Helias Reactor Research Articles

Confinement of transitioning particles in bi-helical Wendelstein-type configurations

Recently, stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor was observed numerically. This validated the theoretical predictions that (i) the stochastic diffusion represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators and (ii) it is possible to prevent the escape of particles to the wall by closing the separatrix between the locally trapped and passing states. It was concluded that, in principle, the separatrix could be made closed, resulting in a reduction of fast ion losses, by compensating for the effect of the helical component of the magnetic field $(1, 1)$ with an enhanced ‘anti-helical’ harmonic $(1, -1)$ ; the enlargement of this harmonic was proposed previously for other reasons. This possibility is explored in this work. Equations of previous relevant works were generalised to include the $(1, -1)$ harmonic. Calculations were carried out for several magnitudes of the ratio of anti-helical to helical magnetic field harmonics. Positive effects were found already at the smallest anti-helical harmonic considered: when the latter ratio is 0.25, transitioning particles with the smallest and intermediate pitch parameters are confined and, moreover, their fraction decreased. When the ratio is 0.85, almost all transitioning particles are confined and their fraction is minimal; well-confined localised orbits dominate at the smallest pitch parameters.

Stochastic diffusion of energetic ions in Wendelstein-line stellarators: Numerical validation of theory predictions and new findings

Stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor is observed numerically for the first time. This validates theory prediction that the collisionless stochastic diffusion of these particles represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators [Beidler et al., Phys. Plasmas 8, 2731 (2001)]. The numerical calculation has also demonstrated a possibility to prevent the escape of particles to the wall by making the separatrix between the locally trapped and passing states closed, as was proposed in Tykhyy et al. [Plasma Phys. Control. Fusion 49, 703 (2007)]. It is found that stochastic regions can vary from very narrow to very wide that occupy almost the whole plasma cross section. It is shown that the fraction of alpha particles with closed separatrix in the population of transition alphas can be considerable. Potentially, this fraction can be increased, and the number of transitioning particles can be reduced by a special optimization of the magnetic configuration, which decreases delayed losses of alphas by means of reducing the separatrix maximum radius.

Theory of stochastic diffusion in Wendelstein-line stellarators in the presence of radial electric field

In optimized stellarators of the Wendelstein line prompt losses of fast ions in superbanana orbits are reduced through a modification of the magnetic configuration by high β (ratio of the plasma pressure to the magnetic field pressure), so that most contours of the longitudinal adiabatic invariant of locally trapped particles are closed inside the plasma volume. However, magnetic drift leads to the transformation of some of these particles into the locally passing ones and vice versa. Orbit transformation upon crossing the separatrix between locally trapped and locally passing states is accompanied by jumps in that lead to collisionless stochastic diffusion (SD), which was shown to be an important mechanism of the loss of energetic ions in the optimized Wendelstein-line stellarators (C D Beidler et al 2001 Phys. Plasmas 8 2731). The theory of SD that took into account the phase space asymmetry between locally passing particles with opposite signs of was developed in (A V Tykhyy 2018 Ukr. J. Phys. 63(6) 495). This work extends that theory to consider the effect of radial electric field E r on SD. It is found that negative E r of such magnitudes as those observed in W7-X and predicted in Helias reactor can mitigate SD losses from the plasma core of NBI ions in W7-X and α-particles in Helias. This loss mitigation occurs because added drift increases the range of pitch angles for which separatrices are closed inside the plasma volume, even while it increases the SD coefficient. This means that E r can be used in addition to magnetic configuration changes for both loss mitigation and energy deposition profile optimization.

