E Giglio

T Le Cornu

Effect of secondary electrons on the patch formation in insulating capillaries by ion beams

Keywords:

The transmission rate of low energy Ar q+ ion beam through a macroscopic glass tube of large aspect ratio is simulated. Secondary electron (SE) emission, induced by ion impacts with the inner surface of the capillary, are taken explicitly into account by adding a SE source term to the charge dynamics equation. We found that the additional SE channel alters significantly the distribution of the deposited charge in the capillary wall. Compared to the case without the SE channel, the electric field generated by the self-organized charge patches is generally weaker, yielding drastically different transmission rates, especially for higher beam intensities. The effect of SEs on the patch formation and resulting transmission rate is found to be significant for SE yields as low as 1 SE per ion impact, in the case of Ar + ions. We propose a numerical experiment that can be tested experimentally, potentially allowing us to conclude if the SE channel is indeed crucial for simulating accurately the guiding of an ion beam through insulating capillaries. In the long run, our simulations may provide theoretical support for measuring the SE yield of low energy ions impacting insulating surfaces at grazing angles.

I. INTRODUCTION

Guiding of low-energy ions by insulating capillaries was first reported by Stolterfoht et al. in 2002 for microcapillaries [1] and later by Ikeda et al. [2] for macroscopic glass capillaries. They found that even though the capillaries were tilted with respect to the beam axis such as no geometrical transmission was allowed, the beam was steered after an initial charge-up phase through the insulating capillary by self organized charge patches. As a result, a part of the beam could be transmitted, with the ions keeping their initial charge state, indicating that the ions never touched the inner wall.

In the past, several authors modeled and simulated the guiding of the injected beam through insulating capillaries. In pioneering simulations, Schiessl at al. allowed the deposited charges to diffuse along the inner surface of the nano-capillary and through the bulk. Assuming an exponential decay of the deposited charges with a rate proportional to the bulk conductivity, they succeeded to reproduce qualitatively the observed trends in PET nano-capillaries [3]. As diffusion currents are rapidly dominated by drift currents in the presents of electric fields, a different approach was adopted in [4][5][6]. In the latter, surface currents were described involving a nonlinear charge drift model where the accumulated charge carriers were field-driven along the surface, with a velocity proportional to their surface mobility. For macroscopic glass capillaries, surface currents were assumed to have no dominant contribution in the charge dynamics and observed trends in macroscopic glass capillaries were qualitatively reproduce by simply adjusting the rate of the exponential charge decay [7,8].

Recently, we presented a model accounting for the dynamics of the deposited charges by means of solving the continuity equations for surface charges at the capillary interfaces. The model, labeled InCa4D, depends explic-itly on the bulk and surface conductivity of the capillary, which must be provided. The model was successfully used to simulate the radial focusing in tapered capillaries [9,10]. The simulated and experimental results given in [9] agreed convincingly well, giving confidence that the model describes reliably the charge dynamics in insulating glass capillaries.

The same numerical code was then used to support theoretically the observed decay rates of charge patches in tilted glass tubes [11]. While, for injected beam intensities below 4 pA the code reproduced qualitatively the observed time evolution of the transmitted fraction, the model predicted a blocking of the transmission for injected intensities above 8 pA. But that result was in disagreement with the observed data. Experimentally, the transmitted beam did not experienced any blocking for injected intensities as high as 35 pA.

Initially, we thought that the culprit for the discrepancy was the value of the surface conductivity used in the model. Indeed, the surface conductivity in glass capillaries is usually not a well-known quantity, as it depends strongly on the surface contamination. We varied thus the surface conductivity in our simulations over three orders of magnitude. But even then, we could not find a single value for the surface conductivity that was able to reproduce even quantitatively the observed transmission rates presented in [11], namely for intensities as low as 0.3 pA and as high as 35 pA. For completeness, we even varied the bulk conductivity in the simulations, which was also unsuccessful. We concluded then that a channel must be missing in the charge dynamics, which seems to be important especially at high beam intensities.

A source term that we neglected up to now in the charge dynamics, is one that accounts for secondary electrons (SEs). When beam ions hit the inner insulating surface of the capillary, SEs are possibly emitted from the impact point with a given initial velocity, guided by the electric field and eventually absorbed by the surface at different locations. Schliessl et al. already included a SE source term in their model to simulate the electron transmission through insulating Mylar capillaries [12]. Also, preliminary calculations including a SE source were presented in [11], where the added SE source term was shown to have a non-negligible effect on the transmission rate.

In the present work, we investigate the influence of the SE channel on the charge patch formation, by monitoring the transmitted beam current through a straight glass capillary, tilted with respect to the beam axis. We want to identify experimental conditions, for which the transmission rate is sensitive to SE yields. The aim is to make numerical prediction with our code that could be verified (or falsified) experimentally. It will hopefully allow us to conclude if adding a SE channel to the charge dynamics is mandatory. If experimental results were to confirm the numerical predictions, it would mean a new milestone in the modeling of the self-organized guiding of ion-beams by insulating capillaries. Last but not least, the presented numerical results could help deducing the SE yield by low energy ions impacting insulating surfaces at grazing angles, simply by recording in time the transmitted beam fraction.

II. MODELING

A. Surface charge dynamics

We propose to simulate the transmission of a low energy Ar q+ ion beam through a macroscopic borosilicate glass tube of dielectric constant ε r = 4.8. For the present work, we consider a capillary tube of length H = 60 mm, inner radius of R 1 = 0.43 mm and an outer radius of R 2 = 0.75 mm, matching the dimensions of the glass tubes sold by Warner instruments. The outer surface, including the entrance and outlet, is metallized and electrically grounded. The surface charge dynamics, on which the simulations are based, was already discussed in [13,14]. We give here merely a brief summary. Cylindrical coordinates (r, θ, z) are used throughout the paper. The injected charges are assumed to accumulate only at the inner interface, so that the electric field in the bulk (E r , E θ , E z ) is divergence-free. The dynamics of the surface charge density σ at the inner surface (r = R 1 ) of the capillary tube is given by the charge conservation equation,

∂σ ∂t + κ s 1 R 1 ∂E θ ∂θ + ∂E z ∂z = -κ b E r + γ . (1)
The first right hand term stands for the charges that are field driven from the inner to the outer grounded surface. The current density through the bulk is proportional to the bulk conductivity κ b , which is considered constant. The second left hand term describes the charge migration along the inner surface, in the angular and ax-ial direction, and is proportional to the surface conductivity κ s . In agreement with the measurement done by Gruber et al. [15], we take for borosilicate glass the common values of κ b = 10 -13 S/m and κ s = 10 -16 S. The source term γ accounts for the current density of injected holes and electrons at the interface.

Using a 2D Fourier transform, equation (1) may be solved conveniently in terms of moments of the charge distribution. We give here merely the starting point and the main result, a detailed discussion can be found in [13,14]. The surface charge density σ and the source term γ may be decomposed on moments with angular and axial indexes m and n,

σ(θ, z, t) γ(θ, z, t) = M m=0 N n=1 σ mn (t) γ mn (t) cos(mθ) sin (k n z) , (2)
with k n = nπ/H. The chosen basis assumes xOz plane symmetry and zero deposited charges at the grounded entrance (z = 0) and outlet (z = H). The simulated results presented in section III used M = 6 and N = 400, corresponding to a spatial resolution of less than 200 µm in both directions. By following the steps outlined in [13,14], one obtains the dynamics of each moment σ mn , which writes,

∂σ mn (t) ∂t = -σ mn (t) τ mn + γ mn (t) . (3)
Remarkably, each moment σ mn is independent from the others and characterized by its proper relaxation time τ mn . The latter depends merely on the electric properties (κ b , κ s , ε r ) and geometric dimensions (R 1 , R 2 , H) of the capillary and can be calculated once for all for each indexes (m, n). Table I gives some relevant relaxation rates that characterize the present capillary. Eventually, equation (3) can be solved numerically using a first-order exponential integrator method,

