 3 H 6 ) to the excited-states ( 3 F 4 to 1 D 2 ). There is no color center absorption in the visible. The UV absorption edge is found at λ UV = 327 nm (for E || c) and 340 nm (for E || b), corresponding to an optical bandgap E g of 3.64-3.80 eV. The absorption cross-sections, σ abs , for the 3 H 6 → 3 H 4 and 3 H 6 → 3 F 4 transitions are shown in Fig. 3(b). For the 3 H 6 → 3 H 4 one, the maximum σ abs is 7.70×10 -20 cm 2 at 802.8 nm and the corresponding FWHM of the absorption peak is 10.0 nm (for E || b). For the second available light polarization (E || c), σ abs is by one order of magnitude smaller: 0.32×10 -20 cm 2 at 792.9 nm. This transition is suitable for pumping of Tm 3+ ions, e.g., by commercial and high-power AlGaAs laser diodes (the "conventional" pump scheme). The maximum σ abs value for the 3 H 6 → 3 H 4 Tm 3+ transition in KY(MoO 4 ) 2 is similar to that in monoclinic Tm:KLu(WO 4 ) 2 , σ abs = 9.5×10 -20 cm 2 at 793.6 nm [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF] however providing a FWHM of the absorption peak of 1.7 nm (light polarization: E || N p ). As a result, Tm:KY(MoO 4 ) 2 is more suitable for diode-pumping because of weaker sensitivity to the temperature drift of the diode emission wavelength. For the 3 H 6 → 3 F 4 Tm 3+ transition in KY(MoO 4 ) 2 , σ abs reaches 3.95×10 -20 cm 2 at 1785 nm (again for E || b). This transition is suitable for in-band pumping of Tm 3+ ions directly to the upper laser level, e.g., by erbium Raman fiber lasers emitting at ~1.7 μm [START_REF] Loiko | In-band pumping of Tm:LiYF 4 channel waveguide: a power scaling strategy for ∼2 μm waveguide lasers[END_REF].

The notable anisotropy of the absorption cross-sections in the (100) plane cannot be assigned to the layered structure and is most probably related to the low symmetry of the Tm 3+ site (C 2 ).

The stimulated-emission (SE) cross-sections, σ SE , for the 3 F 4 → 3 H 6 transition of Tm 3+ were calculated using the Füchtbauer-Ladenburg (F-L) formula [START_REF] Aull | Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections[END_REF]:

, d ) ( ) 3 / 1 ( ) ( 8 ) ( , , rad 2 5 SE   = = c b a i i i i W W c n          (1)
where λ is the light wavelength, ⟨n⟩ is the refractive index, c is the speed of light, τ rad is the radiative lifetime of the emitting state ( 3 F 4 ), W i (λ) is the measured luminescence spectrum for i-th polarization calibrated for the spectral response of set-up and i = a, b, c. The results are shown in Fig. 4 The luminescence decay from the 3 F 4 state is single-exponential yielding a luminescence lifetime τ lum of 2.29 ms, see Fig. 4(b). This agrees with the accommodation of Tm 3+ ions in a single type of sites (symmetry: C 2 ). The luminescence lifetime of the 3 H 4 pump level is 48 μs. This value is expected to be quenched by the cross-relaxation. Both lifetimes were measured for thin (tens of μm) films eliminating the effect of reabsorption (radiation trapping). Indeed, the τ lum ( 3 F 4 ) value obtained using a crystal-plate was much longer, 3.35 ms.

The 3 F 4 → 3 H 6 Tm 3+ transition represents a quasi-three-level laser scheme with reabsorption losses. Thus, the gain cross-sections, σ gain = βσ SE -(1 -β)σ abs , are typically calculated to conclude about the expected emission wavelength, where β = N 2 ( 3 F 4 )/N Tm is the inversion ratio and N 2 is the population of the upper laser level ( 3 F 4 ). The σ gain spectra for the high-gain light polarization E || b are shown in Fig. 5. They are relatively smooth and broad.

