Katja Klumpp

Olivier Darsonville

Juliette Bloor

Spatial variation in vegetation height as an indicator of aboveground carbon stocks in grazed grasslands

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

Results

• Mean annual productivity was greater in the 'Intensive' treatment compared to the 'Extensive' grazing treatment (F 1,11 = 54.5, P < 0.001), but standing biomass showed no significant difference between grazing treatments during the study (Figure 1A/B). • Absolute variation in green vegetation height at the end of the growing season (green height SD) showed a positive relationship with mean annual field-scale standing biomass in both grazing treatments (Figure 1C). • Metrics of green height were unrelated to field-level productivity, and no significant relationship was found between metrics of variation in senescent height and either field-level productivity or standing biomass (P > 0.05).

Take-home Message

Our results suggest that within-field variation in end-of-season green vegetation height may provide an integrated indicator of biomass state during the year (i.e. quantity of standing biomass available for ingestion over time), with implications for the estimation of aboveground carbon stocks and carbon input into the soil. However, simple metrics of within-field variation do not appear to provide useful proxies of biomass fluxes in this grassland system.

Experimental approach

• Measurements were carried over 6 years at a long-term research platform in France (SOERE-ACBB: Laqueuille) on two grazed grasslands (high stocking rate and N inputs, intensive; low stocking rate and no N inputs, extensive). • Field-scale standing biomass and potential productivity was assessed across each paddock at five dates per year during the growing season. • Maximum height of both green and senescent shoots were determined at the end of each grazing season on 30m x 20m grids using a sward stick (117 points per grid, 2.5m distances). Standard deviation (SD) and coefficients of variation (CV) were used to assess the variation in plant height.

Grid measurements at the study site. Photos: C.Schmidt

Background

Spatial heterogeneity in plant and soil properties is known to influence ecosystem functions, but the linkages between spatial variation and ecosystem services in grasslands are unclear. Here we examine within-field variation in sward structure (vegetation height) and test whether indices of spatial heterogeneity can be used as a simple indicator of aboveground production services or carbon stocks over time in upland grasslands.

Left : Study location in the Massif Central region of France ; Right : On-site grazing.

Fig. 1 .

 1 Fig. 1. Interannual variation in field-scale annual biomass production (A) and mean standing biomass (B); data are means ± SE. Relationship between within-field variation in green vegetation height (standard deviation) and estimations of mean annual field-scale standing biomass during the study (C). Grazing treatments are given by: Intensive, organe-filled bars/circles; Extensive, blue-filled bars/triangles.

  of Clermont Auvergne, VetAgro Sup, UMR UREP, Clermont-Ferrand, France


A Hirsch-Passicos

C L C Lacoste

F André

Y Elskens

E D'humières

V Tikhonchuk

M Bardon

Helical coil design with controlled dispersion for bunching enhancement of the TNSA protons

The quality of the proton beam produced by Target Normal Sheath Acceleration (TNSA) with high power lasers can be significantly improved with the use of helical coils. While they showed promising results in terms of focusing, their performances in terms of the of cut-off energy and bunching stay limited due to the dispersive nature of helical coils. A new scheme of helical coil with a tube surrounding the helix is introduced, and the first numerical simulations and an analytical model show a possibility of a drastic reduction of the current pulse dispersion for the parameters of high power laser facilities. The helical coils with tube strongly increase bunching, creating two collimated narrow-band proton beams from a broad and divergent TNSA distribution. The analytical model provides scaling of proton parameters as a function of laser facility features.

I. INTRODUCTION

Since the 2000s, ion acceleration by intense and short laser pulses [START_REF] Daido | Review of laser-driven ion sources and their applications[END_REF][START_REF] Macchi | Ion acceleration by superintense laser-plasma interaction[END_REF] has been a growing research field due to the very interesting properties of laser generated proton beams compared to 'classically' accelerated proton beams: short duration, high current, low emittance, high laminarity and high brightness [START_REF] Macchi | Ion acceleration by superintense laser-plasma interaction[END_REF][START_REF] Roth | Energetic ions generated by laser pulses: A detailed study on target properties[END_REF][START_REF] Borghesi | Multi-mev proton source investigations in ultraintense laser-foil interactions[END_REF][START_REF] Cowan | Ultralow emittance, multi-mev proton beams from a laser virtual-cathode plasma accelerator[END_REF]. Several laser-driven ion acceleration processes are identified, such as the Target Normal Sheath Acceleration (TNSA) [START_REF] Snavely | Intense high-energy proton beams from petawatt-laser irradiation of solids[END_REF][START_REF] Wilks | Energetic proton generation in ultra-intense laser-solid interactions[END_REF], radiation pressure acceleration [START_REF] Sentoku | High energy proton acceleration in interaction of short laser pulse with dense plasma target[END_REF][START_REF] Schlegel | Relativistic laser piston model: Ponderomotive ion acceleration in dense plasmas using ultraintense laser pulses[END_REF] or collisionless shock acceleration [START_REF] Martins | Ion dynamics and acceleration in relativistic shocks[END_REF]. TNSA is of particular interest, as it is the most robust scheme. It is characterized by a large angular divergence (∼40°) [START_REF] Snavely | Intense high-energy proton beams from petawatt-laser irradiation of solids[END_REF] and an exponential energy distribution [START_REF] Snavely | Intense high-energy proton beams from petawatt-laser irradiation of solids[END_REF] with a cut-off energy depending on the laser intensity and energy [START_REF] Daido | Review of laser-driven ion sources and their applications[END_REF][START_REF] Macchi | Ion acceleration by superintense laser-plasma interaction[END_REF].

However, the large angular divergence and spectral distribution of TNSA ion beams are limitations for several potential applications, such as isochoric heating for warm dense matter (WDM) studies [START_REF] Patel | Isochoric heating of solid-density matter with an ultrafast proton beam[END_REF] and radio-isotope production for medical applications [START_REF] Nemoto | Laser-triggered ion acceleration and table top isotope production[END_REF] or neutron production [START_REF] Lancaster | Characterization of 7 li (p, n) 7 be neutron yields from laser produced ion beams for fast neutron radiography[END_REF] for measurements of nuclear cross sections processes relevant to astrophysics.

