Current-free Double Layer Research Articles

Theory of a Stationary Current-Free Double Layer in a Collisionless Plasma

Current-free double layers can develop in a collisionless, inertia-controlled plasma with two electron populations, expanding in a convergent-divergent nozzle. The double layer characteristics depend on whether they develop at the nozzle divergent side, convergent side, or throat. The divergent-geometry double layer describes faithfully the Hairapetian-Stenzel experiment [Phys. Rev. Lett. 65, 175 (1990)10.1103/PhysRevLett.65.175], whereas the two other types correspond with those studied in self-similar expansions and wall-collection models of similar plasmas.

Oblique Double Layers: A Comparison between Terrestrial and Auroral Measurements

The S3-3, POLAR, and FAST satellite auroral observations of parallel and perpendicular electric field structures have been identified as belonging to a large "U"-shaped potential structure that supports oblique electric double layers. This interpretation is verified by terrestrial laboratory measurements of a self-consistently supported three-dimensional oblique current-free double layer. Its width is a few tens of Debye lengths, its oblicity (with respect to the magnetic field) varies from 0 up to 30 degrees, and its strength is a few times the electron temperature.

Increased Upstream Ionization due to Formation of a Double Layer

We report observations that confirm a theoretical prediction 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 theoretical model argues that the increased ionization is needed to balance the difference in diffusive losses upstream and downstream of the expansion region. In our expanding helicon source experiments, we find that the upstream plasma density increases sharply at the same antenna frequency at which the double layer appears.

Radial characterization of the electron energy distribution in a helicon source terminated by a double layer

Electron energy probability functions (EEPFs) are measured across the radius (0⩽r<6.85cm) of a low pressure (0.3mTorr) helicon plasma source terminated by a current-free double layer. The source field of about 130G is generated using a Helmholtz coil pair and the radio frequency (rf) power is maintained at 250W. All EEPFs exhibit a distribution with a temperature Tebulk out to a break energy εbreak and a relatively depleted distribution for higher energies with a lower temperature Tetail. Tebulk and Tetail are about 8eV and 5eV, respectively, for r<4cm and increase up to about 14eV and 9eV near the source wall, i.e., near the rf antenna. εbreak is found to correspond to the potential drop of the double layer for the central part of the source and to the sheath potential near the wall.

Theory of current-free double layers in plasmas

The existence of current-free double layers in unmagnetized plasma is studied by means of the quasipotential method applied to the Vlasov–Poisson system. Crucial for its existence are trapped particle populations that are characterized by notches (dips) in the velocity distribution functions at resonant velocity becoming flat at large amplitude limit. The potential drop across the double layer, or its amplitude ψ, can be arbitrarily strong covering the whole range 0<ψ<∞. Both the small and large amplitude limit are worked out explicitly, inclusively effective kinetic temperatures and pressures. It is, hence, the effective electron (ion) temperature increase (decrease) with increasing potential, caused by the trapped particles, which is responsible for the existence of this two-parameter family of solutions.

Testing a Helicon Double Layer Thruster Immersed in a Space-Simulation Chamber

The Helicon Double Layer Thruster, a new magnetoplasma thruster that accelerates ions to supersonic velocities using a current-free electric double layer, has been tested successfully for the first time inside a space-simulation vacuum chamber. Using a retarding field energy analyzer, the presence of a current-free double layer and the associated ion beam in argon have been confirmed for operating conditions of 0.297 mgs -1 of argon, 53.3 mPa gas pressure, 100 W of radio-frequency forward power at 13.56 MHz, and a maximum axial magnetic field of 138 G. The inductively coupled plasma and ion beam formed have been characterized axially, and the measured beam velocity is about 8.7 kms -1 for these conditions. The effect of moving the Helicon Double Layer Thruster source tube relative to the magnetic field and radio-frequency antenna is investigated, and the pressure dependence of the double layer is measured from 20 to 275 mPa and compared with a recently developed theoretical model. Ions in the Helicon Double Layer Thruster exhaust are also shown to be nonmagnetized, suggesting that ion detachment has occurred.

Collisionless transport of energetic electrons in the solar corona at current-free double layers

