Determination of the mean energy of fast electron losses and anisotropies through thick-target emission on WEST

A new method to obtain the mean energy of fast electron losses in fusion plasmas using a versatile multi-energy hard x-ray (HXR) detector is presented. The method is based on measuring the thick-target emission of tungsten in the divertor region produced by fast electron losses interacting with the target and modeling the tungsten spectra by a Monte Carlo code which simulates the interaction between a beam of electrons and a solid target. The mean energy of the fast electron losses is determined through the comparison between the experimental and synthetic emission. The results show that fast electron losses during lower hybrid current drive discharges at WEST have a mean energy of 90–140 keV and represent only 2% of the total heat flux at the target. Additionally, anisotropic HXR emission has been detected for the first time at the WEST core and edge plasma, with opposite directions. It is due to the forward-peak emission of two distinctive populations of fast electrons: co-current fast electrons in the core and counter-current fast electron losses at the inner strike point. In view of future experiments like ITER where electron cyclotron current drive will generate a fast electron population, this technique could serve as a real-time monitor of fast electron losses and eventually feed an actuator on the current drive generation.


Introduction
Lower hybrid (LH) waves are often used in fusion devices as heating mechanism for electrons and also as a non-inductive current drive [1][2][3].LH waves are absorbed through Landau Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
damping by electrons in the plasma and as a consequence a population of supra-thermal (or fast) electrons is generated.Confined fast electrons drive the plasma current while diffusion of fast electrons makes them leave the confined plasma and eventually hit the plasma facing components.The interaction of fast electrons with the target material produces hard x-rays (HXRs) often with intensities higher than core HXRs due to the material much higher density and Z compared to the plasma, especially in metallic devices.This emission is called thick-target and consists of bremsstrahlung from the slowing down of incident electrons interacting with multiple target atoms, and line-emission from the target material.
Relatively small electron populations can be observed when interacting with high density materials, making HXR emission from solids a very sensitive indicator of fast electrons losses.Fast electrons losses when occurring in high number during lower hybrid current drive (LHCD) might severely impact the plasma current efficiency [4,5].Characterizing the loss of LH generated fast electrons is important for the quantification of power balance, investigating the physics behind current drive loss as well as estimating the power deposited on the plasmafacing components.
WEST (W-for tungsten-Environment in Steady-state Tokamak) is an X-point divertor tokamak with full-tungsten plasma facing components and the capability of long discharge up to 1000 s [6].Heating and current drive power is provided by radiofrequency systems, namely, ion cyclotron system and LH system.
This work estimates the edge fast electron losses generated by LHCD on WEST through a novel method which relies on the flexibility of a multi-energy HXR camera recently installed.This diagnostic provides measurements of thicktarget emission of tungsten in the divertor region at different energies.Win x-ray, an electron-microscope simulating code [7], is used to model the x-rays produced by the electron-target interaction.The comparison between the measured emission and the synthetic spectrum determines an average value for the fast electron energy and the magnitude of fast electron flux and heat flux on the target.This technique was originally developed at Alcator C-Mod for determining the magnitude of the fast electron flux on the molybdenum divertor [8].However, due to the limited energy resolution of the HXR diagnostic, the energy of fast electrons could not be assessed.In this work this technique will quantitively determine the energy of fast electron losses thanks to the energy resolution of the multi-energy HXR camera.