In order to improve the quality of TNSA ion beam, several schemes have been designed to focus, post-accelerate and select in energy ions such as the use of an active plasma lens [START_REF] Yang | Designing of active plasma lens for focusing laser-plasma-accelerated pulsed proton beams[END_REF], magnetic self-focusing in a stack of conducting foils [START_REF] Ni | Feasibility study of the magnetic beam self-focusing phenomenon in a stack of conducting foils: Application to tnsa proton beams[END_REF], proximal target structures [START_REF] Mcguffey | Focussing protons from a kilojoule laser for intense beam heating using proximal target structures[END_REF], target curvature [START_REF] Patel | Isochoric heating of solid-density matter with an ultrafast proton beam[END_REF][START_REF] Bin | Influence of the target frontsurface curvature on proton acceleration in laser-foil interaction[END_REF][START_REF] Carrié | Focusing of laser-accelerated proton beams using curved targets, and improved energy deposition[END_REF][START_REF] Bartal | Focusing of short-pulse high-intensity laseraccelerated proton beams[END_REF][START_REF] Qiao | Dynamics of high-energy proton beam acceleration and focusing from hemisphere-cone targets by highintensity lasers[END_REF] , target shaping [START_REF] Qiao | Dynamics of high-energy proton beam acceleration and focusing from hemisphere-cone targets by highintensity lasers[END_REF][START_REF] Zakova | Improving laser-accelerated proton beam divergence by electric and magnetic fields induced in flat channel-like targets[END_REF], solenoid field [START_REF] Toncian | Ultrafast laser-driven microlens to focus and energy-select mega-electron volt protons[END_REF][START_REF] Harres | Beam collimation and transport of quasineutral laseraccelerated protons by a solenoid field[END_REF] , ultra-thin foil targets [START_REF] Kaymak | Boosted acceleration of protons by tailored ultra-thin foil targets[END_REF], and nano and micro-structured targets [START_REF] Giuffrida | Manipulation of laser-accelerated proton beam profiles by nanostructured and microstructured targets[END_REF]. In particular, Kar et al. [START_REF] Kar | Guided post-acceleration of laser-driven ions by a miniature modular structure[END_REF] developed a dynamic scheme for the focusing, post-acceleration and bunching of a TNSA proton beam. It consists in attaching a helical coil (HC) normally to the rear side of the target foil. The proton beam then propagates along the coil axis. This mechanism is the only one that allows to bunch, collimate and post-accelerate the proton beam at the same time, with a simple set-up as it uses only one laser beam. This scheme modifies the TNSA proton beam distribution through several multi-physics and multi-scale processes: the target is charged positively during the escaping of the most energetic electrons during the TNSA process, this creates a discharge current through the helical coil attached to the rear side of the foil [START_REF] Kar | Guided post-acceleration of laser-driven ions by a miniature modular structure[END_REF][START_REF] Kar | Dynamic control of laser driven proton beams by exploiting self-generated, ultrashort electromagnetic pulses[END_REF][START_REF] Ahmed | Investigations of ultrafast charge dynamics in laser-irradiated targets by a self probing technique employing laser driven protons[END_REF][START_REF] Ahmed | Proton probing of laser-driven em pulses travelling in helical coils[END_REF][START_REF] Aktan | Parametric study of a high amplitude electromagnetic pulse driven by an intense laser[END_REF]. The propagation of the discharge current through the helical coil induces an electromagnetic pulse (EMP) [START_REF] Poyé | Physics of giant electromagnetic pulse generation in short-pulse laser experiments[END_REF][START_REF] Consoli | High power laser sci[END_REF] which can then focus, post-accelerate and energy select the TNSA protons. The helical coil geometry delays and guides both the current and electromagnetic pulse, matching them in speed and position with the proton beam, similarly to radiofrequency accelerators [START_REF] Chick | The helix as a linear accelerator for protons[END_REF][START_REF] Chick | An experimental proton linear accelerator using a helical waveguide[END_REF] and traveling wave tubes (TWT) [START_REF] Pierce | Traveling-wave tubes[END_REF]. TWT are used in the industry as amplificators: a continuous RF signal is sent at an extremity of the helix. A continuous beam of mono-energetic electrons generated from the cathode travels along the longitudinal axis at a speed slightly faster than the RF signal in the helix. The electrons are slowed down by the fields inside the helix and the transferred energy amplifies the RF signal at the exit of the helix. The HC scheme operates the inverse exchange where protons inside the HC gain energy from the fields generated by the current pulse. This scheme has proven to be efficient experimentally in terms of focusing and spectral shaping of the TNSA proton beam [START_REF] Kar | Guided post-acceleration of laser-driven ions by a miniature modular structure[END_REF][START_REF] Kar | Dynamic control of laser driven proton beams by exploiting self-generated, ultrashort electromagnetic pulses[END_REF][START_REF] Ahmed | Investigations of ultrafast charge dynamics in laser-irradiated targets by a self probing technique employing laser driven protons[END_REF][START_REF] Ahmed | Proton probing of laser-driven em pulses travelling in helical coils[END_REF][START_REF] Aktan | Parametric study of a high amplitude electromagnetic pulse driven by an intense laser[END_REF][START_REF] Bardon | Physics of chromatic focusing, post-acceleration and bunching of laser-driven proton beams in helical coil targets[END_REF] but has also shown limitations in terms of the maximum energy of protons and of bunching. This is due to the dispersive nature of HC.

Its impedance varies with the frequency, which modulates the current pulse intensity during its propagation along the helix. The current changes sign along the coil axis, inducing an alternance of accelerating and decelerating fields seen by the protons, leading to a reduction of the cut-off energy and bunching.

In order to go beyond this limitation, several schemes have been introduced: Kar et al. use very short helical coils where the current does not have time to change sign [START_REF] Kar | Guided post-acceleration of laser-driven ions by a miniature modular structure[END_REF],

Robertson et al. use two short helical coils in a row [START_REF] Ferguson | Dual stage approach to laser-driven helical coil proton acceleration[END_REF] and Liu et al. proposed a scheme with two sections of HC to skip phase reversal [START_REF] Liu | Synchronous post-acceleration of laser-driven protons in helical coil targets by controlling the current dispersion[END_REF].

In this article, we propose a new scheme of HC with tube, inspired by broadband highpower pulsed helix TWT [START_REF] Freund | Theory of helix traveling wave tubes with dielectric and vane loading[END_REF][START_REF] Jiao | A key design and experiment of a broadband high-power pulsed helix twt[END_REF]. This scheme allows us to strongly improve the bunching effect of helical coils under the conditions relevant to 100 TW high intensity and short pulse laser facilities such as ALLS [41] and LULI2000 [START_REF] Luli | [END_REF].

We first introduce this new scheme permitting to reduce drastically the dispersion inside the HC, as well as the physics of the dispersion of a current pulse inside a helical coil with tube. We then show the results of Particle-In-Cell (PIC) simulations and of a reduced model [START_REF] Bardon | Dopplight: an efficient model to study and design helical coil targets for laser-driven ion acceleration[END_REF] of the current propagation in HC with and without tube under the conditions relevant to several laser facilities. Finally, we present the impact of a HC with tube on the TNSA spectrum and proton bunching.

II. DESCRIPTION OF A HC WITH TUBE

The approach we propose to reduce the dispersion of helical coils consists in the use of helical coils with tube. In this scheme, shown in Figure 1a, the HC is inserted inside a metallic tube, the HC and the tube are both connected to the ground but the tube is not connected to the TNSA target, making the HC system similar to a coaxial line with a helical conductor inside. This is inspired by broadband high-power pulsed helix Traveling Wave Tubes (TWT), see Figure 1b. The idea behind this scheme is to create a hybrid mode between the very dispersive helical coil and the dispersion-free conducting tube. The dielectric rod used in broadband high-power pulsed helix TWTs, has been suppressed due to the risk of short-circuit with the intense kA current going through the coil. A. Physics of the dispersion of a transient current in a HC with and without tube A model of current propagation was developed in the 1950s for travelling wave tubes (TWT) by Pierce [START_REF] Pierce | Traveling-wave tubes[END_REF] who proposed to approximate the helix wire by an infinitely thin cylinder with an anisotropic conductivity, which is non-zero only in the helical direction.

The equations of this model were then developed into a circuit approach by Kino and Paik [START_REF] Kino | Circuit theory of coupled transmission systems[END_REF]. This model is set in the Fourier domain, under the assumption that the pulse wavelength along the longitudinal axis z is larger than the turn length of the helix. It gives the following dispersion relation:

ω = kc 1 + cot 2 (Ψ) I 1 (α)K 1 (α) I 0 (α)K 0 (α) (1)
where I i and K i are the modified Bessel functions of order i, α(ω) = a k 2 -ω 2 /c 2 , Ψ = arctan( h 2πa ) is the helix angle, a is the radius of the helix and h is the pitch. In particular, in the low frequency limit, (aω/c) cot Ψ 1, one has α 1, so

I 1 (α) ≈ α 2 , I 0 (α) ≈ 1, K 0 (α) ≈ -ln(α), K 1 (α) ≈ 1
α , and k ≈ ω/c. So, at low frequency, the mode phase velocity is close to the light velocity.

On the other hand, for (aω/c) cot Ψ 1, we have α 1, I 0 (α), I 1 (α) ≈ 2 πα e α , K 0 (α), K 1 (α) ≈ π 2α e α , and finally:

ω ≈ kc 1 + cot 2 (Ψ) (2)
So, at high frequency, the phase velocity is reduced to

c √ 1+cot 2 (Ψ)
, which is smaller than c and depends only on the helix pitch and radius.

Thanks to this asymptotic estimate, we could deduce that, in the helix, the low frequency mode propagates faster than the high frequency mode.

In an attempt to reduce the dispersion, in the 1990s, Freund and al. proposed a new theory for an already existing TWT scheme adding a loss-free conducting wall (tube) of radius b to enclose the HC [START_REF] Freund | Self-consistent field theory of a helix traveling wave tube amplifier[END_REF]. The hybrid model is based on the same assumption of an infinitesimally thin helix, with the current propagating in the helical direction, in the Fourier domain. The authors obtain another dispersion relation:

ω = kc/   1 + cot 2 (Ψ) I 1 (α)I 0 (αb/a)[K 1 (αb/a)I 1 (α) -I 1 (αb/a)K 1 (α)] I 0 (α)I 1 (αb/a)[K 0 (αb/a)I 0 (α) -I 0 (αb)K 0 (α)]   (3)
In particular, one returns to the dispersion relation 1 in the limit where b → ∞ then Therefore, the hybrid model combining a regular coil and a non-dispersive tube allows one to control the mode phase velocity and to reduce the dispersion. On the other hand, with the chosen tube geometry (b/a = 1.2), the electric field available to accelerate the protons is reduced by a factor of about 1.5 compared to the free helix.

