© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:0803.2382

Comment on "Using Three-Body Recombination to Extract Electron Temperatures of Ultracold Plasmas"

Yurii V. Dumin

Published Mar 17, 2008• 0 citations

Abstract

In the recent work Fletcher et al. [Phys. Rev. Lett., v.99, p.145001 (2007)] reported on the novel experimental technique, enabling to measure the temperature of the expanding ultracold plasmas over a considerable time interval (up to 60-70 μs). It was unexpectedly found that the electron temperature dropped with time as T_e(t) ~ t^{-α} with α= 1.2 +/- 0.1 \approx 1 instead of α= 2, which would be expected for the adiabatic cooling of electrons in the cloud expanding linearly in time. The above-cited authors supposed that 'the difference is likely due to the significant heating effects from 3-body recombination' (i.e. the inelastic processes), but they did not provide sufficient quantitative estimates supporting such a conclusion. The aim of the present comment is to mention that the experimentally revealed t^{-1}-dependence can be explained under quite general assumptions by the purely elastic processes in the ultracold plasma, as it was done a few years ago in our work [Yu.V. Dumin, J. Low Temp. Phys., v.119, p.377 (2000)]. Therefore, t^{-1}-dependence revealed in the above-cited experiment should be primarily a manifestation of "virialization" of the electron velocities in the regime of strong electron-ion correlations, while the heat release by inelastic processes should be of secondary importance (it might be responsible, particularly, for changing the exponent from -1 to -1.2). This is confirmed also by our ab initio molecular-dynamic simulations taking into account the strong electron-ion correlations (i.e. not based on the PIC method, Vlasov approximation for electrons, etc., which are applicable only to small-angular scattering).

DOI: 10.48550/arxiv.0803.2382

Related papers

Numerical simulation of ultracold plasmas

S. G. Kuzmin, Thomas M. O’Neil

In recent experiments ultracold plasmas were produced by photoionizing small clouds of laser cooled atoms. This paper presents the results of molecular dynamic simulations for the early time evolution of such plasmas. Contrary to earlier speculation, no evidence of strong electron–electron correlations is observed in the simulations even if the initial value of the coupling parameter (Γe=e2/akTe) is much larger than unity. As electron–electron correlations begin to develop, the correlation energy is released to heat the electrons, raising the electron temperature to the point where Γe∼1 and limiting further development of correlation. Further heating of the electrons occurs as a by-product of three-body recombination. When a model of laser cooling is added to the simulation, the formation of strong ion–ion correlation is observed. Contrary to earlier suggestion, the rate of three-body recombination is observed to be in reasonable agreement with the traditional formula, R=3.9×10−9 s−1[n(cm−3)]2[Te(K)]−9/2, but care must be taken to use the correct temporally evolving temperature, Te. The simulations are challenging because it is necessary to follow three-body recombination into weakly bound (high n quasiclassical) Rydberg states, and the time scale for such states is short compared to that for the plasma dynamics. This kind of problem was faced earlier in computational astrophysics when studying binary star formation in globular clusters and the simulation method used here is adapted from such studies.

Physics of Plasmas•Aug 30, 2002•101 citations

Three-Body Recombination and Rydberg Atoms in Ultracold Plasmas

Robert Samuel Fletcher

Ultracold neutral plasmas, created by photoionizing samples of laser-cooled atoms, have well-controlled initial density and temperature parameters. With initial particle peak densities of ~10^15 m^-3, initial ion temperatures in the tens of micro-Kelvin range, and initial electron temperatures with a controllable range of 1-1000 K, these systems provide a means to study otherwise laboratory-inaccessible parameter ranges for plasma research. Furthermore, these plasmas are inhomogeneous, unconfined, and freely expanding into a vacuum. Despite the extraordinarily low electron temperatures, the electron system remains weakly coupled, although the ion system exhibits strong coupling behavior. While the initial electron temperatures are very low in ultracold plasmas, the temperature evolution has only been measured indirectly, in the earliest ~5% of the plasma lifetime, and often with large uncertainties. We present a technique that, with further theoretical support, can provide straightforward temperature measurements throughout the first fifth of the plasma lifetime. By making use of collective modes of the plasma, we fit a model of Tonks-Dattner resonances (electron sound wave propagating in the plasma) to measurements of these resonances and obtain a time-dependent electron temperature measurement for the ultracold plasma. Three-body recombination, a plasma loss process that has a rate scaling with the -9/2 power of the electron temperature, is of obvious interest in these ultracold plasma systems. Several theoretical works have predicted that the three-body recombination rate expression would need to be modified at these low electron temperatures, although the validity of these changes often hinges on the electron system being strongly coupled. We have performed the lowest temperature measurements of three-body recombination rates in a plasma and show that these measurements potentially provide a low-uncertainty means to calculate electron temperatures.