Experimental setup
A multi-energy HXR pinhole camera was recently installed on WEST.Its name is ME-HXR.It is based on the DECTRIS PILATUS3 X 100K-M CdTe detector with 195 (horiz) × 487 (vert) ∼100k pixels (172 µm each).It is a single-photon counting detector with nearly zero dark signal and noise [9].The diagnostic design and its engineering interface with WEST are described in [10].Figure 1 shows a drawing of the diagnostic assembly and the PILATUS3 detector.
The detector has been calibrated in energy at pixel-level in the range 8-100 keV, following a procedure originally implemented by some of the authors and already successfully applied to similar soft x-ray silicon detectors installed in other fusion experiments [11][12][13].The procedure consists in scanning the detector response by varying the voltage of an in-pixel six-bit digital-analog converter while the detector is irradiated by fluorescence from a series of x-ray sources [14].It is the first time this procedure was applied to a CdTe detector.Thanks to it, the lower energy threshold of each pixel can be set independently.This allows great flexibility in allocating the energy threshold among the pixels.Pixels along the columns or rows of the detector can be set to have the same energy threshold to allow spatial resolution along one direction and energy along the other.If fine spatial resolution is needed (1.4 cm), it is possible to set the pixel columns to the same energy and have spatial resolution along the rows of the detector.If coarse spatial resolution is sufficient (∼3 cm), it is possible to set an entire row (aligned in the toroidal direction) to the same energy and repeating the energy subdivisions (E 1 , E 2 , …, E n ) along adjacent rows of the detector to obtain spatial resolution along the vertical direction.Each group of n rows can be considered as a single unit, roughly sharing a line of sight but with different spectral sensitivities.These groups of rows will provide vertical resolution.Photon counts along the same row can be summed up to strongly increase the signal level, alternatively, a row can provide information on the toroidal asymmetry of the HXR radiation.See [10] for illustrated examples of pixel configurations.This extreme flexibility in adjusting spatial, energy and time resolution depending on the physics goal makes this novel imaging x-ray technique quite appealing compared to conventional x-ray tomography systems, for instance pulse-height-analyzers or x-ray detector arrays filtered with metallic foils, which are often constrained by fixed geometry and energy subdivision.
A spatial calibration of the diagnostic was carried out using a radioactive source placed on a movable actuator inside the vacuum vessel [15].The vertical position of the sightlines originating from each pixel was determined by shifting the source along the vertical axis.It was determined that the sightlines cover most of the plasma cross section including the lower divertor (see figure 2).In particular the bottom sightlines intersect the lower divertor next to the inner strike point.This makes the setup optimal for observing the thick-target emission from fast electrons escaping the confined plasma and interacting with the metallic target.For the measurements presented in this work the detector was set using the second configuration described previously, utilizing six energies from 17 to 60 keV.This configuration results in 80 sightlines with 2.7 cm spatial resolution along the vertical direction at the divertor.Counts are summed along the same row, resulting in a total effective area of 5.8 mm 2 per sightline per energy.The integration time was chosen such that the product of the measurement resolutions ∆t∆r 2 ∆E satisfies the relation derived in [17].This relation sets a limit on the simultaneous time, space and energy resolution of the diagnostic, which depends on plasma emissivity, detector geometry and statistical uncertainty associated to the measurements.Aiming for a relative accuracy of the count number ∆N/N ⩽ 0.015 (assuming that the counts follow Poisson statistics, i.e. |∆N| = √ N ), it turns out that the relation is satisfied for ∆t ⩾ 80 ms.Therefore, an integration time 100 ms was chosen for these measurements.The I p flat-top phase of a typical WEST discharge lasts more than 10 s.

