Current-free Double Layer Research Articles

Double layer formation and thrust generation in an expanding plasma using 1D-3V PIC simulation

Due to large particle exhaust velocity and specific impulse, electric propulsion systems have an edge over chemical propulsion for missions targeting regions outside the Earth's atmosphere. Stationary plasma thrusters and helicon plasma thrusters (HPTs) are commonly used electric propulsion devices for a space mission. In HPTs or expanding magnetic field plasma thrusters, plasma expands from the source region to the expansion region in an externally applied expanding magnetic field. Due to plasma expansion in such a magnetic field configuration, a current free double layer is found to form, which accelerates bulk ions, and a directional ion beam is generated, which causes thrust in the opposite direction. A Particle In Cell (PIC) solver with Monte Carlo Collision (MCC) scheme which resolves the axial direction and all three velocity degrees of freedom (1D-3V PIC-MCC) that captures the 2D spatial plasma expansion effect via a 1D flux conserving model is developed to simulate an argon plasma in an expanding magnetic field. Using the 1D-3V PIC-MCC solver, double layer formation due to plasma expansion, thrust generation, and optimization of thrust studies over a large parameter set, such as fill pressure of Ar, is presented. We compare our results with a particle loss model, which is commonly used as the simplest model for HPTs.

Current-Free Electric Double Layer in a Small Collisional Plasma Thruster Nozzle Simulation

A computational fluid dynamics and plasma model of a collisional (∼ a few Torr) radiofrequency (at 13.56 MHz) argon plasma capacitively coupled in a converging-diverging nozzle (applied to the optimisa- tion of electrothermal plasma thrusters for space use) shows the formation of a strong stationary current-free double layer (CFDL) at the 1.5 mm diameter nozzle throat for a downstream pressure of ∼ 0.1 Torr. The cycle average magnitude of the double layer potential is ∆ΦDL = 77 V and the electron temperature at the high potential edge of the double layer is kBTe = 2.64eV, yielding a strength of ∆ΦDL/(kBTe) ∼ 30. The double layer is 1.2 mm wide which corresponds to ∼ 90 Debye lengths. The axial electric field of the double layer accelerates ions along the nozzle to a maximum drift velocity of 17 km s−1, about 3.3 times the ion sound speed, and their kinetic energy is transferred to neutrals by ion-neutral charge exchange col- lisions. The ion transit time τi through the potential structure spontaneously forming at the nozzle throat is about 5 times the radiofrequency excitation period τRF. These findings are discussed in the broader context of double layer physics and the dynamics of their formation as well as in the context of electrothermal thruster optimisation in which neutral propellant heating via ion-neutral charge exchange collisions is the main source of thrust.

Retarded Field Energy Analyzer as a tool to Study the Ion Velocity Distribution Functions on Radio Frequency Argon Plasma in Expanding Magnetic Field at Low Pressures

<p>Plasma expanding in the space along the magnetic filed is well known phenomenon. This plasma device was constructed to investigate the space plasma in laboratory in connection with plasma flows, electron distribution, ion distribution, instability and turbulence. For this purpose, the low-temperature plasma is produced by means of a 13.56 MHz Helicon plasma source at 300-1000 W rf power. The plasma is expanding from the 13.5 cm diameter source into a 150 cm long chamber of 60 cm diameter. Ion energy and its velocity distribution produced by a current-free double layer at the expansion region have been studied by means of retarding field energy analyzers. Furthermore, the effects due to the geometrical shape of the expanding magnetic field in plasma flows have also been investigated.</p><p>Journal of Nepal Physical Society Vol.3(1) 2015: 82-88</p>

Plume Structure and Ion Acceleration of a Helicon Plasma Source

Helicon plasma sources are capable of efficiently ionizing propellants and have been considered for application in electric propulsion. The literature suggests that the ion acceleration mechanism is a current-free double layer. Previous work shows that single-stage helicon thrusters can produce thrust in the range of 1–6 mN, but it is unknown whether the thrust contribution is due to direct ion acceleration versus thermal expansion. The ion energy and current density profiles in the plume of a helicon plasma source are measured across a range of operating conditions: 343–600 W RF power at 13.56 MHz, 50–350 G, and 1.5-mg/s Ar at a pressure of $1.6\times 10^{-5}$ torr-Ar. The plasma potential, electron temperature, and ion number density are also measured inside the discharge chamber and in the plume up to 60 cm downstream of the exit plane and 45-cm radially outward from the device axis. Ions are found to have energies in the range of 20–40 V, with total beam currents in the range of 7–47 mA. The plume has an average divergence half angle of 82°, either evenly distributed across all angles or focused at large angles to the centerline. From these measurements, it is found that the estimated thrust due to ion acceleration is far less than what has been directly measured on the same device in previous work.