•Apr 18, 2008•1 citation

Characteristic features of temperature evolution in ultracold plasmas

Yu. V. Dumin

The theoretical interpretation of recent experiments on the time evolution of the temperature in freely expanding, ultracold plasma clouds released from a magneto-optical trap is discussed. The most interesting result of those experiments was the asymptotic behavior T e ∝ t −(1,2±0.1), instead of the behavior proportional to t −2, which was expected for a rarefied monatomic gas in the inertial expansion stage. It is shown that such a substantially slower temperature fall can be well explained by the specific properties of the equation of state of ultracold plasma with a large Coulomb coupling parameter; whereas the heat release in inelastic processes (in particular, three-body recombination) turns out to be relatively unimportant in the first approximation. This conclusion is confirmed by approximate analytic estimates from the model of virializing the energies of charged particles and also by the results of ab initio computer simulations; moreover, the computations demonstrate that the law of decrease in the electron temperature is established very rapidly, when the virialization criterion begins to be satisfied only to within a factor of order unity.

arXiv:1104.0038•Plasma Physics Reports•Oct 1, 2011•11 citations

Evolution of Temperature in the Ultracold Strongly-Correlated Plasmas

Yurii V. Dumin

We present a theoretical interpretation of the recently revealed features of temperature evolution in the ultracold plasma clouds released from a magneto-optical trap, namely: (a) its independence at the sufficiently large times on the initial plasma parameters and (b) the asymptotics close to t^{-1} instead of t^{-2}, expected for a rarefied ideal gas. It is shown that both these properties can be well explained by the model of virialization of the charged particle velocities in the regime of strong electron-ion correlations, while heating due to inelastic processes (e.g. three-body recombination) should be of secondary importance. These conclusions are confirmed also by the results of ab initio computer simulations.

arXiv:0905.1485•May 10, 2009•0 citations

Comment on "Observation of Collective Modes of Ultracold Plasmas"

Yurii V. Dumin

We discuss a theoretical interpretation of the experiment by Fletcher, Zhang, and Rolston [PRL, 96, 105003 (2006)], who revealed a number of subharmonics of the electron emission under external irradiation of the freely-expanding clouds of ultracold plasmas. The original interpretation of these subharmonics as standing waves of plasma oscillations (the so-called Tonks-Dattner resonances) encounters a number of problems, such as the lack of adequate boundary conditions and incorrect dependence on the plasma temperature and the degree of neutrality. It is the aim of the present comment to mention that a more promising interpretation may be based on the peaks in the efficiency of ionization of the secondary Rydberg atoms, formed during the plasma cloud expansion and cooling. The presence of the last-mentioned peaks is well supported by the independent experiment by Maeda and Gallagher [PRL, 93, 193002 (2004)].

arXiv:0906.5162•Jun 28, 2009•0 citations

Using Three-Body Recombination to Extract Electron Temperatures of Ultracold Plasmas

Robert Samuel Fletcher, X. L. Zhang, S. L. Rolston

Three-body recombination, an important collisional process in plasmas, increases dramatically at low electron temperatures, with an accepted scaling of Te(-9/2). We measure three-body recombination in an ultracold neutral xenon plasma by detecting recombination-created Rydberg atoms using a microwave-ionization technique. With the accepted theory (expected to be applicable for weakly coupled plasmas) and our measured rates, we extract the plasma temperatures, which are in reasonable agreement with previous measurements early in the plasma lifetime. The resulting electron temperatures indicate that the plasma continues to cool to temperatures below 1 K.

arXiv:0706.2672•Physical Review Letters•Oct 3, 2007•77 citations

In the recent work Fletcher et al. [Phys. Rev. Lett., v.99, p.145001 (2007)] reported on the novel experimental technique, enabling to measure the temperature of the expanding ultracold plasmas over a considerable time interval (up to 60-70 μs). It was unexpectedly found that the electron temperature dropped with time as T_e(t) ~ t^{-α} with α= 1.2 +/- 0.1 \approx 1 instead of α= 2, which would be expected for the adiabatic cooling of electrons in the cloud expanding linearly in time. The above-cited authors supposed that 'the difference is likely due to the significant heating effects from 3-body recombination' (i.e. the inelastic processes), but they did not provide sufficient quantitative estimates supporting such a conclusion. The aim of the present comment is to mention that the experimentally revealed t^{-1}-dependence can be explained under quite general assumptions by the purely elastic processes in the ultracold plasma, as it was done a few years ago in our work [Yu.V. Dumin, J. Low Temp. Phys., v.119, p.377 (2000)]. Therefore, t^{-1}-dependence revealed in the above-cited experiment should be primarily a manifestation of "virialization" of the electron velocities in the regime of strong electron-ion correlations, while the heat release by inelastic processes should be of secondary importance (it might be responsible, particularly, for changing the exponent from -1 to -1.2). This is confirmed also by our ab initio molecular-dynamic simulations taking into account the strong electron-ion correlations (i.e. not based on the PIC method, Vlasov approximation for electrons, etc., which are applicable only to small-angular scattering).