σ mn (t+∆t) = σ mn (t)e -∆t τmn +τ mn (1-e -∆t τmn )γ mn (t) (4)
where γ mn (t) is supposed constant during the time step ∆t. The analysis of the charge dynamics in terms of moments is extremely powerful, but would go beyond the scope of this paper. We highlight here only two properties: the total charge of a patch in the capillary is given by the monopole moments (m = 0), which decay with a rate of about 2.5 mHz, or equivalently, with a relaxation time of 400 s. The electric field responsible for the beam deflection is generated by charge moments with higher angular indexes (m ≥ 1). Their rates increase only slightly with the axial index n, but increase grossly linearly with the angular index m ≥ 1. This indicates that the moments σ mn with m ≥ 1 decay predominantly due to charge migration along the inner surface in the angular direction. The latter is controlled by the surface conductivity κ s .

n τ -1 0n τ -1 1n τ -1 2n τ -1 3n τ -1 4n τ -1 5n τ -1 6n 1

B. Ion trajectories

The beam ions are propagated classically using the Hamiltonian equation of motion (EOF). Inside the capillary, the ions feel only the electric field generated by the charge accumulated in the capillary wall. The trajectories do not depend on the charge over mass ratio of the ion, as can be seen easily by putting the EOF into a dimensionless form, see Appendix 1. The initial positions and velocities are sampled as following: the ions are emitted from a source located 50 cm upstream from the capillary entrance. The source is represented by a disc having a diameter of 2 mm, on which the ions are sampled uniformly. The angle between the initial velocity vector and the beam axis is sampled according to a normal distribution having a FWHM of 0.3 • . The projectiles that, after traveling through the 50 cm field free region miss the entrance of the capillary are discarded. Only the trajectories that pass the 0.8 mm ∅ collimator hole in front of the capillary are retained in the calculation. With this method, the injected beam is characterized by divergence with a half-opening angle of 0.36 • and a RMS emittance [16] of 0.5 mm.mrad. For more details see [10].

C. Secondary electrons

We assume that each Ar q+ ion that is not transmitted but hits the inner capillary surface, injects q + N SE holes at the impact point, which are immediately trapped by hole-centers of the insulator. (Factually, in order to speed-up the simulations, each ion injects q r × (q + N SE ) holes at the impact point, where q r = 2000 is the speedup factor. This amounts to saying that each simulated trajectory stands for 2000 ion trajectories.) Among the q + N SE electrons that are ejected from the impact point, q are picked up by the impacting Ar q+ projectile, which becomes neutralized and will no longer be considered. The remaining N SE electrons are field-driven through the capillary until they hit the inner surface and are reabsorbed at a new location, or escape the capillary. The number of ions per unit time that enter the capillary is I in /(qe), where e is the elementary charge and I in the injected intensity. The source term becomes thus,

γ mn (t) = I in qe e(q + N SE )γ h mn (t) -eN SE γ e mn (t) = I in γ h mn (t) + N SE q γ h mn (t) -γ e mn (t) , (5)
where γ h mn (t) and γ e mn (t) are the moments of the probability distribution per unit surface for the injection of holes and electrons at time t, respectively. From Eq. ( 5) we note that the SE channel is only active if the difference γ h mn -γ e mn is non-zero, or alternatively, if the electrons are injected at sufficiently different locations than the holes. We also note that the SE channel is controlled by the ratio N SE /q. This has an interesting consequence: the source term for (i) Ar + ions that emit on average 1 SE per impact and (ii) Ar 3+ ions that emit on average 3 SEs per impact, is eventually the same. Further, highly charged ions, which are expected to generate a number of SEs, N SE , roughly proportional to the ion charge q for a given impact velocity, see Fig. 3 in [17], may finally have a ratio N SE /q similar to that of singly charged ions.

The authors are not aware of published angular and energy distributions of SE emission from borosilicate glass induced by Ar q+ projectiles in the keV range and at grazing angles. The initial conditions of the SEs are thus chosen using commonly observed distributions: the fraction of electrons, leaving a surface element within a narrow angle dφ in a direction making an angle φ to the surface normal, follows a Knudsen cosine law [18], where sin(2φ)dφ gives the fraction of electrons that have velocity vectors between φ + dφ [19]. The initial energy ξ of the SEs is chosen randomly according to the probability law [20],

P (ξ + dξ) = ξ ξ 2 0 exp - ξ ξ 0 dξ , ξ 0 = 2 eV. ( 6
)
which fits reasonably well the energy spectrum of electrons emitted from Al-Mg (15%) alloy bombarded by 50 keV Ar + ions [21], as well as the calculated energy distribution of SE emission from amorphous SiO 2 [START_REF] Schreiber | [END_REF]. It should be mentioned that the distributions for initial conditions for SEs are just estimates, but could be improved in the future.

III. SIMULATED RESULTS

In this study we want to provide simulated results that are sensitive to the absence or presence of the SE channel, so that experimental measurements are able to discriminate between both approaches. Actually, transmitted beam intensities I out can be measured rather precisely. We propose thus to check in how far SEs influence the transmission rates. To that end, we propose to simulate the transmission of a 2.5 keV Ar + beam through the borosilicate glass tube, setting thus q = 1 and N SE /q = N SE . The choice of singly charged Ar + projectiles is motivated by our existing experimental setup in CIMAP. Nevertheless, we want to emphasize that the following simulated results are also valid for multiply charged Ar q+ ions, as long as the extraction potential of the ion source is kept to U s = 2500 V, see dimensionless charge dynamics in Appendix 2. Just keep in mind that in the following figures and discussions, N SE is to be understood as the number of SEs emitted per impact and per charge state q. For example, simulations with Ar + emitting N SE = 1 are also valid for Ar 3+ emitting 3 SEs per impact, while simulations with Ar + emitting on average 1/2 SE are also valid for Ar 6+ emitting 3 SEs per impact.

The capillary has an aspect ratio of 70 and is characterized by a geometrical transmission angle of 0.8 • . The capillary is tilted by 4 • with respect to the beam axis, so that no geometrical transmission is possible. The injected beam is collimated to a diameter of 0.8 mm. The average number N SE of emitted SEs per impact depends on the charge state and kinetic energy of the projectile, its incidence angle with the surface as well as the nature of the insulator. As we did not find measurements of SE yield for keV Ar q+ ions hitting a glass surface at grazing angles, we investigate the transmission rate for different values of N SE /q, namely 1/2, 1, 2, 3 and 4. This should allow us to cover the expected range of SE per impact and give off possible trends. Our numerical code InCa4D is rather CPU efficient, 6 × 10 6 trajectories per 24h, allowing us to explore times T more than twice the longest charge relaxation time of the system, T ≥ 2τ 01 800 sec, giving access to the asymptotic behavior of the transmission rate, if any.

A. Transmitted fraction

We compute the time-evolution of the transmitted fraction, I out (t)/I in for various injected current intensities I in ranging from 0.2 to 40 pA. In Fig. 1 and Fig. 2, we compare numerical results using N SE = 2 to those using N SE = 0. For injected currents below 2 pA, the dynamics of the transmitted fraction are sensibility the same in both cases, see Fig. 1. In particular, the asymptotically transmitted fractions, which increase with the injected beam intensity, are quite close. This means that below a certain intensity threshold, which generates only one or two charge patches, the SE channel has no notable influence on the transmission rate, and experimental results will not be able to discriminate between both approaches.

For injected intensities above 2 pA, the situation is largely different. First, let us consider the simulated transmission rates using N SE = 0, shown in the top panel of Fig. 2. Remarkably, for I in > 3, the beam is no longer transmitted continuously from the start. For example, for I in = 4, 8 and 12 pA, the beam transmission is mostly blocked during the first 140, 380 and 440 sec, respectively, after which the transmitted fractions increase quickly to the asymptotic value of about 90%. For I in = 20 pA, the transmission is outright sparse, with no asymptotic transmission during the first 800 s. For even higher intensities, I in ≥ 21 pA, no transmission is observed. Looking at the trajectories, we found that the beam got stuck in the capillary, while charging the 5 th patch (located around z = 18 mm) until the beam is Coulomb blocked by the charge patch in the capillary. A movie showing the trapping of the injected beam inside the capillary by charge patches, that attain a potential of U s , is given in the supplemental material [23].

