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Helicity Injected Torus (HIT): Sustainment of Stable Equilibria Through Self-organization

This is the Final Progress Report of the Helicity Injected Torus (HIT) program covering May 2016 through December 2020. During this final period the HIT program continued to make advancements in computational modeling, theory, and experimental studies of global self-organization and inductively sustained spheromaks. This included many valuable contributions to the fusion, plasma and physics community, through peer-reviewed publications, PhD theses and conference presentations and posters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Study of magnetic helicity injection in the active region NOAA 9236 producing multiple flare-associated coronal mass ejection events

To better understand a preferred magnetic field configuration and its evolution during coronal mass ejection (CME) events, we investigated the spatial and temporal evolution of photospheric magnetic fields in the active region NOAA 9236 that produced eight flare-associated CMEs during the time period of 2000 November 23-26. The time variations of the total magnetic helicity injection rate and the total unsigned magnetic flux are determined and examined not only in the entire active region but also in some local regions such as the main sunspots and the CME-associated flaring regions using SOHO/MDI magnetogram data. As a result, we found that (1) in the sunspots, a large amount of positive (right-handed) magnetic helicity was injected during most of the examined time period, (2) in the flare region, there was a continuous injection of negative (left-handed) magnetic helicity during the entire period, accompanied by a large increase of the unsigned magnetic flux, and (3) the flaring regions were mainly composed of emerging bipoles of magnetic fragments in which magnetic field lines have substantially favorable conditions for making reconnection with large-scale, overlying, and oppositely directed magnetic field lines connecting the main sunspots. These observational findings can also be well explained by some MHD numerical simulations for CME initiation (e.g., reconnection-favored emerging flux models). We therefore conclude that reconnection-favored magnetic fields in the flaring emerging flux regions play a crucial role in producing the multiple flare-associated CMEs in NOAA 9236.

79 ASTRONOMY AND ASTROPHYSICS↗

Test of Point-Source Helicity Injection for Non-Solenoidal Startup in NSTX

This grant supported research activity focused on the development of Local Helicity Injection (LHI) as a technique for initiation and growth of spherical tokamak plasmas without the use of a traditional ohmic solenoid for magnetic induction. The LHI technique consists of injection of high-density current streams into a vacuum magnetic field consisting of toroidal and vertical fields. Under appropriate conditions, these streams become unstable and support magnetic reconnection to allow the system to reconfigure itself into a tokamak-like plasma magnetic configuration. This research program focused on three aspects of this plasma startup technique: 1) development and tests of appropriate electron current sources that provide sufficiently high injection currents into the near-plasma edge without strongly contaminating the resultant tokamak plasma with impurities; 2) development and validation of a 0-D power balance model to describe the evolution of the plasma current I p (t) during this startup process; and 3) initial estimates of I p levels achievable with this technique in NSTX-U scale plasmas. The 0-D model development included extremely low aspect ratio corrections to analytical formulae for the plasma inductances that produce voltages due to rapid changes in plasma size and location. Applications of this model to sample plasmas in the Pegasus ultra-low aspect ratio tokamak confirms the expectation that I p (t) is dominated by these induced voltages when injection occurs from the outer low-field side of the plasma. Conversly, I p (t) is dominated by an effective toroidal loop voltage arising from helicity conservation when injectors are placed in the inner high-field side divertor region. The activities pursued here, combined with more general research on LHI followed by the Pegasus experiment group, provide the tools needed for initial consideration of a MA-level plasma startup capability for the NSTX-U experiment. Simplified modeling for LHI on NSTX-U indicates that no showstoppers exist, and ~ 0.8MA appears accessible using a moderate current injection facility. However, many issues remain to be resolved to address extrapolating this technique to the larger sizes and magnetic field strengths of NSTX-U and larger fusion-grade tokamaks. These include, among others: I p scaling with helicity drive input; extending current injector technology; understanding electron confinement and the resulting helicity dissipation processes that determine the achievable I p ; the role of plasma stability in controlling the current evolution; and controlling plasma-material interactions and impurity content. These open issues will be further explored in a future experiment dedicated to integrated studies of non-solenoidal startup at higher magnetic fields and plasma currents.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetic reconnection process in transient coaxial helicity injection

