X-ray1,2,3 and radio4,5,6 observations of the supernova remnant Cassiopeia A reveal the presence of magnetic fields about 100 times stronger than those in the surrounding interstellar medium. Field coincident with the outer shock probably arises through a nonlinear feedback process involving cosmic rays2,7,8. The origin of the large magnetic field in the interior of the remnant is less clear but it is presumably stretched and amplified by turbulent motions. Turbulence may be generated by hydrodynamic instability at the contact discontinuity between the supernova ejecta and the circumstellar gas9. However, optical observations of Cassiopeia A indicate that the ejecta are interacting with a highly inhomogeneous, dense circumstellar cloud bank formed before the supernova explosion10,11,12. Here we investigate the possibility that turbulent amplification is induced when the outer shock overtakes dense clumps in the ambient medium13,14,15. We report laboratory experiments that indicate the magnetic field is amplified when the shock interacts with a plastic grid. We show that our experimental results can explain the observed synchrotron emission in the interior of the remnant. The experiment also provides a laboratory example of magnetic field amplification by turbulence in plasmas, a physical process thought to occur in many astrophysical phenomena.
High-resolution X-ray images and radio polarization maps of Cassiopeia A show two distinct strong magnetic field regions3,4,5,6,12. Narrow X-ray filaments, a fraction of a parsec in width, are observed at the outer shock rim at a radius of about 2.5 pc. These structures are produced by synchrotron radiation from ultrarelativistic electrons (with teraelectronvolt energy) and can be explained by magnetic fields of the order of 100 μG or more2,3. The interior of the remnant contains a disordered shell (about 0.5 pc in width at a radius of 1.7 pc) of radio synchrotron emission by gigaelectronvolt electrons4. The inferred magnetic field in these radio knots is a few milligauss, about 100 times higher than expected from the standard shock compression of the interstellar medium15. Optical observations of Cassiopeia A show the presence of both rapidly moving (5,000–9,000 km s−1) and essentially stationary dense knots. Although the moving knots themselves have a high velocity, their overall pattern is nearly stationary10. This led to the suggestion10 that a dense pre-existing inhomogeneous stationary cloud bank could be present. New rapidly moving knots predominantly appear at a position broadly coincident with the shell of bright radio emission6. Sizes of the observed small-scale features within the shell range from 0.01 to 0.1 pc arranged in larger patterns extending to 0.5–2 pc (ref. 16). Interaction between the ejecta and the cloud bank may excite the turbulence that amplifies the magnetic field and makes Cassiopeia A an exceptionally bright radio source4. The interaction is akin to the Rayleigh–Taylor instability otherwise proposed as a source of turbulence and magnetic field at the contact discontinuity between the ejecta and the swept-up ambient medium9 except that the interaction begins with an already disturbed density configuration.
Our experiments focus on magnetic field amplification in a clumpy medium by making in situ magnetic field measurements in the turbulent wake of a laser-produced shock in a plasma. The interaction of a shock with large density perturbations is reproduced in the laboratory by passing a laser-produced shock in a plasma through a plastic mesh with ℓ = 1.1 mm grid cell size, and 0.4-mm-thick wires (see Fig. 1 for details of the experiment). In situ magnetic field measurements are made in the turbulent wake of the shock. Using hydrodynamic scaling relations17,18, our experimental conditions at 0.3 μs after the laser illumination can be scaled to Cassiopeia A signal to noise (SNR) with a probable age tSNR of approximately 310 years, an expansion velocity vSNR of about 4,700 km s−1 and a deceleration parameter vSNRtSNR/RSNR, where RSNR is the shock radius, of about 0.6 (ref. 2; see Supplementary Information for the description of the scaling relations, and Supplementary Table 1). The same scaling relations imply the wire thickness in the mesh corresponds to ∼0.1 pc in the SNR.
Wind tunnel experiments19 with a steady flow have shown that homogeneous turbulence is already well developed at distances d ∼ 20ℓ, motivating us to take our field measurements predominantly at a distance of 2 cm downstream of the grid. Without the presence of the grid, the position (Rs) and properties of the shock wave have been monitored at various times using Schlieren, interferometry and spectroscopy diagnostics (Fig. 2). The shock closely follows a Sedov–Taylor solution20 with . Numerical simulations performed in one-dimensional (1D) spherical geometry with the collisional-radiative hydrodynamic code HELIOS, and in 2D-cylindrical geometry with the magnetohydrodynamic code FLASH (see Supplementary Information for details on the simulations) reproduce well the shock position, peak electron density and temperature values.
