Mathieu Baudin

Basile Vuichoud

Aurélien Bornet

Geoffrey Bodenhausen

Sami Jannin

A Cryogen-Consumption-Free System for Dynamic Nuclear Polarization at 9.4 T

Keywords:

A novel system for dissolution dynamic nuclear polarization based on a cost-effective "cryogen-free" magnet that can generate fields up to 9.4 T with a sample space that can reach temperatures below 1.4 K in a continuous and stable manner. Polarization levels up to P( 1 H) = 60 ± 5% can be reached with TEMPOL in about 20 min, and P( 13 C) = 50 ± 5% can be achieved using adiabatic cross polarization.

Dissolution dynamic nuclear polarization (D-DNP) has become increasingly popular in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI) because it can enhance the signals by several orders of magnitude [START_REF] Ardenkjaer-Larsen | Increase in signal-to-noise ratio of > 10,000 times in liquid-state NMR[END_REF]. D-DNP experiments consist of polarizing nuclear spins in samples doped with radicals or other paramagnetic polarizing agents (PAs), placed in a strong magnetic field (typically 3.35 < B0 < 6. [START_REF] Kiswandhi | Assembly and performance of a 6.4 T cryogen-free dynamic nuclear polarization system[END_REF] T in most laboratories) at typical temperatures 1.2 < T < 4.2 K. The electron spin polarization Pe is saturated (Pe ≈ 0) by microwave irradiation and the DNP effect causes a build-up of the polarization P(I) of protons and other nuclei I = 2 H, 6 Li, 13 C, 15 N, 31 P, etc. The sample is then rapidly dissolved and the nuclear signals are detected in liquid phase in an NMR spectrometer or MRI scanner. The higher the ratio B0/T, the higher the electron polarization Pe, and, concomitantly, the electron spin relaxation times T1e often become longer so that a weak microwave irradiation is sufficient to achieve saturation [START_REF] Lumata | Electron spin resonance studies of trityl OX063 at optimal concentration for DNP[END_REF]. The line-widths of the proton NMR spectra are determined by dipole-dipole couplings and often exceed 40 kHz regardless of B0 so that there is no need for expensive highresolution NMR magnets that can offer a homogeneity B0/B0 < 1 ppb (e.g. proton linewidths of 0.4 Hz out of 400 MHz at 9.4 T) but are not suitable to ramp the B0 field to arbitrary values. For DNP applications, socalled "cryogen-free" or "dry" superconducting magnets that are equipped with built-in helium liquefier and therefore do not require any liquid helium or nitrogen appear more attractive. Such magnets can be ramped to various fields B0 and their modest homogeneity B0/B0 < 10 ppm suffices for DNP. The samples can be cooled using a helium bath cryostat [START_REF] Comment | Design and performance of a DNP prepolarizer coupled to a rodent MRI scanner[END_REF], [START_REF] Wolber | Generating highly polarized nuclear spins in solution using dynamic nuclear polarization[END_REF] that typically consumes more than 10 liters of liquid helium per day of operation, which translates into significant running costs, and the need to refill liquid helium makes it difficult to run extensive series of experiments continuously over several days. Alternatively, a variable temperature insert (VTI) can be used, like in the "Hypersense" marketed by Oxford Instruments, which operates at B0 = 3.35 T and T < 1.2 K. The "SpinLab" polarizer designed by General Electric [START_REF] Ardenkjaer-Larsen | Dynamic nuclear polarization polarizer for sterile use intent[END_REF] is equipped with a cryo-cooler and a sorption pump and operates in "cryogen-free" mode at B0 = 5 T and T < 1.2 K. This sophisticated system (ca 2 M€) has been designed for sterile clinical use, which is not required for most preclinical MRI and spectroscopic applications. The apparatus described by Yoshihara, Can, Karlsson, Lerche, Schwitter, and Comment operates at B0 = 7 T [START_REF] Yoshihara | High-field dissolution dynamic nuclear polarization of [1-13C]pyruvic acid[END_REF]. The system designed by Kiswandhi, Niedbalski, Parish, Wang, and Lumata [START_REF] Kiswandhi | Assembly and performance of a 6.4 T cryogen-free dynamic nuclear polarization system[END_REF] utilizes a variable-field "cryogen-free" superconducting magnet that can be ramped up to B0 = 9 T but was only used at B0 = 6.7 T and is equipped with cryo-coolers that can cool the sample space and DNP assembly down to T = 1.8 K via the Joule-Thomson effect. The DNP system described in a lecture by Bowen, Rybalko, Petersen and Ardenkjaer-Larsen is also based on a dry magnet and can in principle be used at B0 = 3.35, 6.70, and 10.05 T [START_REF] Bowen | Multi-Field Cryogen Free Dissolution-DNP at 3[END_REF].

In this Communication, we describe a DNP polarizer based on a dry magnet that can operate up to B0 = 9.4 T, as first presented at ENC 2017 [START_REF] Baudin | 60% 1H Polarization with DNP < 2 min using a Cryofree 9.4 T d-DNP Polarizer[END_REF]. This value was chosen in order to explore the efficiency of DNP at higher fields than 7 T, where we hope to benefit from a higher thermal electronic polarization at higher temperatures (90.6% at 4.2 K and 9.4 T versus about 80% at 6.7 T). However, we are aware that some DNP mechanisms tend to lose efficiency at higher fields, which could go against the benefits obtained from electronic polarization, and this is why it can easily be energized at lower magnetic fields such as 3.35 and 6.7 T. A VTI that houses both the NMR probe and sample can provide stable temperatures down to T = 1.4 K in a continuous manner over several days. NMR signals can be excited and observed in alternation on two channels, and cross polarization (CP) can be performed to transfer polarization from 1 H to 2 H, 6 Li, 13 C, 15 N, 31 P, etc. [START_REF] Jannin | Lowtemperature cross polarization in view of enhancing dissolution Dynamic Nuclear Polarization in NMR[END_REF]- [START_REF] Batel | Dissolution dynamic nuclear polarization efficiency enhanced by Hartmann-Hahn cross polarization[END_REF]. Both the magnet and the VTI are cooled by means of a helium recycling loop, thus eliminating the need to fill liquid helium, and limiting running costs other than electric power. We present preliminary results obtained with this setup using the inexpensive polarizing agent TEMPOL at 9.4 T and 1.5 K, yielding a proton polarization of P( 1 H) = 60%, with a remarkably short build-up time constant DNP = 120 s, and a carbon-13 polarization of P( 13 C) = 50% in less than one hour (53 min) using 9 adiabatic cross-polarization contacts at intervals of 320 s. A new dissolution system derived from the flow-cell design [START_REF] Chen | Implementation and Characterization of Flow Injection in Dissolution Dynamic Nuclear Polarization NMR Spectroscopy[END_REF] is currently being developed and will be presented elsewhere.

Design of polarizer

Magnet and integrated VTI with helium recycling circuit

The dry magnet (Figure 1) (Cryogenic Ltd., reference J3997) can be ramped up to B0 = 9.4 T. All experiments described in this paper were performed at this field. The magnet is cooled down by an integrated cryocooler (Sumitomo RDK-415D cold head and F-50H compressor) within approximately 30 hours starting from room temperature.

Figure 1: "Cryogen-free" DNP system composed of (1) a helium storage tank (50 cm diameter, 100 cm height), (2) a magnet-VTI system (80 cm diameter, and 93 cm height) with its DNP probe, and (3) a dry pump. Arrows illustrate the helium circuits involved to cool down the magnet, the VTI and the probe.

Figure 2: Schematic of the three helium gas circuits used in the apparatus. (Green) Helium gas is used in a closed circuit between the cold head and the compressor to cool the magnet below 3 K. (Red) The VTI cooling-down circuit starts at the gas storage tank. The helium is liquefied in the helium pot after going through two traps to purify it. It enters into the VTI circuit through a needle valve and is recycled towards the storage tank using the dry pump. (Blue) A circuit connects the probe with two 27-L storage bags for helium gas that is cryo-pumped to cool the sample to 4.2 K or below.

Once it has reached its base temperature (T ≈ 2.5 K), and its magnetic field has been ramped up in approximately 1 hour, a 200 L storage tank containing helium gas at 20 to 30 kPa over atmospheric pressure is connected to the input port of the cryostat. Helium is then cryo-pumped through two active charcoal traps (one external, immersed in liquid nitrogen at 77 K, and one internal operating below 100 K) that prevent impurities from entering into the helium pot where helium is liquefied and stored at 4.2 K. In a few minutes, sufficient liquid helium is collected to fill the 0.5 L helium pot. It is then fed through a manually operated needle valve into the 43.5 mm diameter clear access VTI containing the DNP probe (Figure 3). The VTI is simultaneously pumped (110 m 3 /h) by a dry pump (Edwards iXL120) providing an estimated cooling power of about 0.32 J.s -1 at 1.4 K. The evaporated helium gas is sent back to the gas storage tank to be re-liquefied in the helium pot in a continuous cycle. This cycle is illustrated in Figure 2. A base sample temperature T = 1.49 K can be reached after a delay between 100 and 180 minutes (depending on the initial temperature, the needle valve setting, the temperature of the internal charcoal trap, etc.), with a stability of ± 0.003 K for the VTI and ± 0.007 K for the probe over several days of operation (see Figure 5).

