Beam optics of RF ion sources in view of ITER’s NBI systems

A low beamlet divergence is crucial for the efficiency of the ITER-NBI systems, since it affects the transmission of the beam through the duct. There is a requirement of 7 mrad e-folding divergence for the ITER Heating Neutral Beam. Significantly higher divergences (10–15 mrad) have been observed in RF-source based experiments albeit at low beam energy. This could be the consequence of a broad perpendicular velocity distribution of the H−/D− particles before extraction. This paper explores this hypothesis and its implications for ITER. To estimate H−/D− perpendicular temperatures in the RF-driven BATMAN Upgrade test facility, spatially resolved measurements of the beam power density are compared with IBSimu calculations. The estimated perpendicular temperatures show a strong dependence on the source filling pressure, decreasing from approximately 4 eV at 0.3 Pa to 2 eV at 0.4 Pa. Ion-optics calculations of the ITER-HNB grid system are performed to evaluate whether the temperatures estimated in the BATMAN Upgrade test facility are tolerable in view of beam-grid interaction and beamline transmission. The beamline transmission is fairly insensitive to the perpendicular temperature, but the heat loads at the downstream grids increase with the perpendicular temperature.


Introduction
Neutral Beam Injection (NBI) will deliver 33 MW of heating power to the ITER tokamak by two injectors.A 7 grid system with 1280 apertures accelerates H − /D − up to 1 MeV for each Heating Neutral Beam (HNB) [1].The negative ions are generated in an RF-driven plasma source, extracted by an extraction potential U ext of up to 10 kV, and subsequently accelerated to the full energy in five steps.
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There are strict requirements on the source operating parameters and beamlet properties.The plasma source should operate at filling pressures below 0.3 Pa to keep stripping losses acceptable.It is necessary to homogeneously (±10%) extract current densities of 329 A m −2 in hydrogen, and 286 A m −2 in deuterium [1][2][3].The ITER-HNB divergence should be below 7 mrad for a beamline transmission above 78% [4,5].The divergence is defined as the e-folding halfwidth of the angular distribution; this convention will be used throughout [6].To achieve the challenging source and beam requirements, an R&D program has been established.The test facilities BATMAN Upgrade (BUG), ELISE, and SPIDER are part of the stepladder approach, supported by EUROfusion in WPPrIO [7].Divergences between 10 and 15 mrad have been observed these in RF-source based experiments, albeit at beam energies below 45 keV [8][9][10].Divergences below 7 mrad have been measured at arc-source based experiments, mostly at higher beam energies [11][12][13].
Several campaigns have been performed at the BUG test facility to investigate if the observed divergences are a diagnostic effect, a consequence of the data evaluation procedure, or due to physical effects.Measurements with the BUG-MITICA-Like-Extraction (BUG-MLE) grid system [14] revealed that diagnostic effects contribute to the observed divergences.Beamlets have a horizontal deflection that switches sign row-by-row due to the co-extracted electron deflection magnets, and since light is collected from multiple beamlet rows this broadens beam emission spectra measured along horizontal lines of sight.When the deflection is compensated, the divergence measured by emission spectroscopy decreases substantially [15].Good agreement was found between the divergence derived from emission spectroscopy of a single beamlet and from analysis of the beamlet spatial profile on a CFC tile [16].CFC calorimetry analysis methods were compared in a divergence taskforce coordinated by the ITER-Organization.Although different labs use different functions to fit the beamlet profiles, the main difference between reported divergences is caused by the conversion between fitted beamlet size and divergence, which needs assumptions on the initial beamlet size and propagation towards the CFC [4].A physical effect that could cause divergence differences between sources is the negative ion energy distribution before extraction [4].A higher H − /D − perpendicular temperature increases the divergence mostly at low beam energies, since this contribution to the divergence scales as T ⊥ /E beam , and is thus almost a factor five smaller in the ITER-HNB compared to BUG.However, previous modeling indicates that the perpendicular temperature increases the divergence more than the scaling suggests, and that it reduces the grid clearance which might increase losses in the accelerator [5].
In this paper, spatially resolved measurements of the beam power density in BUG are compared with modelling to estimate the H − /D − perpendicular temperature.Ion-optics calculations of the ITER-HNB grid system are performed to evaluate the contribution of the perpendicular temperature to the divergence as function of beam energy.The ion-optics calculations are combined with the full 3D grid and beamline geometry to calculate the beamline transmission for the estimated perpendicular temperatures.Losses by direct particle interception inside the ITER-HNB grid system are evaluated and compared with literature values.

