With the advent of high-energy-density ͑HED͒ experimental facilities, such as high-energy lasers and fast Z-pinch, pulsed-power facilities, millimeter-scale quantities of matter can be placed in extreme states of density, temperature, and/or velocity. This has enabled the emergence of a new class of experimental science, HED laboratory astrophysics, wherein the properties of matter and the processes that occur under extreme astrophysical conditions can be examined in the laboratory. Areas particularly suitable to this class of experimental astrophysics include the study of opacities relevant to stellar interiors, equations of state relevant to planetary interiors, strong shock-driven nonlinear hydrodynamics and radiative dynamics relevant to supernova explosions and subsequent evolution, protostellar jets and high Mach number flows, radiatively driven molecular clouds and nonlinear photoevaporation front dynamics, and photoionized plasmas relevant to accretion disks around compact objects such as black holes and neutron stars.

Note the title of Sec. V of his more detailed paper (Tonks, 1939): ''Constriction of Arc under its Own Magnetic Field-Pinch Effect.'' According to J. A. Phillips (1987), The term ''pinch effect'' was in fact first used in 1907 by C. Hering, to describe what would now be called ''a sausage instabillity'' of a liquid-metal conductor in induction furnaces.

Collisionless shocks can be produced as a result of strong magnetic fields in a plasma flow, and therefore are common in many astrophysical systems. The Weibel instability is one candidate mechanism for the generation of su ciently strong fields to create a collisionless shock. Despite their crucial role in astrophysical systems, observation of the magnetic fields produced by Weibel instabilities in experiments has been challenging. Using a proton probe to directly image electromagnetic fields, we present evidence of Weibelgenerated magnetic fields that grow in opposing, initially unmagnetized plasma flows from laser-driven laboratory experiments. Three-dimensional particle-in-cell simulations reveal that the instability e ciently extracts energy from the plasma flows, and that the self-generated magnetic energy reaches a few percent of the total energy in the system. This result demonstrates an experimental platform suitable for the investigation of a wide range of astrophysical phenomena, including collisionless shock formation in supernova remnants, large-scale magnetic field amplification, and the radiation signature from gamma-ray bursts.The magnetic fields required for collisionless shock formation in astrophysical systems may either be initially present, for example in supernova remnants or young galaxies 1 , or they may be selfgenerated in systems such as gamma-ray bursts (GRBs; ref. 2). In the case of GRB outflows, the intense magnetic fields are greater than those which can be seeded by the GRB progenitor or produced by misaligned density and temperature gradients (the Biermannbattery effect) 3,4 . It has long been known that instabilities can generate strong magnetic fields, even in the absence of seed fields. Weibel considered the development of an electromagnetic instability driven by the electron velocity anisotropy in a background of resting ions 5 . The signature of the instability is a pattern of current filaments stretched along the axis of symmetry of the electron motion. The process is quite general, and subsequent work has shown that such instabilities can be excited in both non-relativistic and relativistic shocks. This general nature makes the Weibel instability common in astrophysical systems [6][7][8] . The instability provides a mechanism by which the electromagnetic turbulence associated with the formation of collisionless shocks is fed by the flow anisotropy of the protons (and ions) stochastically reflecting off of the shock 9-11 , and leading ultimately to strong particle acceleration in GRB's (ref. 12).

Proton imaging is commonly used to reveal the electric and magnetic fields that are found in high energy density plasmas. Presented here is an analysis of this technique that is directed towards developing additional insight into the underlying physics. This approach considers: formation of images in the limits of weak and strong intensity variations; caustic formation and structure; image inversion to obtain line-integrated field characteristics; direct relations between images and electric or magnetic field structures in a plasma; imaging of sharp features such as Debye sheaths and shocks. Limitations on spatial and temporal resolution are assessed, and similarities with optical shadowgraphy are noted. Synthetic proton images are presented to illustrate the analysis. These results will be useful for quantitatively analyzing experimental proton imaging data and verifying numerical codes.

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