The physics of magnetic reconnection and fast flux closure in transient coaxial helicity injection experiments in NSTX is examined using resistive MHD simulations. These simulations have been performed using the NIMROD code with fixed boundary flux (including NSTX poloidal coil currents) in the NSTX experimental geometry. Simulations show that an X point is formed in the injector region, followed by formation of closed flux surfaces within 0.5 ms after the driven injector voltage and injector current begin to rapidly decrease. As the injector voltage is turned off, the field lines tend to untwist in the toroidal direction and magnetic field compression exerts a radial J × B force and generates a bi-directional radial E{sub toroidal}×B{sub poloidal} pinch flow to bring oppositely directed field lines closer together to reconnect. At sufficiently low magnetic diffusivity (high Lundquist number), and with a sufficiently narrow injector flux footprint width, the oppositely directed field lines have sufficient time to reconnect (before dissipating), leading to the formation of closed flux surfaces. The reconnection process is shown to have transient Sweet-Parker characteristics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Mean-field Ohm's law and coaxial helicity injection in force-free plasmas

A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity {eta} and hyper-resistivity {Lambda} terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Three-dimensional plasmoid-mediated reconnection and the effect of toroidal guide field in simulations of coaxial helicity injection

Physics of three-dimensional plasmoid-mediated magnetic reconnection during transient Coaxial Helicity Injection (CHI) plasma start-up is explored using nonlinear MHD simulations in a spherical tokamak. We numerically examine (i) the role of three-dimensional magnetic fluctuations arising from current-sheet instabilities on the formation of plasmoid-mediated closed flux surfaces, and (ii) the effect of toroidal guide field on the MHD stability during transient CHI. Here, we find that even in the presence of nonaxisymmetric edge magnetic fluctuations, current-carrying axisymmetric (n = 0) plasmoids are rapidly formed while twisted open field lines are being injected and are merged to form a large current-carrying magnetic bubble for plasma startup in a tokamak. Additionally, it is discovered that the 3-D physics response is drastically different for simulations at a higher toroidal field, and complete stabilization of nonaxisymmetric fluctuations was achieved at a higher toroidal flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Extension of Local Helicity Injection Startup Studies to the Urania Experiment (Final Technical Report)

Initiating high-current plasma in a spherical tokamak (ST) without a central solenoid is a critical issue for the development of the ST configuration. The goal of the research funded through this grant was focused on addressing this challenge by demonstrating scalable startup to high plasma current (I p ), while developing a physical understanding and predictive models for non-solenoidal tokamak plasma startup using Local Helicity Injection (LHI). A major objective of this research and development activity was to use scaling experiments to validate a physics understanding that will support deployment of high-current (~1 MA) startup techniques to fusion-scale facilities such as NSTX-U and beyond.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Physics of forced magnetic reconnection in coaxial helicity injection experiments in National Spherical Torus Experiment

We numerically examine the physics of fast flux closure in transient coaxial helicity injection (CHI) experiments in National Spherical Torus Experiment (NSTX). By performing resistive Magnetohydrodynamics (MHD) simulations with poloidal injector coil currents held constant in time, we find that closed flux surfaces are formed through forced magnetic reconnection. Through a local Sweet-Parker type reconnection with an elongated current sheet in the injector region, closed flux surfaces expand in the NSTX global domain. Simulations demonstrate outflows approaching poloidally Alfvénic flows and reconnection times consistent with the Sweet-Parker model. Critical requirements for magnetic reconnection and flux closure are studied in detail. These primary effects, which are magnetic diffusivity, injector flux, injector flux footprint width, and rate of injector voltage reduction, are simulated for transient CHI experiments. The relevant time scales for effective reconnection are τ{sub V}<τ{sub rec}≈τ{sub A}√(S)(1+Pm){sup 1/4}<τ{sub R}, where τ{sub V} is the time for the injector voltage reduction, τ{sub A} is the poloidal Alfvén transit time, τ{sub R} is the global resistive diffusion time, and Pm and S are Prandtl and Lundquist numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Application of Townsend avalanche theory to tokamak startup by coaxial helicity injection

