A. Fruchtman

Penetration and expulsion of magnetic fields in plasmas due to the Hall field

The axial penetration of an azimuthal magnetic field into a short‐duration hollow cylindrical plasma is studied. When the process is so fast that the ion motion is small and the plasma dissipative resistivity, electron inertia, and pressure are small, the evolution of the magnetic field is governed by the Hall field. When the radial current flows inward, the magnetic field penetrates in the form of a Hall‐induced shock wave with a narrow current channel. When outward, the magnetic field does not penetrate the plasma. Moreover, in the latter case the magnetic field is expelled from an initially magnetized plasma. The increase and decrease of the magnetic field intensity in the cylindrical plasma are shown to result naturally from the frozen‐in law.

Control of the electric-field profile in the Hall thruster

Control of the electric-field profile in the Hall thruster through the positioning of an additional electrode along the channel is shown theoretically to enhance the efficiency. The reduction of the potential drop near the anode by use of the additional electrode increases the plasma density there, through the increase of the electron and ion transit times, causing the ionization in the vicinity of the anode to increase. The resulting separation of the ionization and acceleration regions increases the propellant and energy utilizations. An abrupt sonic transition is forced to occur at the axial location of the additional electrode, accompanied by the generation of a large (theoretically infinite) electric field. This ability to generate a large electric field at a specific location along the channel, in addition to the ability to specify the electric potential there, allows us further control of the electric-field profile in the thruster. In particular, when the electron temperature is high, a large abrupt voltage drop is induced at the vicinity of the additional electrode, a voltage drop that can comprise a significant part of the applied voltage.

Two-dimensional equilibrium of a low temperature magnetized plasma

A two-dimensional steady-state model is developed, in which, even though ion inertia is retained, a variable separation allows us to analyse separately the axial and the radial transports. For the axial transport (along magnetic field lines) an integral dispersion relation is derived that includes a nonlinear form that is obtained from the ion–neutral collision operator. The dispersion relation is solved for various values of the Paschen parameter, and the electron temperature and the axial profiles of the plasma density and plasma potential are calculated. The solutions of the dispersion relation are shown to have three asymptotic limits: collisionless, linear diffusion and nonlinear diffusion. For the radial transport, the rate of which is determined by electron cross-field diffusion, the full equations are numerically solved. The calculations are compared to probe measurements performed at various locations inside our helicon source for various magnetic field intensities and wave powers. The proposition that the measured increase in the plasma density with the increase of the magnetic field intensity is a result of an improved confinement, is examined. For the parameters of the experiment described here, this proposition implies that the electron collisionality is much larger than expected from electron–ion and electron–neutral collisions. A different explanation for the dependence of the density on the magnetic field intensity is suggested, that the density increase that follows an increase of the magnetic field intensity results from an improved wave–plasma coupling via the helicon interaction, causing a larger fraction of the total wave power to be deposited inside the helicon source.

A magnetic nozzle calculation of the force on a plasma

The measured axial force imparted from a magnetically expanding current-free plasma has been shown recently [Takahashi, Phys. Rev. Lett. 107, 235001 (2011)] to equal the axial force on that plasma calculated by a two-dimensional fluid model. Here, we calculate the same axial force on the plasma by a quasi one-dimensional model of a magnetic nozzle. The quasi one-dimensional magnetic nozzle model provides us with an estimate of the force on the plasma that is similar to that found by the more accurate two-dimensional model.

Plasma lens and plume divergence in the Hall thruster

The effect of magnetic field curvature on the plume divergence in the Hall thruster is analyzed. The two-dimensional plasma flow and electric field are determined self-consistently within the paraxial approximation in this plasma lens, a nearly axial electric field perpendicular to the curved magnetic field lines. The ion radial velocity along the thruster is described analytically. The authors suggest positioning the ionization layer near the zero of the magnetic field in a reversing-direction field configuration for a minimal beam divergence. They also show that an additional emitting electrode can reduce plume divergence.