At the position of the grid (Rs0 = 1 cm), the flow velocity of the shock is measured to be v0 ∼ 2 × 106 cm s−1 (Mach number ∼9), although this increases on interaction with the grid. The Reynolds number corresponding to this shock radius is Re = v0Rs0/ν ∼ 5 × 104 (ν ≍ 40 cm2s−1 is the plasma viscosity), and the magnetic Reynolds number is Rm = v0Rs0/η ∼ 3−6, with magnetic diffusivity η ≍ 4 × 105 cm2 s−1 (more details are given in the Supplementary Information). As shown in earlier hydrodynamic simulations21 and in FLASH magnetohydrodynamic simulations of the experiment, for large Re, the grid acts as a channel, which accelerates the flow as it passes through the pores, after which the flow velocity decreases. This can be seen in Fig. 1, where, with the grid, the turbulent flow seems to advance more rapidly towards the position of the magnetic field diagnostics. From Schlieren imaging, for all experiments with the grid, the shock is observed to arrive at the position of the probe at .
Figure 3 shows that in the case of a grid, the perpendicular component of the magnetic field is 2–3 times larger than without it. Previous results22 have indicated that perpendicular magnetic fields are produced at the shock front through the Biermann battery mechanism23 owing to misaligned pressure and density gradients. We find that for shocks passing through a grid, magnetic field amplification continues to occur long after the shock has passed, suggesting that an alternative mechanism is at play. This is attributed to the fact that the downstream flow is highly turbulent as a result of the shock–grid interaction. To confirm that the observed field amplification does not depend on the Biermann battery generation at the laser spot, we have run FLASH simulations with the latter process turned on only during the first 30 ns and switched off afterwards (Supplementary Fig. 1). This shows that the measured magnetic field is indeed enhanced as the shock passes through the grid owing, mainly, to the induced turbulence. Assuming a downstream flow velocity of the order 105–106 cm s−1, the field is gradually amplified over a distance of from the grid, before arriving at the probe, further supporting the mechanism of turbulent field amplification occurring by differential rotation induced by the mesh (Supplementary Movies 1 and 2).
The vorticity induced as the shock overtakes the grid acts as a seed for turbulent generation of magnetic field on a smaller scale. Beyond the grid, the vorticity is stretched in the direction of the flow, so that the spatial scale of the largest eddies is Le ∼ 7 mm by the time the shock reaches the induction probe (Fig. 3). As the magnetic Prandtl number is Pm = Rm/Re = ν/η ≍ 10−4, substantially lower than in the SNR case, the resistive scale lies well above the viscous scale and in fact above the energy-containing scale at which the inertial range starts (see below). Resistive diffusion of the magnetic field is increasingly important on smaller scales, although our measured increase in the magnetic field shows that it is not dominant at the scales of interest. Indeed, the measured k-spectrum of the magnetic field is consistent with the Golitsyn (k−11/3) power-law dependence24,25, characteristic of magnetic fluctuations at low Pm (refs 25, 26, 27; Fig. 4). This suggests that turbulent motions are present and amplifying the field at subresistive scales. With a small magnetic Reynolds number, the amplification is due to the stochastic tangling of an imposed field, B0, by turbulent motions, and the saturated level is set by balancing this effect with Ohmic diffusion25,26,27. In our experiment, B0 is the Biermann-battery-generated baroclinic magnetic field in the homogeneous flow. The amplified field scales as |δB| ∼ Rm |B0|, and it remains dynamically unimportant because the Alfvén speed is smaller than the flow velocity (vA ∼ 400–1,400 cm s−1).
FLASH simulations without a grid show that the shock becomes unstable when it is overtaken by the compositional discontinuity between the vaporized carbon target material and the gas, generating vorticity, and therefore magnetic fields, at spatial scales ≲3 mm (Fig. 3). This is the origin of the k-spectrum of the magnetic field without a grid. Simulations with a grid present show that the size of the largest eddies is ∼2 times larger, the flow velocity is ∼50% larger, and thus the magnetic Reynolds number is ∼3 times larger. This is consistent with the higher magnetic field seen in the experimental data.