Experimental methods
Figure 1 shows the BUG test facility, which extracts H − /D − ions from an RF-generated plasma [17].The currently installed BUG-MLE grid system consists of a plasma grid (PG) and extraction grid identical to the ITER-HNB geometry [5,14].Since the beam energy is limited to 45 keV, the acceleration gap is only 12 mm compared to the five 88 mm acceleration stages in the ITER-HNB.All grids have 5 × 14 apertures spaced 20 mm horizontally and vertically; the diameter of the PG apertures is 14 mm.Permanent magnets embedded in the extraction grid deflect co-extracted electrons out of the extracted particle beam.Asymmetric deflection compensation magnets correct the beamlet deflection around the divergence optimum [18].A current of up to 3 kA is driven vertically through the PG to produce a magnetic filter field of up to 6 mT at the upstream side of the PG [8].The filter field suppresses the coextracted electrons, but induces unwanted vertical asymmetries in the plasma due to drifts.The PG can be biased with respect to the source walls to further reduce the coextracted electrons.
A retractable 20 mm thick 1D-CFC beam target measures spatially resolved beam footprints 0.87 m downstream of the grid system [19].The PG apertures can be masked with plugs to isolate a single beamlet, which is fitted with a concentric bi-Gaussian profile: the angular profile originally assumed for the ITER beamlets [1,16].The profiles are fit after 0.5 s of beam, which is a compromise between a high signal-to-noise ratio and low lateral heat conduction in the tile.FEM analysis shows that a point source would have spread to a 4.8 mm width due to lateral heat conduction for this specific CFC material and thickness after 0.5 s [19].
The measured width can be converted to a divergence, but this requires several assumptions.For a point source, the beamlet size σ Point at distance l is given by: where σ 0 is the size of the beamlet at the end of the grid system and θ 1/e is the divergence in the generally used efolding half-width definition [1,6].A point source has an emittance of zero, since there is a perfect correspondence between particle angle and location, which is not a realistic assumption.The size evolution of a drifting beamlet is better described by the Twiss parameter formalism [20,21].If the beamlet is non-focused at the end of the grid system (no correlation between the particle location and angle), the size is described by: Note that both equations (1) and (2) simply expand to lθ 1/e / √ 2 without σ 0 for small divergences.Both formulas tend to the e-folding half-width divergence definition at large l, but differ in their description of the propagation behaviour close to the grid system, which is relevant for the interpretation of diagnostics close to the grids.Figure 2 shows how an identical size on the CFC can result in different divergence interpretations.To eliminate this ambiguity, the beamlets are simulated up to the CFC so that the sizes can be compared directly.With different propagation assumptions, a different divergence is assigned to a beamlet with a 10 mm size on the CFC, as shown for a point source with 2.5 mm initial size (equation (1)), Twiss parameter propagation with 2.5 mm initial size (equation ( 2)), and a point source without initial size, which result in 12.2 mrad, 15.8 mrad, and 16.3 mrad respectively.