Fast magnetic-field penetration into plasmas due to the Hall field

The enhancement of magnetic‐field penetration into short‐duration plasmas by the dissipationless Hall field is examined. Magnetic‐field penetration along a background magnetic field is focused on, where the inductive Hall electric field enables the magnetic field to penetrate as a whistler wave. It is shown that the magnetic‐field evolution, when governed simultaneously by both whistler wave propagation and collisional diffusion, is described by a diffusion equation with a complex diffusion coefficient. The imaginary part of this coefficient is proportional to the Hall resistivity associated with the background magnetic field. In the collisionless limit the governing equation is equivalent to the Schrodinger equation for a free particle, and the magnetic field propagates the way a free‐particle wave packet expands by dispersion rather than by diffusion. This study was motivated by the enhanced magnetic‐field penetration recently observed in the anode plasma of a magnetically insulated ion diode.

Observation of faster-than-diffusion magnetic field penetration into a plasma

Spatially and temporally resolved spectroscopic measurements of the magnetic field, electron density, and turbulent electric fields are used to study the interaction between a pulsed magnetic field and a plasma. In the configuration studied (known as a plasma opening switch) a 150 kA current of 400 ns-duration is conducted through a plasma that fills the region between two planar electrodes. The time-dependent magnetic field, determined from Zeeman splitting, is mapped in three dimensions, showing that the magnetic field propagation is faster than expected from diffusion based on the Spitzer resistivity. Moreover, the measured magnetic field profile and the amplitude of turbulent electric fields indicate that the fast penetration of the magnetic field cannot be explained by an anomalously high resistivity. On the other hand, the magnetic field is found to penetrate into the plasma at a velocity that is independent of the current-generator polarity, contradictory to the predictions of the Hall-field theory...

Magnetic field penetration due to the Hall field in (almost) collisionless plasmas

The fast penetration of magnetic fields into plasmas due to the Hall field is described. The penetration occurs in nonuniform plasmas of a characteristic length smaller than the ion skin depth, it is much faster than the ion motion, and its rate is independent of the resistivity. Some previous results are described: a shock penetration of the magnetic field accompanied by a large energy dissipation, and field expulsion from an initially magnetized plasma. It is then shown how the Hall field can enhance the penetration into a plasma surrounded by vacuum. Finally, it is demonstrated how the evolution of the magnetic field in a plasma that conducts current between electrodes depends crucially on its evolution near the electrodes, when a realistic density profile is taken into account.

Spectroscopic investigation of fast (ns) magnetic field penetration in a plasma

The time‐dependent magnetic field spatial distribution in a coaxial positive‐polarity plasma opening switch (POS) carrying a current ≂135 kA during ≂100 ns, was investigated by two methods. In the first, ionic line emission was observed simultaneously for two polarizations to yield the Doppler and Zeeman contributions to the line profiles. In the second method, the axial velocity distribution of ions was determined, giving the magnetic field through the ion equation of motion. This method requires knowledge of the electron density, here obtained from the observed particle ionization times. To this end, a lower bound for the electron kinetic energy was determined using various line intensities and time‐dependent collisional‐radiative calculations. An important necessity for POS studies is the locality of all measurements in r, z, and θ. This was achieved by using laser evaporation to seed the plasma nonperturbingly with the species desired for the various measurements. The Zeeman splitting and the ion moti...

Spectroscopic investigations of the plasma behavior in a plasma opening switch experiment

The electron density, the electron kinetic energy, the particle motion, and electric fields in a coaxial positive‐polarity plasma opening switch (POS) were studied using spectroscopic diagnostics. A gaseous source that injects the plasma radially outward from inside the inner POS electrode was developed. The plasma was locally seeded with various species, desired for the various measurements allowing for axial, radial, and azimuthal resolutions both prior to and during the 180 ns long current pulse. The electron density was determined from particle ionization times and the electron energy from line intensities and time dependent collisional‐radiative calculations. Fluctuating electric fields were studied from Stark broadening. The ion velocity distributions were obtained from emission‐line Doppler broadenings and shifts. The early ion motion, the relatively low ion velocities and the nearly linear velocity dependence on the ion charge‐to‐mass ratio, leads to the conclusion that the magnetic field penetrat...