As the boundaries of hypersonic flight continue to expand—fueled by both defense imperatives and renewed interest in rapid global access—researchers find themselves increasingly confronted with the intersection of two complex and historically separate domains: high-speed gas dynamics and plasma physics. While both have matured independently over the decades, the specific case of electric discharges in high-enthalpy nonequilibrium flows forces a confluence of these fields that demands new physical insight, modeling frameworks, and experimental techniques.

Nonequilibrium: The Norm, Not the Exception

In many terrestrial and low-speed flow plasma applications, the background gas (before the plasma is generated) is either at room temperature or in a thermodynamically equilibrium at higher temperature. Of course, when electrical breakdown occurs and plasma is created, the plasma is typically in nonequilibrium state, with electron and vibrational temperatures being higher than the translational temperature of the gas molecules, and the number densities of excited and chemically active species at a level much higher than what would be expected in thermodynamic equilibrium.

In contrast, hypersonic shock and boundary layers are in an interesting regime where temperature is high (thousands to tens of thousands of Kelvin in shock layers), but the high thermal energy is distributed unevenly among molecular energy modes before any electric discharge is applied.

This pre-existing thermal nonequilibrium—where translational, rotational, vibrational, and electronic temperatures can differ by orders of magnitude—has major implications for the physics of electric discharges. In such flows, vibrational excitation (which facilitates ionization through stepwise processes) may lag behind translation, while electronically excited species may be under- or over-populated due to radiative or collisional processes that are far from equilibrium.

To put it simply: the “background” gas is itself out of equilibrium, dynamically evolving, and not something that can be treated as a passive medium for plasma formation.

Breakdown in Nonequilibrium Air: More Than a Function of Pressure and Temperature

Electric breakdown—typically described using Paschen’s Law or its high-frequency variants—depends strongly on gas composition, pressure, and the applied electric field. However, in hypersonic nonequilibrium air, we face a situation where the effective breakdown threshold is affected by the state of internal energy modes of air molecules.

Consider a high-altitude flow where translational temperature is ~3,000 K, but vibrational temperature remains near 500 K due to insufficient relaxation time. In such a case, the population of vibrational levels critical for stepwise ionization is diminished. As a result, the reduced electric field E/N required for breakdown is substantially elevated, and the discharge may either fail to ignite or be confined to a narrow pre-ionized region.

Furthermore, the presence of excited atoms (especially metastable oxygen and nitrogen) can contribute additional pathways for ionization and energy transfer—yet the formation and quenching of these states in nonequilibrium flows is not well understood and is often excluded from simplified discharge models.

Pulsed Discharges: A Path Forward in Harsh Environments

Despite these complexities, pulsed discharges—especially in the nanosecond regime—offer a viable route to achieving and sustaining plasmas in challenging flow conditions. Nanosecond pulses can generate high peak electric fields (on the order of tens of kV/cm) over short timescales (10–100 ns), sufficient to cause electron avalanching even in low-density or vibrationally cold air.

The benefit of such short pulses lies in their ability to drive the electron energy distribution function (EEDF) into a non-equilibrium state, where high-energy electrons dominate and drive inelastic processes—dissociation, excitation, and ionization—before heavy species have time to respond thermally.

Yet here again, the interaction with the nonequilibrium background becomes important: the rates of electron-impact reactions are sensitive not just to EEDF shape, but also to the evolving composition of the air (e.g., partial dissociation, presence of O and N atoms, NO formation), which feeds back into discharge sustainment.

Coupling Discharge Models with Flow Solvers

To simulate these interactions accurately, conventional fluid or drift-diffusion models are often insufficient. A good high-fidelity model must resolve:

●     Detailed electron kinetics (including Boltzmann or Monte Carlo solutions for EEDF),

●     Multi-temperature energy modes (T_trans, T_vib, T_rot, T_elec, T_e),

●     Non-equilibrium chemistry (including excited states),

●     And electrodynamic fields (especially in pulsed or microwave regimes).

Researchers are working on integrating such physics into high-fidelity plasma-flow solvers that can capture the coupling between discharge physics and hypersonic gas dynamics. This is not merely an academic exercise—it is essential for designing plasma actuators that actually function in flight-relevant conditions, whether for ignition enhancement, drag reduction, or steering via asymmetric heating.