A series of Omega experiments have produced and characterized high velocity counter-streaming plasma flows relevant for the creation of collisionless shocks. Single and double CH2 foils have been irradiated with a laser intensity of ∼10 16 W/cm 2 . The laser ablated plasma was characterized 4 mm from the foil surface using Thomson scattering. A peak plasma flow velocity of 2,000 km/s, an electron temperature of ∼110 eV, an ion temperature of ∼30 eV, and a density of ∼10 18 cm −3 were measured in the single foil configuration. Significant increases in electron and ion temperatures were seen in the double foil geometry. The measured single foil plasma conditions were used to calculate the ion skin depth, c/ωpi ∼0.16 mm, the interaction length, int, of ∼8 mm, and the Coulomb mean free path, λ mf p ∼27 mm. With c/ωpi int < λ mf p we are in a regime where collisionless shock formation is possible.
Self-organization 1,2 occurs in plasmas when energy progressively transfers from smaller to larger scales in an inverse cascade 3 . Global structures that emerge from turbulent plasmas can be found in the laboratory 4 and in astrophysical settings; for example, the cosmic magnetic field 5,6 , collisionless shocks in supernova remnants 7 and the internal structures of newly formed stars known as Herbig-Haro objects 8 . Here we show that large, stable electromagnetic field structures can also arise within counter-streaming supersonic plasmas in the laboratory. These surprising structures, formed by a yet unexplained mechanism, are predominantly oriented transverse to the primary flow direction, extend for much larger distances than the intrinsic plasma spatial scales and persist for much longer than the plasma kinetic timescales. Our results challenge existing models of counter-streaming plasmas and can be used to better understand large-scale and long-time plasma self-organization.Our experiments were performed at the OMEGA EP laser facility, where two kilojoule-class lasers irradiated two polyethylene (CH 2 ) plastic discs that faced each other at a distance of 8 mm, creating a system of high-velocity laser-ablated counter-streaming plasma flows. The experimental details are described in Fig. 1 and in the Methods. At early times, up to at least 8 ns, intra-jet ion collisions are known to be strong (owing to relatively low-particle thermal velocities) but inter-jet ion collisions are rare (owing to relatively high flow velocities), permitting the evolution of both hydrodynamic and collisionless plasma instabilities 9,10 (Table 1). We visualized the electric and magnetic field structures in the counter-streaming plasmas with short-pulse laser-generated proton beam imaging 11,12 , taken from two orthogonal views to evaluate the possible azimuthal symmetry of the field structures. After roughly 3 ns, caustics (large-intensity variations 13 ) in the proton images indicate the formation of strong field zones within the plasma, probably due to sharp structures with strong gradients, as reported elsewhere 14 . By 4 ns, the features have changed markedly into two large swaths of straight transverse caustics that extend for up to 5 mm. This extent is large compared with the fundamental scale lengths of the plasma (Table 1) such as the Debye length (50,000 times larger) and the ion inertial length (nearly 100 times larger), indicating a high degree of self-organization. This organization
Computer codes are widely used to describe physical processes in lieu of physical observations. In some cases, more than one computer simulator, each with different degrees of fidelity, can be used to explore the physical system. In this work, we combine field observations and model runs from deterministic multi-fidelity computer simulators to build a predictive model for the real process. The resulting model can be used to perform sensitivity analysis for the system, solve inverse problems and make predictions. Our approach is Bayesian and will be illustrated through a simple example, as well as a real application in predictive science at the Center for Radiative Shock Hydrodynamics at the University of Michigan.KEY WORDS: Computer Experiment; Gaussian process; Markov Chain Monte Carlo. arXiv:1208.2716v1 [stat.AP] 13 Aug 2012 occur, for example, because of the presence of reduced order physics in lower fidelity models, different levels of accuracy specified for numerical solvers or solutions obtained on finer grids. In these cases, a higher fidelity model is thought to better represent the physical process than a lower fidelity model, but also takes more computer time to produce an output than a lower fidelity model. So, combining relatively cheap lower fidelity model runs with more costly high fidelity runs to emulate the high fidelity model has been an significant problem of interest (Kennedy and O'Hagan, 2000;Qian et al., 2006 and.Another important application of computer models is that of calibration (e.g., Kennedy and O'Hagan, 2001;Higdon et al., 2004) where the aim is to combine simulator outputs with physical observations to build a predictive model and also estimate unknown parameters that govern the behaviour of the computer model. The latter endeavour amounts to solving a sort of inverse problem, while the former activity is a type of regression problem.Motivated by applications at the Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan, the aim of this work is to develop new methodology to combine outputs from simulators with different levels of fidelity and field observations to make predictions of the physical system with associated measurements of uncertainty. In the spirit similar to Kennedy and O'Hagan (2000 and2001) and Higdon et al. (2004), we propose a predictive model that incorporates computer model outputs and field data, while attempting to find optimal values for some input parameters (i.e. calibration parameters). Different models are specified for each source of data (Kennedy and O'Hagan, 2000;Qian et al., 2006 and. The approach calibrates each computer model to the next highest level of fidelity model, and the simulator of the highest fidelity is then calibrated to the field measurements. All the response surfaces are Gaussian process (GP) models and the various sources of information that inform predictions of the physical system are combined with a Bayesian hierarchical model. The paper is organized as follows: In section 2, we will introduce the prop...
This article reports the observation of the dense, collapsed layer produced by a radiative shock in a laboratory experiment. The experiment uses laser irradiation to accelerate a thin layer of solid-density material to above 100 km/ s, the first to probe such high velocities in a radiative shock. The layer in turn drives a shock wave through a cylindrical volume of Xe gas ͑at ϳ6 mg/cm 3 ͒. Radiation from the shocked Xe removes enough energy that the shocked layer increases in density and collapses spatially. This type of system is relevant to a number of astrophysical contexts, providing the potential to observe phenomena of interest to astrophysics and to test astrophysical computer codes.
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