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Ion Cyclotron Heating in a Levitated Dipole Fusion Reactor

OpenStar Technologies is pursuing the levitated dipole (LD) as a highly modular, loosely-coupled system that leverages their expertise in high temperature superconductor (HTS) technology. The next generation experiment at OpenStar, Tahi (Ma¯ori for “first”), will demonstrate the generation and confinement of fast ions in a levitated dipole for the first time. Ion cyclotron range of frequency (ICRF) heating is a leading candidate for energetic ion formation in Tahi. A frequency in the 10 MHz range will be used for H minority heating or D majority heating with waves launched from an antenna located above the floating coil. Unlike a tokamak, where the targeted cyclotron resonance is typically a vertical path through the center of the plasma, in a dipole the resonance location follows a C-shaped path from the separatrix to the center of the plasma. The value of B also varies significantly within the confined plasma resulting in a large number of cyclotron harmonics present in the low field region. Furthermore, levitated dipoles contain a “first closed flux surface” surrounding the floating coil, in addition to the traditional separatrix /last closed flux surface. Simulation e ff orts using full-wave ICRF codes show that ICRF heating of a levitated dipole reactor is feasible using a pair of toroidal current straps phased to launch the appropriate parallel ( i.e. poloidal) refractive index.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Final Report: Levitated Dipole Experiment

Since the very first experiments with the LDX, research progress was rapid and significant. Initial experiments were conducted with the high-field superconducting coil suspended by three thin rods. These experiments produced long-pulse, quasi-steady-state microwave discharges, lasting more than 10 s, having peak beta values of 20% [Garnier et al., Physics of Plasmas, 13 (2006) 056111]. High- beta, near steady-state discharges have been maintained in LDX for more than 20 seconds, and this capability made LDX the longest pulse fusion confinement experiment operating in the U.S. fusion program. A significant measure of progress in the LDX research program was the routine investigation of plasma confinement with a magnetically-levitated dipole and the resulting observations of confinement improvement. In both supported and levitated configurations, detailed measurements were made of discharge evolution, plasma dynamics and instability, and the roles of gas fueling, microwave power deposition profiles, and plasma boundary shape. High-temperature plasma was created by multi frequency electron cyclotron resonance heating at 2.45 GHz, 6.4 GHz, 10.5 GHz and 28 GHz allowing control of heating profiles. Depending upon neutral fueling rates, the LDX discharges contain a fraction of energetic electrons, with mean energies above 50 keV. Depending on whether or not the superconducting dipole was levitated or supported, the peak thermal electron temperature was estimated to exceed 500 eV and peak densities to approach 1e18 m -3 . We have found that levitation causes a strong inwards density pinch [Boxer et al., Nature Physics, 6 (2010) 207] and we have observed the central plasma density increase dramatically indicating a significant improvement in the confinement of a thermal plasma species.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Diocotron modes in pure electron plasmas in the APEX levitating dipole trap

Abstract Observations of persistent toroidal modes in dipole-trapped pure electron plasmas are presented. Non-neutral electron plasmas were confined by the poloidal magnetic field of the APEX (A Positron Electron eXperiment) levitating dipole trap. The negative bias of the electron emitter was gated to control the filling time. Large amplitude, narrow-band oscillations were consistently observed in wall probe measurements after the fill. The oscillatory image-charge currents induced by the trapped electron plasma typically persisted for many seconds with fundamental frequencies, f 0 = 50 to 500 kHz, that scale with the E → × B → drift velocity. We attribute this feature to the dipole-equivalent of the diocotron mode that is commonly observed in non-neutral plasmas in linear traps.

Deller, A. (ORCID:0000000234301501)↗

Final Report: Levitated Dipole Experiment

Since the very first experiments with the LDX, research progress was rapid and significant. Initial experiments were conducted with the high-field superconducting coil suspended by three thin rods. These experiments produced long-pulse, quasi-steady-state microwave discharges, lasting more than 10 s, having peak beta values of 20%. High-beta, near steady-state discharges have been maintained in LDX for more than 20 seconds, and this capability makes LDX the longest pulse fusion confinement experiment now operating in the U.S. fusion program. In both supported and levitated configurations, detailed measurements are made of discharge evolution, plasma dynamics and instability, and the roles of gas fueling, microwave power deposition profiles, and plasma boundary shape. High-temperature plasma is created by multifrequency electron cyclotron resonance heating allowing control of heating profiles. Depending upon neutral fueling rates, the LDX discharges contain a fraction of energetic electrons, with mean energies above 50 keV. Depending on whether or not the superconducting dipole is levitated or supported, the peak thermal electron temperature is estimated to exceed 500 eV and peak densities reach 10 18 m -3 .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Guiding center equations for the magnetic dipole

Since the discovery of Van Allen radiation belts in the 1960s, observations of energetic ions trapped in the Earth's dipole magnetic field have illustrated the remarkable confinement properties of this configuration. As such, it has been used for confining a hot plasma for nuclear fusion studies, starting from the pioneering work of Bo Lehnert and Akira Hasegawa, in the Levitated Dipole Experiment (LDX) at MIT until 2011 and in the RT-1 experiment at the University of Tokyo. More recently, the dipole has been subject to a renewed interest for fusion studies by a couple of startups and for smaller applications as a cold plasma source. While the equilibrium and magneto-hydrodynamic stability of the dipole have been investigated quite in detail, neoclassical properties of the dipole are comparatively much less known: the dipole is more known in geophysics than in fusion science. For this reason, in this paper, we propose a set of Hamiltonian, guiding-center equations to describe the motion of electrons and ions in a magnetic dipole configuration. We also developed a code, and we show the main features of particle motion, benchmarking our results with the analytical solutions for the bounce and precession motion, which are well documented in the literature. We also draw some general conclusions for the neoclassical transport in usual toroidal confinement schemes, such as the tokamak and the stellarator, pointing out the unique advantages of the dipole in confining energetic particles.

