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In many experiments on single-component plasmas, including antimatter plasmas, the standard diagnostic techniques used to measure the density and temperature are not appropriate. We present a new method for determining the size, shape, average density, and temperature of a singlecomponent plasma confined in a Penning trap from measurements of the plasma mode frequencies.

We use cold plasma theory to calculate the response of an ultracold neutral plasma to an applied rf field. The free oscillation of the system has a continuous spectrum and an associated damped quasimode. We show that this quasimode dominates the driven response. We use this model to simulate plasma oscillations in an expanding ultracold neutral plasma, providing insights into the assumptions used to interpret experimental data [Phys. Rev. Lett. 85, 318 (2000)].PACS numbers: 52.55. Dy, 32.80.Pj, 52.27.Gr, 52.35.Fp Recent experimental [1,2, 3,4,5,6] and theoretical work [7,8,9,10,11,12,13] has studied the formation and evolution of ultracold plasmas. In the laboratory, cold plasmas are created either by directly photo-ionizing laser-cooled atoms, or by exciting the atoms to high-lying Rydberg states that spontaneously ionize. A fraction of the electrons escape the plasma and the resulting electric field drives the ion expansion. Models of the expansion suggest that the density profile in the plasma is approximately Gaussian, and that it expands in a self-similar manner. It can be expressed aswhere σ = σ 2 0 + v 2 t 2 is the time-dependent width of the distribution, v is the asymptotic expansion velocity, and t is time.The experimental justification of this density profile for the case of an expanding plasma is based on the plasma's response to a spatially uniform applied rf field. In those experiments, Xe atoms initially cooled to ∼ 10µK were ionized by a dye laser. The initial electron energy (E e /k B ) ranged from a few to 1000 K, and the initial electron density ranged from 0.2 to 2.5 × 10 9 cm −3 . The plasmas were nearly charge-neutral, and at electron energies above 70 K, the kinetic energy of the electrons allowed significant loss. The resulting net positive charge in the cloud drove the plasma expansion.As the plasma expanded and its density decreased, the applied rf field pumped energy into the plasma. The heating was assumed to be largest where the applied rf frequency matched the local plasma frequency. Because of collisions in the plasma, the local heating presumably raised the overall plasma temperature, and a small number of the more weakly-bound electrons were ejected. The experiment measured the rate at which electrons were ejected from the expanding plasma as a function of time for a fixed applied rf frequency. This signal was presumed to be proportional to the rate at which the rf field heats the plasma, and was a measure of the weighted time-dependent density profile.The peak of this signal was interpreted to correspond to the "average" density of the plasma,with v a constant. This density was experimentally determined by setting the applied frequency ω equal to the average plasma frequency, ω p , and using the relationω p = q 2n (t)/m e ǫ 0 , where q is the electron charge, m e is the electron mass, and ǫ 0 is the permittivity of free space. The derived density,n, is time dependent. For a different applied rf frequency ω, the signal peaks at a different time. A least-squares fit ofn(t) to E...

Spheromaks with lifetimes of 1 ms are produced in the CTX experiment. This paper describes the diagnostics and measurements on plasmas which, for CTX-produced plasmas, are the hottest and longest-lived discharges using a solid copper flux conserver. These spheromaks are formed using a static hydrogen background gas filling the entire vacuum system before the discharge. The density rapidly decays in 150–300 μs from an initial value of (1–3) × 1014 cm−3 to a steady-state plateau with a value of (1–4) × 1013cm−3,determine d by the pressure of the gas fill. A multi-point Thomson scattering system measures the radial profiles of electron temperature and density. Peak temperatures of over 40 eV are observed, and the average temperature increases in time by Ohmic heating from 15 eV to over 30 eV. Equilibrium models for the magnetic field structure are used to calculate values of peak local beta (8–13%), volume-averaged beta (3–8%), and engineering beta (10–25%). The operation with a filling gas results in a reduction of the impurity radiation power as measured by spectroscopy. Improved vacuum practices, discharge cleaning and the use of the static gas fill have resulted in discharges in which the radiation power loss is not dominating the energy balance late in time. Particle loss and the associated ionization and heating of the neutral particles required to maintain the density plateau appear to be the major energy loss processes in the spheromak.

Computations of damped diocotron oscillations ͑quasi-modes͒ are described for non-neutral plasmas and inviscid fluids. The numerical method implements a suggestion made by Briggs, Daugherty, and Levy some 25 years ago ͓Phys. Fluids 13, 421 ͑1970͔͒ to push the branch line that forms the continuum into the complex-plane by solving the mode equation in the complex r-plane. For the special case of power-law density profiles the calculation finds the same quasi-mode frequencies found recently by Corngold ͓Phys. Plasmas 2, 620 ͑1995͔͒. It is found that the feature of the continuum eigenfunctions which indicates the presence of a nearby quasi-mode is continuity of the derivative of the regular part of the eigenfunctions near the singularity. The evolution of Rayleigh modes, found in density profiles with steps, is also studied as the density steps are smoothed.