Landau damping of Alfvénic modes in stellarators

It is found that the presence of the so-called non-axisymmetric resonances of wave–particle interaction in stellarators (which are associated with the lack of axial symmetry of the magnetic configuration, Kolesnichenko et al 2002 Phys. Plasmas 9 517) may have a strong stabilizing influence through Landau mechanism on the toroidicity-induced Alfvén Eigenmodes (TAE) and isomon modes (Alfvénic modes with equal poloidal and toroidal mode numbers and frequencies in the continuum region) destabilized by the energetic ions. These resonances involve largest harmonics of the equilibrium magnetic field of stellarators and lead to absorption of the mode energy by thermal ions in medium pressure plasma, in which case the effect is large. On the other hand, at the high pressure attributed to, e.g., a Helias reactor, thermal ions can interact also with high frequency Alfvén gap modes (helicity-induced Alfvén Eigenmodes and mirror-induced Alfvén Eigenmodes), leading to a considerable damping of these modes. Only resonances with passing particles are considered. The developed theory is applied to various modes in the Wendelstein 7-X stellarator and a Helias reactor, and to two TAE modes in the LHD helical device.

Stellarator nonlinearly saturated periodicity-breaking ideal magnetohydrodynamic equilibrium states

The relaxation of the constraint of periodicity imposed by the external confining magnetic field coils in a nominally 4-field period Helias advanced stellarator configuration produces weak periodicity-breaking deformations of the plasma. The corrugations are driven by the interaction of the pressure gradient with the magnetic field line curvature and correspond to saturated ideal magnetohydrodynamic interchanges with a mode structure dominated by nonresonant Fourier components. The conditions of quasi-isodynamicity of the Helias reactor system investigated are not significantly altered by the periodicity-breaking distortions.

Global hybrid-gyrokinetic simulations of fast-particle effects on Alfvén Eigenmodes in stellarators

Simulations of gyrokinetic energetic ions interacting with the magneto-hydrodynamic (MHD) Alfvén Eigenmodes are presented. The effect of the finite fast-ion orbit width and the finite fast-ion gyroradius, the role of the equilibrium radial electric field, as well as the effect of anisotropic fast-particle distribution functions (loss-cone and ICRH-type distributions), are studied in Wendelstein 7-X stellarator geometry using a combination of gyrokinetic particle-in-cell and reduced MHD eigenvalue codes. A preliminary stability analysis of a HELIAS reactor configuration is undertaken.

HELIAS 5-B magnet system structure and maintenance concept

Work has been continued on the design study of a 5-fold symmetric HELIAS reactor with increased field. The coil shapes were slightly changed from the straightforwardly upscaled W7-X coils to a better suited reactor configuration providing improved plasma confinement and more space for the blanket. This reactor version is now called “HELIAS 5-B”. The previously presented building block structure was adapted to the new shapes and forces, and was further optimized for better load distribution and reduced number of joints. Simplified panels with only one or two plates each are now used.In addition to the previously presented option to separate the whole torus for good access to the in-vessel components, a blanket maintenance concept based on exchange of 400 large blanket segments simultaneously through five vertical ports was devised. Even though this concept is still at an initial state it can be shown that also in a complex stellarator geometry it is possible to have robots running on rails inside the plasma vessel to transport heavy loads.

Coil winding pack FE-analysis for a HELIAS reactor

At the Max-Planck-Institut fuer Plasmaphysik (IPP) a reference design is being created of an upgraded five-periodic HELIAS type stellarator reactor which evolves from Wendelstein 7-X (W7-X) by scaling of the coil centre line geometries by a factor of four. This reactor type was extensively investigated at IPP with regard to physical characteristics and to some extent also to engineering issues. The upgrade concerns an increase of the induction at the plasma axis and correspondingly at the superconductor. The aim is to develop the reactor concept to a stage and such detail that major engineering problems are unveiled, and relevant comparisons with other concepts, including tokamaks, can be drawn in view of upcoming decisions concerning a DEMO reactor. Even though progress in plasma physics, and in particular future results of W7-X and other machines – particularly of ITER – will probably lead to somewhat different coil shapes, no principal changes of the reference design are expected. In this paper the option of a roll-formed square coil cable jacket is investigated. Detailed structural FE analysis of the coil winding pack demonstrates the feasibility of such a conductor which appears to be the most economical option. It also allows sufficient space for a cable current density very similar to that of the ITER TF coil with a similar overall winding pack cross section of ≈0.5 m 2. Already existing Nb 3Sn conductors could thus be safely applied in such a HELIAS reactor. Obvious progress of superconductor technology, particularly concerning Nb 3Al, will be beneficial concerning savings of conductor material, ease of manufacture, higher operation temperature, etc.