In the bottom panel of Fig. 2, the transmitted fractions were simulated using N SE = 2. Unlike the results in the upper panel, for injected intensities I in = 4 , 8 and 12 pA, the beam is transmitted continuously from start, without interruption. The transmission rates keep following the trend observed in Fig. 1, that is, the beam is transmitted as soon as the first patch is formed, with the asymptotic value increasing with the injected beam intensity. The time evolution of the transmitted fractions for this range of intensities is thus radically different from those without SE. Hence, experimental data should allow us to conclude if a SE source term in the charge dynamics Eq. ( 1) is indeed necessary in order to simulate accurately the patch formation.

Remarkably, for I in = 20 pA, the time-evolution of the transmitted fraction is no longer continuous but blocks intermittently for short amounts of time. As as be seen in Fig. 5, the beam gets stuck in the capillary and needs several tens of seconds before the new charge patch is strong enough to deflect the beam out. The Coulomb blocking is however avoided for the range of intensities investigated here, I in ≤ 40 pA.

B. Blocking of the transmission

We computed the transmission rates for different values of N SE /q, namely 1/2, 1, 2, 3 and 4. We increased the current intensity up to 40 pA and checked if the transmission was continuous for at least 800 seconds or if it was blocked for a given period, (see for example the curve for I in = 20 pA in the bottom panel of Fig. 2). The purpose of this study is to investigate the influence of the number of SEs emitted per impact and per ion charge q on the patch formation and resulting guiding. The results are shown in Fig. 3. The blue sticks indicate the range of intensities for which a continuous transmission was monitored once the first patch has been formed, and for which an asymptotic transmitted fraction could be observed, c.f. Fig. 1. The orange sticks indicate the range of intensities for which the transmission rate was not continues in time, but blocked intermittently for one or several periods of time. The red sticks give the range of intensities for which Coulomb blocking was observed.

When looking at the height of the blue bars, we note a positive trend with increasing N SE , indicating that a higher current intensity can be transmitted continuously if more SE are emitted per ion impact. This trend could be expected from Eq. ( 5), which tells us that the SE source term scales linearly with N SE . Let us take an injected beam current of I in = 21 pA for example : figure 3 predicts that such a beam should be guided continuously through the tilted capillary, if at least in average 3 SE are emitted per impact. On contrary, with N SE = 0, the simulations predict that the beam should be Coulomb blocked inside the capillary. In the case where on average 1 or 2 electrons are emitted per ion impact, the beam is expected to blocked intermittently. The secondary electron channel has thus clearly a non-negligible influence on the time-resolved transmitted fraction, especially in the case of relatively high intense ion beams. In the following we will try to explain how the additional SE channel modifies the dynamics of the charge patch formation, resulting in dramatically different time evolution of the transmission rates. The data shown in Fig. 4 are from a simulation using N SE = 4, as it enhances visually the statement, but the conclusions are valid also for other non-zero values of N SE . We investigate the trajectories of SEs that are emitted from different impact points during the injection of the first charge patch. The latter is located in our case typically 3 mm behind the entrance of the capillary, c.f. Fig. 5. Let us consider a cut from the cylindrical inner interface by the xOy plane at z 0 = 3 mm.

In Fig. 4, the cut of the inner surface is represented by the solid black half-circle of equation R 1 u r (θ), where u r (θ) is the radial unit vector. The brown solid curve on top of the black half-circle represents the surface charge distribution σ(θ, z 0 ), after that a charge of Q in = 40 pC has been injected. The brown curve is given by the equation (σ(θ, z 0 ) + R 1 ) u r , so that the difference between the brown and the black curves along u r (θ) gives the surface charge density σ(θ, z 0 ). The accumulated surface charge distribution generates an electric field (not shown) that drives the emitted electrons.

We show several SE trajectories (colored curves inside the half-disk) that have been emitted from different locations of the surface. SEs that are emitted from the central region labeled "c" "fall" predominantly back to the central region from where they were emitted. Secondary electrons that are emitted from lateral regions label "a" and "b" are predominantly field driven toward the central part "c" of the patch, which is at higher potential. As a result, the central region "c" accumulates negative charge coming from the lateral regions, and this flow is proportional to N SE . The SE source term tends thus to redistribute the injected charge more evenly along the angular direction. The difference in the redistribution of the accumulated charge can be appreciated by comparing the cuts of the surface charge distribution with SE (brown solid curve) to the one without SE (orange dashed curve). In terms of moments of the charge injection cross sections, see Eq. ( 5), the SE channel tends to decrease the absolute value of the moments γ mn with angular index m ≥ 1, resulting in the formation of a charge patch that is expected to ultimately deflect less the ions passing nearby. Note that a redistribution of the injected charge along the axial direction exists too, but is grossly averaged out over the mm-scale long charge patch in the z direction.

We also monitored the trajectories of the injected ions through the capillary. We compare in Fig. 5 snapshots of ion trajectories (blue curves) using N SE = 2 (right panels) to those using N SE = 0 (left panels). The red curves shown in the right panels are trajectories of emitted secondary electrons. The gray lines at x = ±0.43 are cuts of the inner interfaces by the xOz plane. The brown curves on top of the gray lines represents cuts of the surface charge distribution, of equation σ(0, z) + 0.43 and -σ(π, z) -0.43. The latter allow us to indicate the location and charge intensity of the charge patches that guide the ions.

After that 60 pC have been injected by the 8 pA ion beam, a first charge patch is formed and the ions are deflected towards the opposite wall. While the deflections in the left panel (without SE) seem slightly stronger than those in the right panel (with SE), the difference in the transmission rate, up to that moment, is still negligible. After that 240 pC have been injected, already three patches have been formed. Now the differences in the trajectories and patch locations between the 2 approaches are substantial. With SEs, the weaker deflections by the first two patches accumulate, so that the third patch is already located near the exit of the capillary. As a result, a major part of the ions is guided through the capillary. Without SEs, the deflection by the first two patches is notably larger and the third patch is formed about 20 mm from the outlet of the capillary. After that 450 pC have been injected, both approaches give completely different results. With SEs, 90% of the injected beam is transmitted while, without SE (left panel), the beam gets stuck in the middle of the capillary. Except for the first charge patch located near the entrance, which is similar in both approaches, the remaining patches have eventually completely different positions and intensities. Hence, for N SE = 2, the less intense charge patches generate weaker electric fields, what results in smaller beam deflections and thus in further separated charge patches.

The lower number of charge patches allow to guide the beam seamlessly (with less rebounds) through the capillary. The reader will find in the supplemental material a movie showing the time-evolution of the trajectories for the case discussed here [24].

IV. CONCLUSION

We investigated numerically in how far SEs alter the dynamics of the patch formation in insulating capillaries, during ion beam is injected. To this end, we added a SE source term to the surface charge dynamics and simulated the trajectories of the beam ions and SE electrons through a tilted glass tube. We monitored the transmitted fraction of a 2.5 keV Ar + ion beam through a straight capillary tilted by 4 • with respect to the beam axis. We varied the beam current over a large range of intensities, from 0.2 to 40 pA and recorded in time the transmitted fraction. The aim was to make numerical predictions with our code that could be tested experimentally. In order to identify possible trends, the simulations were performed with different numbers of emitted electrons per ion impact, namely N SE = 1/2, 1, . . . , 4. We remind that the presented simulations are not only valid for singly charged Ar + ions, but are valid also for higher charge states q of the Ar ion, if N SE is understood as the number of SE per ion charge state q.

Compared to calculations without SE, we found that the SE channel modifies the distribution of the injected charge, when beam ions hit the insulator surface. In particular, the central part of the patch accumulated SEs coming from lateral impact points, resulting in charge patches that are slightly more uniform, generating weaker electric fields in the vicinity of the patches. Those weaker fields deflect less the beam ions and the charge patches are hence further separated, allowing to guide the beam through the capillary with less rebounds. We found that a higher SE yield per impact and per ion charge state, N SE /q, has a more pronounced effect on the redistribution of the injected charge, allowing higher beam intensities to be transmitted without experiencing intermittent blocking.