Computational methods
The IBSimu code is used to simulate the ion-optics of the BUG-MLE and ITER-HNB grid systems [22,23].The simulation domain contains a single aperture; H − /D − ions are injected over the full surface of the simulation domain 2 mm before the PG with a starting energy of 3 eV.The parallel and perpendicular temperature of the ions is varied.In the experiment negative ion production on caesiated surfaces is essential [24].Modelling indicates that directly extracted surface produced ions have a different angular distribution with respect to the ions extracted from the plasma volume [25].Since it is unclear what initial conditions to use for the surface produced ions, and directly extracted ions produce a strongly non-Gaussian feature in the beamlet not confirmed by experiment yet, it is chosen to neglect surface production as usually done in ionoptics codes; all the simulation particles are from the plasma volume.In the plasma region, quasi-neutrality is ensured by an analytical function that generates a charge density of positive hydrogen ions with a temperature of 0.8 eV as used in [26]; the results are not sensitive to this parameter.
To mimic the collisional behaviour of the particles, the magnetic field is suppressed in the plasma region, so that there is an even flux of particles to the extraction aperture.The plasma region is defined as the cells with a potential below 1 Volt; the PG is at a potential of 0 Volt in the simulations.Co-extracted electrons are neglected, as they contribute m H /m e ≈ 43 times less to the space charge at equal current density, which is the upper limit for safe operation of the BUG and ITER sources at full parameters in view of extraction grid heat loads [27].H − /D − can be stripped of the additional electron by interaction with background gas.Stripped electrons are magnetically deflected out of the beam, leading to a decrease of space charge in the grid system.For short grid systems such as BUG and ELISE, the beam contains less than 5% particles that are stripped in the extraction stage as measured with emission spectroscopy at a source filling pressure of 0.3 Pa [28].For the ITER-HNB grid system, a total 30% stripping fraction was calculated at 0.3 Pa source filling pressure, with approximately 10% of the stripping in the extraction stage [3].Stripping losses are the reason for the difference between extracted (E > U ext ) and accelerated (E = E beam ) current density requirements for the ITER-HNB.Since stripping affects the ion-optics to a relatively minor degree, it is chosen to neglect the stripping losses.The horizontal and vertical boundaries are periodic.It is assumed that 10 mm after the last grid, in the experiment the grounded grid (GG), space charge compensation has set in, and there is no net local charge density and associated electric field that changes the particle distribution [29].In the BUG-MLE simulations, the negative ions are tracked up to the CFC.
The calculated power density is convolved with a 4.8 mm wide Gaussian to mimic the heat conduction in the CFC tile.The width and shape of the convolution kernel is based on a FEM calculation of a point source on the CFC tile.The convolved profile is fit with a concentric bi-Gaussian profile.
A single Gaussian divergence is calculated from the particle velocities as: where v ∥ is the axial, and v ⊥ the horizontal or vertical direction.The average velocity needs to be subtracted to get a correct value for non-centred distributions.The initial temperature corresponds to an initial divergence θ T of: where E beam is the beam energy at the exit of the grid system.This equation assumes that the initial particle distribution is accelerated to E beam by an increase of the parallel velocity while the perpendicular velocity is unchanged.Because the divergence is an angle, the initial temperature contribution depends on the beam energy.BUG magnetic fields are calculated with ANSYS, which takes into account the magnet-magnet interaction.ANSYS is also used to calculate the BUG filter field that is generated by a current through the PG.The field of the ITER-HNB permanent magnets are calculated with BioMAGPy, which is based on an integral formulation [30].The transmission function of the ITER-HNB beamline is calculated with ABC3D [31].The calculation of the transmission function is based on the detection of intersections with beamline elements for all the lines of sight between beamlets and diagnostic points.