Numerical analysis of tungsten transport in drift-optimized stellarator with ergodic and nonergodic plasma configurations

The radial transport of tungsten ions in a fusion plasma of the HELIAS stellarator with five magnetic field periods is studied by means of a new numerical code. The code solves guiding center equations for test particles (tungsten ions) with the use of a Runge–Kutta integrating scheme. Coulomb scattering of the tungsten ions on the background plasma particles (electrons, deuterons and tritons) is simulated by means of a discretized collision operator based on the binomial distribution and presented in terms of pitch-angle scattering and energy slowing down and scattering. The coronal model is used to determine the mean charge state of the tungsten ion ensemble ⟨Z(Te, ne)⟩ as a function of background electron temperature and density. Two plasma configurations with and without ergodic confinement regions and both with finite plasma pressure of β = 3% are considered. The nonergodic configuration possesses closed nested magnetic surfaces throughout the entire confinement volume. The ergodic magnetic field configuration is represented through additional magnetic field perturbations. Comparative analysis of the radial transport is performed for a time interval greater by a factor of 15 than the energy confinement time τE = 1.62 s required for the HELIAS reactor. In spite of the fact that the tendency of impurities to penetrate towards the plasma core is observed in both cases, the stochastic scenario exhibits reduced inward impurity flux.

Status of HELIAS reactor studies

In this paper an overview of the helical advanced stellarator (Helias) reactor studies is presented. The Helias reactor (HSR) is a reactor candidate of the optimized stellarator line, developed at the Max-Planck Institut für Plasmaphysik, in Germany. It is an up-scaled version of the Wendelstein 7X, which accommodates a blanket and a shield and combines the modular coils with the optimized properties of the fusion plasma [T. Andreeva, C.D. Beidler, E. Harmeyer, Yu.L. Igitkhanov, Ya.I. Kolesnichenko, V.V. Lutsenko, A. Shishkin, F. Herrnegger, J. Kißlinger, H. Wobig, The Helias reactor concept: comparative analysis of different field period configurations, Fusion Sci. Technol. 46 (2004) 395–400]. A compact reference version is HSR4/18 with 4-field periods and a 18 m major radius. HSR4/18 can stably operate at an average beta 4–5% and to deliver a fusion power of 3 GW. The design of the HSR demonstrates criteria of a safe and reliable route to ignition, a self-sustained burn without external heating, reliability of the technical components and the tritium breeding blanket. The coil system, the vacuum vessel and the shielding blanket are discussed. A more compact HSR3/15 configuration with 3-field periods and a 15 m major radius shows, however, a considerable amount of the bootstrap current and requires further optimization. A quasi-isodynamical configuration without transitional particle orbits was considered as an option, which confines almost 100% energetic particles.

Effects of the radial electric field on the confinement of trapped fast ions in the Wendelstein 7-X and Helias reactor

Confinement of trapped fast ions in the Wendelstein-line stellarators in the presence of the radial electric field, Er, is studied. It is shown that negative electric field improves the confinement; in particular, a radially localized field can play the role of a transport barrier for the ions escaping from the plasma when Er=0. In contrast to this, the positive electric field tends to deteriorate the ion confinement, unless its magnitude is very large. Such a field accompanied by the plasma rotation with the frequency around a certain magnitude, which we refer to as the resonance rotation frequency, leads to a quick particle loss. A possibility of using the plasma rotation with the resonance frequency for the ash removal in a Helias reactor is considered. The mentioned results are obtained analytically and numerically. The analytical consideration was done on the basis of the derived bounce-averaged equations of the particle motion. The numerical calculations were carried out for Wendelstein 7-X [G. Grieger et al., J. Plasma Fusion Res. Series 1, 53 (1998)] and a Helias reactor [J. Kisslinger et al., Proceedings of the 17th International Conference, Yokohama, 1998 (1999), Vol. 4, p. 1239] by the guiding center code ORBIS (ORBits In Stellarators) developed in this work.

