Simon-Hoh Instability Research Articles

Rotating spoke frequency in E × B penning source with two-ion-species plasma

In E B sources with different degrees of magnetization between electrons and ions, collisionless Simon–Hoh instability is prone to be induced, which may result in long-wavelength and low-frequency plasma oscillations along the azimuthal direction known as the rotating spoke. Recent studies have shown that the inertial response of unmagnetized ions is a key factor that affects the rotating spoke frequency, and in-depth studies on the correlation between the ion mass and spoke frequency have been conducted for various types of E B sources (e.g. Hall thruster, magnetron and Penning sources). In the case of the E B Penning source where the generation of desired ion species is maximized through molecular gas discharge, the intrinsic characteristics of the instability dependent on the ion mass inevitably require consideration of the coexistence of various ion species. In this work, we experimentally studied the spoke in the E B Penning source with two-ion-species plasma. By adjusting the mixture ratio of argon and krypton gases, we investigated the changes in instability frequency with electrical diagnostics. Two frequency peaks were clearly observed, with the peaks of lower and higher frequencies corresponding to mode numbers 2 and 3, respectively. The frequencies of each peak shifted to higher values when the argon content in the gas mixture was increased. Finally, the theoretical scaling of the spoke suggests that the changes in the frequencies are proportional to the inverse square root of the effective ion mass.

Theory of gradient drift instabilities in low-temperature, partially magnetised plasmas

A fluid dispersion theory in partially magnetised plasmas is analysed to examine the conditions under which large-wavelength modes develop in Penning-type configurations, that is, where an electric field is imposed perpendicular to a homogeneous magnetic field. The fluid dispersion relation assuming a slab geometry shows that two types of low-frequency, gradient drift instabilities occur in the direction of the $\boldsymbol {E} \times \boldsymbol {B}$ and diamagnetic drifts. One type of instability, observed when the equilibrium electric field and plasma density gradient are in the same direction, is similar to the classic modified Simon–Hoh instability. A second instability is found for conditions in which (i) the diamagnetic drift is in the direction opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift and (ii) the magnitude of the diamagnetic drift is sufficiently larger than the electron thermal speed. The present fluid dispersion theory suggests that the rotating spokes driven by such fluid instabilities propagate in the same direction as the diamagnetic drift, which can be in the same direction as or opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift, depending on the plasma conditions. This finding may account for the observation, in some plasma devices, of the rotation of large-scale structures in both the $\boldsymbol {E} \times \boldsymbol {B}$ and $-\boldsymbol {E} \times \boldsymbol {B}$ directions.

Full fluid moment modeling of rotating spokes in Penning-type configuration

Rotating spokes are observed in a partially magnetized plasma using a two-dimensional full fluid moment (FFM) model. In the present setup, where the radial electric field and plasma density gradient exist in opposite directions, it is observed that the spokes propagate in the direction of the diamagnetic drift and not the E × B drift. This is contrary to the modified Simon–Hoh instability, and the results suggest that the spokes can be driven by a strong diamagnetic drift. Different parameters, including magnetic field amplitude and physical domain size, influence the growth of the rotational instability as well as the dominant wave modes that arise. The propagation speed of the rotating spokes obtained from the FFM simulation are in good agreement with the observations in experimental and other computational work.

Magnetic confinement and instability in partially magnetized plasma

Discharge with an external magnetic field is promising for various applications of low-temperature plasmas from electric propulsion to semiconductor processes owing to high plasma density. It is essential to understand plasma transport across the magnetic field because plasma confinement under the field is based on strong magnetization of light electrons, maintaining quasi-neutrality through the inertial response of unmagnetized ions. In such a partially magnetized plasma, different degrees of magnetization between electrons and ions can create instability and make the confinement and transport mechanisms more complex. Theoretical studies have suggested a link between the instability of various frequency ranges and plasma confinement, whereas experimental work has not been done so far. Here, we experimentally study the magnetic confinement properties of a partially magnetized plasma considering instability. The plasma properties show non-uniform characteristics as the magnetic field increases, indicating enhanced magnetic confinement. However, the strengthened electric field at the edge of the plasma column gives rise to the Simon–Hoh instability, limiting the plasma confinement. The variation of the edge-to-center plasma density ratio (h-factor) with the magnetic field clearly reveals the transition of the transport regime through triggering of the instability. Eventually, the h-factor reaches an asymptotic value, indicating saturation of magnetic confinement.