Modeling
In order to infer the characteristics of the fast electron losses the observed thick-target emission needs to be compared with synthetic x-rays.In this work we utilize a code which was originally developed for electron scanning microscopes, which also observe high-energy electrons impinging on solid surfaces.The code is called Win x-ray [7].It uses a Monte Carlo procedure to model electron collisions with a solid surface and the associated x-ray emissivity while the attenuation of the x-rays in the surface is determined analytically.The x-rays are generated from bremsstrahlung and atomic excitation.The ensemble of individual representative x-rays is combined to generate the expected x-ray spectrum for large sample sizes.The code has been chosen for its simplicity and rapidity in generating x-ray spectra for simple geometries and conventional samples.
We define the emission spectrum simulated by Win x-ray as S(E | E b , I b , Ω), being a function of several parameters: the foremost is the initial electron beam energy E b , beam current I b , and the solid angle of the detector Ω.The beam incidence direction and detector to beam impact direction also affect the spectrum but are fully specified on WEST.The beam incidence direction is the magnetic field strike angle onto the divertor as derived by magnetic equilibrium reconstruction [18].The detector to beam impact direction is determined from the geometry of the ME-HXR, which is a known and calibrated quantity.
The intensity of x-ray emission is inherently linear with I b due to the low probability of electrons to change the solid or to interact with other electrons (i.e. each electron can be treated separately).We therefore normalize the emission spectrum S(E | E b , I b , Ω) to the beam current I b .The viewing geometry is specified by the solid angle (Ω), which can also be used to normalize the spectrum.The resulting spectrum can be expressed as S(E | E b ) and it has units of counts s Next, the spectrum S(E | E b ) is multiplied by the vacuum window transmission, the detector efficiency and the detector response function at a given energy threshold (E th ).The detector response function is show in figure 3 for the six energy thresholds used in these measurements.The same figure also shows the aluminum window transmission (used in the xray detection system) multiplied by the CdTe quantum efficiency.We express the convolution between the spectrum and these factors as S(E | E b , E th ).The resulting spectrum is shown in figure 4 for five electron beam energies in the range 70-190 keV and one detector's energy threshold (17 keV).
Finally, the spectrum is integrated over the photon energy to provide the synthetic integrated emission I syn (E b , E th ).This is the quantity which will be compared with the measured emission in order to infer E b ; the latter is specified in Win x-ray  as a single value which is a large simplification with respect to the spectrum of electron energies observed with LHCD.The determination of E b requires I syn (E b , E th ) to be calculated over a range of E b for the different detector's energy thresholds.I syn (E b , E th ) will be compared with the measured emitted intensity for the various E b at each E th .The electron beam energy will be determined by finding for which value the synthetic emission best matches the measurements for each E th .The final energy of the fast electron losses (E loss ) will be calculated averaging the beam energy over the different E th .
Since there is no initial knowledge of the fast electron distribution in the scrape-off layer (SOL), we treat the fast electrons as monoenergetic and we determine their average or most likely energy.By running again Win x-ray using this energy as input for the beam, the electron flux and heat flux produced by fast electrons will be estimated, understanding the importance of fast electron fluxes in the WEST SOL.

