The drag of spheres and disks has been measured in a flow of liquid sodium within an aligned magnetic field. A slightly viscous, strong field limit is discussed and explored experimentally. In this limit the drag coefficient was found to have an asymptotic dependence proportional to the square root of the interaction parameter, the ratio of magnetic to inertial force, independent of body shape. A physical model is presented along with preliminary verification of its basic characteristics.

This paper reviews recent work on the focusing of high-power relativistic electron beams in diodes and discusses concepts for pulsed fusion based on this technology. The physics of high-current relativistic electron beam focusing using plasmas in high-current diodes is studied experimentally and with computer simulation. The physics of the beam interaction with dense targets and the requirements for break-even are briefly discussed.

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We present results which are encouraging for a multibeam approach to relativisticeleetron-beam-induced pellet fusion. A self-pinched relativistic electron beam with nominal parameters of 1.1 MV, 200 kA, and 5-mm radius has been propagated at atmospheric pressure over distances of up to 1 m. Gross beam stability and reasonable energy transport efficiency have been achieved. A simple Alfv6n-type calculation corroborates the propagation result, and a self-consistent particle simulation indicates the possibility of scaling to very high-iVy beams.The relativistic-electron-beam (REB) approach to inertial-confinement fusion 1 * 2 requires powers in excess of 100 TW delivered to a target. 3 However, pinched-flow REB generators and diodes presently operate below the 10-TW level. One conceptual solution to this problem consists of propagation of many, several-terawatt, pinched REB's to a single target. This approach would allow the REB accelerator to be located at a large distance from the pellet explosion and would require relatively little improvement over presently available diode operation. Establishment of the feasibility of this scheme has two elements:(1) demonstration of "long-distance" propagation of a pinched, high-v/y REB, and (2) demonstration of the superposition (overlapping) of many beams at a pellet. In this Letter, we report the propagation of a pinched REB over distances of up to 1 m and the observation of complete beamcurrent neutralization. This latter result implies that the superposition problem may be reducible to one involving considerations only of singleparticle orbits in the preformed magnetic field of a plasma discharge. The propagation technique employed in this experiment would allow the use of a high-density gas blanket surrounding a thermonuclear target which would be useful for reactor shielding. Previous work has been done on beam propagation and combination in plasma channels. 4 However, the present work employs techniques which might be extrapolated to the currentdensity and geometry requirements of pellet fusion.In the experiments, a pinched REB from the Hydra accelerator 5 was extracted through a 25jutm Mylar vacuum window into the atmosphere. The beam was collimated to 10 mm diameter by an aperture and, after propagation of a few millimeters, it entered the end of a preformed plasma channel (see Fig. 1). The diode parameters were typically 1.1 MV, 250 kA, i//y~5, 100 ns full width at half-maximum (FWHM), and 25 kJ. The hollow cathode was 75 mm o.d. by 25 mm i.d. and a 6-mm anode-cathode gap was used. X-ray measurements made with collimatedp-i-n diodes (described below) indicated that the initial 25 ns of the beam pulse was not incident on the apertured region, but that once the pinch was fully developed (after 35 ns), over 90% of the beam was available for propagation. We estimate that 15 kJ at peak electron current of 200 kA were injected into the channel region. (A 20% allowance for ion current flow has been included.)The beam propagation channel was preformed by exploding 6 tungste...

A technique has been demonstrated for concentrating electron beams to 5xl0 6 A/cm 2 plasmas on the axis of diodes. A two-dimensional particle code has been used to illustrate the importance of both the ExB motion in vacuum and the self-pinch of the beam within the plasma.Interest has increased recently in applying intense electron beams to the problem of pulsed fusion. One of the fundamental requirements in achieving such a goal is the focusing of multimegampere currents onto submillimeter targets. For the last five years or more, fairly extensive beam research has been carried out in propagation and compression of 50~500-kA beams beyond the diode, with current densities of % 10 5 A/cm 2 achieved. Theoretical and experimental studies have indicated the futility of such an approach insofar as the necessary current densities in the 10 9 -10 10 A/cm 2 range are concerned. The goal of the work described here is to utilize the combined effects of azimuthal magnetic fields together with the applied electric field within the beam-generating diode to accomplish the desired results. We will discuss in this paper experimental and computational results giving the properties of self-pinched beams in diodes, and the focusing improvement obtained as a result of placing a current-carrying plasma along the diode axis.It was observed in early experiments with highv/y diodes that when a critical value of the current was reached, self-pinching of the beam occurred. Although the resultant current density at the anode (~ 10 5 A/cm 2 ) was in excess of the space-charge-limited value, the pinch was not reproducible and formed late in the pulse with a radial collapse velocity of -0.1 cm/nsec. Ecker 1 found that impedance values could be correlated at current maximum with a "parapotential" model originated by De Packh. 2 This model treated the electron trajectories as lying along conical equipotentials with an arbitrarily imposed current along the axis, and it did not treat motion across equipotentials at the cathode edge nor at the anode.Recent numerical studies of this problem 8 have shown that although the dominant mechanism in such a self-pinched diode is EXR motion toward the axis, the assumptions of the parapotential model do not apply. These calculations show that a substantial concentration of current will occur on axis of such a diode if a layer of plasma exists near the anode. They also show that the VB drift away from the anode, as well as space charge near the axis, will tend to inhibit the pinch formation. The primary effect of the spacecharge buildup is to distort the equipotentials sufficiently to force electrons into the anode before they reach the diode axis. Experiments have been conducted to minimize both of these detrimental effects in order to further enhance the diode self-pinch.Mosher et al.* showed that exploding wires could be used in low-impedance diodes to achieve output loads in the l-£2 range, and that under certain circumstances an energetic beam could be generated within such a wire. After we noted that in ...