Laser operation

Laser set-up

For the laser experiments, we prepared two samples from the 3 at.% Tm:KY(MoO 4 ) 2 crystal. They were fabricated by mechanical cleaving the crystal using a thin razor blade placed along the (100) crystallographic plane. Only a slight pressure was applied to the blade producing the initial crack which further easily propagated through the crystal cross-section. The samples had a thickness (t) of 70±5 μm and 700±10 μm, referred further as a thin-film and a crystal-plate, respectively. The thickness was measured using a micrometer and confirmed by SEM for the thin-film. It was uniform along the sample cross-section within the specified error. The first sample exhibited elastic deformation at naked eye. No post-cleavage processing (e.g., polishing or coating) was applied. The clean aperture of the samples was more than 1 cm 2 . The samples were fabricated from the bulk crystal oriented by means of single-crystal XRD so that the orientation of the [010] and [001] axes was known.

The samples were placed in a compact plano-plano (microchip) cavity formed by a flat pump mirror (PM) coated for high transmission (HT) at the pump wavelength, ~0.80 μm, and for high reflection (HR) at 1.8-2.1 μm, and a set of flat output couplers (OCs) having a transmission T OC of 0.1%-9% at the laser wavelength, Fig. 6(a). A special band-pass (BP) OC coated for HT at <2 μm and for partial reflection (T OC = 1.5%) at 2.05-2.20 μm was also used. Both the PM and OC were gently pressed towards the crystalline sample, so that the geometrical cavity length L cav ≡ t. The laser element was passively cooled, Fig. 6(b). The laser element was pumped by a fiber-coupled (fiber core diameter: 200 μm, N.A. = 0.22) AlGaAs laser diode emitting up to 17 W of unpolarized output at 802 nm (M 2 ≈ 86). The incident pump power was limited to avoid optical damage at the crystal / mirror interfaces. The pump beam was collimated and focused into the laser element by a lens assembly (1:1 reimaging ratio, focal length f = 30 mm) resulting in a pump spot diameter 2w P = 200±10 μm. Due to the partial reflectivity of the OCs at the pump wavelength (R ≈ 40%), the pumping was in a double-pass. The total pump absorption was taken at its small-signal value, η abs,0 = 6.4% and 47.6% for the thin-film and crystal-plate, respectively. This value does not account for the possible ground-state bleaching; however, it does not overestimate the slope efficiency of the laser. The laser output was separated from the residual pump using a long-pass filter (FEL1000, Thorlabs).

Laser performance

First, we studied the laser performance of the crystal-plate (t = 700 μm), Fig. 7(a),(b). The laser generated a maximum output power of 0.88 W at 1840-1905 nm with a slope efficiency η of 65.8% (vs. the absorbed pump power P abs ) and the laser threshold was at P abs = 210 mW (for T OC = 5%). For higher output coupling, the performance slightly deteriorated probably due to the upconversion losses. For all OCs, the input-output dependences were linear indicating weak thermal effects. The laser polarization was linear (E || b); it was naturally selected by the anisotropy of the gain. Typical spectra of the laser emission are shown in Fig. 7(b). With the increase of T OC , the spectra experienced a blue-shift due to the quasi-three-level nature of the 3 F 4 → 3 H 6 Tm 3+ laser scheme. For example, for small T OC = 1.5%, the laser operated at 1970-1978 nm and for high T OC = 9% -at 1826-1835 nm. This behavior agrees well with the gain spectra for light polarization E || b, Fig. 5. By implementing the band-pass OC, laser emission beyond 2 μm was achieved. The output power reached 0.34 W at 2047-2074 nm with η = 46.7% and a laser threshold of 205 mW. Such a long wavelength emission is ascribed to the electron-phonon coupling with the lowenergy Raman modes of the KY(MoO 4 ) 2 lattice [START_REF] Loiko | Vibronic thulium laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF][START_REF] Loiko | Monoclinic Tm:MgWO 4 crystal: Crystal-field analysis, tunable and vibronic laser demonstration[END_REF].