Results
The measurements presented in this work were taken during the 2023 C7 campaign at WEST.Diverted plasmas in lower single null configuration were obtained during LH heating and current drive experiments.A series of five discharges (57419, 57420, 57421, 57427, 57526) is considered in this analysis with the following plasma parameters.P LH = 1.1−3.Figure 5 shows typical HXR emission profiles measured with the ME-HXR diagnostic during one of these discharges.The profiles are measured at six different lower energy thresholds.Two main features in the profiles are worth pointing out.First, for any thresholds the thick-target emission of tungsten measured by the first sightlines intercepting the target is higher than the core emission measured by the central sightlines.Second, besides the first 10 sightlines intercepting the lower divertor, the HXR profiles feature a clear up/down asymmetry at all considered energies.Sightlines observing the lower half of the plasma cross-section see higher HXR counts compared to those observing the upper half.This asymmetry is not strongly observed in the core, but it is pronounced for sightlines that view the periphery (for instance at Z = ±0.3m).This up/down asymmetry was already reported during LHCD discharge in diverted plasma at Alcator C-Mod [19].Line-integrated HXR count rates from the divertor were observed being several times higher than those from sightlines viewing the opposite plasma-facing surface.Theories suggest this asymmetry is due to trapped fast electrons in the SOL or enhanced fast electron confinement near the plasma X-point [20].
In the analysis presented here the thick-target emission near the strike point will be compared with the results from Win x-ray in order to determine the mean energy of the fast electron losses.From the profiles in figure 5 only the emission from the first sightline for each energy threshold is considered.Emission from the sightlines at Z = −0.4m is taken as background and subtracted from the thick-target emission to account for x-rays coming from sources other than the target (confined fast electrons or deeply trapped).The experimental emission is averaged over one second during the LH flat-top phase of the discharge.This time window includes 10 HXR measurements since the diagnostic was run at 10 Hz.Afterwards the emission is normalized to its value at the lowest energy threshold (17 keV) and compared to the synthetic integrated emission I syn (E b , E th ), which is computed for the same energy thresholds and normalized in the same way.This comparison is presented in figure 6 as a function of the detector's energy threshold.By finding at which E b the synthetic emission best matches the corresponding experimental emission, the fast electron energy is determined for five values of E th (all but E th = 17 keV which was used for the normalization).Next, a weighted mean is performed over these five energies, using as weight the standard deviation of the time average of the experimental emission.This finally results in the mean, or the most likely, energy for the fast electron losses (E loss ) equal to 123 ± 26 keV for the considered discharge.It is evident from figure 6 that the experimental curve does not coincide with any of the synthetic curves in the investigated energy range, and consequently the determined E loss has a rather large uncertainty.This is due to that fact that the actual fast electron distribution in the SOL is not monoenergetic.E loss for the other discharges in this analysis is comprised in the range 90-140 keV.No clear correlation is found with the injected LH power or the wave parallel refractive index.
An estimate of the electron flux within the detector view can be determined.It is given by the ratio between the experimental emission (I exp ) and the modeled one (I syn ) evaluated at the previously determined value of E loss and multiplied by the detector etendue (ε), as defined in the following equation for one detector's energy threshold: Averaging j e over the different E th will provide a mean value of the electron flux for the considered discharge.It results that the electron flux increases from 0.5 to 2 A m −2 as P LH is increased from 1.7 to 3.3 MW.A rough estimate of the heat flux to the target can be calculated by taking the electron flux and multiplying by the energy per particle (q = E loss •j e ).This again assumes that the electron distribution is monoenergetic and moving only towards the target plate.It results that the electron heat flux increases from 50 to 220 kW m −2 as the injected power is increased.
The electron flux is found to quadruple as the input power doubles.This is related to the trend of I exp with P LH , whose slope varies depending on which of the two LH antennas is used.An example is reported in figure 7 for E th = 40 keV during a discharge with stepped P LH power (0-3.2MW) at a lowvarying density (2.7-3.1 × 10 19 m −3 ).In this figure the thicktarget emission is plotted as a function of P LH /n e 2.5 .The exponent 2.5 for the density scaling was found empirically during LHCD efficiency experiments on Tore Supra, which is the old WEST name before the current upgrade [21].In the figure it is visible that the slope of the HXR signal with respect to P LH /n e 2.5 changes.This is due to the different LH antenna used in the discharge: from 0 to 1.1 MW only the LH1 antenna was firing, then from 1.1 MW to 3.2 MW LH2 antenna was added to LH1.The two antennas have different n ∥ spectra and therefore their efficiency in driving a population of fast electrons changes [22].In particular for the LH2 spectrum the negative lobe carries a significant fraction of the power.The negative lobe drives a population of counter-current fast electrons.As it will be shown in the next section, losses from this population of fast electrons are responsible for the thick-target emission observed at the inner strike-point.
The electron flux from fast electron losses is orders of magnitude lower than the typical ground current densities measured by Langmuir probes located on the divertor around the inner strike point (∼1 kA m −2 ) [23].A similar consideration is made considering the value of the heat flux, which is significantly lower than the heat flux measured by Langmuir probes (∼10 MW m −2 ).The current density generated by fast electron losses carries a heat flux which is a small fraction (∼2%) of the observed heat flux.This rules out fast electrons streaming to the divertor plate to be a significant power loss mechanism.With the applied LH representing the sole heating system in these discharges, the edge loss of fast electrons is a small fraction of the changing conducted heat flux.This quantitative measure of the edge fast electron population finds that fast electron edge loss is not a major concern for LHCD current drive efficiency.This is in line with the fact that radial diffusion of fast electrons was found to be weak in large and medium-size tokamaks, with a diffusion coefficient equal to m 2 s −1 for Tore Supra obtained through LH power modulation experiments [24].In the same work it was established that the collisional slowing-down is the main process which drives the fast electron loss process, and thus radial diffusion is not an important loss mechanism.

