ASCOT simulations of 14 MeV neutron rates in W7-X: effect of magnetic configuration
Joona Kontula, Jan Paul Koschinsky, Simppa Äkäslompolo, Taina Kurki-Suonio, W7-X team
AASCOT simulations of W7-X neutron rates: effectof magnetic configuration
J. Kontula , J. P. Koschinsky , S. ¨Ak¨aslompolo ,T. Kurki-Suonio and the W7-X team A Aalto University, Department of Applied Physics, Espoo, Finland Max-Planck-Institut f¨ur Plasmaphysik, Greifswald, Germany A For the Wendelstein 7-X Team, see the author list: T. Klinger et al., Nucl. Fusion59, 112004 (2019). doi.org/10.1088/1741-4326/ab03a7.E-mail: [email protected]
Abstract.
Demonstrating improved confinement of energetic ions is one of the key goals ofthe Wendelstein 7-X (W7-X) stellarator. In the past campaigns, measuring confinedfast ions has proven to be challenging. Future deuterium campaigns would openup the option of using fusion-produced neutrons to indirectly observe confined fastions. There are two neutron populations: 2 .
45 MeV neutrons from thermonuclear andbeam-target fusion, and 14 . . .
45 MeVneutrons from DD fusion and, particularly, on the 14 . .
1. Introduction
Stellarators provide a promising alternative to the conventional tokamak fusionreactor concept. Their advantages are steady-state operation, lack of current-driveninstabilities, and a wide variety of magnetic configurations. However, due to lack ofaxisymmetry they require careful optimization of the magnetic field in order to ensureconfinement of trapped particles. Wendelstein 7-X (W7-X) is an advanced stellaratorlocated at the Max Planck Institute for plasma physics in Greifswald, Germany [1]. Ituses an optimized set of 3D shaped modular coils, as well as planar coils, to achieve a a r X i v : . [ phy s i c s . p l a s m - ph ] S e p SCOT simulations of W7-X neutron rates: effect of magnetic configuration . .
45 MeV neutrons and gamma rays, andtherefore it can measure the neutron flux from DT reactions exclusively. If the flux issufficiently high, even time-resolved measurements can be made. When cross-calibratedwith either the overall neutron rate or the shot-integrated 14 . SCOT simulations of W7-X neutron rates: effect of magnetic configuration .
45 MeV and 14 .
2. Physics of neutron generation in W7-X
There are two reaction channels for pure DD fusion, each of which has approximatelyequal probability: D + D −→ p(3 .
02 MeV) + T(1 .
01 MeV) (50 %) D + D −→ n(2 .
45 MeV) + He(0 .
82 MeV) (50 %)The 1 .
01 MeV tritons born from the first reaction channel can, in turn, partake in DTfusion reactions with deuterium ions: D + T −→ n(14 . α (3 . SCOT simulations of W7-X neutron rates: effect of magnetic configuration ◦ or 27 ◦ from fully perpendicular, depending on the PINI. In the latest W7-Xcampaing, the NBI system was successfully commissioned for hydrogen injection withtwo PINIs. The NBI system in W7-X will be extended for more sources and deuteriumoperation in future experiments [13]. The parameters for deuterium injection are shownin table 1. Table 1.
Planned parameters for W7-X deuterium neutral beam injection.
Acceleration voltage 60 kVMax. number of PINIs 8Beam power (all sources) 15 . E b ); 25% ( E b / E b / R A − B = n A n B δ AB (cid:104) σv (cid:105) AB , (1) (cid:104) σv (cid:105) AB ∝ T − / e T − / , (2)where the delta function ensures that reactions from the same population are not doublycounted. The fusion rate coefficient (cid:104) σv (cid:105) AB has a strong temperature dependency. Fornon-Maxwellian distributions, the cross sections depend similarly on the center-of-massenergy of the reactants. Due to the relatively low thermal ion energies in W7-X, thebeam-target fusion is expected to be the primary production channel, making the beamslowing-down distribution critical in determining the total fusion rate.By using an energy-discriminating neutron detector, such as a scintillating fiber(SciFi) detector [6, 8] and a common detector monitoring the overall neutron rate, it ispossible to separately measure the 2 .