DNP probe and sample cup

The DNP probe (Figure 3) is equipped for microwave irradiation with a 4.5 mm inner diameter waveguide and a home-built mitre bend. Two radio-frequency (rf) saddle coils can be tuned for 1 H and 13 C and adapted to other nuclei. The probe has an 18-mm diameter clear access that can accommodate a home-built sample stick and sample holder with ~650 µL active volume (Figure 4). It has an additional port to allow the user either to evacuate the probe with a turbo pump, or to connect it to two 27 L prefilled helium gas bags (Plastigas®, Linde). The probe is designed to be leak-tight for superfluid helium, so that the user can precisely control the amount of helium gas that is allowed into the inner volume that contains the sample. The copper sample space cavity is sealed from the VTI using bonding assembly silicone (CAF 1 from Bluestar Silicones France SAS). It has been successfully tested with an overpressure of 1 bar in liquid nitrogen prior to its use under DNP conditions. During operation, 54 L of helium gas is liquefied in the probe, leading to about 71 mL of superfluid helium in the sample space. Prior to sample exchange or dissolution, the liquid helium can be evaporated and transferred back into the helium gas bags simply by warming up the probe above 4.2 K with a built-in heater with a 100 Ω resistance. The temperature at the top of the probe is monitored by a Lake Shore CERNOX sensor (model: CX-1030-SD-HT-1.4L). A second ruthenium oxide resistance (Lake Shore RX-102A) is placed inside of the copper cavity next to the sample to monitor its temperature. The base temperature of the probe and sample T < 1.5 K remains stable over several days (Figure 5). Inserting a new sample typically takes at most 40 minutes if one evaporates and re-liquefies all of the ca. 70 mL of liquid helium in the probe (see Figure 6). The build-up of the proton polarization P eq ( 1 H) in thermal equilibrium at 4.2 K (i.e, in the absence of microwave irradiation) can be monitored while the helium is being condensed. In practice, most of the helium remains liquid and one can cool down immediately below 1.5 K in about 10 min by closing the probe's helium supply, if needed after a quick refill.

Microwave source

The microwave source provides ca. 75 mW at 263 ± 1 GHz, generated from a fundamental frequency of about 10.96 GHz (Virginia Diodes synthesizer VDIS-0068) by 4 multiplication steps ( 3 2 2 2, VDI AMC-559). The synthesizer can be programmed to modulate the microwave frequency in a saw-tooth pattern to enhance the efficiency of DNP by saturating a wide range of the EPR spectrum [START_REF] Bornet | Microwave frequency modulation to enhance Dissolution Dynamic Nuclear Polarization[END_REF]. Typical modulation ranges extend over 100 < fµw < 200 MHz, swept every 100 µs (fmod = 10 kHz). An attenuation port on the source enables microwave gating controlled by a 0-5 V signal generated by a Bruker Avance II NMR spectrometer to boost the performance of CP [START_REF] Bornet | Microwavegated dynamic nuclear polarization[END_REF].

NMR circuit and spectrometer

The NMR circuit (Figure 7) features two rf saddle coils with capacitors that are pre-tuned before the probe is cooled down for 1 H and 13 C at 400 and 100 MHz.Tuning and matching is refined after cool-down using external tuning and matching boxes containing two variable capacitors with a range of 8 to 30 pF. These boxes are linked via coaxial cables to two solenoid coils, one for each channel, which are then inductively coupled to the saddle coils of the resonator. This design can be adapted to work with other low- nuclei such as 2 H, 6 Li, 15 N, 31 P, etc. This allows one to polarize low- nuclei by adiabatic CP, which is much faster than direct DNP [START_REF] Jannin | Lowtemperature cross polarization in view of enhancing dissolution Dynamic Nuclear Polarization in NMR[END_REF]- [START_REF] Batel | Dissolution dynamic nuclear polarization efficiency enhanced by Hartmann-Hahn cross polarization[END_REF]. For 1 H, a 10 µs 90° pulse ( B1/(2π) = 25 kHz) was obtained with 60 W output power of the 400 MHz amplifier, and for 13 C, a 12 µs 90° pulse ( B1/(2π) = 20 kHz) with 150 W at 100 MHz.

Sample formulation

TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl) was used as polarizing agent. To optimize its concentration for 9.4 T DNP, TEMPOL was dissolved at concentrations between 25 and 100 mM in a mixture of glycerol-d8/D2O/H2O (v:v:v = 60:30:10). For 13 C polarization experiments with 1.5 M of 99% labelled sodium [1- 13 C] acetate, we used TEMPOL with a concentration of 80 mM.

Reference polarizations P( 1 H) eq and P( 13 C) eq

In order to determine the absolute polarization levels achieved by DNP in the presence of microwave irradiation, the enhanced signals must be compared with reference polarizations, P( 1 H) eq = 0.23% and P( 13 C) eq = 0.058% in thermal equilibrium at 9.4 T and 4.2 K without DNP (i.e., in the absence of microwave irradiation), which can be calculated from Boltzmann's law if the ratio B0/T is known. The 1 H and 13 C signal intensities in thermal equilibrium are weak, and tend to be contaminated by background signals that stem from the sample holder and from the probe (traces of frozen water and of organic materials such as glues, etc.) After measuring 1 H and 13 C signal intensities boosted by DNP, we not only measure 1 H and 13 C signal intensities of the same sample in the absence of microwave irradiation (green curves on Figure 8), but also of the sample holder after removing the sample, and of the probe after removing the sample holder (respectively, red and green curves in Figure 8, which are very similar, thus suggesting that most of the background 13 C signal comes from the probe). The integrated background signals are then subtracted from the integrated 1 H and 13 C signal intensities of the sample in the absence of microwave irradiation, and the difference signal thus obtained is used to estimate the solid-state polarization. Clearly, if the thermal background signal is underestimated, the thermal signal that stems from the actual sample will be overestimated, and the absolute polarization levels (and hence the advantage of DNP) will be underestimated. It may be feared that some of the polarization levels reported in the literature suffer from various artifacts, but the solid-state polarizations reported in this paper were carefully estimated using the aforementioned procedure. 8: To obtain the correct thermal equilibrium 13 C signal at 4.2 K in the absence of microwave irradiation, one must subtract from the raw signal stemming from the sample, sample holder and probe (black) the background signal from the empty sample cup and probe obtained after the DNP experiments (red or green.) The resulting difference (blue) stems only from the sample and reflects the Boltzmann law. This difference must be compared with the signal obtained with DNP and CP to determine the enhancement of the polarization. A similar behaviour is observed for protons and the same procedure is followed to assess their thermal equilibrium signal.

.

Results

Optimization of microwave parameters

The microwave irradiation was optimized to achieve a maximum polarization P( 1 H) for a sample containing 50 mM TEMPOL in a mixture of glycerol-d8/D2O/H2O (v:v:v = 60:30:10) by adjusting the following parameters:

i)

The central microwave frequency fµw;

ii) The range of the frequency modulation fµw, at a constant modulation frequency fmod = 10 kHz;

iii) The microwave power. The samples were frozen immediately after preparation to avoid "ripening" effects, which may occur depending on the delay between mixing of the sample and freezing, due to nanophase separations in glycerol/D2O mixtures. These effects, which can be either favorable or deleterious for the polarization [START_REF] Weber | Sample Ripening through Nanophase Separation Impacts the Performance of Dynamic Nuclear Polarization[END_REF], have not yet been studied at 9.4 T. In the microwave frequency profile (Figure 9), the positive lobe was found at 263.5 GHz, and the negative lobe around 263.75 GHz, with a surprisingly small separation of only 250 MHz. The separation between the two lobes depends on the concentration of TEMPOL. The range of the frequency modulation fµw seemed to have little effect between 100 and 200 MHz (Figure 10). Finally, even with the maximum available power, the microwave amplitude is not quite sufficient to achieve a complete saturation of the EPR transitions (Figure 11).

Optimization of TEMPOL concentration

The DNP enhancements were measured for TEMPOL concentrations ranging from 25 to 100 mM (Figure 12). In all cases, the same mixture of glycerol-d8/D2O/H2O (v:v:v = 60:30:10) was used. The optimal TEMPOL concentration is around 80 mM, which is higher than the optima found at 6.7 T (50 mM) and 3.35 T (30 mM). The best polarization level P( 1 H) = 60 % (± 5%) was achieved repeatedly with 80 mM TEMPOL. This is lower than P( 1 H) > 95% which was recently achieved for a water sample at 6.7 T with the so-called HYPSO-5 polarizing agent [START_REF] Cavaillès | Tailored Microstructured Hyperpolarizing Matrices for Optimal Magnetic Resonance Imaging[END_REF]. On the other hand, the DNP build-up time constant DNP( 1 H) = 120 s with 80 mM TEMPOL at 9.4 T is shorter than DNP( 1 H) = 185 s with 50 mM TEMPOL at 6.7 T [START_REF] Jannin | High field dynamic nuclear polarization at 6.7 T: Carbon-13 polarization above 70% within 20 min[END_REF]. We believe that this can be attributed to the insufficient or inhomogeneously distributed microwave power at 9.4 T and the higher temperature (1.4 K instead of 1.2 K.)