The hot hELicon eXperiment (HELIX) and the large experiment on instabilities and anisotropy (LEIA)

The West Virginia University Hot hELIcon eXperiment (HELIX) provides variable density and ion temperature plasmas, with controllable levels of thermal anisotropy, for space relevant laboratory experiments in the Large Experiment on Instabilities and Anisotropy (LEIA) as well as fundamental studies of helicon source physics in HELIX. Through auxiliary ion heating, the ion temperature anisotropy (T⊥/T∥) is variable from 1 to 20 for parallel plasma beta (β = 8πnkTi∥/B2) values that span the range of 0.0001 to 0.01 in LEIA. The ion velocity distribution function is measured throughout the discharge volume in steady-state and pulsed plasmas with laser induced fluorescence (LIF). The wavelengths of very short wavelength electrostatic fluctuations are measured with a coherent microwave scattering system. Operating at low neutral pressures triggers spontaneous formation of a current-free electric double layer. Ion acceleration through the double layer is detected through LIF. LIF-based velocity space tomography of the accelerated beam provides a two-dimensional mapping of the bulk and beam ion distribution functions. The driving frequency for the m = 1 helical antenna is continuously variable from 8.5 to 16 MHz and frequency dependent variations of the RF coupling to the plasma allow the spontaneously appearing double layers to be turned on and off without modifying the plasma collisionality or magnetic field geometry. Single and multi-species plasmas are created with argon, helium, nitrogen, krypton, and xenon. The noble gas plasmas have steep neutral density gradients, with ionization levels reaching 100% in the core of the plasma source. The large plasma density in the source enables the study of Aflvén waves in the HELIX device.

Experimental investigation of current free double layers in helicon plasmas

The paper presents investigations of current free double layer (CFDL) that forms in helicon plasmas. In contrast to the other work reporting on the same subject, in the present investigations the double layer (DL) forms in a mirror-like magnetic field topology. The RF compensated Langmuir probe measurements show multiple DLs, which are in connection with, the abrupt fall of densities along with potential drop of about 24 V and 18 V. The DLs strengths e ΔVpk Te are about 9.5 and 6, and the corresponding widths are about 6 and 5 D lengths. The potential drop is nearly equal to the thermal anisotropies between the two plasma regions forming the DL, which is present in the plateau region of mirror, unlike the earlier studies on the DL formation in the region of strong gradients in the magnetic field. Also, it presents a qualitative discussion on the mechanism of DL formation.

Observation of multiple current free helicon double layers

A combination of three strong current free double layers (CFDLs) characterized by strength (eΔΦ/Te) ∼ 10 and widths (Δz/λD) ∼ 7.6, 8, and 8.3 has been observed in argon helicon plasma. In contrast to other works report on the same subject, in the present investigations the DLs form in a mirror-like magnetic field topology and present in the plateau regions of magnetic field. Using the measurement of radio frequency compensated Langmuir Probe consistent with the B-dot probe diagnostic, a qualitative mechanism of DL formation has also been discussed.

Time-resolved characterization of the formation of a collisionless shock.

We report on the temporally and spatially resolved detection of the precursory stages that lead to the formation of an unmagnetized, supercritical collisionless shock in a laser-driven laboratory experiment. The measured evolution of the electrostatic potential associated with the shock unveils the transition from a current free double layer into a symmetric shock structure, stabilized by ion reflection at the shock front. Supported by a matching particle-in-cell simulation and theoretical considerations, we suggest that this process is analogous to ion reflection at supercritical collisionless shocks in supernova remnants.

