Toroidal Plasmoid Generation via Extreme Hydrodynamic Shear: Optical and Magnetic Studies

Author: Mendoza, Sean A.

Year: 2026

Degree: Dissertation (Ph.D.)

Advisor: Gharib, Morteza

Committee Members: Hutzler, Nicholas R.; Bellan, Paul Murray; Faraon, Andrei; Gharib, Morteza

Option: Aeronautics

Abstract

Water is a ubiquitous molecule that mediates our interactions with the world and the dynamics of the universe on scales from astrophysical to biomolecular. Controlling its behavior is an essential step in semiconductor manufacturing and water purification. While commonly viewed as a conductive medium, pure water is in fact quite a good insulator, with a resistivity of ρ ≈ 18 MΩ cm. Such purity is typically short-lived; however, water of sufficient purity allows for unique interactions with solid media as a result of its strong polarization and high dielectric strength (ε ≈ 80, dipole moment ρ ≈ 3 D). In contact with normal glass, this leads to electric double layer buildup, where the substrate's superficial atoms -oxygen, typically- preferentially adsorb the polarized hydrogen atoms of the water molecules, resulting in the generation of an electrical potential known as contact electrification. If the fluid is further accelerated against the glass, this effect is amplified via a charge-ripping process whose exact nature is still debated.

In this work, we examine a specific result of this contact electrification and triboelectrification process via the impingement of a high-speed jet of pure water, normal to dielectric substrates - mainly quartz glass and lithium niobate - with velocities up to 250 m s^-1. We observe a velocity-dependent electric field which, at a critical threshold of approximately 120 m s^-1, exceeds the breakdown threshold for electrical discharge in air (≈ 3 MV m^-1), resulting in the formation of a toroidal plasma. We show that the condition of the water, e.g. its resistivity, is essential for this phenomenon, and that the intense shear resulting from this impingement is the primary driver of electrification. By changing the ambient gas to helium or argon, a near-complete shift in the optical spectrum is observed, demonstrating that this is mainly a gas-phase phenomenon.

We further investigate the case of argon, which shows an anomalous pale blue luminescence, and determine that the majority of the visible luminescence in the case of argon is a result of bremsstrahlung radiation, i.e. the deceleration of electrons on impact with argon neutrals, and that a symmetric toroidal core near the jet annulus - functionally a cathode - corresponds to a region of elevated electron temperature within a roughly 10 µm radial extent of the jet surface. The near-perfect symmetry of this interior core, along with the elevated electron energy, suggests that the energy and the symmetry may be related.

Given the non-thermal nature of this plasma, we estimate that a magnetic field of up to approximately 290 mT would be required to balance the nitrogen electron pressure (n_ek_BT_e ≈ 10-68 kPa). To determine whether this is phenomenologically feasible, we develop an approach for magnetic field measurement at extreme proximity via remote sensing, in which the sensing elements are directly embedded into the dielectric target. A lab-grown diamond with a thin 5 µm layer of nitrogen-vacancy (NV^-) centers allows magnetometry within approximately 75 µm of the plasma core while requiring no modification to the flow or plasma field. We are able to remotely perform a vector measurement which demonstrates a magnetic field structure consistent with a negatively charged stream of distilled water, and we measure a field strength of up to ±1 µT at a measurement standoff distance of z = -75 µm, which drops rapidly to about 0.25 µT after the onset of plasma. Based on the extensive averaging times of this embodiment, we conjecture that this drop is a consequence of the pulsatile behavior of the discharge, with a signal outside of the dynamic range of our detector.

We then develop a simple electrostatic and magnetostatic picture of the electric field and currents. An electric field model is built from the measurements and the proposed charge distribution. Treating the system as a single closed current circuit, the azimuthal magnetic field follows directly from the enclosed current by Ampère's law, B_θ = µ₀ I / (2πr), with no field where no net current is enclosed.

We consider two currents within this circuit. A weak fluid charging current, O(10 mA) advected with the jet, accounts for the pre-onset field; because our sensor sits outside the enclosed current - where an axisymmetric current produces no field - the ±1 µT we measure reflects the non-axisymmetric part of the distribution. During breakdown a much larger, highly uncertain discharge current (instantaneous peak O(50 A), pulsed at a duty cycle O(10^-4), so its time-average matches the charging current) gives a surface field O(100 mT) at the nominal core radius r ≈ 100 µm, whose magnetic pressure B_θ²/2µ₀ (~a few kPa) acts outward, tending to expand the current loop. This magnetic pressure is of the same order as the computed electron pressures (10-68 kPa)- likely weaker, but not negligible - and both act outward, so a self-consistent model of the observed structure must account for both. While a real azimuthal magnetic field accompanies the flow, the stark symmetry of the plasma core is more plausibly set by the impinging-jet stagnation hydrodynamics and triboelectric charging than by the magnetic self-field.