1 H to 13

C cross polarization (CP)

Finally, we compared the slow 'direct' build-up of P( 13 C) polarization at 1.4 K (i.e., in the absence of CP) with the accelerated 'indirect' build-up of P( 13 C) polarization promoted by repeated Hartmann-Hahn contacts between the thermal baths of the 1 H and 13 C spins. The sample contained 80 mM TEMPOL, which we had found to be optimal to polarize 1 H, in a mixture glycerol-d8/D2O/H2O (v:v:v = 60:30:10) with 1.5 M isotopically enriched [1-13 C] acetate. Like at B0 = 3.35 and 6.7 T, CP allows one to reach much higher levels of P( 13 C) polarization in a significantly shorter time. As shown in Figure 14, a polarization P( 13 C) = 50 ± 5% was reached in 53 min, after nine CP steps, performed every 5.3 min to allow for the polarization P( 1 H) to be replenished by DNP in the intervals. Satisfactory polarization levels above 40% can be reached in about 20 min. In comparison, the direct DNP build-up with TEMPOL merely reaches P( 13 C) = 18 ± 5% with a time constant DNP( 13 C) of about 1.5 h, although higher levels might be achieved with Trityl and other radicals. The optimum CP conditions were explored systematically (Figure 14): (i) by optimizing the intervals between the CP contacts, (ii) by optimizing the adiabatic sweeps, (iii) by optimizing the rf amplitudes on both channels, and (iv) by switching the microwaves off 0.5 s before CP to allow the electron polarization to return to its equilibrium level after saturation (which significantly extends the proton relaxation time T1 in the rotating frame, and hence makes CP more efficient) [START_REF] Bornet | Microwavegated dynamic nuclear polarization[END_REF]. Other sequences with double adiabatic inversions in place of the spin-lock were tested as well. They seem to reach the maximal polarization faster, and display the same level of performance as the microwave-gated CP sequence. Some typical results are shown in Figure 14, with intervals of 2.7 min and 5.3 min between the CP steps. The best polarization P( 13 C) = 50 ± 5% that could be achieved at 9.4 T is somewhat lower than the record 71% reached at 6.7 T, using a horizontal solenoidal rf coil that precludes dissolution [START_REF] Jannin | High field dynamic nuclear polarization at 6.7 T: Carbon-13 polarization above 70% within 20 min[END_REF]. Note that certain DNP mechanisms like thermal mixing might be less efficient at higher fields. However, for "routine" operation, a polarization P( 13 C) = 50% is commonly deemed to be sufficient for our applications at 6.7 T, and there is need to achieve a higher polarization at 9.4 T.

Dissolution experiments

By adapting a dissolution unit, originally designed for another polarizer, that can inject ca. 5 mL of superheated D2O at about 1 MPa and 180° C, the solution was transferred in a few seconds to our 400 MHz and 800 MHz spectrometers (respectively 9.4 and 18.8 T) through a magnetic tunnel [START_REF] Milani | A magnetic tunnel to shelter hyperpolarized fluids[END_REF], scavenging the radicals after dissolution [START_REF] Miéville | Scavenging Free Radicals To Preserve Enhancement and Extend Relaxation Times in NMR using Dynamic Nuclear Polarization[END_REF]. Various temperatures recorded by inner and outer sensors of the magnet, the cold head's second stage as well as the variable temperature insert (VTI) and probe are shown in Figure 15 before, during and after a dissolution. The sample contained 1.5 M sodium [1- 13 C] acetate and 80 mM TEMPOL in 200 uL. The enhancement for acetate was about 9800 compared to thermal equilibrium, corresponding to a polarization P( 13 C) = 8% at 400 MHz and P( 13 C) = 6.5% at 800 MHz in solution at room temperature. We are however wary of liquid-state polarization estimates which can strongly vary depending on the method used [START_REF] Vuichoud | Measuring absolute spin polarization in dissolution-DNP by Spin PolarimetrY Magnetic Resonance (SPY-MR)[END_REF]. These enhancements are similar to routine experiments in our laboratory using a polarizer at 6.7 T.

Conclusions

We have demonstrated the use of a simple "cryogen-free" 9.4 T polarizer below 1.5 K for dissolution-DNP using TEMPOL nitroxide radicals as polarizing agents. While the use of a "cryogen-free" polarizer seems to be a promising strategy for D-DNP, it remains to be seen after further optimization whether increasing the magnetic field from 6.7 T to 9.4 T brings significant improvements, for instance regarding the optimum radical concentration required to perform CP from 1 H to 13 C. Here, a polarization up to P( 1 H) = 60 ± 5% was obtained with a remarkably short build-up time constant DNP( 1 H) < 120 s. After cross-polarization at 1.5 K, a polarization P( 13 C) = 50% was reached in 53 min, while P( 13 C) > 40% can be obtained within 30 min. CP from 1 H to 13 C may be improved by the use of doubly-tuned rf coils. Another path to achieve higher polarizations might be the use of other free radicals, starting with Trityl for direct 13 C polarization, but also nitroxide derivatives other than TEMPOL with which we obtained all the results presented in this paper. Another option that we are investigating right now is also the CP sequence itself, with the implementation of double adiabatic half passage to replace the spin-lock. Preliminary dissolution experiments were performed, showing the robustness of the apparatus that can withstand the process.

Figure 3 :

 3 Figure 3: DNP probe with a height of 725 mm with ISO-KF 50 junction to the VTI flange at the top, and a copper sample space cavity with 42 mm outer diameter. The probe body is made of stainless steel and has a 24-mm diameter. Reproduced with permission of Cryogenic Ltd.

Figure 4 :

 4 Figure 4: (a) The sample cup (made of PEEK or Teflon) has an 8-mm outer diameter (14 mm for the upper part), and 45 mm total height. (b) The sample insert is made of stainless steel (15 mm diameter, 690 mm height.) The junction with the body of the probe is made with an ISO-KF 25 collar.

Figure 5 :

 5 Figure 5: Temperature of the probe monitored over 14 hours, while 75 mW microwave power is applied continuously. The temperature fluctuations are below 10 mK.

Figure 6 :

 6 Figure 6: Temperatures of the VTI (dashed line) and probe (solid line) monitored for 50 min at intervals of 16 s during sample exchange. Starting at 4.2 K, the VTI temperature reaches approximately 6 K and the probe 9.5 K when a new sample is inserted. The probe returns to 4.2 K in less than 1 min.

Figure 7 :

 7 Figure 7: (a) The rf circuit of each channel between the preamplifier and the cavity. The tuning and matching of the rf coil is refined remotely using variable capacitors (8 to 30 pF) placed in an external box. (b) The double saddle rf coils, which are inductively coupled to two solenoid coils, one for each channel. The copper pieces are glued to a Kel-F support. A hole allows for microwave irradiation.

Figure

  Figure8: To obtain the correct thermal equilibrium13 C signal at 4.2 K in the absence of microwave irradiation, one must subtract from the raw signal stemming from the sample, sample holder and probe (black) the background signal from the empty sample cup and probe obtained after the DNP experiments (red or green.) The resulting difference (blue) stems only from the sample and reflects the Boltzmann law. This difference must be compared with the signal obtained with DNP and CP to determine the enhancement of the polarization. A similar behaviour is observed for protons and the same procedure is followed to assess their thermal equilibrium signal.

Figure 9 :

 9 Figure 9: Typical DNP microwave profile: polarization P( 1 H) for a sample containing 50 mM TEMPOL as a function of the monochromatic microwave frequency (i.e., without frequency modulation, fµw = 0). The dashed line is represented to guide the eye.

Figure 10 :

 10 Figure 10: Effect of the modulation range fµw on the polarization P( 1 H) for a sample containing 50 mM TEMPOL when the central frequency is set on the positive peak at 263.5 GHz in the microwave profile of Figure 9. The dashed line is represented to guide the eye.

Figure 11 :

 11 Figure 11: The effect on the proton polarization P( 1 H) of the microwave power for a sample containing 50 mM TEMPOL at 1.5 K. The dashed line is represented to guide the eye.

Figure 12 :

 12 Figure 12: Proton polarizations P( 1 H) at 1.5 K (filled circles) and 4.2 K (open circles) as a function of the TEMPOL concentration.

Figure 13 :

 13 Figure 13: DNP build-up rate 1/τDNP of the proton polarization P( 1 H) as a function of the TEMPOL concentration in glycerol-d8/D2O/H2O (v:v:v = 60:30:10) at 4.2 K (open circles) and 1.5 K (filled circles).

Figure 14 :

 14 Figure 14: (Red) CP build up of P( 13 C) in a sample of 1.5 M sodium [1-13 C] acetate and 80 mM TEMPOL in 200 uL of a mixture of glycerol-d8/D2O/H2O (v:v:v = 60:30:10) frozen immediately after mixing, with CP contacts using adiabatic excitation and flip-back pulses of 175 µs duration on both channels bracketing a 10 ms spin-lock period, separated by 5.7 min intervals. (Blue) Same as red curve but with CP contacts separated by 2.7 min intervals. (Brown) Same as blue curve, but with two consecutive simultaneous adiabatic inversions of 11 ms duration on both channels without spin-lock period. (Green) Same as red curve, but with simultaneous adiabatic inversions. (Black) The beginning of the direct DNP build-up curve of P( 13 C) on the same sample. (Below) Complete direct DNP build-up curve of P( 13 C) plotted on a logarithmic time-scale. The dashed line indicates the equilibrium value reached by direct DNP after 16 h. All experiments were performed at 1.4 K.

Figure 15 :

 15 Figure 15: Time-evolution of several key temperature sensors of the apparatus before, during and after dissolution. The dissolution itself occurs around 150 s on the graph, after the main pump is switched off and the probe heated to 4.2 K while pressurized gaseous He avoids contamination. The temperature sensors of the magnet indicate a small rise of about 0.3 K, well below the superconducting transition. The dissolution is not performed in the He bath, since the sample is lifted a few centimetres above this bath prior to dissolution.

Acknowledgements

The authors would like to thank Thomas Kress and Dr Dennis Kurzbach for their help in developing the dissolution system. We acknowledge support of the European Research Council under the European Union's Horizon 2020 research and innovation program (ERC Grant Agreement nº714519/HP4all, and ERC Grant Agreement Number 339754/Dilute para-water), the EPFL, the ENS, the CNRS, the Swiss National Science Foundation, and Bruker Biospin.


