Ultrahigh neutral pressures in the sub-divertor of the Large Helical Device

In the Large Helical Device (LHD) a low temperature mode (LTM) of the helical divertor was discovered. It combines particle detachment and very large sub-divertor pressures up to 1.4 Pa. During the LTM, the electron temperature in the divertor was in the range from 0.25 to 0.42 eV so that volume recombination occurred. This result is remarkable because in the stellarators LHD and Wendelstein 7-X only low sub-divertor pressures (0.03–0.3 Pa) were expected and measured up to now due the loss of pressure conservation along flux tubes by an enhanced cross-field transport. It demonstrates that the more complex, three-dimensional divertors of stellarators can achieve a similar performance with respect to particle exhaust and detachment like the geometrically simpler poloidal divertors in tokamaks even if the favorable effect of flux amplification is absent. The LTM of the helical divertor depends, however, on the magnetic configuration, i.e. on geometry. It was only observed in the inward shifted configuration with Rax=3.55  m, but not in the more frequently studied configuration with Rax=3.6  m. A nuclear fusion reactor based on the heliotron concept (DEMO) would benefit from the LTM by the very compact divertor configuration and the excellent performance.


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There are two competing concepts for future nuclear fusion reactors based on magnetic confinement: tokamak and stellarator.In both devices, the power used to heat the plasma, must be radiated away from the plasma or conducted to the vessel walls.The structure designed for this is called the divertor.In a tokamak the magnetic field is axisymmetric and axisymmetric * Author to whom any correspondence should be addressed.
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divertors can be easily realized (also called poloidal divertors).Poloidal divertors have been studied over a long time in order to optimize energy and gas exhaust (see e.g.[1]).For steadystate operation of a fusion device a high gas exhaust rate is necessary for density control and for balancing particle input from pellet injection.The exhausted rate is given by S eff * p.Since the effective pumping speed of the sub-divertor volume S eff is always limited, the sub-divertor pressure p must be as high as possible.As the result of the optimization process, high sub-divertor pressures of a few Pascal and high neutral compression ratios were obtained.
In stellarators the edge plasma is more complex which makes it more difficult to integrate a divertor and three-dimensional (3D) effects play a dominant role.In the existing two large stellarator devices, Large Helical Device (LHD) and Wendelstein 7-X (W7-X), different divertors concepts were realized depending on the field properties.In W7-X the edge is formed by magnetic islands and the plasma is diverted by an island divertor [2].The LHD is a heliotron-type device with a major radius of 3.9 m.The magnetic field is produced by superconducting coils with a poloidal winding number of l = 2 and toroidal field periods of n = 10 [3].Because of the mode spectrum of the magnetic field produced by the helical coils, magnetic islands of different mode numbers are created, and they overlap each other.As a consequence, the intrinsic field line structure of the edge region is stochastic [3].In LHD a helical divertor was installed which was designed for the so called inward shifted configurations with major radii between 3.55 and 3.65 m [4].However, it seems to be difficult to achieve the same exhaust performance as in a poloidal divertor.In both devices much lower sub-divertor pressures were found due to a relatively low electron density in the divertor.As an example, the maximum sub-divertor pressure in W7-X was 0.15 Pa in the high-iota configuration [5], more than one order of magnitude less than in ASDEX Upgrade.The loss of plasma pressure conservation along flux tubes due to enhanced cross-field transport is the reason for that [6].
Recently, in the helical divertor of LHD very high neutral pressures were obtained after a transition to a divertor plasma with a very low temperature.We call this new state the low temperature mode (LTM) of the helical divertor.It was discovered during a study of two magnetic configurations which differed in the position of the magnetic axis.Figure 1 compares two plasma shots-one shot with R ax = 3.6 m (shot number 186681) and another one with R ax = 3.55 m (shot number 185566).The magnetic field was +2.75 T (clockwise directed) and −2.79 T (counter clockwise directed), respectively.
In these shots the plasma density was ramped up to about 15 × 19 m −3 .The plasma was heated with tangential and perpendicular neutral beams.In both plasmas an energy of about 800 kJ was stored, decreasing toward the end of the shot due to the high density at constant heating power.Figure 1 shows also the sub-divertor pressures and the ion saturation currents of the Langmuir probes.The sub-divertor pressures were measured by fast ionization gauges, one located in the 6I section and another one in the 8I section (for the geometry of the set-up see figure 2 in [7]).The letter I stands for inboard side and the number stands for the toroidal position in the LHD.The ion saturation currents were measured with two probe arrays mounted in the target plates in section 8I (see figure 2 in [8] for the geometry of the arrays).Figure 1 shows the sums over the left array, the sums over the right array, and the total ion saturation current giving an approximate measure of the particle fluxes to the targets.
With increasing density, the total ion saturation current (sum of left and right) shows a flattening in both shots and even a slight decrease.This is called particle detachment.Particle detachment was studied in many fusion devices and the physical mechanism is well-known.Note, that the absolute value of the ion saturation current was higher in the 3.55 m configuration.
The sub-divertor neutral pressures were quite different in both shots.With R ax = 3.6 m, the maximum pressure was about 0.2 Pa while with R ax = 3.55 m the sub-divertor pressure rose up to 1.4 Pa.As figure 1 shows, the hydrogen puff rates were not very different in both shots.Thus, it is impossible that a direct gas puff caused the different sub-divertor pressures.
Figure 2 shows the scalings of the sub-divertor neutral pressures (8I) over line-averaged density and ion saturation currents.The line-averaged density was measured with a farinfrared interferometer.In the 3.55 m configuration we found a strong non-linear increase for the 8I position.It can be described by the power function p = a * n b e with a = 0.000 16 and b = 3.6 (up to a density of 12 × 10 19 m −3 ).Here p is in Pa and n e in 10 19 m −3 .In the 3.6 m configuration the increase with density was approximately linear.By the different scalings, the sub-divertor pressure was almost one magnitude higher at the largest density in the magnetic configuration with R ax = 3.55 m.The differences in neutral pressure were observed only above a density threshold (6 × 10 19 m −3 for the 8I position, see figure 2(a)).For the 6I position the threshold was 9 × 10 19 m −3 so that the pressure rise was not as high as in the toroidal section 8I.