Co-and counter-current fast electrons
LH waves predominantly generate co-current fast electrons (main n ∥ lobe being positive).At the same time, a smaller population of counter-current fast electrons is generated by reverse-n ∥ Landau damping (secondary negative n ∥ lobe).At WEST one strike point mainly absorbs the losses from the cocurrent fast electron population and the other from the countercurrent fast electron population.In a top view of the tokamak, the toroidal magnetic field and the plasma current are directed clockwise.Co-current fast electrons flow along the magnetic field lines with direction opposite to the plasma current and the magnetic field.As illustrated in figure 8, the diffusion of co-current fast electrons creates a population with velocity in the direction opposite to ⃗ B p in the SOL.These electrons will stream towards the outer strike point.Conversely, the smaller population of counter-current fast electrons, when diffusing into the SOL, will stream towards the inner strike point.Thus, the outer strike point absorbs co-current fast electrons and the inner one absorbs counter-current fast electrons.A larger population of fast electrons is then expected on the outer divertor.This statement is confirmed by thick-target measurements from the main WEST HXR diagnostic whose sightlines cover both strike points [17].The sightline intercepting the outer strike point observes ∼3 times higher count rates than the sightline observing the inner strike point.
A further confirmation of the presence of two fast electron populations comes from the observation of the anisotropy of the HXR emission.The plasma bremsstrahlung emission during LHCD is strongly peaked in the forward direction with respect to the electron velocity [25].The thick-target bremsstrahlung emission is also stronger in the forward direction with respect to the incident electrons, as observed during electron bombardment of solid targets [26].Due to the main fast electron population flowing opposite to ⃗ I p , we expect the HXR emission from confined fast electrons to be stronger in the direction opposite to ⃗ I p .The ME-HXR diagnostic can be used to assess this anisotropy thanks to its 2D pixelated detector.Each pixel row aligned in the toroidal direction can be divided in two parts: pixels measuring in the forward toroidal direction and pixels measuring in the backward toroidal direction.In figure 9 the HXR vertical profiles corresponding to the forward and backward emission are shown for E th = 17 keV.For the sightlines looking at the confined plasma, the forward emission is slightly higher than backward emission as expected.Their difference is not large due to the small toroidal angle difference of the ME-HXR view (9 • ).For the edge viewing sightlines aiming at the target, the backward radiation is higher than the forward one, thus confirming that the local emission at the inner strike point is due predominantly to counter-current fast electrons interacting with the target.This statement is confirmed by the toroidal profile of the HXR emission from a single row of pixels, depicted in figure 10.Two profiles are plotted, one for an edge sightline and one for a core sightline.Emission from the edge linearly increases moving from forward to backward direction, opposite to the behavior of the core sightline.