Emeline Baudet

Christophe Cardinaud

Remi Boidin

Aurelie Girard

Jan Gutwirth

Petr Nemec

Virginie Nazabal
email: virginie.nazabal@univ-rennes1.fr

Rémi Boidin

Aurélie Girard

Petr Němec

X-ray photoelectron spectroscopy analysis of Ge-Sb-Se pulsed laser deposited thin films

come

I. Introduction

Chalcogenide glasses are amorphous materials based on S, Se or Te element in combination with a suitable element from 13 th (Ga, In), 14 th (Si, Ge) or 15 th (As, Sb) group of the periodical table. They form an important class of inorganic materials studied many years for their specific properties leading to many interesting applications. Amorphous chalcogenides present unusual characteristics such as a wide transparency in the infrared range (≈1-12 μm for sulfides, ≈1-16 μm for selenides and ≈2-20 μm for tellurides) [START_REF] Zhang | Glasses for seeing beyond visible[END_REF][START_REF] Vigreux-Bercovici | Waveguides based on Te2As3Se5 thick films for spatial interferometry[END_REF] , photosensitivity [START_REF] Meneghini | As2S3 photosensitivity by two-photon absorption: holographic gratings and self-written channel waveguides[END_REF][START_REF] Shimakawa | Photoinduced effects and metastability in amorphous semiconductors and insulators[END_REF][START_REF] Nemec | Photo-stability of pulsed laser deposited GexAsySe100x-y amorphous thin films[END_REF][START_REF] Olivier | Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films[END_REF] , high linear-and non-linear refractive index [START_REF] Olivier | Structure, nonlinear properties, and photosensitivity of (GeSe2)(100-x)(Sb2Se3)(x) glasses[END_REF][START_REF] Liu | Second-harmonic generation in Ge-As-S glasses by electron beam irradiation and analysis of the poling mechanism[END_REF][START_REF] Harbold | Highly nonlinear Ge-As-Se and Ge-As-S-Se glasses for all-optical switching[END_REF][START_REF] Lenz | Large Kerr effect in bulk Se-based chalcogenide glasses[END_REF][START_REF] Guignard | Chalcogenide glasses based on germanium disulfide for second harmonic generation[END_REF] and a suitable shaping ability (to fabricate fibers [START_REF] Caillaud | Highly birefringent chalcogenide optical fiber for polarization-maintaining in the 3-8.5 mu m mid-IR window[END_REF][START_REF] Caillaud | Photonic Bandgap Propagation in All-Solid Chalcogenide Microstructured Optical Fibers[END_REF] or thin films [START_REF] Pagani | Instantaneous microwave frequency measurement using four-wave mixing in a chalcogenide chip[END_REF][START_REF] Novak | Positron annihilation lifetime spectroscopy (PALS) studies of gamma irradiated As2Se3 films used in MIR integrated photonics[END_REF][START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 mu m of an integrated platform based on chalcogenide waveguides for sensing applications in the midinfrared[END_REF] ). Thereby various applications were developed using chalcogenide glasses: chemical and biochemical sensors [START_REF] Starecki | Mid-IR optical sensor for CO2 detection based on fluorescence absorbance of Dy3+:Ga5Ge20Sb10S65 fibers[END_REF][START_REF] Michel | Monitoring of pollutant in waste water by infrared spectroscopy using chalcogenide glass optical fibers[END_REF][START_REF] Keirsse | IR optical fiber sensor for biomedical applications[END_REF] , components for high speed

Accepted Article

. all-optical processing of telecommunications signals [START_REF] Eggleton | Chalcogenide photonics[END_REF][START_REF] Gai | Dispersion engineered Ge11.5As24Se64.5 nanowires with a nonlinear parameter of 136W(-1)m(-1) at 1550nm[END_REF] or phase change materials for rewritable data storage [START_REF] Shportko | Resonant bonding in crystalline phase-change materials[END_REF] .

Amorphous chalcogenides are commonly used as thin films, which can be fabricated from a solid material through different physical vapor deposition methods: RF magnetron sputtering [START_REF] Chen | Optical and structural properties of Ge-Sb-Se thin films fabricated by sputtering and thermal evaporation[END_REF][START_REF] Nazabal | Sputtering and Pulsed Laser Deposition for Near-and Mid-Infrared Applications: A Comparative Study of Ge25Sb10S65 and Ge25Sb10Se65 Amorphous Thin Films[END_REF][START_REF] Verger | RF sputtered amorphous chalcogenide thin films for surface enhanced infrared absorption spectroscopy[END_REF] , pulsed laser deposition (PLD) [START_REF] Olivier | Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films[END_REF][START_REF] Nazabal | Sputtering and Pulsed Laser Deposition for Near-and Mid-Infrared Applications: A Comparative Study of Ge25Sb10S65 and Ge25Sb10Se65 Amorphous Thin Films[END_REF][START_REF] Musgraves | Comparison of the optical, thermal and structural properties of Ge-Sb-S thin films deposited using thermal evaporation and pulsed laser deposition techniques[END_REF] , thermal evaporation [START_REF] Chen | Optical and structural properties of Ge-Sb-Se thin films fabricated by sputtering and thermal evaporation[END_REF][START_REF] Musgraves | Comparison of the optical, thermal and structural properties of Ge-Sb-S thin films deposited using thermal evaporation and pulsed laser deposition techniques[END_REF] or electron beam deposition [START_REF] Nazabal | Chalcogenide coatings of Ge15Sb20S65 and Te20As30Se50[END_REF] . Among mentioned methods, PLD seems to be promising for chalcogenide thin films fabrication due to its flexibility, easy control of the deposition process, possibility to fabricate multilayered structures and often stoichiometric material transfer from the target to the films [START_REF] Nemec | Photo-stability of pulsed laser deposited GexAsySe100x-y amorphous thin films[END_REF][START_REF] Olivier | Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films[END_REF] .

From a wide variety of chalcogenide glass-forming systems, Ge-Sb-Se one, especially in thin films form, already proved to offer a great potential for photonic devices such as chemical sensors [START_REF] Verger | RF sputtered amorphous chalcogenide thin films for surface enhanced infrared absorption spectroscopy[END_REF][START_REF] Charrier | Evanescent wave optical micro-sensor based on chalcogenide glass[END_REF][START_REF] Ganjoo | Planar chalcogenide glass waveguides for IR evanescent wave sensors[END_REF] because it does not contain arsenic, which is environmentally improper due to its high toxicity in elemental form [START_REF] Chen | Optical and structural properties of Ge-Sb-Se thin films fabricated by sputtering and thermal evaporation[END_REF] . This system has a large glass-forming region [START_REF] Haisty | ELECTRICAL CONDUCTIVITY AND FORMATION OF CHALCOGENIDE GLASSES IN GE-AS-SE AND GE-SB-SE MELTS[END_REF] which gives the possibility to adjust the chemical composition of the glasses according to required physical characteristics. The optical properties and structure of chalcogenide glasses within the pseudo-binary (GeSe 2 ) 100-x (Sb 2 Se 3 ) x (5 ≤ x ≤ 70) system have previously been characterized [START_REF] Olivier | Structure, nonlinear properties, and photosensitivity of (GeSe2)(100-x)(Sb2Se3)(x) glasses[END_REF][START_REF] Wei | Structural investigation on GexSb10Se90-x glasses using x-ray photoelectron spectra[END_REF] . Reported structural analyses of (GeSe 2 ) 100-x (Sb 2 Se rich glasses seem to contain slightly higher number of homopolar Sb-Sb, Ge-Ge and Se-Se bonds [START_REF] Olivier | Structure, nonlinear properties, and photosensitivity of (GeSe2)(100-x)(Sb2Se3)(x) glasses[END_REF] . When studying Raman spectra of corresponding thin films prepared by pulsed laser deposition in as-deposited state [START_REF] Olivier | Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films[END_REF] , a higher proportion of homopolar Sb-Sb and Ge-Ge bonds

Accepted Article

. has been evidenced in comparison with parent bulk glasses. Consequently, in this paper we aim at studying the bonding arrangement at the surface of (GeSe 2 ) 100-x (Sb 2 Se 3 ) x (0 ≤ x ≤ 60) as-deposited PLD thin films using X-ray photoelectron spectroscopy (XPS) to understand better PLD films' structural organization.

II. Experimental Procedure

Chalcogenide glasses with the (GeSe 2 ) 100-x (Sb 2 Se 3 ) x (0 ≤ x ≤ 60) nominal composition were prepared using the conventional melting and quenching method [START_REF] Olivier | Structure, nonlinear properties, and photosensitivity of (GeSe2)(100-x)(Sb2Se3)(x) glasses[END_REF] . Glasses were synthesized from high purity (5N) commercial elements. Selenium was pre-purified by a static distillation. Elements were weighted in appropriate amounts and introduced in silica ampoules. The ampoules were then evacuated and sealed. The elements were melted in a rocking furnace at 800 °C; ampoules with the melt were quenched in water and finally annealed at 20 °C below glass transition temperature (T g ). Chalcogenide glasses with a diameter of 25 mm and a thickness of 3 mm used as PLD targets were obtained after slicing and polishing the glass rods.

Thin films were obtained by PLD. In detail, Ge-Sb-Se targets were ablated with a KrF excimer laser emitting at 248 nm (Compex 102, Lambda Physik) using 300 ±3 mJ output pulse energy, pulses duration of 30 ns and 20 Hz repetition rate. Laser fluency was set at 2.6 J.cm -2 . Background pressure in the vacuum chamber before deposition was about 3-4.10 -4 Pa.