We hope that in near future experimental measurements will be able to confirm the crucial role of SE in the self-organized guiding of ion beams by insulating capillaries. On request, we would be delighted to perform calculations for capillaries of different nature and geometry that may be used in dedicated experimental setups.

We consider an ion of charge q and mass m, extracted by a potential U s . The initial velocity of the ion is v 0 = 2qU s /m. Only the electric field generated by the deposited charge in the capillary wall acts on the ion. Other forces like the image charge force at the vacuumglass interface are ignored. Introducing the characteristic time t 0 , the equation of motion (EOM) of an ion can be put into a dimensionless form,

d ṽ d t = t 0 v 0 q m U s H Ẽ , with ṽ = v/v 0 t = t/t 0 Ẽ = E(H/U s ) (A.1)
where the tilted quantities are dimensionless. Defining the characteristic time t 0 = v 0 mH/(qU s ) = H/v 0 , the equation of motion (EOM)

d ṽ d t = 1 2 Ẽ . (A.2)
becomes independent of q or m of the ion as well as of the extraction potential of the source U s . The trajectory of the ions depends only on its initial trace-space conditions, that is, on the initial position r and initial direction of the velocity vector v 0 /v 0 .

Surface charge dynamics

In this section, we want to identify the parameters that control the dynamics of the surface charge density Eq.

(3) and show that the dynamics depend explicitly on the ratios U s /I in and N SE /q. Let us first define the characteristic surface charge density σ 0 , From the definition of τ c , we see that the charge dynamics depend on the ratio U s /I in . Consequently, although the EOM does not depend on the beam parameters U s and I in , the transmission rate eventually depends on their ratio via Eq. (A.6). Injecting the source term Eq. ( 5) into Eq. (A.6), one gets finally, ∂ σmn ∂ t = -τ c τ mn σmn + γh mn + N SE q γh mn (t) -γe mn (t) . (A.7) Because of the added SE source term, the charge dynamics and thus the transmission depends now also on the ratio N SE /q.

σ 0 = CU s S 1 = ε 0 ε r U s R 1 ln R2 R1 , (

  Relaxation rates τ -1 mn in (mHz) for angular indexes 0 ≤ m ≤ M = 6 , as well as for 3 different axial indexes n = 1, 2, 10.

FIG. 1 :

 1 FIG. 1: Simulated transmitted fraction of a 2.5 keV Ar + ion beam through the 4 • tilted capillary as a function of the time for different current intensities Iin ranging from 0.2 to 2 pA. Left panel, NSE = 0, right panel NSE = 2.

FIG. 2 :FIG. 3 :

 23 FIG. 2: Simulated transmitted fraction of a 2.5 keV Ar + ion beam through the 4 • tilted capillary as a function of time for different current intensities Iin ranging from 4 to 20 pA. Top panel, NSE = 0, bottom panel NSE = 2

C

  FIG. 4: SE trajectories, projected on the xOy plane for z ∈ [0, 10] mm (1 st patch), at the moment Qin = 40 pC. Black halfcircle stands for the inner surface of radius R1 = 0.43 mm. The brown and the dashed orange curves on top of the black half-circle correspond respectively to the charge density at the inner surface for NSE = 4 SE per ion impact and NSE = 0. Labels a and b indicate two impact points, emitting each 4 SEs.

FIG. 5 :

 5 FIG. 5: Snapshots of simulated ion trajectories (blue lines), projected on the xOz plane, taken at different moments and labeled by the injected charge Qin = 60, 240, 450 pC. Left panels are without SE, NSE = 0. Right panels, 2 SE per impact were considered, NSE = 2. Straight grey lines represent the inner interface of the capillary. The brown curves show the charge density (arb. units) of the charge patches at the inner surfaces. The red lines are the trajectories of SE emitted from the impact points. Injected intensity was Iin = 8 pA.

A. 3 )

 3 where C = 2πε 0 ε r H/ ln R2 R1 and S 1 = 2πR 1 H are respectively the capacity and inner surface of the capillary. Introducing the characteristic charging time τ c as well as the characteristic current density I in /S 1 , equation (3) may be written in the following form,

Acknowledgments

This work was supported by the French research agency Centre National de la Recherche Scientifique via Projet International de Coopération Scientifique (PICS), "Capillaires isolantes comme lentilles électrostatiques auto-organisées" Project No. 245358 Hongrie 2018.


Gábor Paller

Sébastien Aubin

Gábor Élő

Olivier Camp

Cost-efficient Localisation System for Agricultural Use Cases

Keywords: Agriculture, Low-cost Localisation, Trilateration Simulation

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Connected sensor applications in the agriculture domain often require precise localisation functionality. The state-of-the art solution is high-precision dualfrequency GPS receiver with Real-Time Kinematic (RTK) support. Typically these receivers cost 3-4000 USDs and have strict control of purchase which makes them suitable for a costly agricultural machine like a combine-harvester but are prohibitively expensive for localising less valuable moving objects. Precise localisation requirements have arisen in two separate projects run by the institutions collaborating in the research described in this paper. At ESEO, the task is to localise dairy cows with a precision of less than 1 meter. At Széchenyi University our task was to mobilize the agricultural camera sensor [START_REF] Paller | Power consumption considerations of an agricultural camera sensor with image processing capability[END_REF] by mounting it onto a robot vehicle that traverses a predetermined trajectory. For this use case, precise localisation is needed to keep the robot on the tracks (typically dirt roads) used by agricultural machines. We targeted the precision requirement of better than 1 meter in this case too. In both cases, the value of the objects to be tracked does not justify expensive GPS receivers that are also hard to protect against theft on the field.

Even though the requirements seem to be similar, they are not the same. The robot localisation task may allow a limited number of fixed stations while for the cow localisation, the use of such fixed stations is discouraged. The robot's movement is under our control, e.g. it is possible to stop the robot to allow for more precise localisation. For the cows, such "stopping" is not possible.

The paper shall be organised as follows.

• Section 2 presents our findings with regards to the precision of low-cost standalone and differential GPS solutions.

• Section 3 evaluates a low-cost differential solution.

• Section 4 presents behavioural analysis of dairy cows based on publicly available measurement data that supports our proposal for a localisation solution using RTK GPS and short-range localization technologies.

• Section 5 presents our proposal for distance-based short-range localisation technique.

• Section 6 presents our proposal for an angle-based short-range localisation technique.

EVALUATION OF LOW-COST STANDALONE AND DIFFERENTIAL GPS

GPS measurements are subject to satellite and receiver clock errors, ionosphere and troposphere propagation delays, multipath and random noise errors. The most interesting factor of standalone (nondifferential) GPS receivers is the ionospheric delay.

142

The electromagnetic property of the ionosphere influences the electromagnetic signals' propagation speed, including that of GPS signals. As the signal propagation speed is used in the pseudorange calculation (the satellite's distance from the receiver deduced from the signal delay between the satellite and the receiver), changes in the real propagation speed introduce errors into pseudorange calculations. This error ranges from 1 meter to up to 50 meters in case of satellites with low elevation and even higher in case of increased solar activity. Ionospheric delay is complicated from the error correction point of view because it introduces systematic (non-random) location measurement error. Eventually the mean value of this error is close to zero but that needs very long observation period, in the range of several hours [START_REF] Langley | The mathematics of gps[END_REF]. Dual-frequency GPS receivers can filter out this error but these receivers are very costly. Space-Based Augmentation Systems (SBAS) is a differential GPS technology that transfers corrections over satellites that are distinct from GPS satellites, still transmit data on GPS frequencies. SBAS signals are often problematic to receive on ground level. We made measurements with SBAS-equipped GPS receivers to figure out, what precision can be achieved with this technology in our use cases. The SBAS receiver was MediaTek 3339, equipped with ceramic patch antenna or external active antenna. As reference, Ashtech Z-Xtreme highprecision dual-band receiver was used in static survey (non-differential) mode. The measurements were made in the Angers area, France. We also made measurements at a geodetic reference site (Ecouflant I) whose coordinates have been established with high precision by the National Institute of Geographic and Forestry Information (IGN) of France.

