Convenient analytical formula for cluster mean diameter and diameter dispersion after nucleation burst.

We propose an alternative method of estimating the mean diameter and dispersion of clusters of particles, formed in a cooling gas, right after the nucleation stage. Using a moment model developed by Friedlander [S. K. Friedlander, Ann. N. Y. Acad. Sci. 404, 354 (1983)10.1111/j.1749-6632.1983.tb19497.x], we derive an analytic relationship for both cluster mean diameter and diameter dispersion as a function of two of the characteristic times of the system: the cooling time and the primary constituents collision time. These formulas can be used to predict diameter and dispersion variation with process parameters, such as the initial primary constituents' concentration or cooling rate. It is also possible to use them as an input to the coagulation stage, without the need to compute complex cluster generation during the nucleation burst. We compared our results with a nodal code (NGDE) and got excellent agreement.

Design and implementation of a Thomson parabola for fluence dependent energy-loss measurements at the Neutralized Drift Compression eXperiment.

The interaction of ion beams with matter includes the investigation of the basic principles of ion stopping in heated materials. An unsolved question is the effect of different, especially higher, ion beam fluences on ion stopping in solid targets. This is relevant in applications such as in fusion sciences. To address this question, a Thomson parabola was built for the Neutralized Drift Compression eXperiment (NDCX-II) for ion energy-loss measurements at different ion beam fluences. The linear induction accelerator NDCX-II delivers 2 ns short, intense ion pulses, up to several tens of nC/pulse, or 1010-1011 ions, with a peak kinetic energy of ∼1.1 MeV and a minimal spot size of 2 mm FWHM. For this particular accelerator, the energy determination with conventional beam diagnostics, for example, time of flight measurements, is imprecise due to the non-trivial longitudinal phase space of the beam. In contrast, a Thomson parabola is well suited to reliably determine the beam energy distribution. The Thomson parabola differentiates charged particles by energy and charge-to-mass ratio, through deflection of charged particles by electric and magnetic fields. During first proof-of-principle experiments, we achieved to reproduce the average initial helium beam energy as predicted by computer simulations with a deviation of only 1.4%. Successful energy-loss measurements with 1 µm thick silicon nitride foils show the suitability of the accelerator for such experiments. The initial ion energy was determined during a primary measurement without a target, while a second measurement, incorporating the target, was used to determine the transmitted energy. The energy-loss was then determined as the difference between the two energies.

Sheath-induced instabilities in plasmas with E0×B0 drift.

It is shown that ion acoustic waves in plasmas with E0×B0 electron drift become unstable due to the closure of plasma current in the chamber wall. Such unstable modes may enhance both near-wall conductivity and turbulent electron transport in plasma devices with E0×B0 electron drift and unmagnetized ions. It is shown that the instability is sensitive to the wall material: a high value of the dielectric permittivity (such as in metal walls) reduces the mode growth rate by an order of magnitude but does not eliminate the instability completely.

Kinetic theory of plasma sheaths surrounding electron-emitting surfaces.

A one-dimensional kinetic theory of sheaths surrounding planar, electron-emitting surfaces is presented which accounts for plasma electrons lost to the surface and the temperature of the emitted electrons. It is shown that ratio of plasma electron temperature to emitted electron temperature significantly affects the sheath potential when the plasma electron temperature is within an order of magnitude of the emitted electron temperature. The sheath potential goes to zero as the plasma electron temperature equals the emitted electron temperature, which can occur in the afterglow of an rf plasma and some low-temperature plasma sources. These results were validated by particle in cell simulations. The theory was tested by making measurements of the sheath surrounding a thermionically emitting cathode in the afterglow of an rf plasma. The measured sheath potential shrunk to zero as the plasma electron temperature cooled to the emitted electron temperature, as predicted by the theory.

General cause of sheath instability identified for low collisionality plasmas in devices with secondary electron emission.

A condition for sheath instability due to secondary electron emission (SEE) is derived for low collisionality plasmas. When the SEE coefficient of the electrons bordering the depleted loss cone in energy space exceeds unity, the sheath potential is unstable to a negative perturbation. This result explains three different instability phenomena observed in Hall thruster simulations including a newly found state with spontaneous ∼20 MHz oscillations. When instabilities occur, the SEE propagating between the walls becomes the dominant contribution to the particle flux, energy loss and axial transport.

Absence of Debye sheaths due to secondary electron emission.

A bounded plasma where the hot electrons impacting the walls produce more than one secondary on average is studied via particle-in-cell simulation. It is found that no classical Debye sheath or space-charge-limited sheath exists. Ions are not drawn to the walls and electrons are not repelled. Hence the unconfined plasma electrons travel unobstructed to the walls, causing extreme particle and energy fluxes. Each wall has a positive charge, forming a small potential barrier or "inverse sheath" that pulls some secondaries back to the wall to maintain the zero current condition.

Charge and current neutralization of an ion-beam pulse propagating in a background plasma along a solenoidal magnetic field.

The analytical studies show that the application of a small solenoidal magnetic field can drastically change the self-magnetic and self-electric fields of the beam pulse propagating in a background plasma. Theory predicts that when omega_{ce} approximately omega_{pe}beta_{b}, where omega_{ce} is the electron gyrofrequency, omega_{pe} is the electron plasma frequency, and beta_{b} is the ion-beam velocity relative to the speed of light, there is a sizable enhancement of the self-electric and self-magnetic fields due to the dynamo effect. Furthermore, the combined ion-beam-plasma system acts as a paramagnetic medium; i.e., the solenoidal magnetic field inside the beam pulse is enhanced.

Spatiotemporal dynamics of charged species in the afterglow of plasmas containing negative ions.

The spatiotemporal evolution of charged species densities and wall fluxes during the afterglow of an electronegative discharge has been investigated. The decay of a plasma with negative ions consists of two stages. During the first stage of the afterglow, electrons dominate plasma diffusion and negative ions are trapped inside the vessel by the static electric field; the flux of negative ions to the walls is nearly zero. During this stage, the electron escape frequency increases considerably in the presence of negative ions, and can eventually approach free electron diffusion. During the second stage of the afterglow, electrons have disappeared, and positive and negative ions diffuse to the walls with the ion-ion ambipolar diffusion coefficient. Theories for plasma decay have been developed for equal and strongly different ion (T(i)) and electron (T(e)) temperatures. In the case T(i)=T(e), the species spatial profiles are similar and an analytic solution exists. When detachment is important in the afterglow (weakly electronegative gases, e.g., oxygen) the plasma decay crucially depends on the product of negative ion detachment frequency (gamma(d)) and diffusion time (tau(d)). If gamma(d)tau(d)>2, negative ions convert to electrons during their diffusion towards the walls. The presence of detached electrons results in "self-trapping" of the negative ions, due to emerging electric fields, and the negative ion flux to the walls is extremely small. In the case T(i)<