Estimating T ⊥ from BUG measurement data
The BUG-MLE grid system was characterized in an experimental campaign with a single beamlet isolated by masking leaving 36 of the 70 apertures open as shown in figure 1 [18].The spatial profile of the beam on the CFC was fit with a concentric bi-Gaussian, as shown in figure 3 for a typical measurement.The beamlet shape results from a combination of the perpendicular temperature, space charge, electric and magnetic fields, and heat conduction in the CFC tile.Corresponding simulations which include these effects were made with IBSimu, by taking the extraction potential U ext and acceleration potential U acc from the measurement, while varying the current density and perpendicular temperature.For each simulation, the difference with the measured beamlet core size on the CFC was determined, taking the average of the horizontal and vertical size.Figure 4 shows the comparison between the measurement shown in figure 3 which has a core size of approximately 11 mm and simulations with various injected current densities and perpendicular temperatures.The injected current density is an input parameter in the simulations; it is within ±5% of the extracted current density when the beamlet is not overperveant, in which case negative ions are lost on the extraction grid and do not exit the grid system.At low perpendicular temperatures, the simulated beamlet size is smaller than the measured beamlet size, whereas the simulated beamlet size is larger than the measured beamlet size at high perpendicular temperatures.The best matching perpendicular temperature is on the black line where the difference between simulations and measurement is zero.In this example, which has an extracted current density of 127 A m −2 , the best matching perpendicular temperature is 4.1 eV.However, the measured current density is averaged over the whole grid, the value for the single beamlet is prone to be different due to vertical inhomogeneities.A 20% variation with respect to the average current density leads to large error bars on the perpendicular temperature, 4.1 +2.9 −1.9 eV for this specific example.Note that the simulated beamlet size decreases with increasing current density, so that a larger perpendicular temperature is needed to match the measurement.The 4.1 eV perpendicular temperature corresponds to a 10 mrad divergence (equation ( 4)), or a 6.4 mm size on the CFC (equation ( 1)), which is a substantial part of the measured 11 mm.Any broadening mechanism in the experiment that is not present in the modelling will be attributed to the perpendicular temperature with this method, which means the determined values are upper limits.The obtained temperature values are high compared to the maximum tolerable electron temperature of 1-2 eV in the extraction region because of negative ion destruction [24].More realistic negative ion energy distributions might be obtained when taking into account the role of surface production, which requires a different simulation approach [25] This procedure was applied to all discharges in the campaign, which includes both under-and overperveant discharges at different grid potentials.Not all discharges provide contours that allow a temperature determination.Discharges with a reversed filter field are excluded from further analysis since the current density of the single beamlet in relation to the 4. The difference in measured and simulated core size of the beamlet on the CFC is used to determine which perpendicular temperature is the best match for the measurement (big black marker).Small black markers show simulated conditions.A ±20% deviation from the measured average current density leads to large error bars on the perpendicular temperature.average is different compared to discharges with normal filter field direction, and the main influence on the beamlet optics is the result of this difference.Far away from the divergence optimum, which is at a U acc /U ext ratio of 6.5 in the experiment, the fit procedure produces questionable results; only discharges with a U acc /U ext ratio between 5 and 8 are considered.Figure 5 shows the best matching perpendicular temperature for the remaining discharges as function of the source filling pressure.There is a large spread in the determined H − perpendicular temperatures since the plot includes discharges at different grid potentials, extracted current densities, and biasing, but there is a clear dependence on source filling pressure and a weaker correlation with the RF power.Note that most of the data was taken at 0.3 Pa, and this pressure bin has a much larger variation in RF power compared to the other bins, leading to a larger scatter in the perpendicular temperatures.The perpendicular temperature dependence on the source filling pressure is fitted with a power function.Each of the five pressure bins between 0.25 Pa and 0.75 Pa is weighted equally so that the fit is not influenced by the amount of measurements at each filling pressure.Fits of the lower and upper end of the error bars generated with a 20% current density variation show the same dependence on the pressure with an exponent of −2.2 ± 0.2.The shaded region illustrates the large uncertainty on the perpendicular temperatures estimated with this method.In arc-based ion sources, the negative ion temperature was also observed to increase at low filling pressure [32][33][34].Those estimations were made by comparing the H − /D − density and extracted current, by laser-induced photodetachment, and by the scaling of the measured emittance with voltage [32][33][34][35].