Two-dimensional quasi-double-layers in two-electron-temperature, current-free plasmas

The expansion of a plasma with two disparate electron populations into vacuum and channeled by a divergent magnetic nozzle is analyzed with an axisymmetric model. The purpose is to study the formation and two-dimensional shape of a current-free double-layer in the case when the electric potential steepening can still be treated within the quasineutral approximation. The properties of this quasi-double-layer are investigated in terms of the relative fraction of the high-energy electron population, its radial distribution when injected into the nozzle, and the geometry and intensity of the applied magnetic field. The two-dimensional double layer presents a curved shape, which is dependent on the natural curvature of the equipotential lines in a magnetically expanded plasma and the particular radial distribution of high-energy electrons at injection. The double layer curvature increases the higher the nozzle divergence is, the lower the magnetic strength is, and the more peripherally hot electrons are injected. A central application of the study is the operation of a helicon plasma thruster in space. To this respect, it is shown that the curvature of the double layer does not increment the thrust, it does not modify appreciably the downstream divergence of the plasma beam, but it increases the magnetic-to-pressure thrust ratio. The present study does not attempt to cover current-free double layers involving plasmas with multiple populations of positive ions.

Numerical simulation of current-free double layers created in a helicon plasma device

Two-dimensional simulations reveal that when radially confined source plasma with magnetized electrons and unmagnetized ions expands into diverging magnetic field B, a current-free double layer (CFDL) embedded in a conical density structure forms, as experimentally measured in the Australian helicon plasma device (HPD). The magnetized electrons follow the diverging B while the unmagnetized ions tend to flow directly downstream of the source, resulting in a radial electric field (E⊥) structure, which couples the ion and electron flows. Ions are transversely (radially) accelerated by E⊥ on the high potential side of the double layer in the CFDL. The accelerated ions are trapped near the conical surface, where E⊥ reverses direction. The potential structure of the CFDL is U-shaped and the plasma density is enhanced on the conical surface. The plasma density is severely depleted downstream of the parallel potential drop (φ||o) in the CFDL; the density depletion and the potential drop are related by quasi-neutrality condition, including the divergence in the magnetic field and in the plasma flow in the conical structure. The potential and density structures, the CFDL spatial size, its electric field strengths and the electron and ion velocities and energy distributions in the CFDL are found to be in good agreements with those measured in the Australian experiment. The applicability of our results to measured axial potential profiles in magnetic nozzle experiments in HPDs is discussed.

A linear helicon plasma device with controllable magnetic field gradient

Current free double layers (CFDLs) are localized potential structures having spatial dimensions - Debye lengths and potential drops of more than local electron temperature across them. CFDLs do not need a current for them to be sustained and hence they differ from the current driven double layers. Helicon antenna produced plasmas in an expanded chamber along with an expanding magnetic field have shown the existence of CFDL near the expansion region. A helicon plasma device has been designed, fabricated, and installed in the Institute for Plasma Research, India to study the role of maximum magnetic field gradient as well as its location with respect to the geometrical expansion region of the chamber in CFDL formation. The special feature of this machine consisting of two chambers of different radii is its capability of producing different magnetic field gradients near the physical boundary between the two chambers either by changing current in one particular coil in the direction opposite to that in other coils and/or by varying the position of this particular coil. Although, the machine is primarily designed for CFDL experiments, it is also capable of carrying out many basic plasma physics experiments such as wave propagation, wave coupling, and plasma instabilities in a varying magnetic field topology. In this paper, we will present the details of the machine construction, its specialties, and some preliminary results about the production and characterization of helicon plasma in this machine.