45 MeV and 14 . SCOT simulations of W7-X neutron rates: effect of magnetic configuration Figure 1.
Flowchart of the data and tools used. The black arrows represent simulationI/O. the fusion reactivity, the triton slowing-down time, and possible triton orbit losses. Thefirst two are determined by the kinetic profiles, while the losses are determined by themagnetic configuration.The magnetic configuration space studied in this work is spanned by the W7-Xreference magnetic configurations. These consist of high mirror (HM), characterizedby low neoclassical transport and good fast ion confinement; standard (STD) which islocated at the center of the configuration space; low mirror (LM) in which the magneticfield strength is nearly constant along the magnetic axis; inward shifted (IS) and outwardshifted (OS) plasma configurations; low iota (LI) and high iota (HI) configurationswith correspondingly lower and higher edge rotational transform; and low shear (LS)which has a relatively flat rotational transform profile. The same configurations havepreviously been studied for hydrogen beam ion confinement with ASCOT [12], and assuch provide a good reference case for deuterium and triton confinement studies.
3. Numerical approach to triton burnup modeling
For simulating all aspects of triton burnup in W7-X, a staged numerical approach wasadopted. First, the neutral beam injection is simulated with the BBNBI code [15]. Next,a slowing-down simulation of the ionized NBI population was done using the Monte-Carlo orbit following code ASCOT [16]. ASCOT is a comprehensive tool for fast ionsimulations in both tokamaks and stellarators, and has already been successfully usedto predict the beam ion power loads on the plasma-facing components in W7-X [17, 18,19]. The deuterium slowing-down distribution is used as input for the ASCOT FusionSource Integrator AFSI [20], which calculates the DD fusion rates for both reactionchannels. In this work, only the DD → pT channel was considered. The slowing-downdistribution of the 1 .
01 MeV triton population is again calculated with ASCOT, andanother AFSI simulation performed to get the 14 . (cid:104) β (cid:105) = 2 % was used SCOT simulations of W7-X neutron rates: effect of magnetic configuration pol D en s i t y ( m - ) T e m pe r a t u r e ( k e V ) n e n D n C T e T i E r ( k V / m ) Figure 2.
Plasma profiles used for the simulations as a function of ρ (square root ofnormalised toroidal flux). In the upper frame the dashed lines are the species densities;blue for electrons, red for deuterium ions, and yellow for carbon ions. The solid linesshow the electron and ion temperatures. The radial electric field, shown in the lowerframe, is fixed to zero outside ρ = 1 while the plasma profiles are extrapolated linearlyfrom the last two data points. for the plasma profiles, and carbon assumed as the sole impurity. The radial profilesare shown in figure 2. The plasma profiles were originally simulated for a standardconfiguration hydrogen plasma [5], but for the purposes of the deuterium simulationsthe primary plasma species was changed to deuterium while keeping the profile shapeunchanged. The same plasma profiles were used for all of the magnetic configurations.This is not completely rigorous since the magnetic configuration has an effect on thekinetic profiles [24]. However, using the same profiles allows us to isolate the effect of themagnetic configuration. This effect might otherwise be obscured by the profile changes.For the deuterium beam slowing-down simulation, the guiding center approximationwas used. For the 1 .
01 MeV triton simulation, the guiding center approximation is notjustified since the width of the triton gyro orbits at 2 T – the lowest magnetic fieldinside the plasma region of W7-X – can be up to 19 cm, which is of the same orderas the plasma minor radius – approximately 53 cm. This necessitated a full gyro-orbitsimulation for the tritons.
4. Results
For the BBNBI beam injection simulations, the full beam power of 1 .