New insights into the physics of rotating spokes in partially magnetized E×B plasmas

Regions of enhanced light emission rotating in the azimuthal direction (“rotating spokes”) have been observed in different types of partially magnetized E×B plasma devices such as magnetron discharges and Hall thrusters. A two-dimensional Particle-In-Cell Monte Carlo Collision (PIC MCC) model is used to study the formation of these rotating structures. The model shows that these current driven rotating structures are the results of a Simon–Hoh instability evolving into an ionization instability. The spoke is sustained by local electron heating induced by ∇B drift along a double layer separating the cathodic presheath from the plasma at a potential close to the anode potential. The PIC MCC simulations predict that spoke rotation can take place in the +E×B direction and in the −E×B direction depending on the magnetic field intensity.

Micro instabilities and rotating spokes in the near-anode region of partially magnetized plasmas

Electron and ion transport in the near-anode region of a partially magnetized plasma under conditions typical of Hall thrusters or magnetron discharges is studied with fully kinetic, Particle-In-Cell Monte Carlo Collision (PIC-MCC) simulations assuming a uniform magnetic field and no ionization. We derive a simple relation that defines the magnetic field at the transition point between negative and positive sheaths. For magnetic fields around or above this transition point, PIC-MCC simulations show the development of short wavelength azimuthal instabilities that cascade to longer wavelengths (“rotating spokes”) as the magnetic field is increased. Both short-wavelength and large-wavelength fluctuations can coexist under some conditions. A detailed study of the fluid dispersion relation is used to analyze the PIC-MCC results. Small coherent structures can be associated with the destabilization of ion sound waves by density gradient and collisions. Longer wavelengths or rotating spokes are characteristic of the collisionless Simon-Hoh instability. The small structures are dominant for larger plasma density gradients, while the larger structures correspond to smaller density gradients and larger magnetic fields. Anomalous transport associated with these instabilities can be significant, with effective collision frequencies larger than 2×107 s−1 in xenon for magnetic fields above the transition point.

Boundary-induced effect on the spoke-like activity in E × B plasma

The spoke instability in an E × B Penning discharge is shown to be strongly affected by the boundary that is perpendicular to B field lines. The instability is the strongest when bounded by dielectric walls. With a conducting wall, biased to collect electron current from the plasma, the spoke becomes faster, less coherent, and localized closer to the axis. The corresponding anomalous cross-field transport is assessed via simultaneous time-resolved measurements of plasma potential and density. This shows a dominant large-scale E × B anomalous character of the electron cross-field current for dielectric walls reaching 40%–100% of the discharge current, with an effective Hall parameter βeff ∼ 10. The anomalous current is greatly reduced with the conducting boundary (characterized by βeff ∼ 102). These experimental measurements are shown to be qualitatively consistent with the decrease in the E field that triggers the collisionless Simon-Hoh instability.

Modification of the Simon-Hoh Instability by the sheath effects in partially magnetized E × B plasmas

Effects of dissipation on the gradient drift modes in partially magnetized E × B plasmas are studied with emphasis on the sheath effects. It is shown that the dissipation induced instabilities driven by the density gradient and E × B drifts persist in conditions where the criteria for standard Simon-Hoh instability in E × B plasmas are not satisfied.

Nonmodal modified Simon-Hoh instability of a plasma with a shearing Hall current

A new analytical nonmodal approach to investigate the plasma instabilities driven by sheared current is presented and applied to the analysis of the linear evolution of modified Simon-Hoh (MSH) instability of a plasma in an inhomogeneous electric field. We found analytically a strong nonmodal growth for this instability which is missed completely in the normal mode analysis. It dominates the normal mode growth when the shearing rate of the current velocity is above the growth rate of the MSH instability with a uniform current. It also includes the nonmodal growth for subcritical perturbations, which do not develop in plasmas with uniform Hall current.

Scaling of spoke rotation frequency within a Penning discharge

A rotating plasma spoke is shown to develop in two-dimensional full-sized kinetic simulations of a Penning discharge cross-section. Electron cross-field transport within the discharge is highly anomalous and correlates strongly with the spoke phase. Similarity between collisional and collisionless simulations demonstrates that ionization is not necessary for spoke formation. Parameter scans with discharge current Id, applied magnetic field strength B, and ion mass mi show that the spoke frequency scales with eErLn/mi, where Er is the radial electric field, Ln is the gradient length scale, and e is the fundamental charge. This scaling suggests that the spoke may develop as a non-linear phase of the collisionless Simon-Hoh instability.

Structure of nonlocal gradient-drift instabilities in Hall E × B discharges

Gradient-drift (collisionless Simon-Hoh) instability is a robust instability often considered to be important for Hall plasma discharges supported by the electron current due to the E × B drift. Most of the previous studies of this mode were based on the local approximation. Here, we consider the nonlocal model which takes into account the electron inertia as well as the effects of the entire profiles of plasma parameters such as the electric, magnetic fields, and plasma density. Contrary to local models, nonlocal analysis predicts multiple unstable modes, which exist in the regions, where local instability criteria are not satisfied. This is especially pronounced for the long wavelength modes which provide larger contribution to the anomalous transport.