I 1 (αb/a) → I 0 (αb/a), K 1 (αb/a) → 0, K 0 (αb) → 0. Conversely,

III. PARTICLE-IN-CELL SIMULATIONS AND REDUCED MODEL RESULTS

FOR THE CURRENT PROPAGATION OF A TNSA SHOT IN A HC WITH TUBE

In order to validate the theoretical model, we first performed full-scale PIC simulations of TNSA protons with a HC surrounded by a metallic tube using SOPHIE [START_REF] Cessenat | Sophie, an fdtd code on the way to multicore, getting rid of the memory bandwidth bottleneck better using cache[END_REF], an elec- In both cases, the proton and co-moving electron angular distribution has the shape of a super-Gaussian function, defined by the function exp -1 2 (θ/θ p ) 10 , centred around the longitudinal axis and defined by θ p = 19 • while the fast electron population is isotropically ejected in a solid angle of 2π.

A. PIC Simulations

The results of the SOPHIE simulations are presented in Figure 4, which represents the current pulse propagation along the HC axis as a function of time. The impact of the metallic tube around the HC leading to a drastic reduction of the current dispersion can be seen from comparison of the left and right panels. With a single HC, as seen in Figure 4a, we observe many sign alternations of the current pulse propagating along the axis with the phase speed V HC , corresponding to the longitudinal speed of a current pulse going at the speed c along the helical coil:

V HC = hc/ √ h 2 + 4π 2 a 2 .
One can see accelerated parts of the pulse propagating faster than V HC , larger in time and lower in amplitude. All these features are clear signs of the coil's dispersive nature.

On the other hand, in the case of a HC with tube, one can clearly see a pulse of positive current propagating at a constant speed V = 1.2 V HC and spreading temporally by a factor between 2 and 3 depending on the geometry, along with a reduction of amplitude by the same factor. This figure shows a clear reduction of the dispersion in the case of a HC with tube. As one can see in Figure 5, these results are very similar in the case of a higher energy facility, LULI2000. In the case of a HC with tube the positive current pulse propagates at a constant speed V = 1.2 V HC and presents the same temporal spread and amplitude reduction as in the case of the ALLS laser facility.

B. Reduced model results: the DoPPLIGHT code

The workflow of the model DoPPLIGHT [START_REF] Bardon | Dopplight: an efficient model to study and design helical coil targets for laser-driven ion acceleration[END_REF] is presented in Figure 6: it takes as input the helix geometry and the current at the beginning of the helix in the time domain, it then performs the Fourier transform of the current and uses it to calculate the fields according to Maxwell's equations. The boundary conditions are defined at the surface of the coil and tube. Following Pierce [START_REF] Pierce | Traveling-wave tubes[END_REF], the coil is modeled as an infinitely thin cylinder with the current propagating in the helical direction. The tube is modeled as a perfect conductor.

The fields are then transformed in the space-time domain by applying the inverse Fourier transform. The DoPPLIGHT model also calculates the space charge fields for a Gaussian shaped non-relativistic proton beam. The protons and electrons are then injected in the coil and their trajectories are calculated with the Boris pusher with the helix and space charge fields interpolated at each time step on the particle's position. Finally, at the exit of the coil, the code calculates the energy distribution of the protons. DoPPLIGHT operates in a 2D-axi-symmetric geometry; it is time-resolved and not a self-consistent model. The results of the model are shown in Figures 7a and7b. They are very similar to the PIC simulation results: we observe a positive pulse propagating at the same constant speed V = 1.2 V HC with the same temporal spread by a factor of 2 and an associated amplitude reduction by the same factor than in the PIC simulations.

These calculations are performed for several geometries and several laser source terms and we obtain in all cases good agreements between PIC simulations and DoPPLIGHT calculations as can be seen in the supplementary materials. We conclude that themodelisation of HC with tube in DoPPLIGHT is valid. As shown in Figure 8, these results are also valid when the source term is changed for the one of a higher energy facility, similar to LULI200.

IV. EFFECTS OF THE HC WITH TUBE ON THE PROTON SPECTRUM AT THE EXIT OF THE COIL A. Bunching effect

We studied the effects of electro-magnetic fields generated by the dispersion-reduced current pulse on the particle acceleration in the coil. Figure 9 presents the longitudinal field on the coil axis obtained in the simulations with the SOPHIE code at different times. We observe, for the HC with tube, a pulse with a positive longitudinal field followed by a pulse with a negative longitudinal field. The amplitude of these fields decreases with time (by a factor of 3 for the positive field), and their temporal spread increases (by a factor 1.5 for the positive field and by a factor of 2 for the negative field). A modulation appears in the tail of the pulse, but there are no sign changes and no acceleration of the pulse at the front like in the case of the HC without tube. This observation confirms that the dispersion is strongly reduced. This structure of fields produces two important bunches of protons (see orange line in Figure 10a) around the characteristic energy of the HC E HC = 1/2m i V 2 HC : one is more energetic, composed of the protons seeing the accelerating part of the field, another one is less energetic, composed of the protons under the influence of the decelerating field. It also produces a depletion zone situated in between the two bunches, where the proton population is several orders of magnitude less than the bunches. This feature is observed both in PIC simulations and in the reduced model DoPPLIGHT for several coil geometries with constant pitch and diameter, as can be seen in Figure 10 for one set of parameters: I for ALLS. The HC parameters are: length L = 40 mm, radius a = 0.5 mm, wire thickness of 0.02 mm and pitch h = 0.35 mm with a tube of radius b = 0.9 mm, the HC characteristic energy is 2.9 MeV. Spectra obtained with tubes show a significant increase of the proton bunching due to the electromagnetic configuration produced by the tube's addition. The goal now is to be able to generate bunches at predicted energies.

We notice that this particular scheme of HC with tube keeps the focusing effect of the HC without tube, as we observe a stronger focusing of the proton bunch in the high energy population, by a factor between 10 and 100 depending on the geometry. The focusing is in agreement with experiments and with numerical simulations reported in previous works [START_REF] Bardon | Physics of chromatic focusing, post-acceleration and bunching of laser-driven proton beams in helical coil targets[END_REF].

B. Scaling of the bunching

It would be interesting to design helical coils that produce bunches at predicted energies.

We studied the correlation of bunch energy with the HC characteristic energy that depends only on the helix geometric parameters. For that, we made several calculations using DoPP-LIGHT for different laser source terms, corresponding to ALLS and LULI2000, with radii going from a = 0.5 mm to a = 0.8 mm and pitches going from h = 0.3 mm to h = 0.8 mm, i.e. geometries that we can already manufacture. In all calculations, the radius of the tube was b = a + 0.3 mm. We then normalised the characteristic energies of the bunches and of the depletion zone as well as the HC characteristic energy E H C by the input proton spectrum cut-off energy in order to get energy scalings independent of the laser facility. We notice that all these scalings are independent of the coil radius and only depend on the normalised HC's characteristic energy, making it the discriminatory parameter.

As shown in Figure 11 the normalised energy of the bunches and of the depletion zone depend linearly on the normalised HC characteristic energy.

The depletion zone energy corresponds to the velocity V = 1.2 V HC , i.e. the velocity of the positive current pulse observed in previous figures, the least energetic bunch energy corresponds to V = 1V HC and the most energetic bunch corresponds to V = 1.5V HC . These respective deceleration and acceleration are consistent with the two longitudinal fields seen by the proton beam: the first one, shown in Figure 9, is created by the constant positive pulse and the second one is created by the proton space charge field. Having similar shapes, they both accelerate the most energetic protons at the front and decelerate the less energetic protons at the rear. We analyzed the yield of HC with tube, that is, the ratio of the charge at the exit of HC and the charge of the input proton distribution, as a function of HC characteristic energy normalized by the input cut-off energy and as a function of the coil radius. For E HC /E cutof f < 0.5 the yield is constant and only depends on the coil radius, a larger radius corresponds to a higher yield. We then see an increase to an optimal yield value for E HC /E cutof f ≈ 0.8 before decreasing to the previous level when the pulse becomes faster than the most energetic proton and does not impact the proton population anymore.

This yield enhancement is due to the dominant space charge radial field at early times.