In recent experiments ultracold plasmas were produced by photoionizing small clouds of laser cooled atoms. This paper presents the results of molecular dynamic simulations for the early time evolution of such plasmas. Contrary to earlier speculation, no evidence of strong electron–electron correlations is observed in the simulations even if the initial value of the coupling parameter (Γe=e2/akTe) is much larger than unity. As electron–electron correlations begin to develop, the correlation energy is released to heat the electrons, raising the electron temperature to the point where Γe∼1 and limiting further development of correlation. Further heating of the electrons occurs as a by-product of three-body recombination. When a model of laser cooling is added to the simulation, the formation of strong ion–ion correlation is observed. Contrary to earlier suggestion, the rate of three-body recombination is observed to be in reasonable agreement with the traditional formula, R=3.9×10−9 s−1[n(cm−3)]2[Te(K)]−9/2, but care must be taken to use the correct temporally evolving temperature, Te. The simulations are challenging because it is necessary to follow three-body recombination into weakly bound (high n quasiclassical) Rydberg states, and the time scale for such states is short compared to that for the plasma dynamics. This kind of problem was faced earlier in computational astrophysics when studying binary star formation in globular clusters and the simulation method used here is adapted from such studies.

Ultracold neutral plasmas, created by photoionizing samples of laser-cooled atoms, have well-controlled initial density and temperature parameters. With initial particle peak densities of ~10^15 m^-3, initial ion temperatures in the tens of micro-Kelvin range, and initial electron temperatures with a controllable range of 1-1000 K, these systems provide a means to study otherwise laboratory-inaccessible parameter ranges for plasma research. Furthermore, these plasmas are inhomogeneous, unconfined, and freely expanding into a vacuum. Despite the extraordinarily low electron temperatures, the electron system remains weakly coupled, although the ion system exhibits strong coupling behavior. While the initial electron temperatures are very low in ultracold plasmas, the temperature evolution has only been measured indirectly, in the earliest ~5% of the plasma lifetime, and often with large uncertainties. We present a technique that, with further theoretical support, can provide straightforward temperature measurements throughout the first fifth of the plasma lifetime. By making use of collective modes of the plasma, we fit a model of Tonks-Dattner resonances (electron sound wave propagating in the plasma) to measurements of these resonances and obtain a time-dependent electron temperature measurement for the ultracold plasma. Three-body recombination, a plasma loss process that has a rate scaling with the -9/2 power of the electron temperature, is of obvious interest in these ultracold plasma systems. Several theoretical works have predicted that the three-body recombination rate expression would need to be modified at these low electron temperatures, although the validity of these changes often hinges on the electron system being strongly coupled. We have performed the lowest temperature measurements of three-body recombination rates in a plasma and show that these measurements potentially provide a low-uncertainty means to calculate electron temperatures.

The theoretical interpretation of recent experiments on the time evolution of the temperature in freely expanding, ultracold plasma clouds released from a magneto-optical trap is discussed. The most interesting result of those experiments was the asymptotic behavior T e ∝ t −(1,2±0.1), instead of the behavior proportional to t −2, which was expected for a rarefied monatomic gas in the inertial expansion stage. It is shown that such a substantially slower temperature fall can be well explained by the specific properties of the equation of state of ultracold plasma with a large Coulomb coupling parameter; whereas the heat release in inelastic processes (in particular, three-body recombination) turns out to be relatively unimportant in the first approximation. This conclusion is confirmed by approximate analytic estimates from the model of virializing the energies of charged particles and also by the results of ab initio computer simulations; moreover, the computations demonstrate that the law of decrease in the electron temperature is established very rapidly, when the virialization criterion begins to be satisfied only to within a factor of order unity.

We present a theoretical interpretation of the recently revealed features of temperature evolution in the ultracold plasma clouds released from a magneto-optical trap, namely: (a) its independence at the sufficiently large times on the initial plasma parameters and (b) the asymptotics close to t^{-1} instead of t^{-2}, expected for a rarefied ideal gas. It is shown that both these properties can be well explained by the model of virialization of the charged particle velocities in the regime of strong electron-ion correlations, while heating due to inelastic processes (e.g. three-body recombination) should be of secondary importance. These conclusions are confirmed also by the results of ab initio computer simulations.

We discuss a theoretical interpretation of the experiment by Fletcher, Zhang, and Rolston [PRL, 96, 105003 (2006)], who revealed a number of subharmonics of the electron emission under external irradiation of the freely-expanding clouds of ultracold plasmas. The original interpretation of these subharmonics as standing waves of plasma oscillations (the so-called Tonks-Dattner resonances) encounters a number of problems, such as the lack of adequate boundary conditions and incorrect dependence on the plasma temperature and the degree of neutrality. It is the aim of the present comment to mention that a more promising interpretation may be based on the peaks in the efficiency of ionization of the secondary Rydberg atoms, formed during the plasma cloud expansion and cooling. The presence of the last-mentioned peaks is well supported by the independent experiment by Maeda and Gallagher [PRL, 93, 193002 (2004)].

Three-body recombination, an important collisional process in plasmas, increases dramatically at low electron temperatures, with an accepted scaling of Te(-9/2). We measure three-body recombination in an ultracold neutral xenon plasma by detecting recombination-created Rydberg atoms using a microwave-ionization technique. With the accepted theory (expected to be applicable for weakly coupled plasmas) and our measured rates, we extract the plasma temperatures, which are in reasonable agreement with previous measurements early in the plasma lifetime. The resulting electron temperatures indicate that the plasma continues to cool to temperatures below 1 K.