Figure 1 shows the results of a typical measurement at the reference site. The origo of the graph is the IGN reference coordinate for the site, deviation from the origo means measurement error. MTK3339 2 was not able to lock on the SBAS signal (even though the other two modules in its vicinity were eventually able to receive SBAS corrections), this fact is reflected in its much less precise measurements than MTK3339 1 and MTK3339 3. The two modules that did lock on SBAS produced much less precise locations than the 1 meter error required. Even the advanced Ashtech reference receiver had a maximum error that was larger than 1 meter.

The maximum error relative to the reference point measured with the MTK3339 was in the 2.22-11.51 meters range. All the measurements were made in an environment that models agricultural conditions: mostly flat area with minor depressions, low vegeta- tion with occassional trees. The reference coordinates were either taken from the Ashtech receiver (when the measurement was not performed at the geodetic reference point) or were the coordinates specified by IGN for the reference point. The measurement sessions lasted 10 minutes, measured from the moment when all the 3 SBAS receivers locked on the SBAS signal. This could take quite a long time depending on the location and time of the day, it was quite common that 10-15 minutes needed from the first GPS location fix to the first SBAS fix and there were measurements when one module could not even obtain SBAS fix, in spite of the fact that the SBAS receivers were placed very near to each other (3 centimeters). When the SBAS signal was not acquired, the maximum error was 30.89 meters. Our conclusion based on the field measurements is that low-cost GPS receivers even with SBAS differential corrections are not able to satisfy our requirement of 1 meter accuracy. In addition, SBAS signal cannot be reliably acquired on ground level.

EVALUATION OF LOW-COST DIFFERENTIAL GPS

Our measurements presented in section 2 convinced us that a low-cost GPS receiver supporting only the L1 band is only able to support our accuracy requirements if it is used in differential mode. The goGPS software [START_REF] Herrera | goGPS: Open-source MAT-LAB software[END_REF] was created to support exactly these kinds of receivers with dif- ferential support. Readers interested in the details of goGPS should consult the cited references, only a brief overview is presented here.

In order to enhance the baseline accuracy of lowcost receivers, goGPS relies on raw observation data (pseudorange, carrier phase) from the GPS receiver, provided by the u-blox LEA-6T receiver in our case. We used goGPS in off-line mode when the rover and the master are not connected during the measurements. It is possible to set up the system with two low-cost receivers (one in master role located at a well-known coordinate and one in rover role) or with one professional reference station in master role (we used IGN's NGER reference station which is about 10 km from the location where the measurements were made) and a low-cost receiver in rover mode.

Double differencing in differential GPS mode eliminates efficiently the effect of ionospheric delay but other error terms like random noise, multipath effects and receiver clock errors still affect the locations calculated by the goGPS software. Figure 2 shows the maximum position error when the GPS receiver sampling frequency was 1 Hz and 10 Hz as a function of sliding averaging window length. The window length was between 0.5 min and 8 min. The figure demonstrates that the residual position error can be efficiently decreased with low-pass filtering but this affects the temporal sensitivity of the system which cannot be compensated by increasing the receiver's sampling frequency.

The effect of high-quality reference station master vs. using a low-cost receiver as master was also evaluated. High-quality reference station decreases the noise of at least the master receiver. On the other hand, the IGN reference station had a sampling period of 30 seconds. The goGPS software assumes a 1:1 relationship between rover and master samples, discarding rover samples if there is no corresponding master sample. The outcome is a significant reduction of effective sampling frequency which reduces the averaging window size to achieve the same temporal sensitivity. We evaluated the effect in two measurements and we found that the maximum error with low-cost master station was 1.3 meters while the maximum error with IGN master was 3.31 meters. While this measurement cannot be considered extensive, it indicates that high-quality master may improve the accuracy only if its sampling frequency is comparable with that of the rover.

We conclude that goGPS is indeed capable of producing location measurements using data from lowcost receivers if the target is stationary for at least 8-10 minutes. In case of moving targets (in particular in case of targets moving unpredictably like the cows) its error quickly increases so that trajectory tracking becomes impossible.

BEHAVIOURAL ANALYSIS OF DAIRY COWS

In this section we analyse whether it is possible to measure cow location in spite of the restriction imposed by goGPS' deficiency in tracking moving targets. The other use case is simpler as we control the movement of the robot entirely so if there is a need of a precise location fix, we can stop the movement for the required period. Cows, however, move according to their will and if they do not stay stationary for long enough, the low-cost rover will not be able to acquire the target's accurate position even occasionally. This phase of the research was accomplished based on data sets acquired by earlier research projects. [START_REF] Wietrzyk | CRAWDAD dataset nottingham/cattle (v. 2007-12-20)[END_REF] (from now called Nottingham measurement) tracked 6 dairy cows for 2 days using GPS collars. Based on our experiences about GPS accuracy (see section 2), we consider the target stationary if its location does not change more than 3 meters from the baseline position acquired when the assumed stationary period started for 10 minutes. [START_REF] De Weerd | Deriving animal behaviour from highfrequency gps: Tracking cows in open and forested habitat[END_REF] (from now called Weerd measurement) tracked 9 cows for 11 days and added human observations to high-frequency GPS data. Human observations attach 7 labels to high-frequency GPS data of which we considered 5 ("Drinking","Dry forage","Foraging","Standing", "Grooming") as stationary. If the animals stayed for at least 10 minutes in a stationary state, then the time spent in the state was added to the stationary time. The total stationary time was derived in this case entirely from humanobserved labels. We processed only open-field (as opposed to forest) measurement in this paper. Figure 3 presents the stationary time for the Nottingham measurement, by cow. One cow was found to be stationary all the time and its data has been eliminated from this chart. In general, the cows spend 40-90% of their time stationary even though the one with ID of "067" was constantly moving. Eventually on average the 5 cows were stationary for 62.3% of their time.

The Weerd measurement presented much more uniform picture. All the 9 cows were found to be stationary between 79.5 %-89.8 % of the time with an average of 80.9 %. We therefore concluded that even though the movement pattern of the animals depends on the particular cow, it can be assumed with high probability that at least some animals in the group stay stationary for the time period needed for an accurate GPS measurement. These animals can be used as reference points to locate the animals that were found to be moving with short-range distance or angle measurement methods.

DISTANCE-BASED SHORT-RANGE LOCALISATION

The problem of the distance-based short-range localisation is the following. We intend to localise a point with unknown position on a 2D map based on distance measured from reference points with wellknown positions. We can then calculate the position of the unknown point with a trilateration algorithm [START_REF] Cheung | A constrained least squares approach to mobile positioning: Algorithms and optimality[END_REF]. We assume that the cows are equipped with an Ultra-Wideband (UWB) range mea-suring system and a GPS. There are competing UWB technologies on the market that we are still evaluating. UWB system is for the relative distance estimation among the animals and the GPS is for absolute positions. We have to understand how the errors of each system affect the unknown position's estimation error. Trilateration studies often omit the error to simplify the equations' resolution.

The first part of our simulation is a simple problem with N well-known fixed points. If we measure all the distances r n wpt/u between the well-known points with the following coordinate [x n wpt , y n wpt ] with n wpt = 1, ..., N and the unknown point [x u , y u ], we can find the unique point, only if all the well-known points are not aligned. a system with simple circles equations give this results.