Indeed the space charge is stronger where the proton density is higher and the unmodified TNSA proton distribution is composed mostly of low energy protons. As the HC fields are defocusing electrons from the beam and protons are spatially spread according to their energy, the radial space charge fields become dominant and proportional to the proton density. At the position of denser low energy protons, the HC field cannot compensate it even if its geometric speed is synchronised with these protons, and this leads to the loss of a large number of the low energy protons at the entrance of the HC. This can be understood from Figure 13, where the spectrum at the exit of an HC is shown with only the space charge fields acting on the input spectrum. We see that the space charge effects strongly defocus the low energy protons, leaving only the protons of energy E > 0.5E cut-of f . We introduce a new scheme of HC targets that allows to drastically reduce the current dispersion in the coil. This scheme is simple and relatively easy to implement experimentally as it consists of surrounding the HC by a metallic cylinder.

The reduced model DoPPLIGHT is revised in order to take into account the metallic cylinder effects. The model results are in agreement with the large-scale PIC simulations made with the SOPHIE code.

The numerical study, on both SOPHIE and DoPPLIGHT, shows a strong effect in terms of bunching of protons above and below the characteristic energy of the helical coil, while keeping the focusing effect on the proton beam, which was observed in previous works on regular HC targets.

Furthermore, we obtain a scaling of the bunches energy with the HC characteristic energy, which is independent of the energy distribution of injected protons and can be used to design targets for specific energy bunches. Bunching is a feature interesting for applications such as isochoric proton heating, in order to heat a material at a specific depth, or radio-isotope production, which necessitates proton bunches at specific energies for the production of specific reactions.

This new acceleration scheme will be tested on the ALLS facility at INRS where we expect to observe the bunching and to verify both the scaling and the yield optimum demonstrated in this article.

The HC with tube targets can be modified by introducing progressive pitches in order to increase the cut-off energy of the protons by accelerating the longitudinal fields in synchronisation with the proton velocity.

Figure 1 -

 1 Figure 1 -Scheme of : (A) helical coil with tube, (B) broadband high-power pulsed helix TWT [40].

  in the limit b = a the helix current is short circuited by the axial current in the tube, so ω/k = c. Indeed, if b → ∞ we have only the HC and if b → a we get a perfectly conducting tube without dispersion, because that case corresponds to replacing the HC by the tube. We can conclude that the tube mitigates the current dispersion. This mitigation is presented in Figure 2 where the dispersion relation and the phase velocity v ph = ω/k are plotted as a function of the wave vector for different values of b/a.

Figure 2 -

 2 Figure 2 -Dependence of the current frequency (A) and phase velocity (B) on the wave number for a HC of radius a = 0.5 mm, pitch h = 0.35 mm, with tubes of different radii and without tube.

  tromagnetic particle-in-cell code developed at CEA-CESTA. It solves, in a self-consistent way, the Maxwell's equations for the fields propagation in matter using boundary conditions (Perfect electric conductor, dielectric and magnetic materials) and the relativistic dynamics fundamental equation for the propagation of charged particles in vacuum. The geometry is modeled by appropriate boundary conditions at the perfectly conducting surfaces while the particles are injected following the given prescriptions of the temporal, angular and energetic distribution. The particle dynamics, target charging and discharge current propagation are self-consistently simulated.The solid structures in this simulation (target foil, coil, tube and grounds) are modelled with a resolution of ∆x = ∆y = ∆z = 20 µm as shown in Figure3. In this section we present the results for a coil of length L = 40 mm, a coil radius a = 0.5 mm, a pitch h = 0.35 mm and a wire diameter of e = 0.2 mm. The tube is a perfectly conducting cylinder starting 2 mm after the target foil (in cyan In Figure3), internal radius b = 0.9 mm (i.e. ∆r = 0.3 mm between the HC and the conducting tube), and thickness th = 0.1 mm. They are connected together by a perfectly conducting slab of 3.5 mm by 5 mm and of a thickness of w = 0.3 mm at the end opposite to the TNSA target.

Figure 3 -

 3 Figure 3 -Mesh of a HC with tube in SOPHIE. The target is in cyan, the helical coil in red and the target holder and tube in purple.

Figure 4 -

 4 Figure 4 -PIC simulation of the current pulse intensity in kA for an helical coil (A) without tube and (B) with tube as a function of time and along the HC axis. The particles features are defined in Table I for ALLS. The HC parameters are: length L = 40 mm, radius a = 0.5 mm, wire thickness of 0.02 mm and pitch h = 0.35 mm with a tube of radius b = 0.9 mm. The dashed line corresponds to V HC , the geometrical speed of the HC, the dash-dotted line corresponds to V = 1.2 V HC .

Figure 5 -

 5 Figure 5 -PIC simulation of the current pulse intensity in kA for an helical coil (A) without tube and (B) with tube as a function of time and along the HC axis. The particles features are defined in Table I for LULI2000. The HC parameters are: length L = 40 mm, radius a = 0.5 mm, wire thickness of 0.02 mm and pitch h = 0.35 mm with a tube of radius b = 0.9 mm. The dashed line corresponds to V HC , the geometrical speed of the HC, the dash-dotted line corresponds to V = 1.2 V HC .

Figure 6 -

 6 Figure 6 -(A) Schematics of the model DoPPLIGHT (B) Schematics of the helix fields calculation module in DoPPLIGHT.

Figure 7 -

 7 Figure 7 -DoPPLIGHT calculation of the current pulse intensity in kA for an helical coil (A) without tube and (B) with tube as a function of time and along the HC axis. The particles features are defined in Table I for ALLS. The current is defined analytically by a Gaussian function with FWHM τ F W HM = 3 ps and amplitude at z = 0 mm I 0 = 7 kA, delayed with respect to the particule emission by 6 ps. The HC parameters are: length L = 40 mm, radius of the thin cylinder a = 0.5 mm and pitch h = 0.35 mm with a tube of radius b = 0.8 mm. The dashed line corresponds to V HC , the dash-dotted line corresponds to V = 1.2 V HC .

Figure 8 -

 8 Figure 8 -DoPPLIGHT calculation of the current pulse intensity in kA for an helical coil (A) without tube and (B) with tube as a function of time and along the HC axis. The particles features are defined in Table I for LULI2000. The current is defined analytically by a Gaussian function with FWHM τ F W HM = 8.5 ps and amplitude at z = 0 mm I 0 = 30 kA, delayed with respect to the particule emission by 6 ps. The HC parameters are: length L = 40 mm, radius of the thin cylinder a = 0.5 mm and pitch h = 0.35 mm with a tube of radius b = 0.8 mm. The dashed line corresponds to V HC , the dash-dotted line corresponds to V = 1.2 V HC .

Figure 9 -

 9 Figure 9 -Longitudinal field on the HC axis at different times, dashed lines correspond to an HC without tube, full lines to an HC with tube. The particles features set are defined in Table I for ALLS. The HC parameters are: length L = 40 mm, radius a = 0.6 mm, wire thickness of 0.02 mm and pitch h = 0.35 mm with a tube of radius b = 1 mm.

Figure 10 -

 10 Figure 10 -Spectra of accelerated protons: (A) TNSA spectrum (green line), spectrum at the exit of an HC without tube (blue line) and spectrum at the exit of an HC with tube (orange line) in PIC simulations, (B) spectrum at the exit of an HC with tube in PIC simulations (orange line) and in the numerical model DoPPLIGHT (red line). The particles features are in Table I for ALLS. The HC parameters are: length L = 40 mm, radius a = 0.5

Figure 11 -

 11 Figure 11 -Scaling of the energy of the bunch with respect to the HC characteristic energy normalized by the cut-off energy: (A) normalised energy of the most energetic bunch, (B) normalised energy of the least energetic bunch, (C) normalised energy of the depletion zone. Colored dots correspond to DoPPLIGHT calculations, black dots to PIC simulations. Color code shows dependence on the coil radius. All HC are with tube.

Figure 12 -

 12 Figure 12 -Yield of protons at the exit of HC with tube as a function of the HC characteristic energy divided by the input cut-off energy; color code shows dependence on the coil radius.

Figure 13 -

 13 Figure 13 -Proton energy spectrum at the exit of a cone of radius a = 0.5 mm and length L = 40 mm calculated with DoPPLIGHT with only space charge fields for an ALLS-based input spectrum, as defined in Table I

  Previous experimental and numerical works have shown the limitations of post-acceleration and bunching of TNSA proton beams in regular HC targets. This is explained by the current dispersion in the coil, creating an alternance of accelerating and decelerating fields seen by the proton population.