Damping of Alfvén eigenmodes on localized electrons in stellarators

The electron collisional damping of various kinds of Alfvén eigenmodes (AE) in stellarators is studied. Simple expressions for the damping rates of various well-localized AEs are obtained and applied to evaluating the damping rates in the Helias reactor [H. Wobig et al., Fusion Energy 1998, 17th Conference Proceedings, Yokohama, Japan (IAEA, Vienna, 1999), Vol. 4, p. 1235] and quasi-poloidal stellarator [J. F. Lyon et al., Fusion Energy 2002, 19th Conference Proceedings, Lyon, France (IAEA, Vienna, 2002), Paper IC/P-05]. The estimates made indicate that the collisional damping prevents the destabilization of AEs localized at the plasma periphery of the Helias reactor. A new mechanism that can considerably affect the collisional damping of Alfvén waves in stellarators is predicted: it is found that under certain conditions the collisionless orbit transformations between the locally trapped states and locally passing states significantly change the damping rate, so that the latter becomes weakly (logarithmically) dependent on the collision frequency.

The Helias Reactor Concept: Comparative Analysis of Different Field Period Configurations

The Helias reactor (HSR) is an upgraded version of the Wendelstein 7-X (W7-X) experiment. A straightforward extrapolation of W7-X leads to a five-period configuration with a major radius of 22 m. To reduce the size of the reactor, another option with four periods has been investigated. Recent studies have focused on a three-period Helias configuration (HSR3/15i) (major radius 15 m, plasma radius 2.5 m, B = 5 T), which presents a more compact option than the five- and four-period configurations. In HSR3/15i, the resulting magnetic configuration is consistent with the island divertor concept. The stochastic region outside the last magnetic surface is imposed by the remnants of the 3/4 islands and the plasma flows along distinct channels toward the plates. The main problem is due to the high value of the bootstrap current (~1 MA) and alpha-particle losses (estimated as 6%). Further optimization of HSR3/15i can cause the maximum value of the magnetic field at the superconductive coils to be exceeded. There is a trade-off between physics goals (alpha-particle confinement and small bootstrap current) and technical realization (NbTi technology). The comparative analysis of different period configurations will be presented.

Kinetic mirror-induced Alfvén eigenmodes in Wendelstein-type stellarators

Equations of non-ideal Alfvén eigenmodes in stellarator plasmas are derived that take into account the finite ion Larmor radius, the parallel perturbed electric field and dissipative mechanisms. On the basis of these equations, it is shown for the first time that there exist kinetic mirror-induced Alfvén eigenmodes—modes associated with the presence of the mirror Fourier harmonic in the equilibrium configuration (the harmonic that dominates the magnetic field of the optimized stellarators of the Wendelstein line). Destabilization of these modes by fusion-produced α-particles in a Helias reactor is considered.

Improved support concept for the Helias reactor coil system

For the Helias reactor (HSR) a system of non-planar superconducting coils has been developed. The distributions of the magnetic field and the forces are calculated. In order to support the magnetic forces a scheme of mutual support of the coils is applied. The common vault support concept of earlier studies has been modified: Two toroidal support rings, connected to each other, are introduced at the inner part of the coil system. These new rings connect the coils and carry the main part of the centripetal forces. Finite element computations are done with half a field period, taking into account the stellarator symmetry. The mechanical stress and strain distributions inside the coil support structure are analyzed.

The effect of magnetic field modification on heavy ion movement in advanced stellarators and helical devices

Two new physics mechanisms that can be used to shield and exhaust the impurity ions in the toroidal magnetic traps with the rotational transform from the external current coils are considered here. One of them is connected with the stochastic magnetic fields, which can be the barrier for the penetration of impurity ions from the outside in the confinement volume. This way is appropriate in advanced stellarator systems such as the Wendelstein 7 X and the Helias Reactor. Another approach is a possibility to use the process of transition of particles with the blocked trajectories into the helical trapped particles. The particles that should be removed from the center of the confinement volume can go away along the transit trajectories. Such mechanism can be used in the helical device with the noticeable fraction of the transit particles, particularly the large helical device.

