No abstract

A bounded plasma where the electrons impacting the walls produce more than one secondary on average is studied via particle-in-cell simulation. It is found that no classical Debye sheath or space-charge limited sheath exists. Ions are not drawn to the walls and electrons are not repelled. Hence the plasma electrons travel unobstructed to the walls, causing extreme particle and energy fluxes. Each wall has a positive charge, forming a small potential barrier or "inverse sheath" that pulls some secondaries back to the wall to maintain the zero current condition.

Most works on plasma-wall interaction predict that with strong electron emission, a nonmonotonic "space-charge-limited" (SCL) sheath forms where the plasma potential is positive relative to the wall. We show that a fundamentally different sheath structure is possible where the potential monotonically increases toward a positively charged wall that is shielded by a single layer of negative charge. No ion-accelerating presheath exists in the plasma and the ion wall flux is zero. An analytical solution of the "inverse sheath" regime is demonstrated for a general plasma-wall system where the plasma electrons and emitted electrons are Maxwellian with different temperatures. Implications of the inverse sheath effect are that (a) the plasma potential is negative, (b) ion sputtering vanishes, (c) no charge is lost at the wall, and (d) the electron energy flux is thermal. To test empirically what type of sheath structure forms under strong emission, a full plasma bounded by strongly emitting walls is simulated. It is found that inverse sheaths form at the walls and ions are confined in the plasma. This result differs from past particle-in-cell simulation studies of emission which contain an artificial "source sheath" that accelerates ions to the wall, leading to a SCL sheath at high emission intensity.

Hot cathodes are crucial components in a variety of plasma sources and applications, but they induce mode transitions and oscillations that are not fully understood. It is often assumed that negatively biased hot cathodes have a space-charge limited (SCL) sheath whenever the current is limited. Here, we show on theoretical grounds that a SCL sheath cannot persist. First, chargeexchange ions born within the virtual cathode (VC) region get trapped and build up. After the ion density reaches the electron density at a point in the VC, a new neutral region is formed and begins growing in space. In planar geometry, this 'new plasma' containing cold trapped ions and cold thermoelectrons grows towards the anode and fills the gap, leaving behind an inverse cathode sheath. This explains how transitions from temperature-limited mode to anode glow mode occur in thermionic discharge experiments with magnetic fields. If the hot cathode is a small filament in an unmagnetized plasma, the trapped ion region is predicted to grow radially in both directions, get expelled if it reaches the cathode, and reform periodically. Filament-induced current oscillations consistent with this prediction have been reported in experiments. Here, we set up planar geometry simulations of thermionic discharges and demonstrate several mode transition phenomena for the first time. Our continuum kinetic code lacks the noise of particle simulations, enabling a closer study of the temporal dynamics.

A condition for sheath instability due to secondary electron emission (SEE) is derived for low collisionality plasmas. When the SEE coefficient of the electrons bordering the depleted loss cone in energy space exceeds unity, the sheath potential is unstable to a negative perturbation. This result explains three different instability phenomena observed in Hall thruster simulations including a newly found state with spontaneous ∼20  MHz oscillations. When instabilities occur, the SEE propagating between the walls becomes the dominant contribution to the particle flux, energy loss and axial transport.

Two floating sheath solutions with strong electron emission in planar geometry have been proposed, a “space-charge limited” (SCL) sheath and an “inverse” sheath. SCL and inverse models contain different assumptions about conditions outside the sheath (e.g., the velocity of ions entering the sheath). So it is not yet clear whether both sheaths are possible in practice, or only one. Here we treat the global presheath-sheath problem for a plasma produced volumetrically between two planar walls. We show that all equilibrium requirements (a) floating condition, (b) plasma shielding, and (c) presheath force balance, can indeed be satisfied in two different ways when the emission coefficient γ > 1. There is one solution with SCL sheaths and one with inverse sheaths, each with sharply different presheath distributions. As we show for the first time in 1D-1V simulations, a SCL and inverse equilibrium are both possible in plasmas with the same upstream properties (e.g., same N and Te). However, maintaining a true SCL equilibrium requires no ionization or charge exchange collisions in the sheath, or else cold ion accumulation in the SCL's “dip” forces a transition to the inverse. This suggests that only a monotonic inverse type sheath potential should exist at any plasma-facing surface with strong emission, whether be a divertor plate, emissive probe, dust grain, Hall thruster channel wall, sunlit object in space, etc. Nevertheless, SCL sheaths might still be possible if the ions in the dip can escape. Our simulations demonstrate ways in which SCL and inverse regimes might be distinguished experimentally based on large-scale presheath effects, without having to probe inside the sheath.

Contemporary models of bounded plasmas assume that the target plasma electron temperature far exceeds the temperature of the cold electrons emitted from the target, Temit. We show that when the sheath facing a collisional plasma becomes inverted, the target plasma electron temperature has to equal Temit even if the upstream plasma is hotter by orders of magnitude. This extreme cooling effect can alter the plasma properties and the heat transmission to thermionically emitting surfaces in many applications. It also opens a possibility of using thermionic divertor plates to induce detachment in tokamaks.

It is well known that electron emission can restructure the thin sheaths at plasma-facing surfaces. But conventional models assume that the plasma's structure negligibly changes (the “presheath” is still thought to be governed by ion acceleration to the Bohm speed). Here, it is shown by theory and simulation that the presheath can take a fundamentally different structure where the emitted electrons entering the quasineutral region cause numerous changes. Gradients of total plasma density, ion and electron pressures, and electric potential throughout the “inverted” presheath can carry different magnitudes, and opposite signs, from Bohm presheaths.