In order to obtain films with uniform thickness (±2%), off-axis PLD technique with rotating substrates and targets was used. Substrates were silicon wafers (10 × 15 mm) which were positioned parallel to the target surface at a distance of 5 cm. After the deposition, thin film samples around 0.7-1.2 µm were kept under vacuum (5.10 -5 mbars), thus limiting any further surface contamination or chemical degradation (such as oxidation) until XPS surface analysis was carried out. The glass targets used for PLD originate from the glass-forming domain. The

Accepted Article

. PLD process typically exhibits a cooling rate during the film growth much higher than conventional cooling for glass fabrication increasing the vitreous domain for the PLD films. However, to be sure about amorphous state of the films, XRD measurements for PLD films (in particular for GeSe 2 and Se7 targets) were recorded with a D8-Advance diffractometer (Bruker AXS, Germany) with Bragg-Brentano θ-θ geometry (40 kV, 40 mA) using CuKα radiation with secondary graphite monochromator. The XRD patterns were measured at room temperature from 5 to 65° (2θ) within 0.02° steps with a counting time of 5 s per step.

A Kratos Axis Ultra X-ray photoelectron spectrometer was employed to characterize the top surface of as-deposited Ge-Sb-Se thin films using monochromatic Al Kα X-rays (1486.6 eV, 15 kV -15 mA). Survey scans were recorded in the [+1250, -5 eV] binding energy (BE) range using the constant pass energy of 80 eV and energy steps of 0.5 eV. High resolution spectra were further acquired within Sb 3d -O 1s, Se 3d, Sb 4d -Ge 3d core levels, using pass energy of 20 eV and an energy step of 0.1 eV. The analysis was made at 0° take off angle with respect to the normal to the sample surface. Data analysis of the core levels (Ge 2p 3/2 , Sb 3d -O 1s, Se 3d, Sb 4d -Ge 3d) was carried out with standard CASA-XPS software [START_REF] Ai | Luminescence of In2S3 nanocrystallites embedded in sol-gel silica xerogel[END_REF] . Each 3d (Ge, Sb, Se) and 4d (Sb) core-level spectrum is constituted of 3d 5/2 , 3d 3/2 and 4d 5/2 , 4d 3/2 spin orbits doublets. The binding energy scale has been calibrated on the Se 3d 5/2 peak of chalcogenide thin film with the nominal composition Ge 28.1 Sb 6.3 Se 65.6 (x = 10) positioned at 53.75 eV. Afterwards, other samples have been calibrated by aligning the Sb 3d 5/2 peak onto those obtained for previous sample (i.e. 528.85 ± 0.08 eV). An "Offset Shirley" background was used for determining the spectral areas, in which the Linear to Shirley blend ratio was fixed to 1. Line shapes for curve ftting were determined thanks to the analysis of a freshly fractured bulk glass Ge 25 Sb 10 Se 65 , whose structure presents almost only Ge-(Se) 4 and Sb-(Se) 3 environments. For the Sb 4d and Ge 3d spectra an Lorentzian Finite (LF) profile was used, in which the asymmetry parameters were set to unity to achieve a Accepted Article . symmetric line shape; the tail damping and the width of the Gaussian were adjusted to the experimental spectrum, leading to LF (1,1,20,200) and LF(1,1,30,400) for the Sb 4d and Ge 3d components respectively. For the Se3d spectrum a Gaussian-Lorentzian (GL(30)) profile was used. Concerning the fitting parameters, BE were free, Full Width at Half Maximum (FWHM) were free but constraint to be identical for all components of the same element, finally spin-orbit parameters (intensity ratio and BE separation) are fixed to (0.667 -0.57 eV), (0.667 -1.25 eV) and (0.667 -0.87 eV) for the Ge3d, Sb4d and Se3d spectrum respectively.

The chemical composition of (GeSe 2 ) 100-x (Sb 2 Se 3 ) x glassy targets and PLD thin films was measured using a scanning electron microscope with an energy-dispersive X-ray analyzer (EDS, JSM 6400-OXFORD Link INCA). A ZAF (effects of atomic number (Z), absorption within the sample and detector (A), and X-ray-induced fluorescence within the sample (F)) correction was used for the quantitative microanalysis. A Ge 25 Sb 10 Se 65 commercial bulk glass was used to validate the quantification procedure for Ge-Sb-Se glass samples. Atomic percentage of each element (±0.5 and ±1 % for the targets and the films, respectively) was extracted exploiting LLL lines of Ge, Sb and Se element working at 20 kV for the targets and at 10 kV for the films.

III. Results and Discussion

In order to compare the local structural units present in as-deposited (GeSe 2 ) 100-x (Sb 2 Se 3 ) x PLD thin films, XPS was used to describe bonding arrangement at the surface of the layers. Moreover, surface chemical composition was also studied by XPS and the obtained results were compared to EDS data. Fig. 1 shows an example of typical XPS survey spectrum of asdeposited thin film (Ge 23.5 Sb 11.8 Se 64.7 , i.e. x=20). The well-defined peaks are visible for Ge, Sb and Se core level as well as Auger lines (Ge LMM, Sb MNN and Se LMM). No elements

Accepted Article

. other than the thin films' components and residual oxygen were observed in all the (GeSe 2 ) 100-x (Sb 2 Se 3 ) x thin films' XPS survey spectra.

Table I presents the chemical composition data of the as-deposited thin films from (GeSe 2 ) 100-x (Sb 2 Se 3 ) x system determined by EDS in comparison with parent glass targets.

Consequently, the chemical composition of PLD films was studied by XPS and compared to EDS values (Fig. 2). For all the Ge-Sb-Se compositions under study, the agreement between these two methods is fine and very similar general behavior is observed. Thereby, a deficiency in chalcogen content (lower than 4 at. %) and an excess of antimony were observed in comparison with glass targets real composition. The loss of selenium is probably caused by its high volatility compared to germanium and antimony. In the case of germanium, when its content is lower than ≈ 25 at. %, the agreement between the composition of the films and theoretical one is very good as shown in Fig. 2. For higher Ge content, small excess of this element in the films is observed.

The bonding characteristics of as-deposited (GeSe 2 ) 100-x (Sb 2 Se 3 ) x (x values varying from 0 to 60) thin films were studied by analyzing the core level XPS spectra taking into account earlier papers [START_REF] Verger | RF sputtered amorphous chalcogenide thin films for surface enhanced infrared absorption spectroscopy[END_REF][START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF][START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] . Fig. 3 (a,b,c) shows the Sb 4d and Ge 3d core level spectra for films with x=5, x=20 and x=60. The binding energy (BE, eV), the full width at half maximum (FWHM, eV) and the proportion of bonds (%) of the different components used for the fitting of core level spectra of as-deposited thin films are presented in Table II. As expected due to the chemical composition, the Sb core-level spectra area increases with the introduction of antimony (or increase of x value) and a corresponding decrease in the area of Ge core-level spectra is observed.

The Ge 3d core-level spectra presents a primary component at ≈ 30.30 eV (±0.05 eV).

Additional doublets have to be introduced to correctly fit the Ge 3d core-level spectra, one with lower BE value (from 29.57 to 30.04 eV) and one with higher BE value (from 31.40 to Accepted Article . 31.64 eV). The different BE of each structural units is determined by the neighboring atom electronegativity. Accordingly, the binding energy downshift will be larger when the difference of neighboring atom electronegativity is larger. From the electronegativities of Ge, Sb and Se (2.01, 2.05 and 2.55 respectively in view of Pauling scale), the chemical environments can be deduced. The primary component at ≈30. 30 environment. As in the case of Ge 3d core-level spectra, a third doublet is used to correctly fit the Sb 4d core-level spectra of as-deposited thin films and it is attributed to (Se y )-Sb-Ox (at 34.02 eV) [START_REF] Verger | RF sputtered amorphous chalcogenide thin films for surface enhanced infrared absorption spectroscopy[END_REF][START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] . However, (Se y )-Sb-Ox is clearly observed for only (GeSe 2 ) 70 (Sb 2 Se 3 ) 30 asdeposited thin film (Table II). The presence of M-M bonds (M = Ge, Sb) was also demonstrated for bulk Ge-Sb-Se glasses [START_REF] Olivier | Structure, nonlinear properties, and photosensitivity of (GeSe2)(100-x)(Sb2Se3)(x) glasses[END_REF][START_REF] Wei | Structural investigation on GexSb10Se90-x glasses using x-ray photoelectron spectra[END_REF][START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] and thin films [START_REF] Olivier | Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films[END_REF][START_REF] Chen | Optical and structural properties of Ge-Sb-Se thin films fabricated by sputtering and thermal evaporation[END_REF][START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] . Sati et al [START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] used an additional doublet to fit Sb 4d core level (at ≈ 32.20 ± 0.05 eV) which was attributed to a distorted Sb-based trigonal pyramid with substitution of two and more Se atoms by Ge or Sb atoms [START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] . Further, an additional doublet was used to fit the Ge 3d core level spectra at ≈ 29.90 ± 0.05 eV in Ge 28 Sb 12 Se 60 and Ge 32 Sb 8 Se 60 glasses; this doublet was assigned to (Ge,Sb) 2 -Ge-(Se) 2 bonding arrangement [START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] .

In contrast with this XPS analysis of Ge-rich Sb x Ge 40-x Se 60 glasses [START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] , the mentioned additional doublet associated to Sb and Ge entities with a substitution of two and more Se atoms by Ge or Sb atoms were not required for the description of Sb 4d -Ge 3d core level spectra in this work.

