We prove that, at the frequencies generally proposed for extracranial stimulation of the brain, it is not possible, using any superposition of external current sources, to produce a three-dimensional local maximum of the electric field strength inside the brain. The maximum always occurs on a boundary where the conductivity jumps in value. Nevertheless, it may be possible to achieve greater two-dimensional focusing and shaping of the electric field than is currently available. Towards this goal we have used the reciprocity theorem to present a uniform treatment of the electric field inside a conducting medium produced by a variety of sources: an external magnetic dipole (current loop), an external electric dipole (linear antenna), and surface and depth electrodes. This formulation makes use of the lead fields from magneto- and electroencephalography. For the special case of a system with spherically symmetric conductivity, we derive a simple analytic formula for the electric field due to an external magnetic dipole. This formula is independent of the conductivity profile and therefore embraces spherical models with any number of shells. This explains the "insensitivity" to the skull's conductivity that has been described in numerical studies. We also present analytic formulas for the electric field due to an electric dipole, and also surface and depth electrodes, for the case of a sphere of constant conductivity.
In a series of experiments using two-, four-, and eight-beam 10.6-jum-laser irradiation of a variety of target geometries, a significant amount of energy was found to be deposited in regions remote from the focal spots. The deposition patterns can be predicted with a self-generated magnetic field model. PACS numbers: 52.50.Jm Lateral transport of energy away from laser focal spots can play an important role in redistributing energy deposition in laser-fusion targets. Work has been reported investigating the qualitative 1 and quantitative 2 nature of this transport. Recently, using a plasma simulation, Forslund and Brackbill 3 have identified convective transport of electrons in self-generated magnetic fields as an important mechanism for surface transport in laser-irradiated foils. In one simulation with a laser intensity of 5 x 10 13 W/cm 2 in a 60-jum spot and a hot-electron temperature of 20 keV, peak fields of the order of 1 MG were calculated. The calculation has not been performed at higher intensities comparable to those used in experiment (~10 16 W/cm 2 ) because the code does not handle the relativistic effects of the high-energy electrons generated at these intensities. In general, the ratio of electron to magnetic field pressure is of order 1 in a magnetized sheath whose thickness is large compared with the electron gyroradius. This Letter presents experimental evidence for the nonuniformity of energy deposition predicted by the magnetic field model in a variety of target geometries progressing from flats to cylinders to spheres. From the simulations, a simple qualitative moddel has been developed. Briefly, the model describes lateral energy transport by electrons in magnetic fields generated at the periphery of the laser spot by lateral temperature gradients in the corona. These gradients are maintained by electrons confined and drifting in the magnetic field, resulting in the convective transport of energy from the beam spot to the edge of the magnetized region. The interaction of the magnetic field and electrons produces a thermal magnetic wave 4 which propagates across the surface until disrupted by fringing fields at the target edge or by destructive interference with the wave propagating from an adjacent beam.
The presence of superconducting surfaces in the vicinity of current sources may be interpreted in terms of image theory. This concept has both experimental and theoretical practicality. Experimentally, sensing coils for magnetic detection, when placed near such surfaces, perform in a gradiometric fashion. In order to explain this effect explicitly, a theoretical treatment of the magnetic fields in the presence of superconducting surfaces and coils is presented. Expressions are derived for planar and spherical geometries that approximate practical experimental situations. These expressions may be used to predict the expected gradiometric response of a coil as a function of the positions of the source and coil relative to the surface.
C0 2 -laser--driven implosions have been shown to produce compressed plasma densities of the same magnitude as ordinary solids (>2 g/cm 3 ). A variety of diagnostic techniques has been used, including the simultaneous observation of x-ray spectroscopic signatures and nuclear yield. The laser energy on target ranged from 3 to 6 kJ and the half width of the pulse was 600-800 ps. The results of these experiments are compared with numerical hydrodynamic simulations.
An intensity dependence of the absorption of 10-/u m laser light on C02-laser-fusion targets has been observed. Absorption on gold spheres increases from 25%--30% at 10^^ W/cm^ to 50%-60% at 10^^ W/cm^, with most of the variation occurring above 10^^ W/cm^ Concurrently, hot-electron temperature scales as T^ot ^I^'^^ over the entire range. The absorption variation is interpreted as enhanced resonant absorption. It is su^ested that as intensity is increased, the critical surface in the irradiated region becomes increasingly unstable, thereby permitting greater surface distortion and more favorable coupling conditions for resonant absorption.
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