Divergence contributions in the ITER-HNB
The divergence is the result of several mechanisms: the perpendicular temperature, repulsion of the negative ions, and aberrations due to e.g. the magnetic field.This section explores the importance of these contributions for the ITER-HNB grid system at a perpendicular temperature of 1 eV, which is chosen to connect to literature [4].In hydrogen, the full operating parameters are an extraction potential of 7.9 kV, an acceleration potential of 174 kV, and an injected current density of 329 A m −2 [5].In deuterium, the full operating parameters are an extraction potential of 9.0 kV, an acceleration potential of 200 kV, and an injected current density of 286 A m −2 [5].The acceleration potentials are given for a single acceleration stage; the ITER-HNB has five acceleration stages.At reduced potentials, the current density is reduced according to the Child-Langmuir law as: The simulated angular distribution functions are well approximated by a single Gaussian.As shown in figure 6, without magnetic field, the divergence follows a θ 0 + T ⊥ /E beam dependence.Note that the values for H − and D − are not identical since the literature U acc /U ext ratios are slightly different, probably due to a rounding error in the extraction potential for H − .At 1 eV perpendicular temperature, without magnetic field, the modeled divergence is below the 7 mrad requirement above a beam energy of approximately 150 keV in both H and D, as reported in literature [4].The permanent magnets in the grids lead to aberrations in the beamlet and consequently a higher divergence [14].Aberrations due to the magnetic field are more pronounced at lower beam energies since the particles then deviate further from the center of the aperture.Hydrogen beamlets are more affected by the magnetic field due to the lower mass.The different contributions to the divergence are estimated by fitting the beam energy dependence in presence of magnetic field with the following empirical formula: where θ 0 is the space charge contribution to the divergence, T ⊥ /E beam the perpendicular temperature contribution, and θ B E beam δE exp (− E beam δE ) the magnetic field contribution with θ B and δ E describing the magnitude and scaling with beam energy.The space charge and perpendicular temperature term have been used in the literature [4], the magnetic field term is determined by observing the difference between simulations with and without magnetic field.θ 0 is approximately 3.7 ± 0.1 mrad, indicating that a substantial part of the divergence is caused by space charge effects.The remainder of the divergence is caused by the perpendicular temperature, and, to a lesser extent, by the magnetic field.Note that when neglecting the magnetic field contribution, a 3.7 mrad θ 0 suggests a tolerable perpendicular temperature of approximately 10 eV at the full 1 beam energy.

Impact of T ⊥ on ITER-HNB beamline transmission
The impact of various perpendicular temperatures on the ITER-HNB beamline transmission is calculated.The beamline transmission calculation takes into account the full 3D geometry of the beamlets and beamline with the transmission function, and the full angular distribution of the beamlets including the effects of the magnetic fields on the ions.The transmission function describes what fraction of the particles is transmitted as function of the starting angle.The calculation of the transmission function is purely geometric, ABC3D is used, which assumes that the beamlets start as point source and that the particles travel in straight lines [31].Figure 7 shows the transmission function for the ITER-HNB which includes the 1280 beamlets and full beamline geometry [5].Since the neutralizer and residual ion dump are narrow, particles should have a horizontal angle below approximately 6 mrad to ensure transmission; the vertical angle is less critical.
The beamline transmission is the product of the transmission function and the angular distribution of the beamlets.Figure 8 shows the transmission and power losses on individual components as function of divergence for a beamlet that can be described by a single Gaussian without a deflection angle.Also shown is the ideal transmission, which is the  maximum transmission that is possible given the beamline length and size of the blanket opening.The ideal transmission is calculated as a single beamlet passing through the center of the 0.55 m wide and 1.08 m high blanket opening at 26 m [36].The beamline transmission is below the ideal transmission due to the 3D geometry of beamline elements that restrict the transmitted power, such as the residual ion dump.Since the ITER transmission requirement is 78%, the angular distribution of the beamlets should be a single Gaussian profile with a divergence below 7.4 mrad, which is close to the literature value of 7 mrad [4,5].A 7 mrad requirement is stricter than the double Gaussian profile sometimes mentioned in the literature with 85% of the power in a core with a divergence below 7 mrad and 15% in a halo with a divergence in the 15-30 mrad range [1,37].For a core divergence of 7 mrad, the transmission is 74% when the halo is 15 mrad [1], and 70% for a 30 mrad halo [37].Note that these transmissions are calculated for the design geometry, i.e. without randomly distributed beamlet deflections sometimes included to account for possible misalignments.
Figure 9 shows the beamline transmission of the simulated angular distributions in H − and D − for various values of T ⊥ .The beamline transmission is generally higher for deuterium, since it has a lower divergence at identical beam energy because deuterium beamlets are less affected by the magnetic field.Transmission differences between the isotopes are smaller at higher perpendicular temperature.At low beam energies, the hydrogen beamline transmission becomes higher than the deuterium beamline transmission due to losses of highly divergent hydrogen ions inside the grid system which are not counted as beamline losses.Above a minimum beam energy, the beamline transmission is above the requirement; the minimum beam energy depends on the perpendicular temperature.Although the beamline transmission increases as function of beam energy, the extracted power increases as E 5/2 beam , so that the absolute losses in the beamline are highest at full energy.In view of beamline transmission, a perpendicular temperature up to approximately 9 eV is tolerable at nominal operating parameters in both hydrogen and deuterium.