Figure 15 -Figure 16 -Figure 17 -Figure 18 -Figure 19 -

 1516171819 Figure 15 -DoPPLIGHT calculation of the current pulse intensity in kA for an helical coil (A) without tube and (B) with tube as a function of time and along the HC axis. The particles features are defined in Table I for ALLS. The current is defined analytically by a gaussian with FWHM τ F W HM = 3 ps and amplitude at z = 0 mm I 0 = 7 kA, delayed with respect to the particule emission by 6 ps. The HC parameters are: length L = 40 mm, radius of the thin cylinder a = 0.6 mm and step h = 0.3 mm with a tube of radius b = 0.9 mm. The dashed line corresponds to V HC , the dash-dotted line corresponds to V = 1.2 V HC .

ACKNOWLEDGMENTS

The authors are grateful to K. Aliane , O. Cessenat, F. Doveil, D. Minenna and A. Poyé for their help and useful discussions. This work is supported by the CEA/DAM laser-plasma experiments validation project and the CEA/DAM basic technical and scientific studies project. This work was granted access to the HPC resources of IRENE under the allocation No. A0130512899 made by GENCI

Appendix: Supplementary materials

In this appendix, we show the results of PIC simulations and DoPPLIGHT results for the current dispersion in HC with and without tube for different geometries and laser parameters.


Peter W Hadden

Misha Vorobyev
email: m.vorobyev@auckland.ac.nz

William H Hadden
email: williamhadden92@gmail.com

Francesco Bonadonna
email: francesco.bonadonna@cefe.cnrs.fr

Charles N J Mcghee
email: c.mcghee@auckland.ac.nz

Jie Zhang
email: jie.zhang@auckland.ac.nz.

Can penguins (Spheniscidae) see in the ultraviolet spectrum?

Keywords: Spheniscidae, lens, cornea, ultraviolet, Gentoo, King, Little

  L'archive ouverte pluridisciplinaire

Introduction

Ultraviolet (UV) reflectance and ultraviolet-sensitive (UVS) vision are thought to play a role in many avian behaviors, including orientation, foraging and sexual selection [START_REF] Bennett | Ultraviolet vision and mate choice in Zebra Finches[END_REF][START_REF] Johnsen | Ultraviolet plumage ornamentation affects social mate choice and sperm competition in Bluethroats (Aves: Luscinia s. svecica): A field experiment[END_REF]. Color also appears to be important in penguin (Spheniscidae) mate selection [START_REF] Jouventin | Visual and vocal signals in penguins, their evolution and adaptive characters[END_REF][START_REF] Massaro | Carotenoid-derived ornaments reflect parental quality in male and female Yellow-eyed Penguins (Megadyptes antipodes)[END_REF]. The orange beak spots of both King Aptenodytes patagonicus and Emperor A. forsteri penguins have been found to have UV reflectance [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF] and, in the case of the King Penguin, a multilayer photonic microstructure appears to be the source of this reflectance, which is maximal at 367.5 nm [START_REF] Dresp | Ultraviolet reflecting photonic microstructures in the King Penguin beak[END_REF]. Beak reflectance has also been reported in juvenile Gentoo Penguins Pygoscelis papua [START_REF] Vb | UV-reflecting and absorbing body regions in gentoo and King Penguin: Can they really be used by the penguins as signals for conspecific recognition?[END_REF].

However, similar beak reflectance has not been found in 10 other species of penguin, nor on the claws, feathers or skin of any penguin [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF].

This finding, together with the observations that UV reflectance from the beak only appeared when the animal was sexually mature and of pairing behavior, led to the suggestion that such UV reflection could be important in King and Emperor penguin breeding [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF]. This would appear to be supported by a higher UV beak reflectance amongst early pairing King Penguins (the most successful in breeding) and the observation that experimentally reduced UV reflectance from beak spots is associated with delayed pairing [START_REF] Jouventin | UV signals in penguins[END_REF][START_REF] Nolan | Mutual mate choice for colorful traits in King Penguins[END_REF]).

However, this interpretation was challenged on the basis that UVS vision had not been demonstrated in penguins [START_REF] Vb | UV-reflecting and absorbing body regions in gentoo and King Penguin: Can they really be used by the penguins as signals for conspecific recognition?[END_REF], leading to a fierce debate in this journal [START_REF] Jouventin | UV signals in penguins[END_REF][START_REF] Vb | Is there any proof of UV-sensitivity and its role in King Penguins (Aptenodytes patagonicus)?[END_REF][START_REF] Nolan | Mutual mate choice for colorful traits in King Penguins[END_REF].

Ultraviolet-sensitive visual pigments (<400 nm) are widespread in the animal kingdom [START_REF] Hunt | Vision in the ultraviolet[END_REF]) and in birds a UVS visual pigment is thought to have evolved from ancestral violet vision on multiple occasions [START_REF] Wilkie | Spectral tuning of avian violet-and ultraviolet-sensitive visual pigments[END_REF][START_REF] Hart | Avian visual pigments: Characteristics, spectral tuning, and evolution[END_REF], although molecular evidence suggests that UVS cones are more widespread in terrestrial birds than in seabirds [START_REF] Hart | Avian visual pigments: Characteristics, spectral tuning, and evolution[END_REF]. A UVS cone has not been found in penguins; however, a short wavelength 1 (SWS1) cone with maximum sensitivity at 403 -405 nm has been identified in the Humboldt Penguin Spheniscus humboldti [START_REF] Bowmaker | Visual pigments and oil droplets in the penguin, Spheniscus humboldti[END_REF][START_REF] Wilkie | Spectral tuning of avian violet-and ultraviolet-sensitive visual pigments[END_REF], very close to the UV range. More recently, Gentoo Penguins have been shown to respond behaviourally to UV light maximal at 365 nm, tapering to no output at 390 nm [START_REF] Cole | Genomic insights into the secondary aquatic transition of penguins[END_REF]. Although, this visual pigment does not have maximal absorbance in the UV range, it is close to that range (<400 nm) and the absence of UVS visual pigments is not evidence of blindness to UV, as there is a significant secondary absorption (-peak) by all visual pigments in the UV range despite maximum absorbance in the visible spectrum [START_REF] Douglas | The spectral transmission of ocular media suggests ultraviolet sensitivity is widespread among mammals[END_REF]. This can be demonstrated by the ability of aphakic humans to see in the UV spectrum despite lacking a UVS cone [START_REF] Stark | Ultraviolet sensitivity of three cone types in the aphakic observer determined by chromatic adaptation[END_REF].

Because of this secondary absorption, ocular transmission is more critical to UVS vision than the presence of a UVS cone. Many animals have been shown to have ocular media that allow the transmission of near-ultraviolet (near-UV, <400 nm) light, including many bird species [START_REF] Emmerton | Spectral transmission of the ocular media of the Pigeon (Columba livia)[END_REF][START_REF] Siebeck | Ocular media transmission of coral reef fish-can coral reef fish see ultraviolet light?[END_REF][START_REF] Mullen | Studies on UV reflection in feathers of some 1000 bird species: Are UV peaks in feathers correlated with violet-sensitive and ultraviolet-sensitive cones[END_REF][START_REF] Tsukahara | Light transmission of the ocular media in birds and mammals[END_REF][START_REF] Lind | Ultraviolet vision in birds: The importance of transparent eye media[END_REF][START_REF] Olsson | Lens and cornea limit UV vision of birds -a phylogenetic perspective[END_REF]. Although all biological tissues are opaque to light below 300 nm due to absorption by molecules such as nucleic acids and aromatic amino acids, in birds as in mammals the lens is usually more critical than the cornea with regard to UV light transmission, particularly above 345 nm [START_REF] Douglas | A review of vertebrate and invertebrate ocular filters[END_REF][START_REF] Douglas | The spectral transmission of ocular media suggests ultraviolet sensitivity is widespread among mammals[END_REF][START_REF] Olsson | Lens and cornea limit UV vision of birds -a phylogenetic perspective[END_REF].

Clearly, in order for UV reflectance to be important in mate selection such reflectance has to be visible. Given the debate, the primary aim of this study was to determine the ocular transmission of the King Penguin eye and thus determine the potential sensitivity of its visual system to UV light.