96 MW for eachPINI – 15 . SCOT simulations of W7-X neutron rates: effect of magnetic configuration . . ρ (square root of normalised toroidalflux) used in the simulations is that it is interpolated from a regular 3D grid. As the fluxsurfaces are packed more tightly near the plasma core, the spatial resolution of ρ nearthe magnetic axis is poor. Due to this limitation, the radial distributions inside ρ = 0 . ρ = 0 . ρ , i.e., the shell volumes, are different for each configuration,leading to differences in the ion birth density. The large variation in the profiles nearthe axis are mainly caused by the small shell volumes, which exaggerates the differencesbetween configuration.The observed fast ion birth profile is unfavorable for fast ion confinement. W7-Xis optimized for improved fast ion confinement only near the axis, while the BBNBIsimulations predict that over 80 % of the particles are born outside ρ = 0 . SCOT simulations of W7-X neutron rates: effect of magnetic configuration I on i z a t i on r a t e ( s - m - ) HMLMISHISTDOSLILS
Figure 3.
Beam ion birth profiles for the different magnetic configurations. The totalnumber of ionized particles is approximately equal in all of the configurations.
The deuterium beam slowing-down simulations were done using 100 000 markers persimulation. The markers were followed using the guiding-center formalism until theypassed the LCFS or their energy was less than twice the local thermal energy, in whichcase the particle was considered thermalized. For the particles crossing the LCFS, thesimulation was continued in full gyro-orbit mode to account for wall collisions accurately.The resulting radial beam-ion distributions are shown in figure 4. Unlike the deuteriumbirth profiles, the slowing-down density profiles have a flat shape with the density rapidlydecreasing outside ρ = 0 .
8, the profile shape being similar between the configurations.The profile flattening is due to the beam particle loss fraction increasing rapidly towardsthe edge of the plasma, the loss fraction being 2 to 5 times higher at ρ = 0 . . . SCOT simulations of W7-X neutron rates: effect of magnetic configuration B ea m i on den s i t y ( m - ) HMLMISHISTDOSLILS
Figure 4.
Slowing-down distribution of injected deuterium for different magneticconfigurations. The peaked deuterium birth profile is flattened by the larger lossfraction of particles near the edge of the plasma. the particles were lost during their first orbit. Most of the fast ion losses were via driftmotion.The fusion rates between the full 5D slowing-down and thermal distributions werecalculated with AFSI and converted to 1D ρ -profiles for visualization purposes. Onlythe DD → pT reaction channel was calculated: the rates are identical to the otherreaction channel. The AFSI results indicate that the triton birth distribution is peakedin the center of the plasma, as shown in figure 5. This is due to the fact that both theion temperature and the beam ion mean energy – the high energy component of thebeams penetrates the plasma more easily – are centrally peaked and the fusion crosssections have a strong dependence on the ion center-of-mass energy.Of all the simulated scenarios, the high-iota configuration had the highest totaltriton (and 2 .
45 MeV neutron) production rate of 7 . × s − , while the low mirrorconfiguration had the lowest rate at 5 . × s − . A comparison between all magneticconfigurations is shown in figure 6, where the production channels are also separated.In all configurations, the majority of fusion reactions come from the beam-targetproduction channel and the beam-target fusion rate is almost directly proportional tothe mean beam ion density in the plasma, which is in turn determined by the beamion confinement properties of the configurations. The thermonuclear contribution isvirtually identical between the different configurations as the plasma profiles were keptconstant. The beam-beam reactions constitute less than 2 % of the total fusion rate dueto the low density of the beam ions. SCOT simulations of W7-X neutron rates: effect of magnetic configuration DD p T f u s i on r a t e ( s - m - ) HMLMISHISTDOSLILS
Figure 5.
Radial DD → pT fusion rate or, equivalently, 2 .
45 MeV neutron and1 .
01 MeV triton birth rate profiles as a function of ρ for the different magneticconfigurations. The solid lines are the total, the dashed lines the beam-target, andthe dotted lines the thermonuclear DD → pT fusion rates, respectively. H M L M I S H I S T D O S L I L S DD p T f u s i on r a t e ( s - ) Figure 6.
Total DD → pT fusion rates or, equivalently, 2 .
45 MeV neutron and1 .
01 MeV triton birth rates in different magnetic configurations. The rates are splitaccording to their production channels: thermonuclear (blue), beam-target (orange),and beam-beam (yellow).
