Analytic solutions are presented for the orbit of a charged particle in the combination of a uniform axial magnetic field and parabolic electrostatic potential. These trajectories are shown to correspond to the sum of two individually rotating vectors with one vector rotating at a constant fast frequency and the other rotating in the same sense but with a constant slow frequency. These solutions are related to Penning trap orbits and to stochastic orbits. If the lengths of the two rotating vectors are identical, the particle has zero canonical angular momentum in which case the particle orbit will traverse the origin. If the potential has an inverse dependence on distance from the source of the potential, the particle can impact the source. Axis-encircling orbits are where the length of the vector associated with the fast frequency is longer than the vector associated with the slow frequency. Non-axis-encircling orbits are the other way around.

The fundamentals of stereoscopy and their application to dusty plasmas are described. It is shown that stereoscopic methods allow us to measure the three-dimensional particle positions and trajectories with high spatial and temporal resolution. The underlying technical implications are presented and requirements and limitations are discussed. The stereoscopic method is demonstrated for dust particles in dust-density waves under microgravity conditions.

The effect of the finite probe size in plasma fluctuation measurements is revisited for dusty plasmas, where it has been argued that dust leads to a significant low-frequency enhancement in the spectral densities of ion density fluctuations, which can constitute the physical basis of a dust diagnostic technique. Theoretical predictions for the spectral modifications are presented and the dust acoustic mode contribution is analysed. The finite probe size effect is treated within the volume average approach, which introduces geometry dependent form factors that are calculated for spherical and cylindrical probes. The volume average approach is compared with the typically employed cutoff wavenumber approximation for various dust and plasma parameters. The contribution of temperature fluctuations to the spectral density of current fluctuations is also evaluated.

The intense heat and energetic particle fluxes expected in ITER and future magnetic fusion reactors pose prohibitive problems to the design, selection and maintenance of the first wall and divertor. Micropellet injection (MPI) technologies can offer some innovative solutions to the material and extreme heat challenges. Basic physics of micropellet motion, ablation and interactions with high-temperature plasmas and energetic particles are presented first. We then discuss MPI technology options and applications. In addition to plasma diagnostic applications, controlled injection of micropellets of different sizes, velocities and injection frequencies will offer several possibilities: (1) better assessment of the core plasma cooling due to dust produced in situ; (2) better understanding of the plasma–material interaction physics near the wall; (3) new methods for plasma fuelling and impurity control; and (4) techniques for edge cooling with minimal impact on the plasma core. Dedicated small-scale laboratory experiments will complement major fusion experiments in development and applications of MPI.

The fundamentals of the ‘resonance method’ are presented. The method relies on evaluating the dynamic response of one or more dust particles in the sheath of a laboratory plasma to small external perturbations. It allows one to make in situ high-precision measurements of particle properties. It is shown that the particle mass and charge and the strength of the interaction between two particles can be measured. Technical requirements, limitations and application examples are presented and discussed.

Particle image velocimetry is a fluid measurement technique that has been used for more than 20 years to characterize the particle transport and thermal state of dusty plasma systems. This manuscript provides an overview of this diagnostic technique, highlighting the strengths and limitations that are associated with its use. Additionally, the variations of this technique that have been applied in the study of dusty plasma systems will be discussed, along with a small selection of measurements that can be made with the technique. Potential future directions for this diagnostic tool within the dusty plasma community will also be discussed.

Methods of imaging and image analysis are presented for dusty plasma experiments. Micron-sized polymer spheres, electrically suspended in a partially ionized gas, are illuminated by a sheet of laser light and imaged by video cameras. Image analysis methods yield particle positions and velocities of individual particles in each video image. Methods to minimize errors in the particle positions and velocities, which are now commonly used in the dusty plasma community, are described.

We consider two isolated, interacting dust particles confined in plasma. Measurements of normal mode frequencies are used to determine the dust charge, the Debye shielding length and the anisotropy of the confining potential well. For dust particles confined near the sheath edge, the vertical electric field and an effective electron temperature are also determined. This method is used to characterize the sheath above a short rectangular trench in the powered electrode of a radio-frequency discharge.

In this paper a method is described that allows mapping of the forces acting on dust particles in a GEC reference cell. Monodisperse particles are dropped into the plasma environment and their trajectories are tracked using a high-speed camera system to determine local accelerations and respective forces. Collecting data from a large number of particle drops allows the identification of three-dimensional vector fields for the acting forces. The procedure is described and multiple examples in which the method has been applied are given. These examples include a simple plasma sheath, plasmas perturbed by a horizontal and vertical dipole magnet, an array of multiple magnets mimicking the fields found at a lunar swirl, and the fields inside a glass box used for particle confinement. Further applicability in other plasma environments will be discussed shortly.

Two in situ experimental methods are presented in which dust particles are used to determine the extent of the sheath and gain information about the time-averaged electric force profile within a radio frequency (RF) plasma sheath. These methods are advantageous because they are not only simple and quick to carry out, but they also can be performed using standard dusty plasma experimental equipment. In the first method, dust particles are tracked as they fall through the plasma towards the lower electrode. These trajectories are then used to determine the electric force on the particle as a function of height as well as the extent of the sheath. In the second method, dust particle levitation height is measured across a wide range of RF voltages. Similarities were observed between the two experiments, but in order to understand the underlying physics behind these observations, the same conditions were replicated using a self-consistent fluid model. Through comparison of the fluid model and experimental results, it is shown that the particles exhibiting a levitation height that is independent of RF voltage indicate the sheath edge – the boundary between the quasineutral bulk plasma and the sheath. Therefore, both of these simple and inexpensive, yet effective, methods can be applied across a wide range of experimental parameters in any ground-based RF plasma chamber to gain useful information regarding the sheath, which is needed for interpretation of dusty plasma experiments.

In this article, a detailed introduction of the light extinction spectrometry (LES) diagnostics is given. LES allows the direct in situ measurement of the particle size distribution and absolute concentration of dust clouds levitating in plasmas. Using a relatively simple and compact experimental set-up, the dust cloud parameters can be recovered with a good accuracy making minimum assumptions on their physical properties. Special emphases are given to the inversion procedure of light extinction spectra and all the required particle shape, refractive index and light extinction models. The parameter range and the limitations of LES are discussed. Two measurements in low-pressure gas discharges are presented: (i) in a direct-current (DC) glow discharge in which nanoparticles are growing from the sputtering of a tungsten cathode and (ii) in an argon–silane radio-frequency discharge. They demonstrate the capabilities of the LES technique to characterise, in situ and in real-time, the growth dynamics of nanoparticles in the size range 5–100 nm and volume concentrations in the range from a few ppb to a few ppm.