Current-free double layers: A review

During the last decade, there has been an upsurge in the research on current-free DLs (CFDLs). Research includes theory, laboratory measurements, and various applications of CFDLs ranging from plasma thrusters to acceleration of charged particles in space and astrophysical plasmas. The purpose of this review is to present a unified understanding of the basic plasma processes, which lead to the formation of CFDLs. The review starts with the discussion on early research on electric fields and double layers (DLs) and ion acceleration in planar plasma expansion. The review continues with the formation of DLs and rarefaction shocks (RFS) in expanding plasma with two electron populations with different temperatures. The basic theory mitigating the formation of a CFDL by two-electron temperature population is reviewed; we refer to such CFDLs as double layers structures formation by two-temperature electron populations (TET-CFDLs). Application of TET-CFDLS to ion acceleration in laboratory and space plasmas was discussed including the formation of stationary steady-state DLs. A quite different type of CFDLs forms in a helicon plasma device (HPD), in which plasma abruptly expands from a narrow plasma source tube into a wide diffusion tube with abruptly diverging magnetic fields. The formation mechanism of the CFDL in HPD, referred here as current free double layer structure in helicon plasma device (HPD-CFDL), and its applications are reviewed. The formation of a TET-CFDL is due to the self-consistent separation of the two electron populations parallel to the ambient magnetic field. In contrast, a HPD-CFDL forms due to self-consistent separation of electrons and ion perpendicular to the abruptly diverging magnetic field in conjunction with the conducting wall of the expansion chamber in the HPD. One-dimensional theoretical models of CFDLs based on steady-state solution of Vlasov-Poisson system of equations are briefly discussed. Applications of CFDLs ranging from helicon double-layer thrusters (HDLTs) to the accelerations of ions in space and astrophysical plasmas are summarized.

Ion-Current Downstream of a Carbon Dioxide Helicon Double Layer

Energy-resolved ion measurements in a carbon dioxide helicon radio-frequency plasma containing an oblique current-free double layer are obtained using a retarding field energy analyzer for standard operating conditions (i.e., 0.4 mTorr, 250 W, and 140 G). Two ion populations corresponding to thermal ions and an energetic ion beam, respectively, are observed and spatially mapped downstream of the double layer, which is in the region of diverging field lines. The measurements are mirrored about the main reactor axis using cylindrical geometry, and a 3-D image is generated.

Current-free double layers in helicon sources

A model for the formation of a stationary current-free double layer in collisionless plasmas expanding in a magnetic nozzle is presented. The model consists of the dynamics of cold ions, isothermal hot electrons and fere-isothermal, i.e. almost isothermal, cold electrons. It can determine the position and amplitude of the double layer including the jump in cold electron temperature across the layer. The magnitude of the jump is consistent with experimental observations. Plasmas are accelerated mainly by the magnetic nozzle and the contribution from the double layer is small. The important effects of the ion charge state Z on the flow speed at the nozzle throat and at the exit are also discussed. It is found that the Mach number at the magnetic nozzle throat is which can be tested in experiments. The exit velocity also scales as . To increase the thrust power, the ion charge state Z could be an important parameter.

Electron Energy Distribution of a Current-Free Double Layer: Druyvesteyn Theory and Experiments

Electron energy distributions upstream of a current-free double layer (CFDL) contained in a low-collisional plasma are modeled and compared with experimental results. The experimentally observed electron energy probability functions (EEPFs) with a depleted tail above the energy corresponding to the potential drop of the CFDL can be well approximated by a Druyvesteyn distribution function. Theoretical effective electron temperatures for the Druyvesteyn distribution are in good agreement with the values obtained from the experimental EEPFs over the range of pressure where the CFDL is observed.

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.

Transit time instabilities in an inverted fireball. II. Mode jumping and nonlinearities

A fireball is formed inside a highly transparent spherical grid immersed in a dc discharge plasma. The ambient plasma acts as a cathode and the positively biased grid as an anode. A strong nearly current-free double layer separates the two plasmas. Electrons are accelerated into the fireball, ionize, and establish a discharge plasma with plasma potential near the grid potential. Ions are ejected from the fireball. Since electrons are lost at the same rate as ions, most electrons accelerated into the fireball just pass through it. Thus, the electron distribution contains radially counterstreaming electrons. High-frequency oscillations are excited with rf period given by the electron transit time through the fireball. Since the frequency is well below the electron plasma frequency, no eigenmodes other than a beam space-charge wave exists. The instability is an inertial transit-time instability similar to the sheath-plasma instability or the reflex vircator instability. In contrast to vircators, there is no electron reflection from a space-charge layer but counterstreaming arises from spherical convergence and divergence of electrons. While the basic instability properties have been presented in a companion paper [R. L. Stenzel et al., Phys. Plasmas 18, 012104 (2011)], the present paper focuses on observed mode jumping and nonlinear effects. The former produce frequency jumps and different potential profiles, the latter produce harmonics associated with electron bunching at large amplitudes. In situ probe measurements are presented and interpreted.