Little Penguins (Eudyptula minor) and Gentoo Penguins were also available to us in Auckland, New Zealand, and represent a different lineage within Spheniscidae [START_REF] Zusi | An interpretation of skull structure in penguins[END_REF][START_REF] Baker | Multiple gene evidence for expansion of extant penguins out of Antarctica due to global cooling[END_REF][START_REF] Cole | Genomic insights into the secondary aquatic transition of penguins[END_REF], with recent DNA evidence [START_REF] Vianna | Genome-wide analyses reveal drivers of penguin diversification[END_REF] suggesting that King and Emporer penguins form a sister clade to all other extant penguins. Little and Gentoo penguins are also of different sizes [START_REF] Shirihai | A complete guide to Antarctic wildlife: The birds and marine mammals of the Antarctic continent and the Southern Ocean[END_REF], dive to different depths [START_REF] Montague | A maximum dive recorder for Little Penguins[END_REF][START_REF] Culik | Diving energetics in King Penguins (Aptenodytes patagonicus)[END_REF] and inhabit vastly different environments [START_REF] Shirihai | A complete guide to Antarctic wildlife: The birds and marine mammals of the Antarctic continent and the Southern Ocean[END_REF] to the Kings, therefore we also wished to determine if these findings were consistent across all penguins.

Methods

Animals and ethics

Permission was obtained for this study from the New Zealand Department of Conservation (permit numbers 68003-DOA, 28 November 2018 and 89983-DOA, 27 July 2021), Auckland Zoo and SEA LIFE (SL (G) -AR 001). A Little Penguin (L1) was recovered from the wild in the Auckland Region, New Zealand, but was unable to be re-released due to a physical disability not involving the eye. Its exact age was unknown, although it was an adult bird and had passed its first moult. Two Gentoo Penguins were examined, G1 aged 7 weeks (lens) and G2 aged 26 years (cornea and vitreous), as well as two King Penguins, K1 aged 23 months and K2 aged 32 years. The Gentoo and King penguins had spent their life in captivity at SEA LIFE Kelly Tarlton's Aquarium in Auckland, New Zealand and were descended from penguins living in South Georgia. With the exception of K2, all examinations were completed within 6 hours of enucleation post-mortem, and none had any known ocular disease. The vitreous of K2 was examined after 24 hours of refrigeration and this animal had moderate cataract; only the vitreous from this eye was examined (Table 1). Several other eyes of all three species were examined to check the accuracy of the two spectrometers that we used against each other. However, we did not use these results as they were from elderly penguins, hadspent time refrigerated, or both. Moreover, their lenticular ocular transmission was not as great as the penguins that we included in this study, probably because of their age and preservation, and we did not wish to combine the results for fear of underestimating potential ocular transmission in the youngest and healthiest eyes of each species, our primary goal being to determine if the penguin optical media could transmit UV. The results of the right eye of G1 were also discarded, as they were not credible (substantially more than 100% transmission at some wavelengths).

Suggested location of Table 1

Equipment and tissue preparation Two spectrometers were used. The first was a USB2000+ (Ocean Optics, Dunedin, Florida, USA, Fig. 1), which could be transported to peripheral locations. This was used for G1 and K1. The second was a SpectraMax 13x (Molecular Devices Inc, San Jose, CA), into which the eyes or components thereof were inserted, and which could only be used when the central laboratory was accessible (Fig. 2). This was used for L1, G2 and K2. It was only possible to measure vitreous transmission using the SpectraMax 13x.

The spectral transmission of the whole eye, cornea and lens were measured in L1 and K1. In G1, only the transmission of the lens was measured. Vitreous samples of L1, G2 and K2 were also measured, as were the corneas of G2, noting that these were older animals but being reassured of their validity as noted above and in the knowledge that, in all birds, it is the lens that determines ocular transmission in any event [START_REF] Olsson | Lens and cornea limit UV vision of birds -a phylogenetic perspective[END_REF]). To measure transmission through the whole eye, the eye was enucleated and then the posterior pole was removed with a Bard-Parker 15 blade (Aspen Surgical Products, Inc., Caledonia, MI). To measure transmission through the cornea, the cornea was then removed and placed in the spectrometer. Then, having removed the cornea, the vitreous was removed as much as possible without touching the lens, leaving the lens attached to the ciliary body (and thus the rigid ossicular ring) for stability so that we could avoid handling the lens. The residual anterior segment, minus cornea, was then inserted into the spectrometer.

Data acquisition using SpectraMax 13x

A plate blank and a well filled with blackened paper tissue were used to verify the calibration. The tissue being measured was then placed into a plastic tray, cushioned with paper for stability (Fig. 1) and inserted into the machine where it lay immediately above the detector, separated from the latter only by the floor of the clear plastic container. To measure the transmission of the vitreous, a well 14.5 mm high was filled with liquid vitreous. Percentage transmission was directly measured by the machine in steps of 10 nm. This was then calculated as a percentage of the transmission at 700 nm (T  ). Values obtained for light less than 300 nm were ignored as very little light was transmitted at these wavelengths through the plate blank using the SpectraMax 13x and thus the values obtained for transmission of ocular media as a percentage of transmission by the plate blank were erroneous. An exception was made and the value at 290 nm used if necessary to calculate an intercept, using the method described below (primarily the vitreous  50 but also the cornea  10 ).

Suggested location of Figure 1 Data acquisition using Ocean Optics USB2000+

The tissue being measured was placed in a black case that was custom made at the University of Auckland using a 3D plastic printer to keep it steady and to eliminate external sources of light (Fig. 2). Multiple recordings were obtained, and the maximum spectral transmission recorded. For purposes of calibration, the spectrum without light on and with just the xenon light on was recorded using the USB2000+. When the whole eye or the lens (attached to the ciliary body) was being measured, this was placed as close as possible to the detector and cushioned for stability by tissue paper. When the cornea was being measured, it was draped over the detector. The Oceans Optics USB2000+ measured absolute transmission in steps of 0.38 to 0.39 nm. The transmission of each wavelength (T  ) measured using the USB2000+ was calculated by first subtracting the background light (b  ) measured at that wavelength within the closed box from that measured with the Xenon source on (Xe  ) and then comparing that to the light transmitted with both the Xe source on and the optical element under investigation being in the path of the beam (Xt  ).

Thus T  = (Xt  -b  ) / (Xe  -b  )
This was then calculated as a percentage (T % ) of the average transmission between 650 and 750 nm (T 700 ). Due to the small transmission interval of 0.38 to 0.39 nm, there was variability between individual measurements. Therefore, the data was first exponentially smoothed with a damping value of 0.5 using Microsoft 365® Excel. Transmission percentages for light less than 300 nm were ignored on the USB2000+, both for consistency with the SpectraMax and because they appeared to be highly variable, probably a function of how little light was produced by the Xenon source at those wavelengths as compared to background.

Suggested location of Figure 2 Data analysis and plotting

Since, except for G1, both eyes were examined, the results from each eye were first averaged and then the average T  for each species, at 10 nm intervals, was plotted against the respective wavelengths. The wavelength at which the cornea, lens, vitreous and whole eye reached 10% ( 10 ), 50% ( 50 ) and 90% ( 90 ) of that recorded at 700 nm for species was determined by using the forecast function of Microsoft 365® Excel to predict where the 10%, 50% and 90% intercepts would be based on the two recordings 10 nm and 20 nm before 10%, 50% or 90% transmission was reached and the two recordings 10 and 20 nm after.

Results

The averaged transmission curves, combining both eyes of each penguin (except in the case of the lens of G1, which was only the left eye), are presented in figures 3, 4, 5 and 6.  10 , 50 and  90 intercepts are listed in table 2. Suggested location of Figure 3, Figure 4, Figure 5 and Figure 6 Suggested location of Table 2 The dimensions of eyes of these penguins have been the subject of a previous report [START_REF] Hadden | Selected ocular dimensions of three penguin species[END_REF]. The average corneal thickness (measured with ultrasound pachymetry) was 0.303, 0.472 and 0.605 mm in the Little, Gentoo and King penguins respectively, the lens thickness (measured with callipers) 4.0, 7.14 and 7.75 mm, excluding the lens of K2 which was cataractous and 10 mm thick, and the axial length (measured with ultrasound) 17.4, 21.7 and 26.5 mm respectively.

Discussion

Importance of UV reflectance in King Penguin mate selection

Because of reduced lenticular UV transmission, the eye of the King Penguin transmitted very little UV light, with almost all light at wavelengths less than 370 nm being blocked and 50% transmission only being reached at 406 nm. In King Penguins, the only part of the body that reflects UV are the orange bands of the beak [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF]. The UV peak in these bands, according to the literature, is at 401 nm in museum specimens and 380 nm in live penguins [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF]. In a King

Penguin taxidermy available at CEFE (Univ Montpellier, CNRS, EPHE, IRD, Montpellier, France), the UV peak of the bands of the beak, as measured with an Avantes spectrophotometer, is at 360 nm (FB personal data). Our results, showing that no light below 370 nm and only half of the light even at 400 nm is transmitted to the retina in this species, suggests that the use of UV in mate choice behaviour [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF][START_REF] Nolan | Mutual mate choice for colorful traits in King Penguins[END_REF]) should be reconsidered, or at least confirmed with further experimental protocols. We also note that, in the later paper [START_REF] Nolan | Mutual mate choice for colorful traits in King Penguins[END_REF]), the range of the spectrum examined in the experiment was from 320 nm to 450 nm, thus including some visible light (> 400 nm), which could have been easily perceived by King Penguins.