The second experiment consisted of inserting the crystal-film into the laser cavity, Fig. 7(c),(d). The maximum output power was 131 mW at 1801-1872 nm with η = 45.2% and a threshold of only 35 mW (for T OC = 1.5%). The emission was linearly polarized (E || b). With the increase of the output coupling, the laser threshold increased: from 13 mW for the smallest T OC = 0.1% up to 54 mW for T OC = 9% still remaining relatively low. The slope efficiency first increased with T OC (so that the optimum transmission of the OC is expected to lie between T OC = 0.1% and 1.5%) and, furthermore, decreased for T OC > 1.5%. The latter effect is probably due to stronger energy-transfer upconversion (ETU) associated with higher population of the upper laser level 3 F 4 (higher inversion rate β) at increased output coupling. The ETU has a direct influence on the laser threshold [START_REF] So | A power-scaling strategy for longitudinally diode-pumped Tm:YLF lasers[END_REF]. However, it also leads to a stronger heat dissipation and more severe thermo-optic effects in the gain medium thus affecting the slope efficiency in an indirect way.

The lower slope efficiency achieved with the crystal-film laser as compared to the crystalplate one is ascribed to higher passive losses originating from possible mechanical distortion and bending of the film. We expect that such losses can be eliminated by further optimizing the cleaving procedure.

The blue-shift of the emission spectra with the output coupling was also detected, Fig. 7(d). The spectra contained equidistant spectral lines separated by Δλ = 12.2 nm at ~1.85 μm (for T OC = 1.5%-9%). This is ascribed to the etalon effect of the uncoated laser element. The free spectral range (FSR) of the Fabry-Perot etalon with a thickness t and a refractive index n g (n g ≈ n assuming a weak dispersion) at normal incidence is Δλ FSR ≈ λ 2 /(n g t). From this formula, we get the etalon thickness of 71 μm for n = 2.0 in good agreement with the measured thickness.

The Tm:KY(MoO 4 ) 2 lasers operated in the fundamental transverse mode. The beam quality parameters measured using an ISO-standard method employing a focusing lens M 2

x,y < 1.2 (x = b, y = c).

Conclusion

To conclude, the orthorhombic double molybdate crystal Tm:KY(MoO 4 ) 2 is a promising material for efficient ~2 μm lasers owing to its easy growth, high available doping levels, intense, broad and strongly polarized absorption and emission bands and Raman activity. The layered structure of KY(MoO 4 ) 2 promotes the anisotropy of its optical properties and allows one to fabricate easily laser-quality crystal plates and films with a thickness ranging from few mm down to tens of μm. This feature is of interest for microchip and thin-disk lasers. In particular, the long lifetime of the upper laser level of Tm 3+ is attractive for passively Qswitched sub-nanosecond microchip lasers. In the present work, we achieved ~2 μm CW laser action in single-crystal plates (sub-mm) and films (sub-100 μm) featuring up to 65.8% slope efficiency and almost watt-level output for passively-cooled devices.

Fig. 1 .

 1 Fig. 1. (a) Photograph of the as-grown 3 at.% Tm:KY(MoO 4 ) 2 crystal boule. The growth direction is along the [100] axis (vertical); (b) Scanning Electron Microscope (SEM) image of the side surface of a cleaved single-crystal film indicating the crystallographic directions.