Impact of T ⊥ on ITER-HNB grid heat loads
The ITER-HNB grids should handle the heat load due to the beamlet, halo, stripped particles, and secondary electrons.Design optimizations were based on heat load calculations with a cylindrically symmetric potential and a 0.18 eV perpendicular temperature [38].Recent efforts used a 3D potential which includes the effects of the magnetic field and a 1 eV perpendicular temperature [39].This section analyzes the impact of the perpendicular temperature on the power losses inside the ITER-HNB grid system.Only beamlet particles impinging on the grids are considered, which is a small fraction of the total power to the grids at perpendicular temperatures up to 1 eV, where most of the heat loads are due to co-accelerated electrons and H/D generated by stripping [39].However, when the beamlet clearance becomes too small, the direct particle losses could increase abruptly with the perpendicular temperature.
The loss of beamlet particles inside the grid system is larger for hydrogen than deuterium, in absolute value and as fraction of the extracted power, because hydrogen is more affected by the magnetic field.At higher perpendicular temperatures, there are more losses in the accelerator due to direct particle interception, mostly on the GG.At nominal operating parameters in H, there is 0.1 MW of power scraped by the GG at a perpendicular temperature of 1 eV, and 0.6 MW at 4 eV which corresponds to approximately 1% of the beamlet particles.
The amount and location of beamlet losses depend on the current density.At low current densities, the beamlet is scraped by the downstream grids, whereas the extraction grid scrapes the beamlet at high current densities.Figure 10 shows the power of directly intercepted H − particles for the different grids at a perpendicular temperature of 1 and 4 eV calculated for a (U ext -U acc ) of (7.9-174) kV.At an increased perpendicular temperature, variations in current density are more critical in view of power intercepted by the last two grids (AG4 and GG).More detailed modelling that includes secondary particles is necessary to define operational boundaries in terms of the current density and perpendicular temperature in view of power loads to the grids.

