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. 2015 Jul 7;112(27):8211-5.
doi: 10.1073/pnas.1502079112. Epub 2015 Jun 22.

Developed Turbulence and Nonlinear Amplification of Magnetic Fields in Laboratory and Astrophysical Plasmas

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Free PMC article

Developed Turbulence and Nonlinear Amplification of Magnetic Fields in Laboratory and Astrophysical Plasmas

Jena Meinecke et al. Proc Natl Acad Sci U S A. .
Free PMC article

Abstract

The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe.

Keywords: galaxy clusters; laboratory analogues; lasers; magnetic fields; turbulence.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Colliding jet configuration for the generation of turbulence. Two carbon foils (100 μm thick, with density 1.13 g/cm3) are separated by 60 mm in a 1±0.2 mbar argon gas-filled chamber. Each target is ablated by three frequency-doubled (527-nm-wavelength) laser beams with a laser spot diameter of 300 μm. The total laser illumination onto each foil is 240±30 J in a 1-ns pulse length. An induction coil ( 200-MHz bandwidth, with four twisted pair coils wound around the axis of a 1×1 mm2 plastic core) is placed at equal distance between the foil targets. Additional details are given in ref. . (A) Schlieren image (using a 532-nm-wavelength probe and 5-ns CCD gate width) of the jet formations at t=500 ns after the laser shot. (B) The jets collide at t=800 ns, and (C) turbulence develops by t=1,500 ns. (D) Magnetic field (Top) and mass density (Bottom) from a FLASH simulation of the two jets at t=500 ns. (E) Same as D but at t=800 ns. (F) same as D but at t=1,500 ns. (g) Schlieren synthetic image obtained by postprocessing the FLASH results at t=500 ns using Spect3D (34). (H) Same as G but at t=800 ns. (I) same as G but at t=1,500 ns. The measured and simulated Schlieren images are similar at t=500 ns and 800 ns, but differ at t=1,500 ns. The difference is likely due to a slight angle between the directions the two jets are moving, which allows part of the jets to continue beyond the initial interaction region. This produces a much larger turbulent region in the experiment than in the simulation, where the 2D cylindrical geometry prevents us from accommodating this situation. Since the FLASH simulations are 2D cylindrical, the plane that most closely corresponds to the experimental data is the one that is perpendicular to the page and connects the two target foils. This plane does not contain the induction coil probe.
Fig. 2.
Fig. 2.
Characterization of jet propagation and collision. (A) Measurement of the jet leading edge vs. time from Schlieren data (blue symbols) and FLASH simulations (dashed green line). The FLASH simulation was calibrated to match the position of the leading edge of the jet at 800 ns for the measured value of the total laser energy for that data point. (Inset) The electron density profile obtained by interferometry at t=800 ns compared with FLASH predictions. The density has been averaged over a volume of 5 mm radius from the axis connecting the two target foils. (B) Spatially resolved electron temperature profile of a single jet (blue symbols) and colliding jets (red symbols) at t=800 ns obtained from the measured argon spectral lines (see Supporting Information for details). Solid lines (blue, single jet; red, colliding jets) correspond to the predicted temperature values from FLASH simulations at t=800 ns, averaged over the same volume as the electron density. Dashed lines are the results from the same FLASH simulations at t=1,500 ns. (Inset) An example of the argon spectral line at t=800 ns and 3 cm from the carbon foil target (averaged over 0.1 cm).
Fig. S1.
Fig. S1.
Effect of the Biermann battery mechanism on the magnetic field in the interaction region of the colliding jets experiment. The top half of the image shows the magnetic field strength at t = 1 µs in a FLASH simulation of the colliding jets experiment in which the Biermann effect was turned off at t = 716 ns (i.e., just before the two jets collide). The bottom half of the image shows the same, except the Biermann effect was on throughout the simulation. Comparison of the two images shows that the morphology and the overall value of the magnetic field are similar in both cases, demonstrating that the Biermann battery mechanism has only a small effect on the magnetic field in the interaction region.
Fig. S2.
Fig. S2.
Pinching of the jets by the wrap-around shock in the argon gas. The six panels show close-up images of the shock produced by the carbon ablated by the laser, and the carbon jet at (left to right, top to bottom) 20 ns, 40 ns, 60 ns, 80 ns, 120 ns, and 160 ns showing the logarithm of the density (dens, top) and the target (targ) material fraction (bottom). The images show that the carbon plasma produced by ablation of the target by the laser has just enough time to engulf the carbon foil target, wrap around it, and launch a shock in the argon gas before the jets are able to get ahead of it. As a result, the shock pinches the carbon jets. This pinching effect produces ripples in the faces of both jets that cause the fronts to become unstable.
Fig. S3.
Fig. S3.
