International collaboration on development of a stellarator confinement database has progressed. More than 3000 data points from nine major stellarator experiments have been compiled. Robust dependences of the energy confinement time on the density and the heating power have been confirmed. Dependences on other operational parameters, i.e. the major and minor radii, magnetic field and the rotational transform , have been evaluated using inter-machine analyses. In order to express the energy confinement in a unified scaling law, systematic differences in each subgroup are quantified. An a posteriori approach using a confinement enhancement factor on ISS95 as a renormalizing configuration-dependent parameter yields a new scaling expression ISS04; . Gyro–Bohm characteristic similar to ISS95 has been confirmed for the extended database with a wider range of plasma parameters and magnetic configurations than in the study of ISS95. It has also been discovered that there is a systematic offset of energy confinement between magnetic configurations, and its measure correlates with the effective helical ripple of the external stellarator field. Full documentation of the International Stellarator Confinement Database is available at http://iscdb.nifs.ac.jp/ and http://www.ipp.mpg.de/ISS.

Regression analyses have been carried out for the international stellarator database which includes 859 discharges from the medium-sized helical devices ATF, CHS, Heiliotron E, W7-A and W7-AS. Recent results from enhanced confinen1ent regime such as H mode and reheat mode are excluded from the database. Optimum fit of all devices is given by the following expression (International Stellarator Scaling 95, ISS95), No dependence of 'tE on the isotropic mass is indicated in the data set. No distinct difference between ECH and NBI can be diagnosed. Because of the different density ranges in the two heating methods, a possible difference might, however, be hidden in the density scaling properties. The density dependence of 'tE also turns to be more complicated than a simple power law. Figure 1 shows a comparison of all data together with ITER L mode database with the ISS95 expression. Although it is crucial to use the appropriate definition of a and -t in the comparison of stellarators and tokamaks, the ISS95 scaling describes tokamak data in L mode very well. In other words, also, the stellarator and the tokamak L mode are of comparable confmement quality.In Fig.1, the data of heliotron/torsatron devices and shearless stellarator have opposite offsets with respect to the ISS95 scaling. It should be noted that data stored in the database are primarily obtained in each standard operation.Operational modes with better confinen1ent are obtained by means of intense wall conditioning and tailoring the magnetic geometry in each device. The ISS95 scaling should be recognized as an L-mode-like scaling. The ISS95 scaling is based on the selection of the iotadependent scaling for heliotron/torsatron confinen1ent. It was tested whether the choice of the radial position at which the -t value is taken influences the results. Regressions using -t at p = 1/3 or 1 do not, however, qualitatively change the results. If the iota-independent scaling is selected, the offsets reduces to a level similar to that when the LHD-scaling expression is used. The next generation experiments LHD and W7-X will allow to distinguished more clearly between the two scaling expression.The predicted operational regime in LHD is also illustrated in Fig. 1, which suggests that the operational regime of LHD will be close to those of the present large tokamaks in L mode.

The paper presents a study of empirical scaling of energy confinement observed experimentally in stellarator/heliotron devices (Heliotron E, Wendelstein VII-A, L2, Heliotron DR) for plasmas heated by electron cyclotron heating and/or neutral beam injection. The proposed scaling of the gross energy confinement time is: , where P is the absorbed power (MW), n is the line average electron density (1020 m−3), B is the magnetic field strength on the plasma axis (T), a is the average minor radius (m) and R is the major radius (m). The empirical scaling of the density limit obtainable under the optimum condition is proposed to be: . These scalings for helical systems are compared with those in tokamaks. The energy confinement scaling has a similar power dependence as the L-mode scaling of tokamaks. The density limit scaling for helical systems seems to indicate an upper limit of the achievable density similar to that in many tokamaks. From the energy confinement time and the density limit , a beta limit can be derived: , which can be lower than the stability/equilibrium beta limit. Thus, from the viewpoint of designing a machine, the values of B, a and R should be selected with care because the dependence of the confinement time (or nτET) and of the above beta limit on these values is different.

Demonstrating improved confinement of energetic ions is one of the key goals of the Wendelstein 7-X (W7-X) stellarator. In the past campaigns, measuring confined fast ions has proven to be challenging. Future deuterium campaigns would open up the option of using fusion-produced neutrons to indirectly observe confined fast ions. There are two neutron populations: 2.45 MeV neutrons from thermonuclear and beam-target fusion, and 14.1 MeV neutrons from DT reactions between tritium fusion products and bulk deuterium. The 14.1 MeV neutron signal can be measured using a scintillating fiber neutron detector, whereas the overall neutron rate is monitored by common radiation safety detectors, for instance fission chambers. The fusion rates are dependent on the slowing-down distribution of the deuterium and tritium ions, which in turn depend on the magnetic configuration via fast ion orbits. In this work, we investigate the effect of magnetic configuration on neutron production rates in W7-X. The neutral beam injection, beam and triton slowing-down distributions, and the fusion reactivity are simulated with the ASCOT suite of codes. The results indicate that the magnetic configuration has only a small effect on the production of 2.45 MeV neutrons from DD fusion and, particularly, on the 14.1 MeV neutron production rates. Despite triton losses of up to 50 %, the amount of 14.1 MeV neutrons produced might be sufficient for a time-resolved detection using a scintillating fiber detector, although only in high-performance discharges.