Territorial characteristics of low frequency electrostatic fluctuations in a simple magnetized torus

This paper presents an experimental investigation of turbulence in simple toroidal plasma devices without rotational transform. It is argued that Rayleigh–Taylor (flute interchange) mode may be one of the source mechanisms for the observed turbulence but is not sufficient to explain its observed global characteristics. Taking BETA device as an example, we show that pure Rayleigh–Taylor mode cannot explain (i) the observation of mode maximum at the location other than where density scale length is minimum, (ii) the comparable value of amplitude level of fluctuations in good curvature region, and (iii) the decrease in the mode amplitude with increasing magnetic field. Investigations have revealed that there exists not only poloidal plasma flow but also that it is sheared. Including this effect explains the first observation. However, modification brought about by velocity shear in the Rayleigh–Taylor mode still does not explain our second and third observations. We have taken an approach that since Rayleigh–Taylor is not excited in a good curvature region, it cannot be the source of turbulence there. Nor is it defensible to say that turbulence born in a bad curvature region is carried over through E×B rotation to the good curvature region. Consequently, we have invoked cross-field Simon–Hoh instability for this region. Experimental evidence supporting our proposal is presented. This paper concludes that toroidal devices have simultaneous existence of different self-consistent sources of turbulence in different regions of the device.

Modified Simon-Hoh Instability in a magnetized inhomogeneous dusty plasma

The modified Simon-Hoh Instability (MSHI) in an inhomogeneous plasma in presence of charged dust grains is investigated where the ions and dust are unmagnetized but electrons are strongly magnetized. Our dispersion relation matches exactly to the dispersion equation (18) of Sakawa et al.15, when we withdraw the contribution of dust grains from our expression. The growth rates of MSHI in presence of dust grains, shows either comparable or lower than that of dust free plasma.

Growth and nonlinear evolution of the modified Simon-Hoh instability in an electron beam-produced plasma

The growth and nonlinear evolution of the modified Simon–Hoh instability (MSHI) is observed in a weak electron beam-produced collisionless cylindrical plasma, in which electrons are strongly magnetized and the ions are essentially unmagnetized. The evolution of this instability occurs through a sequence of sideband instabilities, thought to be induced by trapped ions, and a period doubling sequence. Transient study of the MSHI reveals that the growth rate of the MSHI is extremely rapid; of the order the instability frequency.

Collisionless Simon–Hoh instability in a strongly double-sheared electric field

It has been shown in an earlier paper [Phys. Fluids B 5, 344 (1993)] that the ion flow speed of a plasma can be much smaller than the E×B speed in a strongly double-sheared electric field. In this paper, the stability of the plasma is investigated. It is found that a new instability, driven by the difference between the ion and electron flow speed, occurs and may dominate the Kelvin–Helmholtz (KH) instability in a nonuniform plasma. This new instability has a driving mechanism similar to that of the Simon–Hoh instability and is thus called the collisionless Simon–Hoh (CSH) instability. When the CSH instability dominates, the plasma does not become more unstable as the electric field is increased, in contrast to scenarios where the KH instability is dominant.

Excitation of the modified Simon–Hoh instability in an electron beam produced plasma

An intermediate frequency (fci≤f≤fce) electrostatic instability has been observed in an electron beam produced, cylindrical plasma column. This instability has been identified as a new instability, the modified Simon–Hoh instability (MSHI), which has an instability mechanism similar to the Simon–Hoh instability (SHI). This instability can occur in a cylindrical collisionless plasma if a radial dc electric field exists and if this radial dc electric field and the radial density gradient are in the same direction. The origin of the dc electric field is found to be the difference between the ion and the electron radial density profiles. In such a plasma if the ions are essentially unmagnetized but the electrons are magnetized, a velocity difference in the θ direction can arise because of the finite ion Larmor radius effect. This leads to a space charge separation between the electron and ion density perturbations in the θ direction. The consequent perturbed azimuthal electric field Eθ1 and the enhancement of the density perturbation by the Eθ1×B0 velocity occur in the same manner as in the SHI. The instability frequency is decided by the ion azimuthal drift velocity. This new instability has been investigated through experiments and theory.

Nonlinear evolution of the modified Simon-Hoh instability via a cascade of sideband instabilities in a weak beam plasma system.

The modified Simon-Hoh instability is observed in a collisionless cylindrical plasma, produced by a weak electron beam, in which electrons are strongly magnetized and the ions are essentially unmagnetized. The nonlinear evolution of this instability occurs through a sequence of sideband instabilities, thought to be induced by trapped ions, and can lead to a chaotic state.