Context. Impinging electron beams in the solar chromosphere generate hard X-ray radiation (HXR) through the collisional Bremstrahlung thick target model. The deduced electron distributions usually exhibit a broken-power-law. Assuming that the initial distribution function was a drift-Maxwellian, this indicates that the distribution of energetic electrons changes in the course of their propagation, from the looptop acceleration site to the high density chromosphere, via a collisionless scattering mechanism. Aims. The formation of a broken-power-law spectrum via the particle interaction with the current-free weak double layers (DLs) in a reverse current beam plasma system. Methods. The unstable waves generated in current-free coronal plasmas are first studied by means of a linear instability analysis. For most probable coronal plasma parameters, a one-dimensional electrostatic Vlasov-code simulation is performed to understand the nonlinear evolution of the instabilities and their influences on the electron distribution. Results. DL structures cause a dissipation of low energy beam electrons and a stagnation of return-current electrons. Fast electron holes are formed, a secondary two-stream instability, caused by the DL-accelerated electrons. Electron and ion heating by DLs also takes place. Conclusions. The plasma distributions of energetic electrons in the solar corona evolve via their interactions with nonlinear largeamplitude phase-space structures. At the late stage of evolution, the low-energy electrons are slowed down while the high energy part stays uninfluenced after the appearance of DLs. A major part of the return-current electrons change their direction to that of the injected beam. As a result the distribution becomes a broken-power-law as observed by chromospheric HXR radiation.

Measurement of the energy distribution of trapped and free electrons in a current-free double layer

In the high potential plasma, upstream of the double layer, the measured electron energy distribution function (EEDF) shows a very clear change in slope at energies (εbreak) corresponding to the double layer potential drop. Electrons with lower energy are Maxwellian with a temperature of 8eV, whereas those with higher energy have a temperature of 5eV. The EEDF in the downstream plasma has a temperature of 5eV. Over the range of pressures wherein the double layer and accelerated ion beam are detected by analysis of a retarding field energy analyzer, the strength of the double layer corresponds to the energy where the slope changes in the EEDF (εbreak). We deduce that the downstream electrons come from upstream electrons that have sufficient energy to overcome the potential of the double layer, and that only a single upstream plasma source is required to maintain this phenomenon.

Langmuir probe data analysis for a magnetized inductive radio-frequency discharge

The properties of an inductively coupled argon plasma in a uniform magnetic field, at pressures of the order of 0.1 Pa, in the presence of a weak current-free electric double layer, are measured with a plane Langmuir probe. The static current-voltage probe characteristics, recorded on the symmetry axis of the experimental device, both in the plasma source and in the main chamber of the setup, showed the existence of two electron populations with different temperatures. The axial profiles of plasma parameters, such as the plasma potential and the cold and hot electron temperatures, offered a new insight into such a complex system. However, both the external magnetic field and the two electron populations contribute to the difficulty of calculation of the local plasma density. A method for solving this problem, involving the definition of an effective electron temperature, is also presented.

Xenon ion beam characterization in a helicon double layer thruster

A current-free electric double layer is created in a helicon double layer thruster operating with xenon and compared to a recently developed theory. The Xe+ ion beam formed by acceleration through the potential drop of the double layer is characterized radially using an electrostatic ion energy analyzer. For operating conditions of 500W rf power, 0.07mTorr gas pressure, and a maximum magnetic field of 125G, the measured beam velocity is about 6kms−1, the beam area is about 150cm2, and the measured beam divergence is less than 6°.

Experiments and theory of an upstream ionization instability excited by an accelerated electron beam through a current-free double layer

A low-frequency instability varying from 10 to 20kHz has been discovered in the presence of a current-free double layer (DL) in a low-pressure expanding helicon plasma. The instability is observed using various electrostatic probes, such as Langmuir probes floating or biased to ion saturation and emissive probes measuring the plasma potential. A retarding field energy analyzer measuring the ion energy distribution function downstream of the double layer is used together with the LP to simultaneously observe the DL and the instability, confirming their coexistence. The frequency of the instability decreases with increasing neutral pressure, increases with increasing magnetic field in the source and increases with increasing rf power. A theory for an upstream ionization instability has been developed, in which electrons accelerated through the DL increase the ionization upstream and are responsible for the observed instability. The theory is in good agreement with the experimental results and shows that the frequency increases with the potential drop of the double layer and with decreasing chamber radius.

Upstream Ionization Instability Associated with a Current-Free Double Layer

A low frequency instability has been observed using various electrostatic probes in a low-pressure expanding helicon plasma. The instability is associated with the presence of a current-free double layer (DL). The frequency of the instability increases linearly with the potential drop of the DL, and simultaneous measurements show their coexistence. A theory for an upstream ionization instability has been developed, which shows that electrons accelerated through the DL increase the ionization upstream and are responsible for the observed instability. The theory is in good agreement with the experimental results.

Theory for Formation of a Low-Pressure, Current-Free Double Layer

A diffusion-controlled theory is developed for the formation of a low-pressure, current-free double layer just inside an upstream insulating source chamber connected to a larger diameter, downstream chamber. The double layer is described using four groups of charged particles: thermal ions, monoenergetic accelerated ions flowing downstream, accelerated electrons flowing upstream, and thermal electrons. The condition of particle balance upstream is found to determine the double layer potential. The double layer disappears at very low pressures due to loss of ionization balance upstream and due to energy relaxation processes for ionizing electrons at higher pressures, in good agreement with experiments.