Conclusions
Divergences above the 7 mrad ITER-HNB requirement, in the range 10-15 mrad, have been observed in RF-source based experiments at approximately 1/20 of the ITER-HNB beam energy, especially at low filling pressures.It is the working hypothesis that the high divergences are the result of a velocity distribution of the H − /D − particles before extraction.The physical mechanism behind the pressure dependence of the H − /D − temperature is unclear at the moment, but a similar dependence has been observed in volume production dominated arc sources [32,34,40].H − perpendicular temperatures were estimated in the RF-driven BATMAN Upgrade test facility by comparing thermographic measurements of a single beamlet with modelling.Any broadening mechanism in the experiment that is not present in the modelling will be attributed to the perpendicular temperature with this method, which means the determined values are upper limits.The estimated perpendicular temperature shows a strong dependence on the source filling pressure: it decreases from approximately 4 eV at 0.3 Pa to 2 eV at 0.4 Pa.The temperature estimation depends strongly on the current density of the single beamlet, taken here from the grid averaged value; current measurements of a single beamlet are highly desirable.
The contribution of the perpendicular temperature to the divergence for the ITER-HNB grid system was analyzed with ion-optics calculations in H and D with and without magnetic field.The divergence is systematically higher in hydrogen compared to deuterium because it is more affected by the magnetic field on account of its lower mass.Above a perpendicular temperature of 1 eV, the perpendicular temperature dominates, and isotope differences become smaller.
The full ITER-HNB 3D beamline geometry was used to calculate the transmission function, which describes the transmission as function of starting angle averaged over all the beamlets.Applying the transmission function to undeflected single Gaussian beamlets, yields a divergence requirement of 7.4 mrad, which is close to the 7 mrad literature value [4,5].The transmission of the modeled angular distributions, which include asymmetries and deflection, decreases at lower beam energies.The maximum power loss in the beamline occurs at nominal operating parameters.At the nominal operating parameters, the transmission requirement of 78% is satisfied up to a perpendicular temperature of approximately 9 eV.Since this is much higher than the temperatures estimated in the BATMAN Upgrade test facility, the measured divergences at low energies are compatible with the 7 mrad divergence and 78% transmission requirement at the full energy.
The loss of beamlet particles inside the ITER-HNB grid system was analyzed.This is generally a small fraction of the total power to the grids, most of the heat loads are due to coaccelerated electrons and H/D generated by stripping, but direct particle losses could increase abruptly with the perpendicular temperature when the grid clearance becomes too small [39].At higher perpendicular temperatures, scraping on the last acceleration grid and GG increases.At higher perpendicular temperatures, variations in the extracted current densities are more critical in view of power intercepted by the last two grids; more detailed modelling is necessary to define operational boundaries.

Figure 1 .
Figure 1.Schematic of the BUG test facility, with a single beamlet isolated by masking plugs in the upper half of the PG.

Figure 2 .
Figure 2.With different propagation assumptions, a different divergence is assigned to a beamlet with a 10 mm size on the CFC, as shown for a point source with 2.5 mm initial size (equation (1)), Twiss parameter propagation with 2.5 mm initial size (equation (2)), and a point source without initial size, which result in 12.2 mrad, 15.8 mrad, and 16.3 mrad respectively.

Figure 3 .
Figure 3.A single beamlet profile measured after 0.5 s of beam, shown with the Gaussian size of the core (black) and halo (white) indicated.

Figure 5 .
Figure 5.The H − perpendicular temperatures estimated on basis of best matching simulations to BUG-MLE CFC measurements, show a dependence on the source filling pressure, and a weak correlation with the RF power.The gray band indicates the error bar, which is based on a ±20% deviation of the current density from the measured average.

Figure 6 .
Figure 6.The simulated ITER-HNB divergence for H − and D − with and without magnetic field at a T ⊥ of 1 eV.Without magnetic field, the divergence follows a θ 0 + √ T ⊥ /E beam dependence.The magnetic field increases the divergence, especially at lower beam energies.

Figure 7 .
Figure 7.The calculated transmission function of the ITER-HNB beamline has a steep dependence on the horizontal angle of the particles.

Figure 8 .
Figure 8.The power to the different components in the ITER-HNB beamline is shown as function of the divergence.The ITER-HNB neutral beam transmission is above the 78% target for a divergence below 7.4 mrad.

Figure 9 .
Figure 9.The calculated ITER-HNB transmission for various perpendicular temperatures in H − and D − .The required 78% is indicated by the gray shaded area.

Figure 10 .
Figure 10.The power of directly intercepted H − is shown for the grids of the ITER-HNB at a perpendicular temperature of 1 and 4 eV.The shaded gray area is outside the nominal operating point ±10%.