Hamiltonian mechanics↗

A new frontier in laboratory physics: magnetized electron–positron plasmas

We describe here efforts to create and study magnetized electron–positron pair plasmas, the existence of which in astrophysical environments is well-established. Laboratory incarnations of such systems are becoming ever more possible due to novel approaches and techniques in plasma, beam and laser physics. Traditional magnetized plasmas studied to date, both in nature and in the laboratory, exhibit a host of different wave types, many of which are generically unstable and evolve into turbulence or violent instabilities. This complexity and the instability of these waves stem to a large degree from the difference in mass between the positively and the negatively charged species: the ions and the electrons. The mass symmetry of pair plasmas, on the other hand, results in unique behaviour, a topic that has been intensively studied theoretically and numerically for decades, but experimental studies are still in the early stages of development. A levitated dipole device is now under construction to study magnetized low-energy, short-Debye-length electron–positron plasmas; this experiment, as well as a stellarator device that is in the planning stage, will be fuelled by a reactor-based positron source and make use of state-of-the-art positron cooling and storage techniques. Relativistic pair plasmas with very different parameters will be created using pair production resulting from intense laser–matter interactions and will be confined in a high-field mirror configuration. We highlight the differences between and similarities among these approaches, and discuss the unique physics insights that can be gained by these studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Laser refrigeration of optically levitated sodium yttrium fluoride nanocrystals

Solid state laser refrigeration can cool optically levitated nanocrystals in an optical dipole trap, allowing for internal temperature control by mitigating photothermal heating. This work demonstrates cooling of ytterbium-doped cubic sodium yttrium fluoride nanocrystals to 252 K on average with the most effective crystal cooling to 241 K. The amount of cooling increases linearly with the intensity of the cooling laser and is dependent on the pressure of the gas surrounding the nanocrystal. Furthermore, cooling optically levitated nanocrystals allows for crystals prone to heating to be studied at lower pressures than currently achievable and for temperature control and stabilization of trapped nanocrystals

36 MATERIALS SCIENCE↗

Observation of weakly damped modes using high resolution measurement of turbulence in a dipole confined plasma

When plasma is confined by a levitated superconducting current ring, the turbulent radial particle flux changes the direction depending upon the gradient of the particle number within tubes of equal magnetic flux [Garnier et al., Phys. Plasmas 24, 012506 (2017)]. When the density profile is highly peaked, the particle flux is outward. When the density profile is less peaked, turbulence drives an inward “particle pinch.” This change in the direction of particle flux coincides with a reversal of the mean toroidal propagation direction of turbulent fluctuations. Previously, only the mean wavenumber of the fluctuations was reported. The mean wavenumber was computed from the ensemble correlation between two probes. Here, the full frequency-wavenumber power spectrum of the saturated turbulence is calculated by applying Capon’s “maximum likelihood method” to floating potential measurements from an array of probes. The power spectrum shows that the highest intensity modes are due to unstable entropy modes, and the less intense modes coincide with weakly damped convective cells, which rotate toroidally in the direction opposite to the unstable modes. Because the weakly damped modes make up a significant fraction of the fluctuating power, these measurements imply that saturated turbulence in a dipole-confined plasma involves the excitation of weakly damped rotating convective cells.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Positron orbit effects during injection and confinement in a magnetic dipole trap

Lossless injection of positrons into a magnetic dipole trap and their subsequent confinement have been demonstrated. Here, we investigate by numerical single-particle simulations how the radial distribution of positrons in the trap is affected by the measurement itself, the choice of injection parameters, the asymmetry of the electric potential, and by elastic collisions. The results are compared to experimental data. A comprehensive understanding of these effects is a milestone on the road to creating an electron–positron plasma in a trap with a levitating superconducting coil.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The one-dimensional camelback potential in the parallel dipole line trap: Stability conditions and finite size effect

We recently demonstrated a magnetic parallel dipole line (PDL) system that serves as a unique diamagnetic trap with a fascinating one-dimensional camelback potential along its longitudinal axis. The system can be realized with a pair of transversely magnetized cylindrical magnets and a cylindrical graphite rod as the trapped object. In this paper, we present more detailed experimental and theoretical studies of the finite size effect of the rod and its impact on the stability and oscillation dynamics of the trap. We show that the camelback potential effect only occurs when the length of the PDL system is beyond certain critical length (L C ). The length of the trapped rod determines the “effective camelback potential” and is subject to maximum and minimum values for the trap to be stable. Both length and radius of the rod determine the damping dynamics or the quality factor of the oscillator. Finally, these characteristics are important for designing the PDL trap system for various sensing applications, for example, we demonstrated a PDL trap gas viscometer system through measurement of the oscillation damping time constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