As results from XPS data analysis performed in this study, the proportion of Sb-(Se) 3 arrangements increases from 3.9 at.% (for x=5) to 28.4 at.% (for x=60) and the proportion of Ge-(Se) 4 arrangements decreases from 33.1 at.% (for x=0) to 7.9 at.% (for x=60) (Table 2). These values confirm that the amorphous network of as-deposited thin films slowly evolves from a [GeSe 4/2 ] tetrahedra dominated structure to a [SbSe 3/2 ] trigonal pyramidal one. Furthermore, the proportion of (Ge,Sb)-Sb-(Se) 2 bonds ranges from 6.5 to 21 % (from x=5 to 20) and then this proportion decreases to 7.5 % (x=60) (Table II). Similarly, the proportion of (Ge,Sb)-Ge-(Se) 3 bonds increases from 10.3 to 29.5 % from x=0 to 50 and then decreases to 16.6 % for x=60 (Table II). The lower value observed for x=30 film could be related to more important amount of (Se y )-Sb-O x (11.7 %) and (Se y )-Ge-O x (5.8 %) bonds at the surface of the films. Fig. 5 presents the M-M bonds proportions (at. %) i.e. Ge-Ge, Sb-Sb and Ge-Sb bonds observed in Ge3d and Sb4d core level spectra. Introduction of antimony in thin films' network leads to M-M bonds increase first due to (Ge,Sb)-Ge-(Se) 3 and then to (Ge,Sb)-Sb-

Accepted Article

.

(Se) 2 . The decrease of M-M bonds observed for x > 30 can be explained by the glass network character which evolves to a network dominated by [SbSe 3 ] pyramids (Table 2). Raman analysis of PLD as-deposited thin film is somewhat different [START_REF] Olivier | Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films[END_REF] . In fact, a decrease of Ge-Ge bonds (at ≈ 170 and ≈ 270 cm -1 ) is observed with the introduction of antimony in thin films network. Furthermore, proportion of Sb-Sb bonds (at ≈ 155 cm -1 ) seems to slightly increase with x values and Raman spectra are dominated by Sb-Se (≈ 190 cm -1 ) bonds for as-deposited thin films with x>50.

In the case of XPS analysis of selenium, two doublets (3d 5/2 and 3d 3/2 ) were used to fit correctly Se 3d core level spectra. Fig. 3 (d, e andf) illustrates fitting of Se 3d core level spectra for x=5, 20 and 60. The Se 3d core level spectra presents a main component located from 53.47 to 53.78 eV depending on composition which can be attributed to the (Ge,Sb)-Se-(Ge,Sb) entities (Table 2). The second doublet, located from 54.02 to 54.35 eV, is assigned to the Se-Se-(Ge,Sb) entities [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF][START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF][START_REF] Chen | Optical and structure properties of amorphous Ge-Sb-Se films for ultrafast all-optical signal processing[END_REF] 2). The content of (Ge,Sb)-Se-(Ge,Sb) (80.8 -89.9 %) and Se-Se-(Ge,Sb) (10.1 -19.2 %) bonds is almost independent of composition for all (GeSe 2 ) 100-x (Sb 2 Se 3 ) x thin films (Table 2). Due to the comparable electronegativities of Ge and Sb, the contributions from Ge and Sb are similar but not exactly the same. Indeed, Sati et al. [START_REF] Sati | Structure of SbxGe40-xSe60 glasses around 2.67 average coordination number[END_REF] reported higher FWHM values for the two doublets attributed to (Ge,Sb)-Se-(Ge,Sb) and Se-Se-(Ge,Sb) environments (0.8-0.9 eV) in comparison to doublets of binary Ge-Se chalcogenide glasses (0.6-0.7 eV). In the case of Ge-Sb-Se sputtered thin films, FWHM values of those doublets are also higher (0.9-1.0 eV) [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] . In the line with mentioned data, XPS bands of as-deposited PLD thin films present also higher FWHM values (0.8-1.0 eV, Table 2), similar to Ge-Sb-Se bulk glasses and sputtered thin films.

Accepted Article

. Our previous XPS analysis [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] performed with RF sputtered thin films with the nominal composition Ge 28.1 Sb 6.3 Se 65.6 (x=10) presents comparable proportion of M-M bonds as follows. Considering the closest chemical composition of as-deposited PLD thin films (i.e. comparison with the films sputtered at Ar pressure of 1.10 -2 mbar), the proportion of (Ge,Sb)-Ge-(Se) 3 entities is about 14.1% (Table 2) and 12% for as-deposited PLD and sputtered thin films, respectively. In the same way, the proportion of (Ge,Sb)-Sb-(Se) 2 entities is about 11.5% (Table 2) and 9% for PLD and sputtered thin films, respectively. As mentioned above, local structure analysis of (GeSe 2 ) 100-x (Sb 2 Se 3 ) x bulk glasses [START_REF] Olivier | Structure, nonlinear properties, and photosensitivity of (GeSe2)(100-x)(Sb2Se3)(x) glasses[END_REF] , PLD [START_REF] Olivier | Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films[END_REF] and sputtered thin films [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] (for x=10 and x=50) using Raman spectroscopy has been previously reported. The presence of homopolar Ge-Ge bonds in Ge 2 Se 6/2 and Ge-Ge m Se 4-m (m = 1,2,3,4) species and Sb-Sb(Ge) bonds of Se 2 Sb-Sb(Ge)Se 2(3) structural units in PLD films was confirmed by Raman spectroscopy.

On the other hand, M-M bonds proportion seems to be to some extent overestimated by XPS analysis for as-deposited PLD thin films with the nominal composition Ge 12.5 Sb 25 Se 62.5 (x=50). In fact, the proportion of (Ge,Sb)-Ge-(Se) 3 entities is about 29.5% (Table II) and 7% for as-deposited PLD and sputtered thin films, respectively. Further, the proportion of (Ge,Sb)-Sb-(Se) 2 entities is about 15.0% (Table II) and 0% for PLD and sputtered thin films, respectively. This is consistent with Raman analysis of sputtered thin films [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] which demonstrates that for higher Ar pressure, the M-M bonds are almost not observed. If we consider the Raman spectroscopy data for sputtered film deposited with Ar pressure lower than 1.10 -2 mbar, the spectrum of PLD film (x=50) looks like Raman spectra of such sputtered films. The PLD film Raman spectrum shape is between those of two sputtered films (7.5.10 -3 and 5.10 -3 mbar). From XPS analysis, the proportion of (Ge,Sb)-Ge-(Se) 3 entities for these two sputtered films is 19% and 47%, respectively. The semiquantitative analysis of Raman spectra of PLD film (x=50) compared to sputtered films let

Accepted Article

. expect proportion of (Ge,Sb)-Ge-(Se) 3 entities around 22-25%. Thus, the general agreement between Raman and XPS analysis is good keeping in mind that only first ten nanometers are probed by XPS. Although, it seems that there is a slight overestimation of (Ge,Sb)-Ge-(Se) 3 entities by the XPS analysis of PLD film (x=50).

The BE values found for PLD layers are in good agreement with sputtered thin films' XPS analysis: Ge-(Se) 4 and Sb-(Se) 3 entities are located at 30.29 and 32.71 eV and 30.37 and 32.73 eV for as-deposited PLD and sputtered thin films with the nominal composition Ge 28.1 Sb 6.3 Se 65.6 (x=10). For Sb-rich thin films, mentioned two main entities are located at 30.32 and 32.78 eV and 30.34 and 32.71 eV for as-deposited PLD and sputtered thin films, again in very good agreement.

Likewise, Se-Se homonuclear bonds were also revealed in Raman and XPS analysis of RF sputtered thin films with the nominal chemical composition Ge 28.1 Sb 6.3 Se 65.6 (x=10) and Ge 12.5 Sb 25 Se 62.5 (x=50) [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] . The comparison of PLD and sputtered layers with x=10 gives the proportion of Se-Se-(Ge,Sb) entities about 13.6% (Table 2) and 14% for as-deposited PLD and sputtered thin films (at 1.10 -2 mbar Ar) [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] , respectively. In layers with x=50, the content of Se-Se-(Ge,Sb) entities is about 16.2% (Table 2) and 22% for as-deposited PLD and sputtered (at 1.10 -2 mbar) thin films, respectively. Binding energies revealed for PLD thin films are also in agreement with those observed for RF sputtered thin films. For x=10 films, Se-Se-(Ge,Sb) entities are located at 54.30 eV (Table 2) and 54.32 eV for as-deposited PLD and sputtered (1.10 -2 mbar Ar pressure) layers, respectively [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] . For Sb-rich thin films (x=50), these entities are situated at 54.06 eV (Table 2) and 54.10 eV for PLD and sputtered (1.10 -2 mbar Ar pressure) layers, respectively [START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] . Raman data analysis of RF sputtered thin films also revealed the presence of Se-Se bonds, especially for higher Ar pressure, with the amplitude increase of the band located at ≈265 cm -1 33 . These results also agree with previous XPS data obtained for RF sputtered thin film with the nominal composition Ge 25 Sb 10 Se 65 ; the

Accepted Article

. proportion of Se-Se-(Ge,Sb) is about 13% (for 5.10 -3 mbar) and 29% (for 5.10 -2 mbar) [START_REF] Verger | RF sputtered amorphous chalcogenide thin films for surface enhanced infrared absorption spectroscopy[END_REF] . The proportion of Se-Se homonuclear bonds is surprisingly high in these both compositions (x=10 and x=50) close to stoichiometric composition or with deficit in chalcogen element as shown in Table I with relatively low content of M-M bonds. As it was already mentioned in previous work [START_REF] Verger | RF sputtered amorphous chalcogenide thin films for surface enhanced infrared absorption spectroscopy[END_REF][START_REF] Baudet | Structural analysis of RF sputtered Ge-Sb-Se thin films by Raman and X-ray photoelectron spectroscopies[END_REF] , another contribution to this second Se 3d core level component spectrum might be considered: Se involved in bonds between two [GeSe 4/2 ] tetrahedra connected by edges could also contribute to Se-Se-(Ge,Sb) component.

