Numerical MHD simulations are used to gain insight into how sawteeth are affected by three-dimensional shaping from the Compact Toroidal Hybrid (CTH) stellarator field. CTH is a small stellarator-tokamak hybrid and sawteeth are sometimes seen on soft x-ray signals when operating with tokamak like profiles. We use NIMROD to compute numerical solutions having repeated sawtooth relaxations for a sequence of configurations with increasing helical stellarator field strength. The experimentally observed trend of the sawtooth period decreasing as the helical field strength is increased is recovered in the simulations. Careful attention to numerical convergence was required to obtain the results, and these considerations may be relevant to simulations of other phenomena in devices with non-axisymmetric plasmas such as perturbed tokamaks, RFPs, and stellarators.
Tokamak-like sawtooth oscillations are observed in the Compact Toroidal Hybrid (CTH), a current-carrying stellarator. CTH has the unique ability to change the amount of the applied vacuum rotational transform from external stellarator coils relative to the rotational transform generated by the internal plasma current to investigate the effects of strong three-dimensional magnetic shaping on sawtooth behavior. The observed sawteeth in CTH, for plasmas with monotonically decreasing rotational transform profiles dominated by the plasma current, have characteristics of those observed on tokamaks including (1) a central emissivity rise and then a sudden crash with a well-defined inversion radius, (2) the presence of an m = 1 emissivity fluctuation, and (3) the normalized inversion surface radius scales with the total edge rotational transform. We explore the properties of an ensemble of discharges in CTH in which the fractional rotational transform, defined as the vacuum rotational transform divided by the total rotational transform, is systematically varied from 0.04 to 0.42 to observe changes in sawtooth oscillation dynamics. Over this range of the fractional rotational transform, the measured sawtooth period decreased by a factor of two. At a high fractional rotational transform, the sawtooth amplitude is observed to consist of only low-amplitude oscillations while the measured crash time of the sawtooth oscillation does not appear to have a strong dependence on the amount of the fractional transform applied. Experimental results indicate that the low-amplitude sawteeth are accompanied by a decrease in the sawtooth period and predominantly correlated with the mean elongation (due to the increasing fractional rotational transform) of the non-axisymmetric plasmas within CTH rather than other global equilibrium parameters.
Understanding the role of physical processes contributing to breakdown is critical for many applications in which breakdown is undesirable, such as capacitors, and applications in which controlled breakdown is intended, such as plasma medicine, lightning protection, and materials processing. The electron emission from the cathode is a critical source of electrons which then undergo impact ionization to produce electrical breakdown. In this study, the role of secondary electron yields due to photons (γ ph) and ions (γ i) in direct current breakdown is investigated using a particle-in-cell direct simulation Monte Carlo model. The plasma studied is a one-dimensional discharge in 50 Torr of pure helium with a platinum cathode, gap size of 1.15 cm, and voltages of 1.2–1.8 kV. The current traces are compared with experimental measurements. Larger values of γ ph generally result in a faster breakdown, while larger values of γ i result in a larger maximum current. The 58.4 nm photons emitted from He(21P) are the primary source of electrons at the cathode before the cathode fall is developed. Of the values of γ ph and γ i investigated, those which provide the best agreement with the experimental current measurements are γ ph = 0.005 and γ i = 0.01. These values are significantly lower than those in the literature for pristine platinum or for a graphitic carbon film which we speculate may cover the platinum. This difference is in part due to the limitations of a one-dimensional model but may also indicate surface conditions and exposure to a plasma can have a significant effect on the secondary electron yields. The effects of applied voltage and the current produced by a UV diode which was used to initiate the discharge, are also discussed.
Low edge safety factor operation at a value less than two (q(a)=1/ι̷tot(a)<2) is routine on the Compact Toroidal Hybrid device with the addition of sufficient external rotational transform. Presently, the operational space of this current carrying stellarator extends down to q(a)=1.2 without significant n = 1 kink mode activity after the initial plasma current rise phase of the discharge. The disruption dynamics of these low edge safety factor plasmas depend upon the fraction of helical field rotational transform from external stellarator coils to that generated by the plasma current. We observe that with approximately 10% of the total rotational transform supplied by the stellarator coils, low edge q disruptions are passively suppressed and avoided even though q(a) < 2. When the plasma does disrupt, the instability precursors measured and implicated as the cause are internal tearing modes with poloidal, m, and toroidal, n, helical mode numbers of m/n=3/2 and 4/3 observed on external magnetic sensors and m/n=1/1 activity observed on core soft x-ray emissivity measurements. Even though the edge safety factor passes through and becomes much less than q(a) < 2, external n = 1 kink mode activity does not appear to play a significant role in the disruption phenomenology observed.
Non-axisymmetric free-boundary equilibrium reconstructions of stellarator plasmas are performed for discharges in which the magnetic configuration is strongly modified by ohmically driven plasma current. These studies were performed on the compact toroidal hybrid device using the V3FIT reconstruction code with a set of 50 magnetic diagnostics external to the plasma. With the assumption of closed magnetic flux surfaces, the reconstructions using external magnetic measurements allow accurate estimates of the net toroidal flux within the last closed flux surface, the edge safety factor, and the plasma shape of these highly non-axisymmetric plasmas. The inversion radius of standard sawteeth is used to infer the current profile near the magnetic axis; with external magnetic diagnostics alone, the current density profile is imprecisely reconstructed.
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