Trapping and violent turbulent mixing of the argon gas and the carbon in the jets when the two jets collide. (Upper) Close-up images of the interaction region at 600, 800, and 1,500 ns, showing the logarithm of the density (top) and the target material fraction (bottom). (Lower) Close-up images of the interaction region at the same three times, showing the radial velocity vr perpendicular to the axes of the jets (top) and the velocity vz parallel to the axes of the jets (bottom). The images show that the mixing between the argon gas and the jets is thorough and persists for 0.5 µs.
Fig. S4.
Fig. S4.
Radiative cooling of the plasma. (A) Calculation of the Planck mean emission opacity (κP) for argon as a function of typical values of density and temperature expected in the experiment. (B) 1D radiation hydrodynamic simulation with the code HELIOS showing the rapid cooling of an argon plasma sphere initialized with radius of 0.5 cm, Te=3 eV, mass density of 9×106 g/cm3, and outward radial velocity of 14 km/s. Results from a calculation performed with multigroup radiation diffusion turned on are shown with solid lines. Results from a similar calculation but without radiation diffusion are shown with dashed lines.
Fig. S5.
Fig. S5.
Effect of radiative cooling in the interaction region of the colliding jets experiment. The top half of the image shows Te in the interaction region at t = 1 µs in a FLASH simulation of the colliding jets experiment in which multigroup radiation diffusion (and therefore radiative cooling) was turned off at t=716 ns (i.e., just before the two jets collide). The bottom half of the image shows the same, except multigroup radiation diffusion was on throughout. Comparison of the two images shows Te is a factor of 3 larger in the first case, demonstrating that radiative cooling is very important in the interaction region.
Fig. S6.
Fig. S6.
Measurement of spectral lines. Argon spectral lines at t=800 ns and 2 cm from the carbon foil target (averaged over 0.1 cm) for a single-jet experiment. Spectral fit performed with the code PrismSPECT is also shown.
Fig. S7.
Fig. S7.
Turbulent line broadening. The measured argon spectral line at 461 nm at 3 cm from the carbon foil target for colliding jets (solid red line) and a single jet (solid blue line). A PrismSPECT calculation for an ion density of 1.6×1017 cm−3 and an electron temperature of 3.5 eV is also shown (dashed black line).
Fig. S8.
Fig. S8.
Time evolution of spectral line widths. The measured argon spectral line at 440 nm (Left) and 461 nm (Right) at 3 cm from the carbon foil target for a single jet (Upper) and colliding jets at various times after the interaction (Lower).
Fig. 3.
Fig. 3.
Power spectra of turbulence. (A) Plot of the density fluctuation power spectrum P(k)=|nk/n0|2, where nk is the discrete Fourier transform of the space-dependent electron density and n0 is its average value. In Schlieren imaging, the measured signal intensity is proportional to (n/y+n/z)dx, where n is the electron density, x,y are the image plane spatial coordinates, and z is the depth (35). Therefore, under the assumption that turbulence is statistically homogeneous across the jet interaction region, the discrete Fourier transform of the central region of the jet collision in Fig. 1C directly gives nk. The power spectrum is arbitrarily normalized so that P(k)1 at the largest scale. The solid red curve corresponds to the experimental data, while the black and green symbols correspond to the inferred density spectrum in the Coma cluster obtained from CHANDRA and XMM satellite observations, respectively (25). (B) Plot of the magnetic energy spectrum M(ω)=|B(ω)|2, where B(ω) is the discrete Fourier transform of the total magnetic field for the cases both with a single jet (blue solid line) and with colliding jets (red solid line). The slope of the spectrum in the case of colliding jets is shallower than in the case of a single jet (where it is consistent with the k11/3 Golitsyn spectrum, assuming conversion from frequencies to wavenumbers according to Taylor hypothesis, ωv0k). This gradual shallowing of the spectrum with increasing Rm is a signature of the dynamo precursor regime (31). The measured frequency spectrum, ω7/3, can be argued to correspond to wavenumber spectrum, k1.9, in the case of colliding jets, where Taylor's hypothesis is inapplicable (see Supporting Information).
Fig. 4.
Fig. 4.
Time evolution of the magnetic field. (A) The magnetic field components measured at 3 cm from the carbon foil in the case of a single jet (see Fig. 1 for the axis coordinates). (B) Magnetic field components measured in the case of jet collision. The time resolution of the magnetic field traces is 10 ns. These have been extracted from the recorded induction coil voltages. Details are given in ref. . The initial (t<100 ns) high-frequency noise due to the laser–plasma interaction with the target has been filtered. The dashed lines in both panels correspond to the average azimuthal magnetic field obtained from the FLASH simulations in a volume of radius 1 mm and length 3 mm centered at the midpoint between the two target foils. Due to cylindrical symmetry of the simulation domain, the measured component that is closest to the calculated one is Bz.

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