Discussion and future developments
This analysis showed that the intensity of x-rays for a given electron flux is higher for thick-target emission due to the density of solid tungsten.The large variation in particle density and in Z from the tungsten surface to the deuterium plasma makes the wall significantly more sensitive to high energy electrons.The quantitative analysis shows that a relatively small population of fast electron losses colliding with the wall can cause significant x-ray emission.The features induced by thick-target emission strongly weight the profile and can easily overwhelm the core emission.
No direct measurement of the energy of the fast electron losses on the target was made at WEST.Nevertheless, the energy of LH-driven fast electron losses in the magnetic ripple was determined based on calorimetric and current measurements on Tore Supra.Those measurements showed that, for values of I p and n e similar to those in the current WEST experiments, the energy of fast electron losses was ∼100 keV, which is compatible with our findings [18].WEST has a lower magnetic ripple than Tore Supra (3% instead of 6% at the edge [27]), however the magnetic field coils and the LHCD system remained the same [6], therefore the energy of fast electrons escaping the confined plasma is expected to be comparable in the two tokamak versions.Those measurements also showed that the energy of fast electron losses scales with I p and n e , while it is not sensitive to P LH .This effect is confirmed by our measurements which found no clear correlation between E loss and P LH .Our measurements were carried out at fixed values of I p and n e , so the relationship between E loss and these two quantities could not be assessed in this campaign, but it will be investigated in the future.
Our mean value for the energy of the fast electron losses is compatible with HXR measurements carried out with the main WEST HXR diagnostic, which measures x-rays up to 200 keV [17].These measurements indicate that an electron tail is pulled out up to 100-200 keV [28].The existence of an electron tail at those energies is confirmed by LH ray-tracing and Fokker-Planck calculations done with the suite of codes C3PO/LUKE/R5-X2 [29].
Regarding the possible sputtering of tungsten by fast electrons, the estimated energy is below the incident-electron sputtering threshold energy for tungsten, equal to 728 keV [30].
The maximum energy to which electrons can be accelerated by a wave with parallel refractive index n ∥ is given by the resonance condition for values of the counter-current n ∥ used in these discharges (−2.8 to −1.4), corresponds to an energy of 35-220 keV.
Our value for the fast electron energy lies within this interval.Nevertheless, this equation assumes that n ∥ is equal to the one set on the antenna waveguide, whereas the real value of n ∥ might vary while the wave propagates through the plasma.In fact, during the wave propagation n ∥ might undergo a downshift or upshift and hence the wave accelerates the electrons at higher or lower energies.The variation of n ∥ during the wave propagation has been observed with ray-tracing simulations at WEST [31] and full-wave simulations at Alcator C-Mod [32].Moreover, besides the LH waves, the residual DC field also accelerates the electrons.In these discharges there is a residual DC field revealed by a non-vanishing loop voltage (∼0.2-0.4V) that provides further acceleration to the electrons.This additional source of energy contributes to the non-monoenergetic nature of the electron distribution function.
Besides the non-monoenergetic nature of the electron distribution function a further source of uncertainty in this method may originate from the variation of the electron incident angle due to the fast electron pitch angle.As reported in [33], depending on the electron pitch angle, the actual incident angle of electrons can be significantly different from the initial magnetic field inclination (1 • ), reaching up to 20 • .We performed a sensitivity analysis and found that the determined fast-electron energy does not depend much on the incident angle, varying only by 1 keV by increasing the incident angle from 1 • to 20 • .
The magnetic configuration flexibility of WEST does not allow to move the strike points location towards the high field side in order to have both strike points within the ME-HXR camera view.On the other hand, by applying this technique to the main WEST HXR system we could estimate the energy and flux of both co-current and counter-current fast electron losses.Any asymmetry of the electron distribution in the core plasma which carries the current will also lead to an asymmetry in the distribution of fast electrons which diffuse into the SOL.It can then be expected that an asymmetry in x-ray production will be observed on the inner and outer strike points due to LHCD fast electrons.This will be the subject of a future investigation.
In the future at WEST it will be interesting to study the thick-target emission produced by fast electrons generated by the electron cyclotron (EC) system (under installation).EC, when used in current drive mode (ECCD), will generate a fast electron population similarly to LHCD [34].
Another project would be to include the thick-target emission modeled by Win x-ray in the suite of codes C3PO/LUKE/R5-X2, in order to fully reproduce the x-rays generated both in the core plasma and at the edge.

Conclusion
The method presented here, first of its kind, allowed determining a mean value for the energy of the fast electron losses at WEST, as well as the electron flux and heat flux to the target, understanding the magnitude of fast electron particle flux and heat flux in the WEST SOL.In addition, the powerful diagnostic allowed to observe for the first time at WEST the anisotropy of the core and edge HXR emission.
This powerful and flexible tool can be used to monitor fast electron losses, especially in view of bigger experiments like ITER, where ECCD is planned to be used for current drive and control of neoclassical tearing modes [35].Simulations show that the slow-down time of fast electrons generated by ECCD in ITER is much longer than that of thermal electrons.Before they slow down, the fast electrons will be transported along the perpendicular (to the magnetic field) direction due to plasma turbulence and may end up to the target [36].In this scenario the ME-HXR diagnostic could be integrated in the plasma control system and be used to monitor the losses and eventually to reduce them by optimizing the current density.Moreover, the diagnostic could be employed to observe losses of fast electrons generated at the plasma startup by the high toroidal electric field [12].In view of a possible application of this diagnostic to ITER, the effect of a large neutron flux on this kind of detector must be fully assessed.

