Scott D. Baalrud

Global nonambipolar flow: Plasma confinement where all electrons are lost to one boundary and all positive ions to another boundary

A new mode of plasma confinement is demonstrated in which essentially all positive ions leave the plasma to only one boundary while essentially all electrons are lost to a different boundary. Sheaths near the plasma boundaries are entirely responsible for this global nonambipolar flow. The bulk plasma remains quasineutral and unperturbed even when all electrons are lost to only one, physically small, location. A necessary condition for global nonambipolar flow depends on the ratio of electron collection area to ion collection area. The plasma electron temperature is significantly higher in the global nonambipolar mode than in the typical ambipolar mode due to a relative increase in confinement of high-energy electrons and a relative decrease in confinement of low-energy electrons.

Reduced magnetohydrodynamic theory of oblique plasmoid instabilities

The three-dimensional nature of plasmoid instabilities is studied using the reduced magnetohydrodynamic equations. For a Harris equilibrium with guide field, represented by Bo=Bpotanh(x/λ)y+Bzoz, a spectrum of modes are unstable at multiple resonant surfaces in the current sheet, rather than just the null surface of the poloidal field Byo(x)=Bpotanh(x/λ), which is the only resonant surface in 2D or in the absence of a guide field. Here, Bpo is the asymptotic value of the equilibrium poloidal field, Bzo is the constant equilibrium guide field, and λ is the current sheet width. Plasmoids on each resonant surface have a unique angle of obliquity θ≡arctan(kz/ky). The resonant surface location for angle θ is xs=λarctanh(μ), where μ=tanθBzo/Bpo and the existence of a resonant surface requires |θ|<arctan(Bpo/Bzo). The most unstable angle is oblique, i.e., θ≠0 and xs≠0, in the constant-ψ regime, but parallel, i.e., θ=0 and xs=0, in the nonconstant-ψ regime. For a fixed angle of obliquity, the most unstable wave...

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth dη≡SL-1/2LνA/γ, where SL is the Lundquist number, L, the length of the current sheet, νA, the Alfven speed, and γ, the growth rate. Modifications to a recent resistive MHD analysis [N. F. Loureiro et al., Phys. Plasmas 14, 100703 (2007)] arise when collisions are sufficiently weak that dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (di/L)6/13SL7/13νA/L and the number of plasmoids as (di/L)1/13SL11/26, compared to SL1/4νA/L and S3/8, respectively, in resistive MHD.

Kinetic theory of the presheath and the Bohm criterion

A kinetic theory of the Bohm criterion is developed that is based on positive-exponent velocity moments of the plasma kinetic equation. This result is contrasted with the conventional kinetic Bohm criterion that is based on a v−1 moment of the Vlasov equation. The salient difference between the two results is that low-velocity particles dominate in the conventional theory, but are essentially unimportant in the new theory. It is shown that the derivation of the conventional kinetic Bohm criterion is flawed. Low-velocity particles can cause unphysical divergences in the conventional theory. These divergent contributions are avoided with this new approach. The two theories are compared using example distribution functions from previous presheath models. The importance of ion–ion and electron–electron collisions to determining the particle distribution functions throughout the presheath is also discussed. A kinetic equation that accounts for wave–particle scattering by convective instabilities is used to show that ion-acoustic instabilities in the presheath of low temperature plasmas (where Te Ti) can cause both ions and electrons to obtain Maxwellian distribution functions near the sheath.

Nonambipolar electron source

A radio frequency (rf) plasma-based electron source that does not rely on electron emission at a cathode surface has been constructed. All of the random electron flux incident on an exit aperture is extracted through an electron sheath resulting in total nonambipolar flow within the device when the ratio of the ion loss area to the electron loss area is approximately equal to the square root of the ratio of the ion mass to the electron mass, and the ion sheath potential drop at the chamber walls is much larger than Te∕e. The nonambipolar electron source (NES) has an axisymmetric magnetic field of 100G at the extraction aperture that results in a uniform plasma potential across the aperture, allowing the extraction of all the incident electron flux without the use of grids. A prototype NES has produced 15A of continuous electron current, using 15SCCM (SCCM denotes cubic centimeter per minute at STP) Ar, 1200W rf power at 13.56MHz, and 6 times gas utilization. Alternatively 8A of electron current can be pro...