Variation between species

The cornea of all specimens examined absorbed almost all light at or below 300 nm (Fig. 3), consistent with what is known about the absorption of all biological tissues generally [START_REF] Douglas | A review of vertebrate and invertebrate ocular filters[END_REF]. However, in contrast to King Penguin, the lens of the Little Penguin did not further restrict the ability of UV light to be perceived at the retina and thus the animal will be more sensitive to light of these wavelengths. The Gentoo Penguin eye would appear to lie somewhere between these two, although clearly the optical transmission would enable it to see the 365 nm torch previously reported [START_REF] Cole | Genomic insights into the secondary aquatic transition of penguins[END_REF]. The behavioural relevance of this finding in these species is unclear. In regard to mate selection, adult Gentoo Penguins have no body parts that reflect UV, although beak reflectance has been reported in juveniles [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF][START_REF] Vb | UV-reflecting and absorbing body regions in gentoo and King Penguin: Can they really be used by the penguins as signals for conspecific recognition?[END_REF].

Why are shorter wavelengths transmitted more readily through the lenses of Little and Gentoo penguins but absorbed in the King? There is a weak association between lens thickness and UV transmission in birds [START_REF] Olsson | Lens and cornea limit UV vision of birds -a phylogenetic perspective[END_REF], presumably because of the increased tissue thickness across which light can be absorbed. However, the difference in UV transmission between the lens of the Little Penguin and the King Penguin is much more marked than that between the corneas of the two species, despite both anatomical structures being proportionately thicker in the King Penguin [START_REF] Hadden | Selected ocular dimensions of three penguin species[END_REF]. Furthermore, despite the aforementioned weak association, many birds have a higher  0 than would be expected from eye size; for instance, the Long-eared Owl Asio otus has a 7.0 mm thick lens but a lenticular 0 of 323.6 nm [START_REF] Olsson | Lens and cornea limit UV vision of birds -a phylogenetic perspective[END_REF]).

An environmental difference seems unlikely, despite the habitat of King and Little penguins being markedly dissimilar, because of the relatively high UV transmission of the Gentoo Penguin lens despite a habitat much more similar to the King Penguin than to the Little Penguin. Both King and Gentoo penguins predominantly breed on subantarctic islands, although the gentoo can also be found on the Antarctic Peninsula and both can be found as rare vagrants on the New Zealand mainland [START_REF] Shirihai | A complete guide to Antarctic wildlife: The birds and marine mammals of the Antarctic continent and the Southern Ocean[END_REF]. The Gentoo and King penguins in our study were also both of South Georgian descent and therefore share the same pelagic environment, although King Penguins hunt in open pelagic waters down to 300 m, which seems to correlate with their main prey, the midwater lanternfishes Myctophidae [START_REF] Kooyman | Diving behavior and energetics during foraging cycles in King Penguins[END_REF], while gentoos, which at South Georgia have been recorded diving to over 100 m [START_REF] Croxall | Diving patterns in relation to diet of gentoo and macaroni penguins at South Georgia[END_REF], are both nearshore benthic and pelagic foragers, consuming crustaceans, particularly Antarctic krill Euphasia superba and Themisto gaudichaudii, as well as fish [START_REF] Xavier | Sexual and individual foraging segregation in Gentoo Penguins Pygoscelis papua from the Southern Ocean during an abnormal winter[END_REF][START_REF] Mcclintock | Intertidal foraging by Gentoo Penguins in a macroalgal raft[END_REF]. The latitudes in which they live means that the hours of night and day are more a function of seasonality than time of day and they forage at all times of the year. By contrast, Little Penguins (grouping both Eudyptula minor and E. novaehollandiae together) inhabit mainland New Zealand, southern Australia and Tasmania [START_REF] Shirihai | A complete guide to Antarctic wildlife: The birds and marine mammals of the Antarctic continent and the Southern Ocean[END_REF][START_REF] Grosser | Multivariate skeletal analyses support a taxonomic distinction between New Zealand and Australian Eudyptula penguins (Sphenisciformes: Spheniscidae)[END_REF]. They feed on small shoaling fish (particularly Clupeiformes), cephalopods and crustaceans such as krill and forage at shallower depths, around 10-50 m [START_REF] Montague | A maximum dive recorder for Little Penguins[END_REF][START_REF] Gales | Foraging behaviour of the Little Penguin, Eudyptula minor: Initial results and assessment of instrument effect[END_REF][START_REF] Chiaradia | Diving behaviour of Little Penguins from four colonies across their whole distribution range: Bathymetry affecting diving effort and fledging success[END_REF][START_REF] Iida | Seasonal variability of phytoplankton biomass and composition in the major water masses of the Indian Ocean sector of the Southern Ocean[END_REF]. Little Penguins also breed in burrows, under rocks and in other hollows, in dunes or amongst vegetation, rather than on the harsher shores of South Georgia; they can be active at night but are predominantly diurnal foragers [START_REF] Shirihai | A complete guide to Antarctic wildlife: The birds and marine mammals of the Antarctic continent and the Southern Ocean[END_REF]).

The lower latitudes in which Little Penguin live, with illumination coming from more directly overhead, means that the Little Penguin lives in a generally brighter environment; the atmospheric transmission of UV also increases with increasing solar elevation in a similar fashion to light in the visible spectrum [START_REF] Spitschan | Variation of outdoor illumination as a function of solar elevation and light pollution[END_REF]. However, if this greater luminance is the explanation for increased UV transmission in the Little Penguin, it is one that is contrary to the tendency of diurnal mammals to block UV [START_REF] Douglas | The spectral transmission of ocular media suggests ultraviolet sensitivity is widespread among mammals[END_REF].

It might be that the larger eyes of the larger King Penguin block UV light to maximise the increased visual acuity their size affords, since the elimination of UV reduces chromatic aberration, to which their large pupils renders them more sensitive; elimination of UV will also reduce Rayleigh scatter [START_REF] Walls | The occurrence of colored lenses in the eyes of snakes and squirrels, and their probable significance[END_REF][START_REF] Pye | To add another hue unto the rainbow-near ultraviolet in nature[END_REF][START_REF] Douglas | The spectral transmission of ocular media suggests ultraviolet sensitivity is widespread among mammals[END_REF][START_REF] Olsson | Lens and cornea limit UV vision of birds -a phylogenetic perspective[END_REF]. Also, given the -peak in the UV range possessed by all visual pigments, allowing the transmission of UV light would make the task of color differentiation much more difficult [START_REF] Pye | To add another hue unto the rainbow-near ultraviolet in nature[END_REF]. There would appear to be a correlation between larger eyes, which generally possess higher spatial sensitivity given that more pixels (photoreceptors) can be made available per visual angle, and lack of transparency of the lens to UV [START_REF] Walls | The occurrence of colored lenses in the eyes of snakes and squirrels, and their probable significance[END_REF][START_REF] Ambach | Spectral transmission of the optical media of the human eye with respect to keratitis and cataract formation[END_REF][START_REF] Tsukahara | Light transmission of the ocular media in birds and mammals[END_REF][START_REF] Douglas | The spectral transmission of ocular media suggests ultraviolet sensitivity is widespread among mammals[END_REF]. Furthermore, the ocular media of raptors, which are notable for their excellent spatial sensitivity, up to 140 cycles / degree in the Golden Eagle Aquila audax, are relatively opaque to UV, with 50% transmissions ranging from 369 nm to 394 nm in those that have been studied, although this does not include the Golden Eagle [START_REF] Reymond | Spatial visual acuity of the eagle Aquila audax: A behavioural, optical and anatomical investigation[END_REF][START_REF] Lind | Ultraviolet sensitivity and colour vision in raptor foraging[END_REF][START_REF] Potier | Visual acuity in an opportunistic raptor, the chimango caracara (Milvago chimango)[END_REF]. In humans, a drop in potential visual acuity has been documented in pseudophakic individuals who have intraocular lenses that do not absorb UV, although intraocular lenses may introduce retinal images that do not occur in the phakic eye [START_REF] Rog | Ultraviolet effects on visual acuity in pseudophakia[END_REF]). On the other hand, the potential spatial resolution of the King Penguin eye (20.40 cycles / degree in water) is only marginally greater than that of the Little Penguin (17.07-17.46 cycles / degree in water), despite its greater size, because of a lesser ganglion cell density [START_REF] Coimbra | Retinal ganglion cell topography and spatial resolving power in penguins[END_REF]. Of course, this resolution was based on morphological ganglion cell counts rather than actual measurements of acuity so may not reflect the true spatial sensitivity. urthermore, UV transmission is of less relevance underwater, the environment in which penguins forage, because it is more rapidly attenuated than are wavelengths in the visible spectrum [START_REF] Williams | Optical properties of the ocean[END_REF]). Attenuation also increases with depth, which suggests it may be even less relevant in the deeper diving King Penguin than in the Little Penguin, although the latter forage in more estuarine waters where UV attenuation is higher [START_REF] Zielinski | Subsea optics: an introduction[END_REF].