Figure 2(b) shows the pressure over the total ion saturation current which is a measure for the particle flux to the divertor target plates.In the 3.6 m configuration, the maximum current is about 2 A. In the 3.55 m configuration, the maximum value is about 2.8 A. For a high value of the ion saturation current, i.e. for a high particle flux to the target, the neutral pressure can vary one order of magnitude up to 1.4 Pa.This is the state of particle detachment where the ion saturation current flattens or even decreases.It is very remarkable, that the subdivertor pressure strongly rises despite a very small increase of the particle flux in the detachment phase.This proves clearly that the sub-divertor pressure was decoupled from the particle source in the helical divertor.There must be another reason for the strong sub-divertor pressure rise than the particle flux.Furthermore it is interesting to note that the very high subdivertor pressures were only observed in a particle flux range which cannot be achieved in the 3.6 m configuration.
Further insight into the underlying process was gained through divertor spectroscopy [9].The divertor spectroscopy observed the 3I section which allowed the direct access of the divertor plasma without crossing the main plasma (see figure 3(a)).
The analysis of Balmer series lines indicated that the divertor plasma was very different in both magnetic configurations for densities larger than 6 × 10 19 m −3 .Figure 3 shows a change of the upper state population densities feeding the atomic transitions for the H β , H γ , and H δ spectral lines, in the 3.55 m configuration case.At 3.4 s, the population densities did not follow a Boltzmann distribution, which is very typical for ionizing plasma conditions.In such a plasma the hydrogen levels are populated by electron excitation from the ground From 3.5 s on, the character of the population densities significantly changed.They can by described by a Boltzmann distribution, i.e. the quantum levels 4, 5, and 6 were in partial local thermal equilibrium (see [10]).An electron temperature of 0.25 eV was derived from a Boltzmann plot immediately after the transition.At such a low temperature, plasma recombination occurred in the divertor volume, not on the targets.We call the new plasma state the LTM of the helical divertor.It lasted from 3.5 to 4.8 s.Temperatures were between 0.25 and 0.42 eV (see figure 4(b)).The characteristic time scale for an equilibrium setting of the pressure in the sub-divertor space was 0.5 s, which was less than the duration of the LTM.In shot 186681 with R ax = 3.6 m no such transition was observed.The divertor plasma was always ionizing, i.e. the electron temperatures were not low enough for volume recombination.The conclusion is that the different scalings of the sub-divertor pressures were caused by the transition into the LTM in the 3.55 m configuration.
A possible reason for the differences between the configurations could be a different electron temperature in the upstream position.Figure 4(a) shows the edge temperature approximately at the separatrix measured by Thomson scattering.The dependence on line-averaged density was the same for both configurations.At low density, the edge temperature was about 200 eV while at the highest densities, it was about 50 eV.Somewhat higher values were measured for the 3.55 m configuration.
A striking difference was, however, the amount of carbon radiation in the divertor.Figure 4(b) shows the maximum value of CIII 464.7 nm emission over time for both configurations.In the 3.6 m configuration, the CIII emission followed approximately the density while in the 3.55 m configuration a maximum at 3.5 s was observed after a steep rise.At 3.5 s the difference in carbon radiation was about a factor of 5. Due to the high radiative losses, the temperature dropped down and volume recombination was observed at 3.5 s for the first time.Because the carbon radiation stayed high in the divertor, the divertor plasma remained in the LTM until the end of the shot.
Figure 5 compares the profiles of the ion saturation currents and the connection lengths for the different magnetic configurations.We took the current profiles at 3.5 s shortly after the transition into the LTM.In the 3.55 m configuration, we see two distinct peaks at 30 and at 50 mm.Their positions approximately agree with the connection lengths peaks.These peaks are not so pronounced or absent in the 3.6 m configuration.The higher particle flux in the 3.55 m configuration is very likely one cause of the large difference of the carbon radiation.
One must note that the transition into the LTM had a special character.Usually, the increase of the carbon radiation is accompanied by a slow cooling of the divertor plasma.However, the transition occurred suddenly within 100 ms (this value results from the temporal resolution of the divertor spectroscopy) and the final state was a plasma with a very low electron temperature (0.25 eV).Such a rapid transition is reminiscent of an instability of the thermal front as analyzed in [11].Furthermore, no thermal instability of the Marfe type was observed which occurs in the LHD at low edge temperatures of about 30 eV [12].Figure 4(a) shows that the edge temperatures were always above the Marfe threshold.
It is reasonable to assume that the electron density in the divertor n div drives the sub-divertor neutral pressure.The general relation between divertor and upstream densities n u is described by −3 [13].P SOL is the total power entering the plasma edge.If the momentum loss factor f m due to the perpendicular interaction is zero, the exponent in the scaling of the sub-divertor pressure would be 3 as known from tokamaks.For a stellarator like LHD or W7-X, the momentum loss factor is much larger than 0 and a linear scaling is expected SOL n u [13].A linear scaling was indeed observed in the 3.6 m configuration (see figure 2(a)).We are therefore dealing with a different physical process in the 3.55 m configuration.
The ratio of the flux through the pumping gap to the flux to the divertor targets is called particle collection efficiency [5].After the transition to the LTM at 3.5 s, this efficiency was much higher.When the electron temperature was about 10 eV, the divertor plasma plugged the pumping gap by ionization.At temperatures below 1 eV such a plugging did not exist.The pumping gap was suddenly open for the neutrals, so that they reached more easily the sub-divertor space resulting in the observed increase of the sub-divertor neutral pressure up to 1.4 Pa.
Such a pressure is comparable to the values obtained in the poloidal divertor of the ASDEX Upgrade tokamak.Here the typical pressure in an H-mode discharge was 2 Pa and in a density limit discharge up to 5 Pa [14].This result demonstrates that the helical divertor in LHD has an excellent performance by a combination of particle detachment and high sub-divertor pressures.The key factor is the magnetic configuration.The helical divertor was designed to work with the inward shifted configurations with R ax = 3.55-3.65m, but the LTM was observed only in the 3.55 m configuration, the most inward shifted configuration.The close distance of the X-point to the dome and the target plates allows a very compact construction of the divertor unit in a stellarator fusion reactor.