Determining the Bohm criterion in plasmas with two ion species

A model that uniquely determines the flow speed of each ion species at the sheath edge of two ion species plasmas is developed. In this analysis, ion-ion two-stream instabilities can play an important role because they significantly enhance the friction between ion species. Two-stream instabilities arise when the difference in flow speeds between the ion species exceeds a critical value: V1−V2≡ΔV≥ΔVc. The resultant instability-enhanced friction rapidly becomes so strong that ΔV cannot significantly exceed ΔVc. Using the condition provided by ΔV=ΔVc and the generalized Bohm criterion, the speed of each ion species is uniquely determined as it leaves a quasineutral plasma and enters a sheath. Previous work [S. D. Baalrud et al., Phys. Rev. Lett. 103, 205002 (2009)] considered the cold ion limit (Ti→0), in which case ΔVc→0 and each ion species obtains a common “system” sound speed at the sheath edge. Finite ion temperatures are accounted for in this work. The result is that ΔVc depends on the density and the...

Theory for the anomalous electron transport in Hall effect thrusters. I. Insights from particle-in-cell simulations

Using a 1D particle-in-cell simulation with perpendicular electric, E0, and magnetic, B0, fields, and modelling the azimuthal direction (i.e., the E0 × B0 direction), we study the cross-field electron transport in Hall effect thrusters (HETs). For low plasma densities, the electron transport is found to be well described by classical electron-neutral collision theory, but at sufficiently high densities (representative of typical HETs), a strong instability is observed to significantly enhance the electron mobility, even in the absence of electron-neutral collisions. This instability is associated with correlated high-frequency (of the order of MHz) and short-wavelength (of the order of mm) fluctuations in both the electric field and the plasma density, which are shown to be the cause of the anomalous transport. Saturation of the instability is observed to occur due to a combination of ion-wave trapping in the E0 × B0 direction, and convection in the E0 direction.

Theory for the anomalous electron transport in Hall effect thrusters. II. Kinetic model

In Paper I [T. Lafleur et al., Phys. Plasmas 23, 053502 (2016)], we demonstrated (using particle-in-cell simulations) the definite correlation between an anomalously high cross-field electron transport in Hall effect thrusters (HETs), and the presence of azimuthal electrostatic instabilities leading to enhanced electron scattering. Here, we present a kinetic theory that predicts the enhanced scattering rate and provides an electron cross-field mobility that is in good agreement with experiment. The large azimuthal electron drift velocity in HETs drives a strong instability that quickly saturates due to a combination of ion-wave trapping and wave-convection, leading to an enhanced mobility many orders of magnitude larger than that expected from classical diffusion theory. In addition to the magnetic field strength, B0, this enhanced mobility is a strong function of the plasma properties (such as the plasma density) and therefore does not, in general, follow simple 1/B02 or 1/B0 scaling laws.

Response of the plasma to the size of an anode electrode biased near the plasma potential

As the size of a positively biased electrode increases, the nature of the interface formed between the electrode and the host plasma undergoes a transition from an electron-rich structure (electron sheath) to an intermediate structure containing both ion and electron rich regions (double layer) and ultimately forms an electron-depleted structure (ion sheath). In this study, measurements are performed to further test how the size of an electron-collecting electrode impacts the plasma discharge the electrode is immersed in. This is accomplished using a segmented disk electrode in which individual segments are individually biased to change the effective surface area of the anode. Measurements of bulk plasma parameters such as the collected current density, plasma potential, electron density, electron temperature and optical emission are made as both the size and the bias placed on the electrode are varied. Abrupt transitions in the plasma parameters resulting from changing the electrode surface area are identified in both argon and helium discharges and are compared to the interface transitions predicted by global current balance [S. D. Baalrud, N. Hershkowitz, and B. Longmier, Phys. Plasmas 14, 042109 (2007)]. While the size-dependent transitions in argon agree, the size-dependent transitions observed in helium systematically occur at lower electrode sizes than those nominally derived from prediction. The discrepancy in helium is anticipated to be caused by the finite size of the interface that increases the effective area offered to the plasma for electron loss to the electrode.

Particle-in-cell simulations of a current-free double layer

Current-free double layers of the type reported in plasmas in the presence of an expanding magnetic field [C. Charles and R. W. Boswell, Appl. Phys. Lett. 82, 1356 (2003)] are modeled theoretically and with particle-in-cell/Monte Carlo simulations. Emphasis is placed on determining what mechanisms affect the electron velocity distribution function (EVDF) and how the EVDF influences the double layer. A theoretical model is developed based on depletion of electrons in certain velocity intervals due to wall losses and repletion of these intervals due to ionization and elastic electron scattering. This model is used to predict the range of neutral pressures over which a double layer can form and the electrostatic potential drop of the double layer. These predictions are shown to compare well with simulation results.