For the triton slowing-down simulation, 100 000 markers were randomly sampledfrom the 5D triton birth distribution and simulated with ASCOT using the full-orbit formalism. The resulting radial triton slowing-down distributions are shown infigure 7. The total triton power loss fraction was between 42 % to 51 % in the differentconfiguration, which is much higher than for deuterium ions. This is not surprising, sincethe triton Larmor radius can be up to half the plasma minor radius. The loss fraction
SCOT simulations of W7-X neutron rates: effect of magnetic configuration den s i t y ( m - ) T r i t on HMLMISHISTDOSLILS
Figure 7.
Slowing-down distribution of tritons for the different magneticconfigurations. The profiles are highly peaked in the plasma core, where the tritonbirth rate is the highest and loss fraction lowest. increases radially from over 50 % for tritons born near the axis to over 80 % for thoseborn outside ρ = 0 .
9. Due to this and the centrally peaked triton birth profiles, thetriton slowing-down profiles are highly peaked in the plasma core. The profile shape issimilar between the configurations, and the differences lie in the total integrated numberof tritons in the plasma.The triton losses are highly dependent on the particle initial pitch, and the tritonslowing-down distributions have a distinct gap at low pitch values. This is due to thefact the energetic particles in this gap are on trapped orbits and are lost from the devicevia magnetic drifts. They thus have little time to contribute to the fast-ion distribution.This process is illustrated by figure 8, where the total amount of lost particles is shownas a function of the initial pitch and the time it takes for the particle to be lost. Lessthan 2 % of the particles are also lost via first-orbit losses at times less than 10 − s.Apart from the collisional losses at t > − s, the tritons are lost at practically theirfull 1 .
01 MeV energy.An initial AFSI estimation of the DT fusion rate from the reactions between beamdeuterium and fast tritons yielded only 10 neutrons / s, which is only one per mill of thetotal neutron birth rate of more than 10 neutrons / s. Due to this, only plasma-tritonreactions were included in subsequent analysis. The reason for the low contribution ofthe beam-triton reactions is that, from the 1 .
01 MeV triton point of view, the beam ionenergy is practically the same as the thermal ion energy and the beam density is morethan two orders of magnitude lower than the plasma density. The radial profiles of the
SCOT simulations of W7-X neutron rates: effect of magnetic configuration -1 -0.5 0 0.5 1 Pitch angle ( ) -8 -6 -4 -2 T i m e ( s ) -3 Figure 8.
Amount of lost particles as a function of initial pitch ξ and loss timefor the standard configuration triton slowing-down simulation. The color axis is thenormalized number of markers in each histogram slot. The particles can be categorizedto first-orbit losses at t ≤ − s, losses of trapped orbits at t ≤ − s, and collisionallosses at t > − s. DT fusion rates are shown in figure 9.The total DT fusion rates in all of the configurations were between 1 . × s − and 1 . × s − ; the total rates for all configurations are shown in figure 10. Variationbetween the configurations for the DT fusion rates are smaller than for the DD fusionrates, and the triton burn-up ratio was approximately 0 . .
05 % to 0 .
45 % [25]. The constant burn-up ratio implies that the DT fusion rate is mainly determined by the triton slowing-downdistribution and consequently effected by the triton confinement properties.
To assess the sensitivity of the neutron rate on the plasma kinetic profile, one additionalsimulation was performed for the standard configuration. In this simulation, the centralplasma density was halved to 10 m − and the central temperature doubled to 3 keV.This maintains the same volume-averaged beta value ( (cid:104) β (cid:105) = 2 %) while increasing thefusion reactivity and the triton slowing-down time.The NBI shine-through fraction was 14 . SCOT simulations of W7-X neutron rates: effect of magnetic configuration D T n H e f u s i on r a t e ( s - m - ) HMLMISHISTDOSLILS
Figure 9.
Total DT fusion rates as a function of radial coordinate ρ for the differentmagnetic configurations. The fusion rates are even more centrally peaked and theabsolute differences between configurations further reduced compared to the tritonbirth distributions. H M L M I S H I S T D O S L I L S D T n H e f u s i on r a t e ( s - ) Figure 10.
