skip to main content


This content will become publicly available on April 1, 2025

Title: Simulations of radiatively cooled magnetic reconnection driven by pulsed power

Magnetic reconnection is an important process in astrophysical environments, as it reconfigures magnetic field topology and converts magnetic energy into thermal and kinetic energy. In extreme astrophysical systems, such as black hole coronae and pulsar magnetospheres, radiative cooling modifies the energy partition by radiating away internal energy, which can lead to the radiative collapse of the reconnection layer. In this paper, we perform two- and three-dimensional simulations to model the MARZ (Magnetic Reconnection on Z) experiments, which are designed to access cooling rates in the laboratory necessary to investigate reconnection in a previously unexplored radiatively cooled regime. These simulations are performed in GORGON, an Eulerian two-temperature resistive magnetohydrodynamic code, which models the experimental geometry comprising two exploding wire arrays driven by 20 MA of current on the Z machine (Sandia National Laboratories). Radiative losses are implemented using non-local thermodynamic equilibrium tables computed using the atomic code Spk, and we probe the effects of radiation transport by implementing both a local radiation loss model and$P_{1/3}$multi-group radiation transport. The load produces highly collisional, super-Alfvénic (Alfvén Mach number$M_A \approx 1.5$), supersonic (Sonic Mach number$M_S \approx 4-5$) strongly driven plasma flows which generate an elongated reconnection layer (Aspect Ratio$L/\delta \approx 100$, Lundquist number$S_L \approx 400$). The reconnection layer undergoes radiative collapse when the radiative losses exceed the rates of ohmic and compressional heating (cooling rate/hydrodynamic transit rate =$\tau _{\text {cool}}^{-1}/\tau _{H}^{-1}\approx 100$); this generates a cold strongly compressed current sheet, leading to an accelerated reconnection rate, consistent with theoretical predictions. Finally, the current sheet is also unstable to the plasmoid instability, but the magnetic islands are extinguished by strong radiative cooling before ejection from the layer.

 
more » « less
Award ID(s):
2213898
NSF-PAR ID:
10501826
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ; ; ; ; ;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
Journal of Plasma Physics
Volume:
90
Issue:
2
ISSN:
0022-3778
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Large-eddy simulation was used to model turbulent atmospheric surface layer (ASL) flow over canopies composed of streamwise-aligned rows of synthetic trees of height,$h$, and systematically arranged to quantify the response to variable streamwise spacing,$\delta _1$, and spanwise spacing,$\delta _2$, between adjacent trees. The response to spanwise and streamwise heterogeneity has, indeed, been the topic of a sustained research effort: the former resulting in formation of Reynolds-averaged counter-rotating secondary cells, the latter associated with the$k$- and$d$-type response. No study has addressed the confluence of both, and results herein show secondary flow polarity reversal across ‘critical’ values of$\delta _1$and$\delta _2$. For$\delta _2/\delta \lesssim 1$and$\gtrsim 2$, where$\delta$is the flow depth, the counter-rotating secondary cells are aligned such that upwelling and downwelling, respectively, occurs above the elements. The streamwise spacing$\delta _1$regulates this transition, with secondary cell reversal occurring first for the largest$k$-type cases, as elevated turbulence production within the canopy necessitates entrainment of fluid from aloft. The results are interpreted through the lens of a benchmark prognostic closure for effective aerodynamic roughness,$z_{0,{Eff.}} = \alpha \sigma _h$, where$\alpha$is a proportionality constant and$\sigma _h$is height root mean square. We report$\alpha \approx 10^{-1}$, the value reported over many decades for a broad range of rough surfaces, for$k$-type cases at small$\delta _2$, whereas the transition to$d$-type arrangements necessitates larger$\delta _2$. Though preliminary, results highlight the non-trivial response to variation of streamwise and spanwise spacing.

     
    more » « less
  2. Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius$R$and axial length$10{\rm \pi} R$at friction Reynolds numbers up to$Re_\tau =5200$using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor$\lambda$overshoots by$2\,\%$and undershoots by$0.6\,\%$the Prandtl friction law at low and high$Re$ranges, respectively. In addition,$\lambda$in our results is slightly higher than in Pirozzoliet al.(J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichiet al.(Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to$y^+=250$, has not yet developed a plateau farther away from the wall in the pipes even for the$Re_\tau =5200$cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with$Re_\tau$– are lower in the pipe than in the channel, but the difference decreases with increasing$Re_\tau$. While the wall value is slightly lower in the channel than in the pipe at the same$Re_\tau$, the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a$k^{-1}$dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.

     
    more » « less
  3. We extend the Matsuno–Gill model, originally developed on the equatorial$\beta$-plane, to the surface of the sphere. While on the$\beta$-plane the non-dimensional model contains a single parameter, the damping rate$\gamma$, on a sphere the model contains a second parameter, the rotation rate$\epsilon ^{1/2}$(Lamb number). By considering the different combinations of damping and rotation, we are able to characterize the solutions over the$(\gamma, \epsilon ^{1/2})$plane. We find that the$\beta$-plane approximation is accurate only for fast rotation rates, where gravity waves traverse a fraction of the sphere's diameter in one rotation period. The particular solutions studied by Matsuno and Gill are accurate only for fast rotation and moderate damping rates, where the relaxation time is comparable to the time on which gravity waves traverse the sphere's diameter. Other regions of the parameter space can be described by different approximations, including radiative relaxation, geostrophic, weak temperature gradient and non-rotating approximations. The effect of the additional parameter introduced by the sphere is to alter the eigenmodes of the free system. Thus, unlike the solutions obtained by Matsuno and Gill, where the long-term response to a symmetric forcing consists solely of Kelvin and Rossby waves, the response on the sphere includes other waves as well, depending on the combination of$\gamma$and$\epsilon ^{1/2}$. The particular solutions studied by Matsuno and Gill apply to Earth's oceans, while the more general$\beta$-plane solutions are only somewhat relevant to Earth's troposphere. In Earth's stratosphere, Venus and Titan, only the spherical solutions apply.

     
    more » « less
  4. Two common definitions of the spatially local rate of kinetic energy cascade at some scale$\ell$in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’$R>0$,$Q>0$quadrant, where$R$and$Q$are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when$R$is large.

     
    more » « less
  5. This paper considers the initial stage of radiatively driven convection, when the perturbations from a quiescent but time-dependent background state are small. Radiation intensity is assumed to decay exponentially away from the surface, and we consider parameter regimes in which the depth of the water is greater than the decay scale of$e$of the radiation intensity. Both time-independent and time-periodic radiation are considered. In both cases, the background temperature profile of the water column is time-dependent. A linear analysis of the system is performed based on these time-dependent profiles. We find that the perturbations grow in time according to$\exp [(\sigma (t) t)]$, where$\sigma (t)$is a time-dependent growth rate. An appropriately defined Reynolds number is the primary dimensionless number characterising the system, determining the wavelength, vertical structure and growth rate of the perturbations. Simulations using a Boussinesq model (the Stratified Ocean Model with Adaptive Refinement) confirm the linear analysis.

     
    more » « less