Neutral-plasma oscillations at zero temperature

Abstract

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...

Heating mechanisms in radio-frequency-driven ultracold plasmas

“…Plasma resonance can be detected as an increased yield of electrons leaving the UCP [10]. Combined with knowledge of the mode properties [11], this can be used to determine the plasma density and expansion as a function of time. Using the same technique, the presence of acoustic or Tonks-Dattner modes in an UCP has been observed in addition to the fundamental mode [12].…”

Ultracold Plasma Expansion in a Magnetic Field

“…UCPs thus provide a testing ground to study basic plasma theory in a clean and simple system, and we need fields of only tens of Gauss to observe significant effects on the expansion dynamics (for our system the electrons are magnetized, while the ions are not). All previous studies of ultracold plasma expansion, both experimental [2,3,4,5] and theoretical [6,7,8,9], focus on free expansion in the absence of magnetic fields.In this work, we present the first measurement of UCP expansion in a magnetic field. By extracting the ions with a high voltage pulse onto a position-sensitive detector, we image the ion distribution of an UCP expanding in a uniform magnetic field.…”

Waves in Rydberg plasmas

“…However, we should notice that Rydberg states are also excited in the case of direct ionization. The result is a low ionized plasma where the remaining neutral atoms have highly excited energy states [3][4][5].…”