The Effect of Distance Measurement Error

In the first simulation we tried to find how an error on distance measurement could affect the reconstruction of the unknown point. The aim of this simulation is to verify if we can reconstruct the position of an unknown point and to determine what is the error of the unknown point estimation in the presence of distance measurement error. We have tried N = {4, 5, 6, 10, 20}. We chose the location of these well-known points according to real grazing situation. In [START_REF] Dumont | Consistency of animal order in spontaneous group movements allows the measurement of leadership in a group of grazing heifers[END_REF], the domestic herbivores used to graze in group. Few animals are alone. The selected plot is an area of maximum 300 meters × 300 meters. As example, this is the coordinate for 10 fixed points: ; [-5, 90]. A random point is picked in the area. The exact radius could be calculated with the knowledge of the fixed points and random point coordinates. A different random error of ε meters is added to each radius to reflect the error. Finally this overdetermined system is described in the following equation:

                       (x u -x 1 ) 2 + (y u -y 1 ) 2 -( (x 1 -x u ) 2 + (y 1 -y u ) 2 + ε 1 ) 2 = 0 . . . (x u -x N ) 2 + (y u -y N ) 2 - ( (x N -x u ) 2 + (y N -y u ) 2 + ε N ) 2 = 0
(1) This system in this form is a non-linear least-squares problem. We use iterative non-linear least-squares algorithm to solve these equations due to distance mea- surement errors. In our simulation each ε n wpt is a random value between ±2 meters. Using Python's scipy package, we iterate the process 1 000 times to act as a Monte-Carlo test and we repeat the process with 100 random and unknown points. Figure 4 represents the ideal situation with 10 well-known points. Figure 5 represents the error after 1 000 iterations for a given list of well-known points.

The results are presented in table 1 with regards to different number of fixed points. ∆ max is the difference between the maximum error and the minimum error for all the situations. So it is the upper bound of the error for all the situations (and iterations). ∆ mean(ε Xu ) represent the upper bound of the mean of errors on one axis. max(σ 2 X u

) is the maximum of the variance in all the situations. [ X u ; Y u ] is a N × 2 matrix size of all the estimation results of the unknown point.

We have started the iterative algorithm (least squares() the scipy Python library) from the same initial point and we experienced that the results were slightly different after the end of each iterative process. Therefore we executed the iterative process several times and we took the mean of the results. Our experience is that this mean value is of better quality than any of the standalone results.

In the following simulations, however, we considered that each distance measurement has a different measurement error. We consider that we only have one chance to calculate the unknown position to save power in the real case.

The main problem of this simulation is to help the algorithm to find the correct minimal solution. Optimisation functions are very susceptible to initial state. When the number of well-known points is not enough, a good solution is hard to find. That why the variances are very high for 4 and 5 fixed well-known points. Moreover, in 4 and 5 fixed points, we try to model a real grazing situation, so animals are really close. A group of reference points that are close to each other could behave as if they were one point. This situation is not suitable to estimate the position if no reference points are available that are far away from this group. The reason of this phenomenon is the small distance between the first points, the large distance to the last point, and the addition of a random error.

In conclusion, our simulation shows it is important to have at least 3 fixed points which are far away to be sure of the good problem resolution. This result is interesting to minimise the calculation load in an embedded system and to help us to evaluate the number of UWB anchors. Moreover, if a group of cows is close to each other, it is possible to activate only a part of the GPS receivers in the group to save power.

Effect of Reference Point Position Error

We consider using GPS to obtain the coordinates of the fixed points and to use UWB to measure the distance between the fixed points and the unknown point.

In that case, the GPS error may introduce a more significant error source. We made a second simulation to understand the consequence of a GPS localisation error in the reconstruction of the unknown point. In this situation, we consider no distance measurement error.

The aim is to reduce the system to linear equations. The new system can be written as: This could be put in a matrix form (equation 3). Subtracting the last equation from the other equations is arbitrary.

                       (x N -x 1 ) • x u + (y N -y 1 ) • y u = 1 2 (r 2 1 -r 2 N + x 2 N -x 2 1 + y 2 N -y 2 1 ) . . . (x N -x N-1 ) • x u + (y N -y N-1 ) • y u = 1 2 (r 2 N-1 -r 2 N + x 2 N -x 2 N-1 + y 2 N -y 2 N-1 )) (2)
Gβ = F (3)
where

G =    x N -x 1 y N -y 1 . . . . . . x N -x N-1 y N -y N-1   , β = x u y u , F = 1 2 •    r 2 1 -r 2 N + x 2 N -x 2 1 + y 2 N -y 2 1 . . . r 2 N-1 -r 2 N + x 2 N -x 2 N-1 + y 2 N -y 2 N-1   
The localisation estimation could be found with this linear equation using the standard linear least-squares method (eq. 4).

β = (G T G) -1 G T F (4)
β is the estimated coordinate.

To visualize the problem, the figure 6 represents 10 fixed points with 1 000 different simulated errors added to them and the estimation of the unknown point. One larger patch in this figure represents a reference point with a set of error values added.

The results of this simulation are presented in table 2. For 10 fixed points in this configuration, the results are good. In some cases with few fixed points, this table show some variance problem. Sometime the simple resolution does not work and the result of the least-squares solution exhibits a large error. A lowpass filter that we did not implement could be used to control the problem.

The calculation takes approximately 20 to 50 seconds with the linear least-square method and 520 seconds to 715 seconds with the iterative non-linear algorithm proportion to the number of fixed points depending on the number of fixed points. The processor used is an Intel i7-4700MQ, 2.4 GHz and the computer is equipped with 16 GBytes of volatile memory.

We can conclude that linear least-square algorithm could be used if we have enough separate fixed points. If we have enough computation resources and not enough separate fixed points, we could use non-linear least-square techniques to find the correct unknown point. We can see that for a same measurement error, in our case ±2 meters, with enough separated fixed points, the estimation is better if we assume that the measurement error is introduced into the fixed points' positions. In our real study, the distance measurement could be given by UWB which have, theoretically, a better accuracy than ±2m. Finally the error position could only depend on the effect of reference point position error. But we have to do other simulation and try.

ANGLE-BASED SHORT-RANGE LOCALISATION

Beside distance-based short-range localisation, we investigated whether we can build an in-house angle-ofarrival (AOA) short range localization system. This localisation method depends on a direction-sensitive antenna. The antenna rotates and finds out the angle of signals from stations with known locations. These stations can either be fixed to the ground or mounted to a moving platform which stops for long enough time periods so that it can be localised accurately (see section 3).

Our AOA localisation method is based on the prin- [START_REF] Cheung | A constrained least squares approach to mobile positioning: Algorithms and optimality[END_REF]. We assume, however, that instead of the fixed stations measuring the angle of the mobile station's beacon signal, it is the mobile station that measures the angle of the fixed stations' beacon signal. So equation ( 47) in [START_REF] Cheung | A constrained least squares approach to mobile positioning: Algorithms and optimality[END_REF] changes to equation 5. where N is the number of the fixed stations whose angle is measured. N is at least 3 but the measurement may be overdetermined where N > 3 hence linear least-square solution is calculated.

tan(r AOA,i ) = sin(r AOA,i ) cos(r AOA,i ) = y i -y x i -x (
β = (H T H) -1 H T k (8)
We have made simulations to estimate the localisation accuracy. Figure 7 shows the localisation error measured in a simulation with varying angle measurement error and distance between the mobile station and the fixed stations. The 4 fixed stations were arranged in a square, the mobile station was from equal distance from all the fixed stations. The distance shown in the figure is the distance between the mobile station and any of the fixed stations. We assumed that there is a fixed measurement error (x axis). The angle measurement error was added to the exact angles so that the distance between β and β is maximal and this maximum error is shown in the figure.

With the distance of 50 meters, the required localisation precision can be achieved only if the angle measurement error is less than 1 degree. We built a simple prototype to verify how easily these requirements can be implemented based on Atmel ATmega328P MCU (Arduino Pro Mini) and Nordic nRF24L01P RF module, operating in the 2.4 GHz band. The sender unit was equipped with a simple omnidirectional stick antenna and the receiver unit was equipped with a 9 dBm PCB Yagi antenna. By turning around the Yagi antenna, the angle range (0 degree being the direction of the sender) was identified where the sender's data can be received. Unfortunately the nRF24L01P module has no Received Signal Strength Indicator (RSSI) feature, the signal is either present or not. This means that there is a minimum distance to the sender because if the receiver is closer to the sender than the minimal distance, the signal can be received independently of the angle of the receiver's antenna. This restriction can be mitigated by a receiver that provides RSSI along with the received data packets.