Total D-T fusion rates in different magnetic configurations. The relativedifferences between configurations are smaller than for the D-D fusion rates. down. The total 2 .
45 MeV neutron and triton birth rates were found to increase from6 . × s − to 2 . × s − due to the increased beam-plasma and thermonuclearfusion reactivities. The beam-beam fusion rate also increased by more than an orderof magnitude. The triton power losses however remained virtually identical (47 % to48 %). The total 14 . . × s − , which is more than eighttimes larger than for the high-density scenario. Increasing the plasma temperature thusdominates over the differences between magnetic configurations. SCOT simulations of W7-X neutron rates: effect of magnetic configuration
5. Conclusions and further work
In this work we have verified that while the confinement of fast ions depends not onlyon the plasma profiles but also strongly on the magnetic configuration in W7-X, thisdifference does not extend to the DD and DT fusion rates, which are mainly governedby the kinetic profiles. In order to isolate the effect of the magnetic configuration onthe neutron rates, the plasma profiles were left unchanged between the configurations.In reality the temperature and density will differ between magnetic configurations [24].Since the plasma profiles were kept identical, the only difference in fast ionconfinement and the fusion rates comes from the magnetic field configuration. Themagnetic geometry has the largest effect on the fast ion losses near the plasma edge,where most of the NBI ions are born. Consistently, differences of up to 80 % were foundin deuterium beam confinement between configurations, causing significant differences inthe slowing-down distribution function. On the other hand, fusion occurs predominantlyin the plasma core, where the configuration effects are weaker. Due to this, the tritonbirth rates differ only up to 18 % between configurations.This configuration difference is smaller for tritons, since they are mainly bornin the plasma core; the triton power-loss fraction was between 42 % to 51 % in allof the configurations. Of the studied magnetic configurations, the high-iota scenariowas found to have the highest DT fusion and 14 . . × s − neutrons produced. Consistently, the low-iota configuration resulted inthe least amount of 14 . . × s − . The differences are neverthelessinsignificant compared to the effect of changing the kinetic profiles, where the total14 . (cid:104) β (cid:105) constant.These simulations were done using all of the proposed NBI injectors in W7-Xsimultaneously, with a total power of 15 . .
84 MW, i.e., using half of the injectors. This wouldapproximately halve the beam-target and beam-beam fusion rates presented in thiswork, depending on which PINIs are operated. Simulation using experimental plasmaprofiles and limited number of PINIs are thus required for more realistic neutron rateestimates once the experimental limitations of DD operation in W7-X are clarified.Earlier estimates [7] suggest that a total neutron production rate of 10 s − ,integrated over the plasma volume, would be needed for time-resolved neutronmeasurements with a SciFi detector. This estimate includes a simple estimation of theneutron propagation to the detector. Based on the ASCOT simulations, the amount of14 . s − . Nevertheless, time-resolved SciFi measurementsmight be possible in high-performance phases with higher ion temperature and higherbeta.5The volume-integrated neutron production rate is not directly comparable to theneutron signal at the detector, as the neutron distribution has both spatial and velocitydependence. Thus, the next step towards a more reliable neutron signal estimate wouldbe a realistic simulation of the 2 .
45 MeV and 14 . r L of1 .
01 MeV tritons in W7-X is similar to 3 . r ∗ = r L /a , where a is the machine minor radius, of particles would be smallerin a HELIAS due to the larger machine size and higher magnetic field. Acknowledgments
The calculations were performed on Marconi-Fusion, the High Performance Computerat the CINECA headquarters in Bologna (Italy). The computational resources providedby Aalto Science-IT project are also acknowledged. This work was partially funded bythe Academy of Finland project No. 298126. This work has been carried out within theframework of the EUROfusion Consortium and has received funding from the Euratomresearch and training programme 2014-2018 and 2019-2020 under grant agreement No633053. The views and opinions expressed herein do not necessarily reflect those of theEuropean Commission.
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