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Research on magnetic confinement of high-temperature plasmas has the ultimate goal of harnessing nuclear fusion for the production of electricity. Although the tokamak1is the leading toroidal magnetic-confinement concept, it is not without shortcomings and the fusion community has therefore also pursued alternative concepts such as the stellarator. Unlike axisymmetric tokamaks, stellarators possess a three-dimensional (3D) magnetic field geometry. The availability of this additional dimension opens up an extensive configuration space for computational optimization of both the field geometry itself and the current-carrying coils that produce it. Such an optimization was undertaken in designing Wendelstein 7-X (W7-X)2, a large helical-axis advanced stellarator (HELIAS), which began operation in 2015 at Greifswald, Germany. A major drawback of 3D magnetic field geometry, however, is that it introduces a strong temperature dependence into the stellarator’s non-turbulent ‘neoclassical’ energy transport. Indeed, such energy losses will become prohibitive in high-temperature reactor plasmas unless a strong reduction of the geometrical factor associated with this transport can be achieved; such a reduction was therefore a principal goal of the design of W7-X. In spite of the modest heating power currently available, W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas3,4. The triple product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible1,5. Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization.

The two leading concepts for confining high-temperature fusion plasmas are the tokamak and the stellarator. Tokamaks are rotationally symmetric and use a large plasma current to achieve confinement, whereas stellarators are non-axisymmetric and employ three-dimensionally shaped magnetic field coils to twist the field and confine the plasma. As a result, the magnetic field of a stellarator needs to be carefully designed to minimize the collisional transport arising from poorly confined particle orbits, which would otherwise cause excessive power losses at high plasma temperatures. In addition, this type of transport leads to the appearance of a net toroidal plasma current, the so-called bootstrap current. Here, we analyse results from the first experimental campaign of the Wendelstein 7-X stellarator, showing that its magnetic-field design allows good control of bootstrap currents and collisional transport. The energy confinement time is among the best ever achieved in stellarators, both in absolute figures (τE> 100 ms) and relative to the stellarator confinement scaling. The bootstrap current responds as predicted to changes in the magnetic mirror ratio. These initial experiments confirm several theoretically predicted properties of Wendelstein 7-X plasmas, and already indicate consistency with optimization measures. Results from the first experimental campaign of the Wendelstein 7-X stellarator demonstrate that its magnetic-field design grants good control of parasitic plasma currents, leading to long energy confinement times.

This paper shows with the help of numerical simulations that one may be able to achieve physical conditions necessary for hydrogen metallization by imploding appropriately designed multilayered targets that are irradiated by intense beams of energetic heavy ions. In these calculations we consider the beam parameters that will be available at the GSI accelerator facility by the end of the year 2001 when the upgrade of the present facility will be completed.

At the synchrotron SIS of GSI (Gesellschaft für Schwerionenforschung, Darmstadt, Germany) the energy deposition of intense heavy ion beams in solid targets can be employed to create dense plasmas by isochoric heating and quasi-adiabatic compression. Typical beam parameters are 2.1010Ar18+ions of 300 MeV/u. The stored beam energy of ca. 40 J is deposited in the solid state targets within 250 ns, leading to a specific energy deposition of about 1 kJ/g. Target materials are rare gas crystals, metals especially lead and solid hydrogen or deuterium. Diagnostic tools are high speed and fast shutter, intensified cameras, pressure sensors and spectroscopes. With this experimental setup it was for the first time possible to record the heavy ion beam induced hydrodynamic motion of lead and the emission in the visible range of neon. Though experimental details are different, both in lead and in neon initial pressure values of 0.1-0.3 GPa and temperature of ca. 0.1 eV were measured. Combining the respective properties of lead and hydrogen in compound targets and with the improved beam parameters after the intensity upgrade at SIS we intend to join the experimental activities to produce metallic hydrogen.

Experimental investigations of heavy-ion-generated shock waves in solid, multilayered targets were performed by applying a Schlieren and a laser-deflection technique. Shock velocity and the corresponding pressures, temporal and spatial density profiles inside the material compressed by multiple shock waves, and details of the shock dynamics were determined. Important for equation-of-state and phase transition studies, such experiments extend their relevance to inertial confinement fusion and astrophysical fundamental research.

The article presents the results of the experimental research on precision measurement of total stopping range and energy deposition function of intermediate and heavy ion beams in cold solid matter. The “thick target” method proves to be appropriate for this purpose. Two types of detectors were developed which provide an error of the total stopping range measurement of less than 3% and of the beam energy deposition function of about 7%. The experiments with 58Ni+26, 197Au+65, and 238U+72 ion beams in the energy range 100–300 MeV/u were performed on SIS-18 (Gesellschaft für Schwerionenforschung, Darmstadt) in 1999–2001. The measured data on the total stopping ranges for the above ion species in bulk and foiled Al and Cu targets are presented. The investigation showed that there is a noticeable discrepancy between the measured stopping ranges and the theoretically predicted ones. Also, it was shown that realistic ion energy deposition depends on the type of target (bulk or foiled). Further investigation is necessary to clarify the latter.