The measurements were made on an agricultural field that serves as a pasture. The sender's transmission power was set to one of the 3 levels the nRF24L01P supports. The receiver was located at a specified distance from the sender and the antenna was rotated. The angle when the signal appeared and when the signal disappeared was recorded. With this simple method the direction of the sender was identifiable with 1 degree precision. The minimum and maximum distances with different power levels were the following: PA MIN: 4-20 meters, PA LOW: 22-41 meters, PA HIGH: 31-70 meters.

CONCLUSIONS

Low-cost, accurate localisation is often required in agricultural applications. We found that low-cost GPS modules are inadequate but in differential setup certain low-cost modules are able to produce the required accuracy if the target is stationary for at least 8-10 minutes. Certain cows (but not all of them) were found to satisfy the criteria for being stationary for 40-80 % of their grazing time. Movements have to be tracked by an auxiliary technology. We made simulations for two of such technologies: distance-and angle-based short-range localisation technology. In case of distance-based, the effect of distance measurement error results in worse position estimation than the effect of reference point measurement error. Angle-based short-range localisation turned out to be more cost-efficient but also more problematic, due to the rapidly growing localisation error as the distance between the mobile and the fixed station grows.

Figure 1 :

 1 Figure 1: Results of one measurement at Ecouflant I site.

Figure 2 :

 2 Figure 2: Maximum position error as a function of sampling frequency and averaging time.

Figure 3 :

 3 Figure 3: Stationary time per cow, Nottingham measurement.

  [0, 0] ; [0, 5] ; [-10, 10] ; [-10, -6] ; [100, 100] ; [10, -8] ; [70, -40] ; [80, -45] ; [75, -35]

Figure 4 :

 4 Figure 4: Optimal situation for 10 fixed points.

Figure 5 :

 5 Figure 5: Example of the error repartition on x and y.

Figure 6 :

 6 Figure 6: Representation of 10 fixed points with simulated error added to them and the effect of the error of the localisation of the unknown point.

  5) where r AOA,i is the angle of the ith fixed station as measured by the mobile station, x i , y i is the known position of the ith fixed station, and β = x u y u is the unknown position of the mobile station. By bringing this set of equations to a linear matrix form, we get H =    -sin(r AOA,1 ) cos(r AOA,1 ) . . . . . .-sin(r AOA,N ) cos(r AOA,N ) sin(r AOA,1 ) + y 1 cos(r AOA,1 ) . . .-x M sin(r AOA,N ) + y M cos(r AOA,N )

Figure 7 :

 7 Figure 7: AOA localisation accuracy as a function of the distance to the fixed stations and angle measurement error.

Table 1 :

 1 Statistics on all the unknown point estimation in distance error situation in meter.

	n wpt pts 4 5 6 10 20	x (meter) ∆ max mean(ε X Y u y (meter) 23.6 -0.1 39 2.4 24.6 0.1 43.9 24.32 -0.1 37.8 3.8 23.6 0.0 43.0 12.5 0.0 5.5 0.3 14.8 0.0 7.8 9.7 0.0 2.9 0.2 9.9 0.0 2.7 6.2 0.0 1.2 0.1 6.4 0.0 1.0	) ∆ mean(ε Yu ) 2.4 4.0 0.3 0.1 0.1

u ) ∆ mean(ε Xu ) max(σ 2 X u ) ∆ max mean(ε Y u ) max(σ 2

Table 2 :

 2 Statistics on all the unknown point estimation in fixed points error situation in meters. max mean(εX u ) ∆ mean(ε Xu ) max(σ 2 X u ) ∆ max mean(ε Y u ) ∆ mean(ε Yu ) max(σ 2

	n wpt pts 4 5 6 10 20 n wpt pts 4 5 6 10 20	linear least-squares solution ∆ max mean(ε X u ) ∆ mean(ε Xu ) max(σ 2 x (meter) X u ) ∆ max mean(ε Y u ) ∆ mean(ε Yu ) max(σ 2 y (meter) Y u 4•10 6 49.1 4341 15•10 9 4•10 6 -50.9 4473 16•10 9 128.3 0.0 1.7 223.6 134.6 0.0 1.9 269.1 19.7 0.0 0.3 9.6 18.4 0.0 0.5 10.5 19.9 0.0 0.4 10.0 20.0 0.0 0.5 12.6 12.7 0.0 0.4 5.0 12.3 0.0 0.3 5.6 non-linear least-squares solution x (meter) y (meter) ∆ Y u 338 -0.1 5.9 178 370 0.1 189 344.8 0.1 5.6 169.4 368.5 0.1 6.3 167.0 13.8 0.0 0.2 5.8 15.6 0.0 0.3 9.2 9.4 0.0 0.2 2.6 10.0 0.0 0.2 2.8 7.2 0.0 0.1 1.4 6.4 0.0 0.1 0.9	) )
	ciples described in

ACKNOWLEDGEMENTS

The Hungarian side of the research is supported by the AgroDat.hu project (project code: VKSZ 12-1-2013-0024), financed by the Government of Hungary. I thank ESEO for co-financing my research stay in Angers, France where part of the research was done. The French side of the research is financed by the region of "Pays de la Loire" (Vagabond project).


PALEOAESTHETICS AND THE PRACTICE OF PALEONTOLOGY. Derek D. Turner.

2019. Cambridge: Cambridge University Press. 83 pp. $18.00 (Softcover).

In this volume of the Cambridge Elements in the Philosophy of Biology, Derek Turner brings to light the aesthetics embedded in the practice of paleontology. Turner's claim runs along two directions. The first one uncovers the intermixing of epistemic and aesthetic values occurring in the study of fossils, and how the acquired knowledge about the deep past eventually transforms one's aesthetic appreciation of fossils and landscapes. It is to this deepening of experience that Turner refers when using the neologism 'paleoaesthetics'. The second one focuses on the role of aesthetic judgments in the interpretation of fossil data and the solving of problems. From the epistemic to the aesthetic and back again, this essay forces the reader to critique the too often assumed incompatibility between the two dimensions. Turner makes the decision to explicitly address his peers in the philosophy of science community from the very first line, but historians of paleontology and geology have much to gain from this contribution as well.

Due to the synthetic nature of this essay, Turner's ambition is kept to a strict formula: "My primary goal is to show that the paleosciences have an aesthetic dimension" (Turner 2019, p. 5). This approach facilitates readers' task of exploring their own line of questioning about how paleontology is done and what it does. In the first part of his demonstration, Turner mentions a trip he took to Dinosaur Provincial Park in Alberta, Canada, where he came across a bed of fossilized freshwater clam shells. Drawing from contributions in environmental studies, Turner explains how the experience of these fossils in situ, enhanced by the scientific knowledge of their origins, completely reconfigured his sense of place within the park. Paleontology not only has epistemic outcomes, but it also reshapes the perception of landscapes by focusing on their fossil details.