Figure 1 .
Figure 1.Drawing of the ME-HXR diagnostic with the PILATUS3 CdTe detector.The 2D pixelated detector with independent energy threshold allocation among the pixels allows spatial resolution along the vertical and toroidal direction simultaneously, as well as energy and temporal resolution.

Figure 2 .
Figure 2. Vertical arrangement of the ME-HXR sightlines in the WEST vacuum vessel.Gray lines represent the magnetic flux surfaces computed with the equilibrium reconstruction code NICE [16].Black contour is the vacuum vessel with main plasma facing components (divertor, baffles, antenna protecting limiters).Red contour is the last closed flux surface and the two red crosses are the strike points on the lower divertor.For illustration purposes in the top image only 24 of the total 80 sightlines are shown.In the bottom image the actual sightlines are shown.

Figure 3 .
Figure 3. Detector's response function for several lower energy thresholds.The slope at high energy is due to charge-sharing between adjacent pixels.In black the aluminum window transmission multiplied by the CdTe efficiency.The spikes at 26 and 31 keV correspond to the fluorescence of Cd and Te.

Figure 4 .
Figure 4. Synthetic HXR tungsten spectra for various monoenergetic electron beams in the range 70-190 keV and for a detector's energy threshold of 17 keV.Tungsten x-ray emission lines from K shell are visible at ∼60 keV.
3 MW from two antenna launchers (LH1 and LH2), I p = 0.4 MA, volume-average n e ∼ 3 ×10 19 m −3 , LH wave parallel refractive index (n ∥ ): main positive lobe of the antenna spectrum in the range 1.8−2, secondary negative lobe of the antenna spectrum in the range -2.8 to -1.4.

Figure 5 .
Figure 5. Line-integrated HXR vertical profiles at different energy thresholds averaged over one second during the LH flat-top phase of the discharge.The profiles are obtained summing up the counts along the pixel rows of the detector (toroidal direction).The profiles are plotted as a function of the Z coordinate at the vacuum vessel geometrical center (R = 2.5 m).The sightlines at the extreme bottom intersect the target and measure the thick-target emission.Error bars show the standard deviation of the time average.

Figure 6 .
Figure 6.Colors: synthetic integrated W spectra for different electron beam energies as a function of the detector's energy threshold.Black: experimental emissions measured at different energy thresholds.Error bars represent the standard deviation of the time average.From the comparison between the modeled results and the measurements an average value of the electron beam energy is obtained (E loss ).

Figure 7 .
Figure 7. Line-integrated HXR emission at E th = 40 keV from a sightline intercepting the target as a function of P LH /ne2.5 .The measurements are taken from a single discharge (57428) where the input power was increased initially using the LH1 antenna only (from 0 to 1.1 MW), then using LH1+LH2 (from 1.1 to 3.2 MW).The two antennas have different n ∥ spectra and thus their efficiencies in driving a population of fast electrons at the edge varies, as such the HXR count rate exhibits a different slope.

Figure 8 .
Figure 8.The diffusion of the larger population of co-current fast will create a population with velocity in the direction opposite to − → Bp in the SOL (in green).Illustrated in the figure, co-current electrons when escaping the plasma at the midplane will preferably end up at the outer strike point (in blue).The electrons which are observed at the inner strike point are likely generated by reverse-n ∥ Landau damping.

Figure 9 .
Figure 9. Line-integrated HXR vertical profiles at E th = 17 keV obtained by averaging over the counts from the pixels looking at the forward emission (opposite to the direction of ⃗ Ip) and the pixels looking at the backward emission (same direction as ⃗ Ip).Error bars show the standard deviation of the time average.

Figure 10 .
Figure 10.Line-integrated HXR toroidal profile at E th = 17 keV for (a) an edge sightline intercepting the divertor and (b) a core sightline looking at the confined plasma.The toroidal view of the ME-HXR is not centered at 0 • but it is instead slightly tilted towards negative angles.The emission is expected to peak at full tangential view, i.e. a toroidal angle of 90 • and −90 • for the two cases, respectively [25].