At the Gesellschaft für Schwerionenforschung (GSI, Darmstadt) intense beams of energetic heavy ions have been used to generate high-energy-density (HED) state in matter by impact on solid targets. Recently, we have developed a new method by which we use the same heavy ion beam that heats the target to provide information about the physical state of the interior of the target (Varentsov et al., 2001). This is accomplished by measuring the energy loss dynamics (ELD) of the beam emerging from the back surface of the target. For this purpose, a new time-resolving energy loss spectrometer (scintillating Bragg-peak (SBP) spectrometer) has been developed. In our experiments we have measured energy loss dynamics of intense beams of 238U, 86Kr, 40Ar, and 18O ions during the interaction with solid rare-gas targets, such as solid Ne and solid Xe. We observed continuous reduction in the energy loss during the interaction time due to rapid hydrodynamic response of the ion-beam-heated target matter. These are the first measurements of this kind. Two-dimensional hydrodynamic simulations were carried out using the beam and target parameters of the experiments. The conducted research has established that the ELD measurement technique is an excellent diagnostic method for HED matter. It specifically allows for direct and quantitative comparison with the results of hydrodynamic simulations, providing experimental data for verification of computer codes and underlying theoretical models. The ELD measurements will be used as a standard diagnostics in the future experiments on investigation of the HED matter induced by intense heavy ion beams, such as the HI-HEX (Heavy Ion Heating and EXpansion) EOS studies (Hoffmann et al., 2002).

The dynamics of low entropy weak shock waves induced by heavy ion beams in solid targets was investigated by means of a schlieren technique. The targets consist of a metallic absorber for the beam energy deposition followed by a plexiglass block for optical observations. Multiple waves propagating with supersonic velocities at 15 kbar pressures were observed in the plexiglass, for pressures of up to 70 kbar numerically calculated in the absorbers. Pressures in the megabar ranges are predicted for a near future beam upgrade, enabling studies of phase transition to metallic states of H, Kr, and Xe.

The hydrodynamic response of metal targets to volume heating by energy deposition of intense heavy-ion beams was investigated experimentally. Recent improvements in beam parameters led to a marked increase in specific deposition power: 2·1010 40 ions of 300 MeV/u focused to a spot size of 300 μm (σ) × 540 μm (σ) yield a specific deposition energy in solid lead of approximately 1 kJ/g in the Bragg peak, delivered within 250 ns [full width at half maximum (FWHM)]. This value allowed us for the first time to observe heavy-ion-beam-induced hydrodynamic expansion of metal volume targets. Measurements comprise expansion velocities of free surfaces of up to 290 ± 20 m/s, surface temperatures of ejected target matter of 1600–1750 K, and pressure waves in solid metal bulk targets of 0.16 GPa maximum absolute value and 0.8 μs FWHM. The experimental results agree well with the results of a 2D hydrodynamic code. Inside the interaction zone, which can only be accessed by simulation, maximum temperatures are 2800 K and maximum pressures are 3.8 GPa.18+ ions of 300 MeV/u focused to a spot size of 300 μm (σ) × 540 μm (σ) yield a specific deposition energy in solid lead of approximately 1 kJ/g in the Bragg peak, delivered within 250 ns [full width at half maximum (FWHM)]. This value allowed us for the first time to observe heavy-ion-beam-induced hydrodynamic expansion of metal volume targets. Measurements comprise expansion velocities of free surfaces of up to 290 ± 20 m/s, surface temperatures of ejected target matter of 1600–1750 K, and pressure waves in solid metal bulk targets of 0.16 GPa maximum absolute value and 0.8 μs FWHM. The experimental results agree well with the results of a 2D hydrodynamic code. Inside the interaction zone, which can only be accessed by simulation, maximum temperatures are 2800 K and maximum pressures are 3.8 GPa.

An energy loss of 240 MeV argon ions in a Z-pinch helium plasma has been for the first time observed throughout the entire pinching process. Standard Stark broadening analysis gives an electron density ranging from 4 to 6 × 1017 cm−3 during the pinch. To deduce stopping power from the energy loss, the target thickness of the helium plasma has been evaluated assuming the mean charge of helium based on thermal equilibrium. The observed electron density and the mean charge of helium give a target thickness of 30 ± 3 μg cm−2 from 1 μs to 1.8 μs after the discharge ignition. The measured stopping power exceeds a tabulated value for cold helium gas by a factor of 2 to 3 around the time of the first pinch. The experimental stopping power is compared with theoretical values calculated using an equation of stopping power for a partially ionized plasma.

This article reports on the interaction between slow ions and a partially ionized plasma. Temporal evolutions of energy loss and charge distribution of 2.4 MeV oxygen beams in the laser-induced polyethylene plasma were measured. The charge distribution showed strong stripping ability in the early phase of the plasma. Stopping power deduced from the experimental energy loss was 1.9 times larger than that for the solid. The effective charge of the projectile ion was estimated from the yields of 4+ and 6+ states. The peak value of the effective charge was 1.4 times larger than that of the solid. The stopping power equation given by Sigmund was extended for the partially ionized plasma and it could reproduce the measured energy loss.

The energy loss of heavy ions in matter is completely different from the case of laser beams. Whereas laser radiation produces a plasma on the surface of the target and heats the volume mostly by shock waves, heavy ions penetrate deep into the target with an almost-constant energy loss in the beginning and a very high energy loss at the end of the range, the so called “Bragg peak.” This special behavior offers excellent possibilities for the examination of critical points of different materials, the measurement of benchmarks for equations of state, production and detection of X-rays and XUV radiation, investigations in physics of overdense plasma, and many more topics. In particular, heavy ion beams are considered to be a very efficient driver for an inertial confinement fusion power plant. Thus, research on the elementary processes of the energy deposition of heavy ions in matter with respect to inertial fusion energy is of primary interest.

In the version of this Article originally published, and in the associated Publisher Correction, the members of the W7-X Team were not included. All versions of the Article, and the Publisher Correction, have now been amended to include these team members.

In the version of this Article originally published, A. Mollén’s affiliation was incorrectly denoted as number 10; it should have been 1. Throughout the Article, some technical problems in typesetting meant that the tilde symbol above b and one instance of a superscript 2 were too high to be visible; see the correction notice for details. Finally, the citation to ref. 35on page one of the Supplementary Information was incorrect; it should have been to ref. 36. These issues have now been corrected.