The idea that paleontology can carve new perspectives within landscapes opens a promising field of historical inquiry. The philosophical nature of Turner's reasoning leads him to discuss such issues as the distinction between beauty and aesthetics and the identification of science with disenchantment; nonetheless, the historian is called upon to answer questions about when and how paleontology came to influence the appreciation of landscapes. Just as Turner highlights the fact that the philosophy of paleontology has traditionally favored epistemological approaches, the history of the interpretation of fossils has primarily been concerned with theoretical frameworks. Such a realization is not meant to diminish the importance of work that has already been done, but it merely suggests that other points of view remain. The complex historical career of fossils as epistemological objects has been thoroughly addressed by scholars such as Martin Rudwick and David Sepkoski. The study of how the modern interpretation of fossils shapes our aesthetic appreciation of landscapes through an emphasis on their temporal nature can provide a valuable opportunity to revisit our current narrative of paleontology. To legitimize his own experience in Dinosaur Provincial Park, Turner alludes to the literary tendencies that paleontologists have deployed in their popular works to aesthetically engage with landscapes in reaction to the fossils they find. Just as with any other form of aesthetic engagement and appreciation, paleoaesthetics must have a history. Fossils, although observed and collected for centuries, were only recently recognized as constitutive parts of landscapes. Turner's newly coined term, 'paleoaesthetics', encourages a historical investigation into the interplay between scientific conceptions of fossils and the ways in which to experience the deep past. If one approaches classical texts in earth sciences by Georges Cuvier (1769-1832), Charles Lyell (1797-1875) or even Ferdinand Hayden (1829-1887) later in the nineteenth century while asking this question, the development of paleoaesthetic experiences might become more apparent. More than a superficial byproduct of paleontological research, this kind of relation to landscapes and their fossil content could be recognized as a major cultural transformation in attitudes toward the earth and its history. If one is to investigate the history of the interpretation of fossils, the history of their aesthetic appreciation should also be taken into consideration, and the pertinence of paleoaesthetics should be tested.

The second contribution that Turner's essay makes to the history of paleontology touches on the subject of visual arts and their relation to scientific knowledge-making. After having demonstrated the mutual reinforcement of epistemic and aesthetic dimensions within the practice of paleontology, Turner addresses the problem of aesthetic biases potentially at play in the interpretation of paleontological data. The traditional representation of dinosaurs fighting each other in paleoart pieces is chosen as a revealing case study of this issue. By pointing out the obvious aesthetic biases and artistic conventions that can influence images of the deep past, Turner wants to push the limits of his hypothesis. The question is not whether we should try to banish any sort of aesthetics from the practice of paleontology. Having demonstrated how aesthetic experiences are inextricably connected to the study of fossils, the problem is where the balance lies between the aesthetic and the epistemic when investigating the deep past. This question paves the way toward a history of paleoart, strictly defined as the artistic depiction of extinct species and environments in a scientific setting, which would go beyond the biographies of predominant artists, such as Benjamin Hawkins (1807-1894) and Charles Knight (1874Knight ( -1953)) This short essay does not give Turner the opportunity to expand on the implications of his concept of paleoaesthetics, but it does provide enough insight for the historian to begin the search for clues about the development of paleoaesthetic postures and experiences. The historical elucidation of our connection with the deep past is especially relevant today as we face the challenge of harmonizing geological, political, and economic timescales.

Victor Monnin University of Strasbourg

Augustin Cournot Doctoral School victor.monnin@gmail.com

  . Recently, the richly illustrated volume Paleoart: Visions of the Prehistoric Past (2017), edited by Zoë Lescaze (reviewed in 2018 by Warren D. Allmon in Earth Sciences History 37(1): 218-222), offers the first visual map to undertake such a critical journey. The question raised by Turner's essay could help revive the historical project first initiated by Martin Rudwick in Scenes from Deep Time (1992) and more recently picked up by Ralph O'Connor in The Earth on Show (2007). The historical overlap and interactions between artistic practices and epistemic methods applied to the interpretation of fossils remains quasi terra incognita.


Putting the history of palaeontology to work

In the last few years, the Earth sciences community has grown acutely aware of its lack of racial, gender and cultural diversity. As shown by the latest controversy over the repatriation from Germany of a Ubirajara jubatus specimen found in Brazil, palaeontology in particular finds itself at the centre of serious conversations regarding unethical practices and colonial legacies. A few examples of recent initiatives and publications illustrate the urgency of such issues shaped by the rich and complex history of palaeontology.

In 2017, filmmaker Lexi Jamieson Marsh and palaeontologist Ellen Currano launched a touring exhibition, The Bearded Lady Project, featuring black and white photographs of women palaeontologists wearing fake beards. This original initiative unravelled the stereotypes and gender biases that have long been defining the exclusive identity of palaeontologists and field scientists in general. In 2020, palaeontologists studying amber fossils from Myanmar were asked to stop acquiring new specimens in view of the humanitarian crisis happening in the Kachin region. This call raised the question of the extent of palaeontologists' ethical responsibilities regarding the wider ecosystem of their research. Finally, last year, a team of young scholars, led by Nussaïbah Raja and Emma Dunne, published the results of a scientometric study showing how the colonial past is still determining access to the fossil record and research opportunities.

None of these issues exists in a historical vacuum. Therefore, a better and more widely shared understanding of palaeontology's complex history could shed some much-needed light on some of the pressing challenges faced by the palaeontological community, especially by its younger and rising members.

The question is: how could the history of palaeontology be better integrated into the training of palaeontologists to foster an always more inclusive, ethical and sustainable research community? The goal of this communication is to encourage future collaborations between historians and palaeontologists for the benefit of all the stakeholders of palaeontological research.

In a recent note published in this same Newsletter (106), historian Chris Manias highlighted that "palaeontologists and connected branches of natural history have recently been engaging in highly reflective ways with the history of their fields, with an agenda towards decolonizing them". Indeed, a significant number of scientific actors have been acknowledging the complex heritage of their disciplines and the collections they work with. Recently, palaeobiologist Pedro Monarrez and colleagues published an article discussing the extractive nature of palaeontology and the various manifestations of racism and colonialism lingering in geosciences academia. Palaeoartists, such as Mark Witton, have also begun to address the often-problematic legacies of their predecessors. Such communications recognize the social and ethical benefits of investigating the history of palaeontology.

The problem is that the history of palaeontology is either not being systematically taught to palaeontology students or mostly being taught as a chronicle of 'discoveries' made by a selected few (and mostly Western men). Such a narrative provides a skewed vision of the historical development of palaeontology, ignoring not only the multiplicity and diversity of actors involved in scientific work, but also the situatedness of this work. Instead of providing the new generations of palaeontologists with the tools to think holistically about their science and understand its current ethical and policy challenges, such a vision of history prevents them from doing so. In other words, upcoming palaeontologists do not need to learn more about the history of their discipline, they need to engage with it with a sense of purpose.

Coincidentally, the palaeontological community can rely on the recent efforts of an active and growing contingent of historians of science, who are critically revising the history of palaeontology among other Earth sciences. Many historians are now giving particular attention to the entanglements of the reconstruction of deep time with colonialism, capitalism and extractive economies. Through these new analytical lenses, the past of palaeontology no longer appears as the epic story of 'fossil hunters' excavating exceptional specimens around the world, but as a series of histories involving a variety of scientific and non-scientific actors evolving in different social, economic and political contexts. These efforts represent a valuable resource for the palaeontological community to actively engage with the legacies crippling its efforts in diversification and ethical advancement. Finding ways to introduce the new historiography of palaeontology to students would help them navigate through the changing landscape of ethical standards, policies and laws that characterize the palaeontological field today. Through the discussion of the history of their discipline, they could imagine more sustainable and inclusive ways of studying the deep past. Just as students are being taught that the study of the fossil record can improve our understanding of present and future ecosystems, they should also be taught that the study of the historical record of their discipline can help them evaluate and improve their own practice and institutions.

Integrating this new historiography to palaeontology curricula raises obvious logistical and methodological questions, such as: who will teach this content to students? How much time can be reasonably allocated to discussing history? Where can palaeontologists and students follow recent developments in the historiography of palaeontology and Earth sciences? Which specific issues should the teaching of history be focusing on? Where could historians and palaeontologists regularly share their respective concerns and insights? These questions can only be answered through active discussions and collaborations between historians and palaeontologists. The sharing of resources, priorities and ideas is bound to prompt the emergence of specific, practical solutions, which could in time serve as templates for more ambitious educational reforms. The relationship between the history of science and science is a convoluted one. It had and will have its ups and downs. One thing remains for certain though -it is as critics of science that historians can provide their highest form of support to the scientific endeavour. While palaeontologists wrestle with complex issues regarding the future of their community, historians of palaeontology must also reflect on their own ethical responsibilities and how they can put their expertise to work.

Victor Monnin

Archives Henri-Poincaré, University of Strasbourg, France