It is worthy to mention that other techniques were already used for the structural analysis of Ge-Sb-Se glasses, for example neutron diffraction, X-ray diffraction or extended X-ray fine structure analysis. Pethes et al. [START_REF] Pethes | Chemical Short-Range Order in Selenide and Telluride Glasses[END_REF] used the reverse Monte-Carlo simulation technique [START_REF] Mcgreevy | REVERSE MONTE CARLO SIMULATION: A NEW TECHNIQUE FOR THE DETERMINATION OF DISORDERED STRUCTURES[END_REF] to investigate Ge 20 Sb 5 Se 75 , Ge 20 Sb 15 Se 65 and Ge 20 Sb 20 Se 60 glasses. All three glass compositions show a structure mostly described by the chemically ordered network model in which Ge-Se and Sb-Se bonds are preferred. For calculations using the reverse Monte Carlo method, homopolar Se-Se bonds in Se-poor glass and M-M bonds in Se-rich glass are not needed which is distinctive to the analysis performed by XPS spectroscopy for physical vapor deposited Ge-Sb-Se films. However, the rapid quenching during the synthesis of the thin films is likely to generate more defects than parent glasses and deviate from a perfect chemically ordered network model.

IV. Conclusion

In this paper, amorphous chalcogenide thin films with the nominal composition (GeSe 2 ) 100- Table I. Theoretical and real chemical composition (at. %) determined by EDS for chalcogenide glass targets (GeSe 2 ) 100-x (Sb 2 Se 3 ) x (±0.5 %) and corresponding thin films prepared by pulsed laser deposition (±1 %).

  3 ) x glasses based on Raman scattering spectroscopy reveal a progressive change in the glassy network structure with the introduction of Sb 2 Se 3 into GeSe 2 amorphous matrix. In order to allow the insertion of [SbSe 3/2 ] entities, it is first favoring edge-shared [GeSe 4/2 ] entities to the detriment of [GeSe 4/2 ] tetrahedra linked by the corners. At intermediate Sb 2 Se 3 content, glassy network contains significant number of [SbSe 3/2 ] trigonal pyramids. Finally, Sb 2 Se 3

  eV is assigned to the regular Ge-(Se) 4 environment corresponding to [GeSe 4/2 ] tetrahedra. The doublet observed at lower BE (from 29.57 to 30.04 eV) should be attributed to the (Ge,Sb)-Ge-(Se) 3 environment i.e. to a distorted tetrahedra where one Se atom is substituted with Ge or Sb atom (because of their very similar electronegativities) forming M-M bonds. Finally, the doublet at higher BE value (from 31.40 to 31.64 eV) is attributed to the oxide (Se y )-Ge-O x because of the high electronegativity of O (3.44) 25 . In analogy, three doublets are used to describe the Sb 4d core-level spectra. The primary component is located from 32.66 to 32.78 eV and is attributed to the regular Sb-(Se) 3 arrangement of [SbSe 3/2 ] trigonal pyramid. M-M bonds are also observed with the second doublet located at lower BE (from 32.23 to 32.65 eV) and attributed to (Ge,Sb)-Sb-(Se) 2

Fig. 4a shows

  Fig.4ashows normalized core level band of Sb 4d -Ge 3d for (GeSe 2 ) 100-x (Sb 2 Se 3 ) x

  . A very slight shift towards lower energies was observed for PLD films with the introduction of antimony as shown in Fig. 4b. Therefore Se-Se-(Ge,Sb) and Se-(Ge,Sb) 2 arrangements are shifted from 54.35 to 54.02 eV (from x=0 to x=40) and from 53.75 to 53.47 eV (from x=5 to x=40) (Table

x (Sb 2

 2 Se 3 ) x (x = 0, 5, 10, 20, 30, 40, 50 and 60) were deposited by PLD with chemical composition relatively close to the targets' composition. Nevertheless, EDX and XPS analysis, performed on glass targets and as-deposited thin films, reveals a small deficit in Accepted Article . chalcogen element (Se) and an excess of Sb in the PLD films. The as-deposited thin films were characterized by X-rays photoelectron spectroscopy in order to describe bonding arrangement at the surface films. XPS investigations confirm the presence of the two main regular units Ge-(Se) 4 and Sb-(Se) 3 . The Sb core level spectra amplitude increases logically with introduction of antimony so the amorphous network of as-deposited thin films slowly evolves from a [GeSe 4/2 ] tetrahedra dominated structure to a [SbSe 3/2 ] pyramidal one. The (Ge,Sb)-Ge-(Se) 3 and (Ge,Sb)-Sb-(Se) 2 environments, corresponding to distorted tetrahedra or trigonal pyramid where one chalcogen element is substituted with Ge or Sb atom(s) forming M-M bonds, were also observed. The proportion of M-M bonds increases with the introduction of antimony (from x=0 to x=40) first due to (Ge,Sb)-Ge-(Se) 3 and then thanks to (Ge,Sb)-Sb-(Se) 2 entities' appearance. The study of Se 3d core level spectra reveals the presence of two entities: (Ge,Sb)-Se-(Ge,Sb) and Se-Se-(Ge,Sb). XPS analysis of asdeposited thin films seems to overestimate Se-Se homonuclear bonds, thus this component could contain also Se involved in two [GeSe 4/2 ] tetrahedra connected by edges.

Figure captions Fig 1 .

 captions1 Figure captions

Fig. 2 .

 2 Fig. 2. Comparison of chemical composition of (GeSe 2 ) 100-x (Sb 2 Se 3 ) x PLD films determined

Fig. 3 .

 3 Fig. 3. XPS spectra of as-deposited (GeSe 2 ) 100-x (Sb 2 Se 3 ) x PLD thin films. Data fitting of Ge

Fig. 4 .

 4 Fig. 4. Normalized core level band of Ge 3d -Sb 4d (a) and Se 3d (b) of (GeSe 2 ) 100-

Fig. 5 .

 5 Fig. 5. M-M bonds (M = Ge, Sb) proportions (at. %, ±1 %) in Ge 3d and Sb 4d core level

Table II .

 II Binding energy (BE, eV, ±0.05eV), full width at half maximum (FWHM, eV, ±0.05eV), proportion of bonds (% bonds , ±1%) and atomic ratio (% at , ±1%) of the different components used for the fitting of Se 3d 5/2 , Ge 3d 5/2 , Sb 4d 5/2 and Sb 3d 5/2 core level spectra of as-deposited (GeSe 2 ) 100-x (Sb 2 Se 3 ) x thin films prepared by pulsed laser deposition.

	ccepted Article .	x=0 x=5 x=10 x=20 x=30 x=40 x=50 x=60	Theoretical composition %Ge %Sb %Se %Ge Target composition %Sb %Se 33.3 -66.7 36.5 -63.5 39 Thin film composition %Ge %Sb %Se -61 30.6 3.2 66.1 31.0 3.4 65.6 33 4 63 28.1 6.3 65.6 28.3 6.8 64.9 30 8 62 23.5 11.8 64.7 23.1 13.0 63.9 24 15 61 19.4 16.7 63.9 19.5 17.8 62.7 19 21 60 15.8 21.1 63.2 14.9 22.3 62.8 15 26 59 12.5 25.0 62.5 12.1 25.4 62.5 13 27 61 9.5 28.6 61.9 10.4 29.1 60.5 9 29 62

Acknowledgments

This work was financially supported by the Czech Science Foundation (Project No. 16-17921S). This work was also supported by the grants LM2015082, CZ.1.05/4.1.00/11.0251 and Barrande 7AMB17FR058 project from the Czech Ministry of Education, Youth and Sports of the Czech Republic and PHC-Barrande (2017-2018) from French Ministery of Education and Research.

Accepted Article


Guido Ciraolo
email: guido.ciraolo@l3m.univ-mrs.fr

Philippe Ghendrih

Yanick Sarazin

Cristel Chandre

Ricardo Lima

Michel Vittot

Marco Pettini

Control of test particle transport in a turbulent electrostatic model of the Scrape Off Layer

Keywords: turbulence, control, passive tracers, nonlinear dynamics PACS: 05.45.Gg, 52.25.Fi, 52.25.Xz, 52.35.Ra, 47.27.Rc

Introduction

Cross-field turbulent transport in the Scrape-Off-Layer (SOL) has a strong influence on divertor ef-ficiency and thus on the overall performance of discharges. Recent experiments as well as numerical investigations suggest a non diffusive transport in the SOL. The transport seems to be characterized by large intermittent events which propagate ballistically with large velocities. On the one hand SOL turbulence can cross H-mode barrier and connect SOL and core turbulence, destabilizing the pedestal stable region. On the other hand, when large intermittent events propagate in the far SOL, they can modify the recycling pattern and consequently the wall particle content and thus the wall tritium inventory. Furthermore, such a convection of hot ion over-densities can lead to localised heat deposition on components that are not designed to sustain meaningful plasma energy deposition. A strategy to control intermittent transport can therefore prove to be highly valuable to achieve high performance operation.

Several experiments [1,2] have been dedicated to the control of turbulence in magnetized plasmas. Although a modelling of some of the experiments has been achieved, there was to date no theoretical backing for such a procedure. Our aim is to develop such a theoretical background and proceed by steps towards a realistic turbulence control scheme. In the present paper, we apply the control strategy derived for Hamiltonian systems to the transport of test particles in an electrostatic potential which exhibits key features of the turbulent electrostatic potential generated by the Tokam code. This is a 2D non-linear fluid code based on interchange instability [3,4].

The investigation of passive tracer dynamics has demonstrated to be a powerful tool for a deeper understanding of fluid and plasma turbulence, even if, in the case of plasmas, one has to be cautious about the limits of its applicability due to the backreaction of turbulence on electro-magnetic fields. [5,6,7,8].