Figure 1 .
Figure 1.Time traces of two plasma shots with different positions of the magnetic axis: 3.6 and 3.55 m. (a), (g) heating powers, (b), (h) hydrogen puff rates, (c), (i) stored energy, (d), (j) line-averaged densities, (e), (k) sub-divertor neutral pressures, and (f ), (l) ion saturation currents of the target mounted Langmuir probe arrays.In the 3.55 m configuration, the low temperature mode of the divertor was detected, which is indicated by the vertical lines.

Figure 2 .
Figure 2. Sub-divertor neutral pressures (8I position) as a function of the line-averaged density (a) and the ion saturation current (b).

Figure 3 .
Figure 3. (a) Set-up of the divertor spectroscopy observing the 3I section and (b) population densities of hydrogen the energy of the level for n = 4, 5, and 6 at the transition into the low temperature mode (LTM).It occurred between 3.4 and 3.5 s.In the LTM, the occupation of the hydrogen levels was described by a Boltzmann distribution which allowed a determination of the temperature (0.25 eV at 3.5 s).

Figure 4 .
Figure 4. Electron temperatures in the plasma edge versus line-averaged density (a) and electron temperature in the divertor time during the LTM derived from the Boltzmann plots (b).The carbon radiation from the divertor spectroscopy is also shown for both magnetic configurations (b).

Figure 5 .
Figure 5. Profiles of saturation currents from the Langmuir probe arrays 8L and 8R with overlaid connection length plots for both magnetic configurations.The longer the flux tube, the more particles are collected from the plasma which strike at the target plates.The data is from the beginning of the LTM at 3.5 s.