  (a). Tm:KY(MoO 4 ) 2 belongs to the orthorhombic centrosymmetric crystal class (sp. gr. Pbna -D 14 2h , No. 60). No traces of any other impurity phases are found. The lattice constants for the 3 at.% Tm-doped crystal were determined using the Rietveld refinement to be a = 18.2012(9) Å, b = 7.9301(5) Å, c = 5.0666(4) Å, α = β = γ = 90°, the calculated density ρ calc is 4.0897(4) g/cm 3 (the number of the structural units Z = 4). The reduced chi-squared value of χ 2 = (R wp /R exp ) 2 for this fit is 1.802 (R wp = 8.65%, R exp = 4.80%). The initial set of atomic coordinates for undoped KY(MoO 4 ) 2 was taken from [8]. The structure of Tm:KY(MoO 4 ) 2 consists of continuous belts of edge-sharing distorted [YO 8 ] octahedra arranged parallel to the b-axis. In the a-b plane, they share corners with the [MoO 4 ] tetrahedra. The radicals [Y(MoO 4 ) 2 ] -form porous layers parallel to the b-c plane. The linkage of these layers along the a-axis is weak, which explains the excellent cleavage along the (100) plane. Tm 3+ ions substitute for Y 3+ in a single site (coordination number (C.N.) by oxygen is VIII, C 2 symmetry). This is favored by the closeness of ionic radii of Tm 3+ (0.994 Å) and Y 3+ (1.019 Å).

Fig. 2 .

 2 Fig. 2. (a) Rietveld refinement of the X-ray powder diffraction (XRD) pattern of the 3 at.% Tm:KY(MoO 4 ) 2 crystal; numbers indicate the Miller's indices (hkl) (sp. gr. Pbna); (b) Polarized Raman spectra of the Tm:KY(MoO 4 ) 2 crystal for the a(ij)a geometries, where i, j = b or c (Porto's notations), λ exc = 488 nm.

Fig. 3 .

 3 Fig. 3. Absorption of the Tm:KY(MoO 4 ) 2 crystal: (a) full absorption spectrum; (b) absorption cross-sections, σ abs , for the 3 H 6 → 3 F 4 and 3 H 4 transitions for polarizations E || b and E || c.

  (a). The maximum σ SE is 2.70×10 -20 cm 2 at 1856 nm with an emission bandwidth (FWHM) of >110 nm (for E || b). Tm:KY(MoO 4 ) 2 exhibits a notable anisotropy of the SE crosssections: the ratios σ SE (b) : σ SE (c) = 7.5 and σ SE (b) : σ SE (a) = 5.7 at ~1.86 μm, which is a prerequisite for a linearly polarized laser output.

Fig. 4 .

 4 Fig. 4. Emission properties of the Tm:KY(MoO 4 ) 2 crystal: (a) stimulated-emission (SE) crosssections, σ SE , for the 3 F 4 → 3 H 6 transition, light polarizations are E || a, b, c; (b) luminescence decay curve from the 3 F 4 state, λ exc = 800 nm, λ lum = 1860 nm.

Fig. 5 .

 5 Fig. 5. Gain cross-sections, σ gain = βσ SE -(1 -β)σ abs , for the 3 F 4 ↔ 3 H 6 transition of Tm 3+ in KY(MoO 4 ) 2 : β = N 2 ( 3 F 4 )/N Tm is the inversion ratio, the light polarization is E || b.

Fig. 6 .

 6 Fig. 6. (a) Scheme of the diode-pumped microchip Tm:KY(MoO 4 ) 2 lasers: LDlaser diode, PMpump mirror, OCoutput coupler, Fcut-off filter; (b) photograph of the laser.

Fig. 7 .

 7 Fig. 7. Diode-pumped laser performance of (100)-oriented cleaved (a,b) thin-film (t = 70 μm) and (c,d) crystal-plate (t = 700 μm) 3 at.% Tm:KY(MoO 4 ) 2 crystal: (a,c) input-output dependences, ηslope efficiency; (b,d) typical spectra of the laser emission measured at maximum P abs . The laser polarization is E || b.

Funding

Spanish Government (MAT2016-75716-C2-1-R (AEI/FEDER,UE), Generalitat de Catalunya (2017SGR755); Russian Foundation for Basic Research (RFBR) (19-32-90199).

Disclosures

The authors declare no conflicts of interest.