Limitations and further work

We suspect there is an artifactual drop-off in the transmission of the left lens of G1, particularly above 50% transmission, given that the rise in shortwave transmission is less rapid above this point than in the King Penguin despite a much lower 0 and a substantially lower  0 . This could be due to a greater separation of the tissue from detector in the USB2000+ by mistake, increasing chromatic aberration which is more significant at shorter wavelengths. This could also have been the reason why the reading from the right lens was not credible. There was also a dip in transmission at 410 to oxygenated hemoglobin, and we speculate that some tissues may have been contaminated by blood when they were dissected out and placed in the spectrometer. Such contamination may mean that the 0 measurements are less reliable than the others, particularly in the case of the cornea of G2 and the lens of G1.

In the future, more individuals per species across different ages could be tested to confirm these results and, for those species that can see UV, experimental behavioural protocols should be designed to confirm the use of potential UV cues. In addition, more species of penguin could be studied to determine if the apparent relationship between size and UV transmission in these three species of penguin is consistent across the family. For instance, it would be useful to know whether the lens of the larger Emperor Penguin blocks UV light, given that it shares the same lineage as the King and UV reflection off the beak has been demonstrated [START_REF] Jouventin | Ultraviolet beak spots in King and Emperor penguins[END_REF]. It would also be interesting to understand if Galápagos (Spheniscus mendiculus) or African (Jackass, Black-footed, Spheniscus demersus) penguins, which inhabit yet lower latitudes than the Little Penguin, transmit UV to a similar extent to that observed in the similarly sized but subantarctic Gentoo Penguin. It would also be useful to correlate behaviour and vision between species with different UV transmissions, for instance in mate choice. Previous authors have speculated that, since the UVS form of the SWS opsin is ancestral, a lens that transmits UV may also be ancestral [START_REF] Olsson | Lens and cornea limit UV vision of birds -a phylogenetic perspective[END_REF]. Investigation of the spectral transmission of oil droplets in the retina would also be instructive, as light passes through them before being detected by cone photoreceptor outer segments. The King Penguin retina has been found to contain only pale green droplets, similar to nocturnal birds. This may reflect a habitat of little colour and their need to see well at depth in a dark sea, necessitating maximisation of retinal sensitivity. Maximal absorption of these droplets was between 500 and 600 nm; the absorption in UV wavelengths was not measured but it was approximately 0.35 at 400 nm [START_REF] Gondo | Comparative histophysiological study of oil droplets in the avian retina[END_REF]. Humboldt Spheniscus humboldti and Rockhopper Eudyptes chrysocome penguins were found to have droplets of four different colours, similar to diurnal birds and potentially because they live in areas with vegetation [START_REF] Gondo | Comparative histophysiological study of oil droplets in the avian retina[END_REF]. The closer phylogenetic relationship [START_REF] Cole | Genomic insights into the secondary aquatic transition of penguins[END_REF] and, for the Little Penguin, habitat similarity might suggest that Gentoo and Little penguin oil droplets may be more akin those in Humboldt and Rockhopper penguins than to those in King Penguins. However, they have not been examined in this regard and the similarly related Magellanic Penguin Spheniscus magellanicus was found to possess yet different droplets [START_REF] Suburo | Environmental adaptations in the retina of the Magellanic Penguin: photoreceptors and outer plexiform layer[END_REF]. Finally, cataract is known to be associated with UV exposure [START_REF] Delcourt | Lifetime exposure to ambient ultraviolet radiation and the risk for cataract extraction and age-related macular degeneration: The alienor study[END_REF]. Although UV radiation has been shown to cause cataract in Sprague-Dawley rats [START_REF] Michael | Dose-response function for lens forward light scattering after in vivo exposure to ultraviolet radiation[END_REF], where it is unlikely that the lens constitutes an additional barrier to UV transmission over and above the cornea [START_REF] Douglas | The spectral transmission of ocular media suggests ultraviolet sensitivity is widespread among mammals[END_REF], it would be useful to know if absorbing this energy in the lens rather than transmitting it increases the risk of cataract; if this was the case, there may be a relationship between lack of UV transmission and increased incidence of cataract. On the other hand, absorbing UV in the lens may reduce the risk of UVinduced retinal damage [START_REF] Vb | Risks, especially for the eye, emanating from the rise of solar UV-radiation in the Arctic and Antarctic regions[END_REF].

Conclusions

Because of the UV absorbing characteristics of the King Penguin lens, its ability to perceive UV will be poor and well-nigh impossible below 370 nm. Gentoo and Little penguins, on the other hand, can perceive near UV light almost down to 300 nm, near the transmission cut off of the cornea and biological tissues in general. Therefore, UV reflectance should be of much lesser importance in the behaviour of the King Penguin than of its smaller relatives.

Table legends

Table 1 Demographic data of penguins with, in brackets, the names and / or identification numbers, where known, for each penguin. Fresh means the ocular examination was completed within 6 hours of death, without being stored in any medium Table 2 The wavelength at which transmission reached 10% 10 ), 50%  50 ) and 90%  90 ) of the transmission at 700 nm for each of the cornea, lens and whole eye. Footnotes: a. The  10 values were unable to be calculated as the eyes never recorded less than 10% transmission even at the lowest wavelength tested, 230 nm. b. The whole eye of the Gentoo Penguin was not examined

Figure legends

Fig. 1 The 3D printed box in which the eye or components thereof were placed, to measure their spectral transmission using the Oceans Optics USB2000+ instrument. The fiber optic cables delivering the xenon light source (left) and the receiver (right) were screwed in at opposite ends. A lid was placed on top to eliminate room light while the experiment was undertaken Fig. 2 The tray in which the eyes were placed to be examined by the SpectraMax 13x, in this case the left and right eyes of Little Penguin Eudyptula minor L1. Note the tissue paper holding the eye stable and central Fig. 3 Averaged transmission of light through the cornea of Little (Eudyptula minor), Gentoo (Pygoscelis papua) and King (Aptenodytes patagonicus) penguins L1, G2 and K1. Note a dip in transmission maximum around 400-420 nm in G2. Created with Microsoft 365® Excel Fig. 4 Averaged transmission of light through the lens of Little (Eudyptula minor), Gentoo (Pygoscelis papua) and King (Aptenodytes patagonicus) penguins L1, G1 (left eye only) and K1. Note that L1 transmits much more of the shorter wavelengths than does K1, while G1 is intermediate between the two. The rise in shortwave transmission is less rapid in G2, especially above 50%, which may be the result of methodological error (see discussion). Created with Microsoft 365® Excel

Fig. 5

 5 Fig. 5 Averaged transmission of light through the vitreous of Little (Eudyptula minor), Gentoo (Pygoscelis papua) and King (Aptenodytes patagonicus) penguins L1, G2 and K2. Created with Microsoft 365® Excel

  Figure 1 526

No funding was received for conducting this study. The authors have no relevant financial or nonfinancial interests to disclose.

Ethics approval

All procedures performed in the study were in accordance with the ARVO Statement for Use of Animals in Ophthalmic Vision and Research. Ethical approvals were obtained from the New Zealand

Data availability

The raw data that support the findings of this study are available in the Digital Science (London, UK) online open access repository, https://doi.org/10. 17608/k6.auckland.c.6427706.v1

Author contributions

PH, MV, JZ and CM conceived and designed the research. PH, WH and JZ conducted the experiments. PH, WH and JZ analysed the data. PH, MV and FB interpreted the data. CM and JZ provided resources and supervision. PH and FB wrote the manuscript. All authors read and approved the manuscript.