Our strategy is to define a small apt modification of the system which enhances confinement, at low additional cost of energy [9,10,11]. In the present case it consists in reducing the chaotic diffusion of charged test particles advected by the E × B drift motion. This effect is obtained by adding a small control term to the turbulent electric potential and comparing the chaotic diffusion of the test particles advected by the original electric potential and by the modified one.

In the case of turbulence with intermittent bursts of transport, one has to specify the control strategy: Either one aims at controlling turbulence in between the bursts of transport with a fluctuation level of the order of 2 %, or one aims at controlling the intermittent events with fluctuation levels larger than 10 %. The former is comparable to the case of homogeneous turbulence and is readily achieved while the latter is more challenging and is presently investigated.

The paper is organized as follows: In Section 2 the 2D model for SOL turbulence is recalled as well as its nonlinear transport properties. In Section 3 the procedure for the computation of the control term is described and the results of its application to the E × B drift motion of charged test particles are presented.

Interchange turbulence in the Scrape Off Layer

SOL turbulence is specific with respect to core turbulence due to the sheath boundary conditions that strongly reduce the parallel current flowing on each flux tube. Regimes with reduced parallel current are then very sensitive to charge separation via the curvature drift since the parallel current is less effective to balance the charge separation. In fact, the interchange instability, hence curvature charge separation combined to a density gradient, in conjunction with the sheath resistivity have been proposed to explain the very large fluctuation levels reported in the SOL [12,13]. We consider here this model of SOL turbulence in the limit T i ≪ T e . In this model two balance equations are used, the particle balance that governs the density transport, and the charge balance which takes the form of an evolution equation for the vorticity ∆φ, where φ is the electric potential, due to the ion inertia terms. Further simplifications are introduced in the flute limit, hence with weak parallel gradients such that the average along the field lines can be performed. The system is thus reduced to a two dimensional and two field model, n the density and φ the plasma potential normalised to T e /e. ∂ ∂t

-D∇ 2 ⊥ + {φ} n = σ n n + S n ∂ ∂t -ν∇ 2 ⊥ + {φ} ∇ 2 ⊥ φ + g∂ y n = σ φ n (1)
In these equations time is normalised to the ion Larmor frequency Ω i and space is normalised to the so-called hybrid Larmor radius ρ s . D and ν stand for the collisional transverse diffusion and viscosity (normalised to the Bohm values), S is the density source term, here localised radially and constant in time and along the poloidal angle θ. σ n and σ φ are the sheath controlled particle flux and current to the wall, σ n = σ exp (Λ -φ) and σ φ =σ 1exp (Λ -φ) where σ = ρ s /qR stands for the normalised saturation current. The operator {φ}F = {φ, F } = ∂ x φ∂ y F -∂ y φ∂ x F is the electric drift convection term. At first order in the fluctuation magnitude, sheath loss terms can be linearised to yield the Hasegawa-Wakatani coupling term σ (n -φ) [14]. The interested reader can refer to Refs. [3,4] for more details on Eqs. (1), the assumptions of this model and its transport properties.

Large systems with 512ρ s in both the radial and poloidal directions are simulated for about 200 SOL confinement times (typically 1500 turbulence correlation times). A localised particle source, with Gaussian shape in the radial direction and width 8.5ρ s and no dependence in poloidal angle or time, splits the box in two regions, an unstable region where the average density gradient is negative and exceeds the threshold of the interchange turbulence, and a stable region with positive gradient of the average density and where the system is stable with respect to the interchange mechanism. A contour plot of the electric potential at a given time is shown in Fig. 1. Typical power spectra of the potential in the x and y direction are shown in Fig. 2.

In the following Section we study the effect of the control term on E × B drift motion of charged test particles.

Turbulent potential and test particle dynamics

In the guiding center approximation, the equations of motion of a charged test particle in presence of a strong toroidal magnetic field and of a time dependent electric field are [15]

ẋ = d dt x y = c B 2 E(x, t) × B = c B -∂ y φ(x, y, t) ∂ x φ(x, y, t) , ( 2
)
where φ is the electric potential, E = -∇φ, and B = Be z . We study the 2D dynamics of test particles obeying to Eq. ( 2), where the considered turbulent potential is generated by Eqs. (1). We consider a reduced selected spatial region and we impose periodic boundary conditions in x, y directions. More precisely we choose a square box of 256ρ s × 256ρ s , not too close to the source region (in Fig. 1 the selected square box is between x ∈ [100, 356] in the radial direction and y ∈ [1,256] in the poloidal direction). This allows one to avoid the complex analysis of diffusive transport in finite systems, namely where the sources and sinks play an important role.

With such an infinite system, one can use a straightforward calculation of diffusion coefficients to characterize the turbulent transport. Since we are interested in long time behaviour of test particle dynamics, we impose periodic boundary conditions also in time. Periodicity in time provides a means to generate appropriate statistics with long time series. The underlying assumption is that all meaningful time scales of the system are shorter than the chosen period. A snapshot of the turbulent potential in the selected spatial region after the filtering procedure for imposing periodic boundary conditions is shown in Fig. 3. In what follows we denote V (x, y, t) the filtered potential. Therefore the potential V (x, y, t) is L x = 256ρ s periodic in the x-direction, L y = 256ρ s periodic in the y-direction and T = 256 50 Ω -1 i periodic in time.

In order to have a 1-periodic dependence in (x, y, t) for simplicity, we perform the change of variables

x = x L x , ỹ = y L y , t = t T . (3)
It follows that Fig. 3. Snapshot of the electric potential V (x, y, t) for t = 100 over the spatial grid of 256ρs × 256ρs obtained from the original potential φ represented in Fig. 1 after the filtering in space and time.

dx d t = T L x dx dt = - T L x ∂V ∂y . ( 4
From

∂V ∂y = ∂V ∂ ỹ dỹ dy , (5)
we get

dx d t = - T L x L y ∂ Ṽ (x, ỹ, t) ∂ ỹ . (6)
Thus the equations in the (x, ỹ, t) variables are equivalent to the equations in the (x, y, t) variables if the potential is multiplied by a factor T LxLy . The test particle dynamics governed by Eq. ( 2) is studied with the aid of numerical simulations. Since the potential is given over a spatio-temporal grid, the estimation of the electric field which acts on the particle trajectories is computed using a four point bivariate interpolation in space and a linear interpolation in time [START_REF] Abramowitz | Handbook of Mathematical functions[END_REF]. The time integration is performed using a fourth order Runge-Kutta scheme.

We consider a set of M particles (M of order 1000) uniformly distributed at random at t = 0 and we study the diffusion properties of the system. We verified that for the values of the parameters in the range of interest the mean square displacement r 2 (t) is a linear function of time and we computed the corresponding diffusion coefficient

D ⋆ = lim t→∞ r 2 (t) t ,
as a function of the amplitude of the turbulent potential. In Fig. 4 the results obtained for small values of the electric potential are shown. The first step in the computation of the appropriate modification of the potential which entails a re- duction of chaotic diffusion is the Fourier expansion of the electric potential, i.e.

V (x, y, t) = k1,k2,k3

V k1k2k3 e 2πi(k1x+k2y+k3t) .

Then we compute ΓV , that is the time-integral of V ,

ΓV = k1,k2,k3 =0 V k1k2k3 2πik 3 e 2πi(k1x+k2y+k3t) , (8)
and the constant part of V with respect to time that is written RV :

RV = k1,k2
V k1k20 e 2πi(k1x+k2y) .

The control term f 2 is given by the Poisson bracket between ΓV and (R + 1)V ,

f 2 = - 1 2 {ΓV, (R + 1)V } = - 1 2 ∂ΓV ∂x ∂(R + 1)V ∂y - ∂ΓV ∂y ∂(R + 1)V ∂x . (10)
A contour plot of f 2 at a fixed time is depicted in Fig. 5. Finally we study the test particle dynamics in the modified potential V + f 2 . The comparison between the diffusion coefficient obtained with and without the control term is shown in Fig. 4. One readily observes two main features, on the one hand the control term exhibits higher frequencies than the turbulent electrostatic field, typically a factor 2 larger has expected from the quadratic form of the control term, Eq.( 10), on the other hand the magnitude of the control term is more than a factor 10 smaller. This reduction compensates for the increase of the electric field via the increased frequencies. A significant reduction of D ⋆ is observed in the controlled case. These preliminary results obtained for small amplitudes of the electric potential show that the control strategy we propose can be applied to much more turbulent flows than the one considered in [9]. Further investigations on the efficiency domain of the control term and its robustness are required.

Discussion and conclusion

In this paper, we have shown that the procedure developed to control turbulent diffusive transport of test particles can be applied to particles transported in a realistic turbulent electrostatic potential. The procedure to compute a low magnitude control term provides an efficient turbulence reduction is presented. For this test of the control strategy the turbulent field is simplified to simplify the analysis of test particle transport. More generally, the proof of principle that a control strategy can be efficient is tested on the simplest available model. When comparing the diffusion coefficient of the test particles in the uncontrolled system to that in the controlled case, a typical factor 3 reduction of the diffusion coefficient is achieved with a factor 10 lower magnitude of the control term. Far more investigation is still required on the way towards realistic control systems for the turbulent transport, however, the present paper shows that a theory based starting point is available.

Fig. 1 .Fig. 2 .

 12 Fig.1. Snapshot of the electric potential φ(x, y, t) for t = 100 obtained by Eq. (1) on a spatial grid of 512ρs × 512ρs.

Fig. 4 .

 4 Fig.4. Test particle diffusion coefficient D ⋆ versus a (magnitude of the potential) in log-lin scale obtained for the turbulent potential V without (full squares, solid line) and with (full circles, dashed line) the addition of the control term f 2 given by Eq. (10).

Fig. 5 .

 5 Fig.5. Contour plot of the control term f 2 (x, y, t) for t = 100 given by Eq. (10).