α-particle transport induced by Alfvén eigenmodes in the Helias reactor

It is shown that in the Helias reactor [1], depending on the ratio γL/γd with γL(d) the linear growth (damping) rate of the Alfvén eigenmode (AE), there are three regimes of the transport of α-particles resonant with AEs. (i) For 1<γL/γd<<10 the transport is determined solely by the pitch-angle scattering of αs trapped by an AE. In this regime τα>>τs, with τα(s) the α-particle confinement (slowing down) time. (ii) For γL/γd∼10 the dominant transport mechanism is the adiabatic convection of the slowing-down αs trapped by an AE, with particle `life time' in resonance with AE limited by pitch-angle scattering. In this regime τα∼τs. (iii) For γL/γd>> 10 the transport become stochastic with τα<<τs.

Alfvén eigenmodes and their destabilization by energetic circulating ions in Wendelstein-line stellarators*

Instabilities of the Alfvén eigenmodes (AEs) that can be driven bycirculating energetic ions in optimized stellarators of theWendelstein line (Helias configurations) are considered. It isstressed that the Alfvén instabilities in stellarators mayconsiderably differ from those in tokamaks because specificAlfvén eigenmodes and specific resonances of the wave-particleinteraction appear when magnetic configurations arenon-axisymmetric. An important role of the continuum damping inlow-shear stellarators is revealed. Aimed to calculate thecontinuum damping, a set of resistive magnetohydrodynamic (MHD) equations, whichgeneralize the ideal MHD AE equations obtained in Kolesnichenko et al (Kolesnichenko Ya.I. et al 2001Phys. Plasmas 8 491), is derived. The derived equations are solvednumerically to investigate the damping of the AEs of global character in a Helias reactor.

Alfvén instabilities driven by circulating ions in optimized stellarators and their possible consequences in a Helias reactor

This work investigates circulating-particle-induced Alfvén instabilities in optimized stellarators of the Wendelstein line [F. Wagner, Trans. Fusion Tech. 33, 67 (1998)]. A general expression for the growth rate of the instabilities is obtained and analyzed. It is shown that the absence of the axial symmetry makes it possible that various types of Alfvén eigenmodes will be destabilized; both the kind of destabilized Alfvén eigenmodes and the type of the resonances driving the instability may differ from those in tokamaks. In particular, an important role of the helicity-induced resonance is predicted. The discovered new resonances may considerably increase the instability growth rate of both the “gap” modes and the eigenmodes residing below cylindrical Alfvén continuum. The upper limits of the local energy losses of circulating α-particles caused by various Alfvén instabilities in a four-period Helias reactor [C. D. Beidler et al., in Fusion Energy 2000, 18th International Atomic Energy Agency Conference Proceedings, Sorrento, 2000 (International Atomic Energy Agency, Vienna, 2001), Report IAEA-CN-77/FT/4] are evaluated. It is found that certain destabilized Alfvén eigenmodes will affect only alphas with the energy well below 3.5 MeV, which seems to open a possibility to remove the helium ash by exciting the corresponding Alfvén eigenmodes by either energetic particles or an antenna system.

The Helias reactor HSR4/18

The Helias reactor is an upgraded version of the Wendelstein 7-X experiment. A straightforward extrapolation of Wendelstein 7-X leads to HSR5/22, which has 5 field periods and a major radius of 22 m. HSR4/18 is a more compact Helias reactor with 4 field periods and an 18 m major radius. Stability limit and energyconfinement times are nearly the same as in HSR5/22, thus the same fusion power (3000 MW) is expected inboth configurations. Neoclassical transport in HSR4/18 is very low, and the effective helical ripple is below 1%. The article describes the power balance of the Helias reactor, and the blanket and maintenance concepts. The coil system of HSR4/18 comprises 40 modular coils with NbTi superconducting cables. The reduction from 5 to 4 field periodsand the concomitant reduction in size will also reduce the cost of the Helias reactor.