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Physical review. E

Reply to “Comment on ‘Ultracold plasma expansion in quadrupole magnetic field' ”

Sergey Ya. Bronin, Evgenii Vladimirovich Vikhrov, B. B. Zelener, B. V. Zelener

Published Aug 21, 2024• 1 citation
Publisher

Abstract

In this Reply, we respond to the Comment by Schlitters et al. on our recent work [Phys. Rev. E 108, 045209 (2023)10.1103/PhysRevE.108.045209], where we present simulation results of ultracold Sr plasma expansion in a quadrupole magnetic field using a molecular-dynamics method. In the Comment, Schlitters et al. present their experimental results, some of which, from their point of view, contradict our simulation results and others that confirm the experiments of Gorman et al. [Phys. Rev. Lett. 126, 085002 (2021)10.1103/PhysRevLett.126.085002] and our results. In addition, Schlitters et al. also provide results that were not described in our work. Here we show that there is not a contradiction but a misunderstanding of our results. This is due to the fact that simulations allow the use of processing methods that are difficult to obtain in experiment. We also present different simulation results related to expansion velocity variations that reflect the experimental results of Schlitters et al. and provide an explanation for the origin of these variations.

DOI
10.1103/physreve.110.027202

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Comment on “Ultracold plasma expansion in quadrupole magnetic field”

Matthew Schlitters, Matthew Miller, Ben Farley +1 more

Bronin et al. [Phys. Rev. E 108, 045209 (2023)2470-004510.1103/PhysRevE.108.045209] recently reported molecular-dynamics simulations of ultracold neutral plasmas expanding in a quadrupole magnetic field. While the main results are in agreement with prior experimental measurements, we present data showing oscillations not captured in the simulations of Bronin et al. Plasmas formed using pulsed or continuous-wave ionization processes have similar confinement times.

Physical review. E•Aug 21, 2024•2 citations

Ultracold plasma expansion in quadrupole magnetic field

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We present simulation results of ultracold Sr plasma expansion in a quadrupole magnetic field by means of molecular dynamics. An analysis of plasma evolution influenced by a magnetic field is given. Plasma confinement time behavior under variation of magnetic field strength is estimated. Similarity of the time dependence of the concentration and distribution of ion velocities against the parameters of the plasma and magnetic field is established. Simulation results are in agreement with the experimental ones.

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

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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).

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Vyacheslav I. Yukalov

Nonadiabatic dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, has been considered in my earlier paper [V. I. Yukalov, Phys. Rev. A 56, 5004 (1997)]. The main result of this paper is that an unusual semiconfining regime of motion was found, when atoms are confined from one side of an axis, but are not confined from another side. The author of the Comment [V. E. Shapiro, Phys. Rev. A 60, 719 (1999)] expressed doubts on the validity of this result, advancing several concrete questions. In the present reply I answer all of these questions and show that they do not invalidate the possibility of realizing the semiconfining regime of motion.

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Abstract The results of calculations using the molecular dynamics method of low-frequency ion oscillations in ultracold plasma, previously observed in the experiment, are presented. Oscillations of the radial velocity of ions and changes in the direction of their flows during the expansion of ultracold plasma in a quadrupole magnetic field are detected. This is due to the influence of the magnetic field on the charge imbalance, which leads to the simultaneous existence of potential wells for both electrons and ions. Ion temperature oscillations with a frequency close to the ion plasma frequency are also detected. Satisfactory agreement with the experiment is obtained.

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Shan Wu, Shi-Sen Ruan, Ze Cheng

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Physical Review Letters•May 29, 2014•1 citation
In this Reply, we respond to the Comment by Schlitters et al. on our recent work [Phys. Rev. E 108, 045209 (2023)10.1103/PhysRevE.108.045209], where we present simulation results of ultracold Sr plasma expansion in a quadrupole magnetic field using a molecular-dynamics method. In the Comment, Schlitters et al. present their experimental results, some of which, from their point of view, contradict our simulation results and others that confirm the experiments of Gorman et al. [Phys. Rev. Lett. 126, 085002 (2021)10.1103/PhysRevLett.126.085002] and our results. In addition, Schlitters et al. also provide results that were not described in our work. Here we show that there is not a contradiction but a misunderstanding of our results. This is due to the fact that simulations allow the use of processing methods that are difficult to obtain in experiment. We also present different simulation results related to expansion velocity variations that reflect the experimental results of Schlitters et al. and provide an explanation for the origin of these variations.
We present simulation results of ultracold Sr plasma expansion in a quadrupole magnetic field by means of molecular dynamics. An analysis of plasma evolution influenced by a magnetic field is given. Plasma confinement time behavior under variation of magnetic field strength is estimated. Similarity of the time dependence of the concentration and distribution of ion velocities against the parameters of the plasma and magnetic field is established. Simulation results are in agreement with the experimental ones.
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).
Nonadiabatic dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, has been considered in my earlier paper [V. I. Yukalov, Phys. Rev. A 56, 5004 (1997)]. The main result of this paper is that an unusual semiconfining regime of motion was found, when atoms are confined from one side of an axis, but are not confined from another side. The author of the Comment [V. E. Shapiro, Phys. Rev. A 60, 719 (1999)] expressed doubts on the validity of this result, advancing several concrete questions. In the present reply I answer all of these questions and show that they do not invalidate the possibility of realizing the semiconfining regime of motion.
Abstract The results of calculations using the molecular dynamics method of low-frequency ion oscillations in ultracold plasma, previously observed in the experiment, are presented. Oscillations of the radial velocity of ions and changes in the direction of their flows during the expansion of ultracold plasma in a quadrupole magnetic field are detected. This is due to the influence of the magnetic field on the charge imbalance, which leads to the simultaneous existence of potential wells for both electrons and ions. Ion temperature oscillations with a frequency close to the ion plasma frequency are also detected. Satisfactory agreement with the experiment is obtained.