Ultrafast optical field-ionized gases: A laboratory platform to study kinetic plasma instabilities

Kinetic instabilities commonly arise from anisotropic (different properties in different directions) electron velocity distributions within ionospheric, cosmic and terrestrial plasmas. But only a handful of experiments have validated that theory so far. Ultrafast laser pulses can be used during optical field ionization of atoms to generate plasmas with known anisotropic electron velocity distributions to understand the phenomenon in practice. In a recent study, Chaojie Zhang and an interdisciplinary research team in the departments of Electrical and Computer Engineering, and Physics and Astronomy in the U.S., showed that plasma underwent two-stream filamentation following ionization—but prior to collision-based thermalization of the constituent electrons.

They observed Weibel instabilities (present in homogenous or nearly homogeneous plasma) that isotropized (similar properties in all directions) the electron distributions. The researchers measured the polarization-dependent frequency and growth rates of these kinetic instabilities using Thomson scattering (TS) of a probe laser, which agreed well with the kinetic theory and simulations. The research team demonstrated an easily deployable laboratory platform to study kinetic instabilities within plasma; the results are now published in Science Advances.

Plasmas are susceptible to kinetic instabilities when the velocity distribution of its constituent plasma electrons, ions or both becomes nonthermal. Physicists can experimentally validate the theory of these instabilities if they have direct knowledge of the initial velocity distribution functions of such plasma species. With the advent of intense ultrashort-pulse, near-infrared lasers, researchers have ionized atoms and/molecules of a gas in a few laser cycles to generate anisotropic or nonthermal electron velocity distribution (EVD) functions. The process is known as optical field-induced or tunnel ionization (OFI). The ability to initiate velocity distribution functions will allow researchers to quantitatively test the kinetic theory of plasmas on ultrafast time scales, prior to electron-electron (e-e) collisions and ion thermalization. However, the mechanisms and time-scale in which plasma electrons evolved from an anisotropic state to a thermal state remains an unsolved experimental problem in basic science.

As a result of the extremely broad range of situations that gives rise to kinetic instabilities including gamma ray flashes, electron positron plasmas, magnetic fields, proton synchrotrons, solar corona and interplanetary media. A voluminous body of theoretical work exists on the kinetic theory of plasmas. In this work, the research team first briefly described three of the most frequently studied kinetic instabilities enabled by OFI plasma for quantitative study in the lab. For example, when plasma electrons are composed of two or more co- or counter-propagating streams (beams) they can become unstable. While a great deal of theoretical work exists on kinetic instabilities in plasmas, they remain to be further verified in the lab. Research teams had previously studied these instabilities by passing relativistic electron beams through plasmas or by creating two interpenetrating plasmas.

In this work, Zhang et al. showed that an ultrafast OFI (optical field induced ionization) helium plasma with a known polarization-dependent anisotropic electron velocity distribution (EVD) was susceptible to kinetic streaming, filamentation and Weibel-like filamentation instabilities. They measured the growth rates and frequencies of these instabilities using time-resolved Thomson scattering. They compared the measurements against self-consistent (exact) particle-in-cell (PIC) computer simulations and with theory thereafter, and observed good agreement.

In the experiments and simulations, the team initialized anisotropic EVD (electron velocity distribution) functions by ionizing the first and the second helium (He) electron either using circularly polarized (CP) or linearly polarized (LP) Ti-Sapphire laser pulses. They monitored the ionization potential of the electron as the laser intensity required to ionize more than 90 percent of the He atoms via a tunneling mechanism developed elsewhere. During the experiments, the EVD function of the second He electron was 'hotter' than the first He electron. Zhang et al. obtained the results after the passage of linear pulses from a 3-D particle-in-cell (PIC) simulation, which they built using the OSIRIS code. The electron momentum distribution resembled a "double donut" shape for circularly polarized (CP) lasers and a two-temperature distribution in the direction of linearly polarized (LP) lasers. They confirmed the plasmas produced in this way to have EVD functions. The values measured by the research team agreed excellently with the values expected from the PIC simulation.

The research team then used 2-D simulations of optical field ionization (OFI)-triggered kinetic streaming and filamentation instabilities in a He plasma. Accordingly, both streaming and filamentation instability began to grow immediately after the creation of plasma. They observed the streaming instability to eventually saturate and dampen very quickly and Zhang et al. therefore similarly expected the filamentation instability to have comparable temporal behavior. At later stages, Weibel-like filamentation instability driven by a reduced but finite temperature anisotropy of the electrons began to dominate in the plasma.

To obtain further information on kinetic instability, Zhang et al. probed a wave vector. For this, they used either a 400 nm laser or an 800 nm laser with a 5nm bandwidth and 100 femtosecond (fs) pulse width and probed electrostatic components of plasma instabilities. They measured the spectra and observed two notable features. At first, the electron feature grew and saturated to dampen within a time frame much shorter than the time for electron-electron collision. Next, the spectral shift of the electron feature showed anomalous behavior from the usual Langmuir wave (electrostatic plasma oscillations). The peak frequency of the electron feature and existence of the zero-frequency feature were essential evidence for Zhang et al. to corroborate streaming and filamentous instabilities in the setup. The research team investigated further streaming, filamentation and Weibel instabilities induced by circular polarization lasers extensively within the experimental system.

The scientists also tracked the evolution of electron velocity distributions and temperature anisotropy of optical field ionization in a 2-D simulation. They consistently modeled ionization and evolution of the plasma in the simulation while excluding Coulomb collisions to isolate the effect of instabilities on temperature anisotropy. They observed kinetic instabilities in the experiments, owing to which the anisotropy of the plasma rapidly dropped.

As the Weibel instability saturated in the simulation, the magnetic fields self-organized to a quasi-helical structure as predicted elsewhere. Using further simulations, Zhang et al. confirmed that electron collisions did not play a significant role during the first 10 picoseconds after plasma formation. During this time, kinetic instabilities dominated isotropization of the plasma, however, eventually the collisions will thermalize the plasma.

The research team also investigated the kinetic instabilities induced by linear polarization lasers, which showed contrasting results to the circularly polarized lasers. In this instance, the instability was driven by reflected electrons, which propagated through slower moving electrons. The frequency spectrum of the mode was narrower than with CP lasers. The experimental process also took longer for the streaming instability to grow and saturate. Zhang et al. observed a remarkable agreement between the measurements and simulation.

In this way, Chaojie Zhang and colleagues showed the possibility of generating "designer" EVDs using a combination of conditions including different polarizations, wavelengths, intensity profiles and ionizing media. The team controlled the drift velocity and transverse temperatures of the streams by changing the polarization ellipticity to suppress streaming or filamentation instabilities. The researchers showed that ultrafast OFI plasmas were nonthermal with a large velocity anisotropy. The plasmas underwent streaming and filamentous instabilities, followed by Weibel-like filamentation instability to isotropize the plasma. When they measured the polarization-dependent frequency and growth rate of these kinetic instabilities, the results agreed well with the kinetic theory and simulations. The research team thus developed and demonstrated an easily deployable platform to study plasma kinetic instabilities in the lab.

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