Figure 3 shows that amplification occurs over distances much larger than the aperture of the grid. The slope of the normalized two-point cross-correlation function of the measured magnetic field at d = 2 cm and d = 3 cm from the grid position (see Supplementary Information for the mathematical definition and Supplementary Fig. 2) shows an amplification rate γ = 4 × 105 s−1. This rate at the outer scale must be comparable to the Ohmic dissipation rate. Estimating this scale to be ∼Le = 7 mm (Fig. 3), we measure . This timescale gives a good order-of-magnitude estimate of the effective stretching rate of the chaotic flow behind the grid and therefore of the typical minimal rate of magnetic field amplification one should expect in an astrophysical plasma, where resistivity is low and Rm is large. From our scaling relations, this laboratory stretching rate corresponds to a growth rate γSNR ∼ 0.4 × 10−3 yr−1 on spatial scales ∼1 pc in the SNR. At smaller scales in our experiment, where resistivity dominates, there are still sustained magnetic fluctuations (Fig. 4). The timescale for the resistivity–chaotic–tangling balance to be established at those scales is η/ℓe2, where ℓe is of order 1 mm (which is the induction coil size, and therefore the measurement resolution limit). The fact that the Golitsyn spectrum extends at least to these scales is an indirect confirmation that turbulence is established25, with inertial-range motions tangling the magnetic field much faster than the motions at the energy-conserving scale (Le). At scales of order ℓe, the corresponding timescale is ns in the laboratory, translating to yr in the SNR over distances ∼0.25 pc.
The observed variability of visible moving knots in the inner regions of the remnant is of the order of 10 yr (ref. 10). The radio emission from Cassiopeia A can be characterized as a bright disordered ring of emission coincident with the cloud bank10 surrounded by a polarized radio plateau of lower brightness with a predominantly radially stretched magnetic field extending to the outer shock seen in X-rays7. X-ray emission similarly consists of an inner ring of non-thermal emission broadly coincident with the cloud shell and an outer rim revealing the position of the outer shock28. The outer X-ray rim is thin because high-energy synchrotron-emitting electrons cool rapidly immediately downstream of the shock. The reverse shock, or shocks, may also accelerate the electrons needed for synchrotron emission at the inner ring.
Magnetic field amplification in Cassiopeia A can be thus understood as being partly due to amplification by cosmic rays at the shock and partly by the interaction, at a smaller radius, between ejecta and a clumpy medium. The latter process can be directly inferred from the experiment and its simulation. Our results are consistent with these observations, namely that a rotational flow, driven by a shock passing through a stationary density perturbation, is necessary to both amplify and sustain strong magnetic fields in an expanding magnetized plasma over distances corresponding to many times the scale of the initial density perturbation. Indeed, Fig. 3 shows a disordered magnetic field, stretched from the grid position to the outer shock, matching the extent of the observed synchrotron emission. On the other hand, as also indicated in Fig. 3, in the absence of such perturbations (that is, without a grid), the magnetic field remains confined only to the outer rim. Our experimental work thus agrees with earlier numerical modelling of shock waves interacting with a clumpy medium13,14,15, and it shows that magnetic fields can, on average, be amplified by the shock-induced rotational flow to values ∼3 higher than expected from the jump conditions alone.
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We thank the Vulcan technical team at the Central Laser Facility of the Rutherford Appleton Laboratory for their support during the experiments; in particular, R. Clarke, M. Notley and R. Heathcote. A.R.B. acknowledges valuable discussions with H. Li (Los Alamos National Laboratory). The research leading to these results has received financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreements no. 256973 and 247039, LASERLAB-EUROPE grant agreement No. 284464, the US Department of Energy under Contract No. B591485 to Lawrence Livermore National Laboratory, and Field Work Proposal No. 57789 to Argonne National Laboratory. Partial support from the Science and Technology Facilities Council and the Engineering and Physical Sciences Research Council of the United Kingdom (Grant No. EP/G007187/1) is also acknowledged. The work of R.P.D., C.C.K., M.J.M. and W.C.W. was supported by the USDOE under grant DE-NA0001840.
The authors declare no competing financial interests.
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Meinecke, J., Doyle, H., Miniati, F. et al. Turbulent amplification of magnetic fields in laboratory laser-produced shock waves. Nature Phys 10, 520–524 (2014). https://doi.org/10.1038/nphys2978
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