Operating Radio Frequency Antennas Immersed in Vacuum: Implications for Ground-Testing Plasma Thrusters

O PERATING RF antennas in a vacuum presents several challenges that are relevant to the ground testing of plasma propulsion systems such as the Helicon Double Layer Thruster (HDLT) prototype. Antennas immersed in vacuum can come into contact with the plasma and, if one end of the antenna is grounded, direct currents flow from the plasma to ground. To the authors’ knowledge, these issues have not been investigated previously in the context of plasma propulsion. However, in asymmetric plasma discharges, which are used in materials processing, the RF biased substrate or electrodes are frequently immersed in the vacuum (and plasma) and biased negatively via a dc blocking capacitor. This enables the energies of the ions impinging the substrate to be controlled independently of the current to the substrate, which is important for various processing techniques [1]. Immersed RF antennas have also been employed in plasma immersion ion implantation (PI) devices [2]. In magnetically confined fusion experiments, the RF antennas are usually shielded with a Faraday cage to prevent the antenna from coming into contact with the plasma. This shielding reduces the power coupling of the plasma to the antenna and hence the efficiency of the system. The RF antenna in the H1 Heliac experiment [3], however, is in direct contact with the plasma and is used to increase the temperature of the plasma. The antenna, which is driven at 7 MHz, is shaped like a loop in the plane of the last closed flux surface, and one end of the antenna is grounded. This allows a direct current toflow from the plasmavia the antenna to ground.Currents of approximately 90 A and plasma potentials of 100 V have been measured during typical operation of the H1 Heliac. The HDLT is a new plasma propulsion concept based on the discovery by various researchers of energetic ion beams formed by a current-free electric double layer in low-pressure helicon plasmas [4,5]. The HDLT is electrodeless, does not require a neutralizer, can operate with a wide variety of propellants [6,7] and produces a verylow-divergence ion beam (less than 10 for argon and 6 for xenon) [8] that can be steered magnetically [9,10]. A prototype of the HDLT has been developed and an initial testing campaign was conducted in the CORONA space simulation chamber [11]. This has been followed by a more extensive testing program with the HDLT prototype immersed in a smaller vacuum chamber [12–14]. In this work, several deleterious phenomena are described that have been observed during this testing program. To alleviate these problems, modifications to the RF (13.56 MHz) matching box and antenna assembly have been implemented. These phenomena, their consequences, and the solutions implemented here are also relevant to ground testing other plasma thrusters such as the new VASIMR VX-200 prototype [15] and other concepts using RF or helicon antennas [16–24].

The effects of downstream magnetic field on current-free double layers and beam formation in the Njord helicon plasma device

The Njord device was constructed with the aim of investigating instabilities and turbulence in plasmas with flows and beams, which are common also in space plasmas. Njord is an inductively coupled helicon plasma device with 13.56 MHz RF power inserted into the working gas by means of a saddle antenna through a 13.8 cm inner diameter Pyrex tube. The source plasma expands through a 7 cm long and 20 cm wide port into a 0.6 m diameter and 1.2 m long chamber. Two magnetic field coils around the source and one additional downstream coil produce a magnetic field of about 25 mT at maximum.We have characterized current-free double layers in argon plasmas, and we find that they are generated at the position where the plasma expands into the main chamber. Further, the effect of shaping the magnetic field from an expanding one to a mirror shaped field by means of the downstream coil has been investigated. The downstream density and the plasma potential increase significantly when all the magnetic field lines in the source are passing also through the port–dome intersection without intersecting the port walls. The ion beam disappears when the plasma potential increases up to a potential similar to that in the source.

Time-resolved measurements of double layer evolution in expanding plasma

Observations in steady-state plasmas confirm predictions that formation of a current-free double layer in a plasma expanding into a chamber of larger diameter is accompanied by an increase in ionization upstream of the double layer. The upstream plasma density increases sharply at the same driving frequency at which a double layer appears. For driving frequencies at which no double layer appears, large electrostatic instabilities are observed. Time-resolved measurements in pulsed discharges indicate that the double layer initially forms for all driving frequencies. However, for particularly strong double layers, instabilities appear early in the discharge and the double layer collapses.