A theory for formation of a low pressure, current-free double layer

A theory is developed for the formation of a low pressure, current-free double layer just inside an upstream dielectric source chamber connected to a larger diameter, downstream metallic expansion chamber. The double layer is described using four groups of charged particle: thermal ions, mono-energetic accelerated ions flowing downstream, accelerated electrons flowing upstream and thermal electrons. The accelerated electrons are formed downstream from an initially nearly half-Maxwellian electron distribution. A fifth group of counter-streaming electrons formed by the reflection of the accelerated electrons from the sheath at the insulated end wall of the source chamber is used to enforce the condition that the double layer be current-free. The condition of particle balance upstream is found to determine the double layer potential. The double layer is found to disappear at very low pressures due to loss of ionization balance upstream and due to energy relaxation processes for ionizing electrons at higher pressures. The theory is found to be in good agreement with the experiments.

The Current-Free Electric Double Layer in a Coronal Magnetic Funnel

Current-free double layers (CFDLs) have been recently discovered in a number of laboratory devices, when a low collisional plasma is forced to expand from a high magnetic field source region to a low magnetic field diffusion region. This experimental setup bears a striking resemblance to the natural conditions prevailing in the magnetic funnels of the solar corona. It was commonly thought that magnetic-field-aligned potential disruptions were driven by electron currents, although the theoretical possibility of a CDFL has been known of for some time. Given its recent experimental verification, we make here a contribution to solar plasma physics by investigating the possibility of CFDLs in coronal funnels, which have much in common with the laboratory experiments. Therefore, CFDLs may play an important role in supplying and accelerating plasma in coronal funnels.

Physical mechanism of current-free double layers

Undriven double layers observed in plasmas expanding along magnetic fields are the result of a sheath instability connected with the Bohm criterion. Diverging magnetic field lines cause the presheath acceleration of ions, causing a potential jump resembling that of a double layer. The process stops when it runs out of energy.

Plasma expansion from a dielectric electron cyclotron resonance source

The boundary conditions in an electron cyclotron resonance (ECR) source have been modified to mimic the operating conditions where current-free double-layers (DLs) have been recently measured in rf helicon plasmas. The plasma is heated or generated by the ECR at 875 G inside a dielectric source tube, and expands into a grounded diffusion chamber (terminated by a glass plate) by a rapidly decreasing magnetic field. Preliminary studies of the plasma expansion have been performed. For the present conditions (1 mTorr, 500 G and 500 W), no DL is observed near the source exit and the plasma diffusion is well described by a Bolzmann expansion.

Experimental Evidence of a Double Layer in a Large Volume Helicon Reactor

The self-consistently generated current-free electric double layer (DL) is shown to scale up with the source tube diameter and appears not to be affected by rf driving frequency and changes in reactor geometry. This Letter presents the first simultaneous measurements of local plasma potential and beam energy as a function of axial position. The DL is shown to be no more than 5 mm thick (20 D lengths) and positioned just downstream of the maximum in the magnetic field gradient. Furthermore, its position relative to the magnetic field is observed to be invariant as the magnetic field is translated axially. Measurements of the potential drop across the DL are presented for pressures down to 0.09 mTorr and the DL strength (phiDL/T(e)) is determined to be between 5 and 7.

The ion velocity distribution function in a current-free double layer

A portable, low-power, diode laser-based laser-induced fluorescence (LIF) diagnostic incorporating a heated iodine cell for absolute wavelength reference was installed on the Chi-Kung helicon source [K. K. Chi, T. E. Sheridan, and R. W. Boswell, Plasma Sources Sci. Technol. 8, 421 (1999)] to measure the ion velocity distribution function of argon ions as they transited a current-free double layer (DL) created where the solenoidal magnetic field diverges at the junction of the plasma source and the diffusion chamber. Based on LIF measurements of the transiting ion beam energy, the strength of the potential drop across the DL increases with decreasing neutral pressure and increasing magnetic field strength in the source. The location of the double layer also moves further downstream of the helicon source with increasing pressure. LIF measurements of the ion beam energy were found to be in good agreement with measurements obtained with a retarding field energy analyzer and also with numerical predictions.

Observations of Ion-Beam Formation in a Current-Free Double Layer

With nonperturbative laser-induced fluorescence measurements of ion flow, we confirm numerical simulations of spontaneous electric double-layer (DL) formation in a current-free expanding plasma. Measurements in two different experiments confirm that the DL is localized to the region of rapidly diverging magnetic field. The measurements indicate that the trapped ion population is a single Maxwellian, that the spatial gradient of the energy of ions accelerated through the DL matches the magnetic field gradient, and that DL formation is triggered when the ion-neutral collisional mean-free path exceeds the magnetic field gradient scale length.