Townsend avalanche theory is employed to model and interpret plasma initiation in NSTX by Ohmic heating and coaxial helicity injection (CHI). The model is informed by spatially resolved vacuum calculations of electric field and magnetic field line connection length in the poloidal cross-section. The modelis shown to explain observations of Ohmic startup including the duration andlocation of breakdown. Adapting the model to discharges initiated by CHI offers insight into the causes of upper divertor (absorber) arcs in cases where the discharge fails to initiate in the lower divertor gap. Finally, upper and lower limits are established for vessel gas fill based on requirements for breakdown and radiation. It is predicted that CHI experiments on NSTX-U should beable to use as much as four times the amount of prefill gas employed in CHI experiments in NSTX. This should provide greater flexibility for plasma start-up, as the injector flux is projected to be increased in NSTX-U.

NSTX↗

A current-driven resistive instability and its nonlinear effects in simulations of coaxial helicity injection in a tokamak

An instability observed in whole-device, resistive magnetohydrodynamic simulations of the driven phase of coaxial helicity injection in the National Spherical Torus eXperiment is identified as a current-driven resistive mode in an unusual geometry that transiently generates a current sheet. The mode consists of plasma flow velocity and magnetic field eddies in a tube aligned with the magnetic field at the surface of the injected magnetic flux. At low plasma temperatures (∼10–20 eV), the mode is benign, but at high temperatures (∼100 eV) its amplitude undergoes relaxation oscillations, broadening the layer of injected current and flow at the surface of the injected toroidal flux and background plasma. The poloidal-field structure is affected and the magnetic surface closure is generally prevented while the mode undergoes relaxation oscillations during injection. This study describes the mode and uses linearized numerical computations and an analytic slab model to identify the unstable mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reduction of plasma density in the Helicity Injected Torus with Steady Inductance experiment by using a helicon pre-ionization source

A helicon based pre-ionization source has been developed and installed on the Helicity Injected Torus with Steady Inductance (HIT-SI) spheromak. The source initiates plasma breakdown by injecting impurity-free, unmagnetized plasma into the HIT-SI confinement volume. Typical helium spheromaks have electron density reduced from (2–3) × 10{sup 19} m{sup −3} to 1 × 10{sup 19} m{sup −3}. Deuterium spheromak formation is possible with density as low as 2 × 10{sup 18} m{sup −3}. The source also enables HIT-SI to be operated with only one helicity injector at injector frequencies above 14.5 kHz. A theory explaining the physical mechanism driving the reduction of breakdown density is presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulation of multi-pulse coaxial helicity injection in the Sustained Spheromak Physics Experiment

Nonlinear, numerical computation with the NIMROD code is used to explore magnetic self-organization during multi-pulse coaxial helicity injection in the Sustained Spheromak Physics eXperiment. We describe multiple distinct phases of spheromak evolution, starting from vacuum magnetic fields and the formation of the initial magnetic flux bubble through multiple refluxing pulses and the eventual onset of the column mode instability. Experimental and computational magnetic diagnostics agree on the onset of the column mode instability, which first occurs during the second refluxing pulse of the simulated discharge. Our computations also reproduce the injector voltage traces, despite only specifying the injector current and not explicitly modeling the external capacitor bank circuit. Furthermore, the computations demonstrate that global magnetic evolution is fairly robust to different transport models and, therefore, that a single fluid-temperature model is sufficient for a broader, qualitative assessment of spheromak performance. Although discharges with similar traces of normalized injector current produce similar global spheromak evolution, details of the current distribution during the column mode instability impact the relative degree of poloidal flux amplification and magnetic helicity content.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Erratum: “Initial characterization of electron temperature and density profiles in PEGASUS spherical tokamak discharges driven solely by local helicity injection” [Phys. Plasmas 28, 102504 (2021)]

Here, this article describes errata in 'Initial characterization of electron temperature and density profiles in PEGASUS spherical tokamak discharges driven solely by local helicity injection,' Phys. Plasmas 28, 102504 (2021) that correct reported electron temperature values and their implications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