Carl Ekdahl

Image charge focusing of relativistic electron beams

Experimental results are reported on the transport of a relativistic electron beam by image charge effects. The transport system consisted of a cylindrical metal tube periodically interrupted by transverse conducting grids with high transparency. Partial cancellation of the beam electric fields increased the space‐charge‐limited current level, allowing propagation in a magnetically self‐pinched mode. A 400‐keV, 4‐kA beam traveled 30 cm in high vacuum through 10 focusing foils. Capture of the beam was almost 100% efficient; beam emittance was not severely degraded during capture and transport. The radius of the self‐contained beam was 1.4 cm; the beam position was centered by the image current in the transport tube to within 1 mm. The favorable results imply that image charge focusing could be considered for transport in high‐current linear induction accelerators.

Aliasing errors in measurements of beam position and ellipticity

Beam position monitors (BPMs) are used in accelerators and ion experiments to measure currents, position, and azimuthal asymmetry. These usually consist of discrete arrays of electromagnetic field detectors, with detectors located at several equally spaced azimuthal positions at the beam tube wall. The discrete nature of these arrays introduces systematic errors into the data, independent of uncertainties resulting from signal noise, lack of recording dynamic range, etc. Computer simulations were used to understand and quantify these aliasing errors. If required, aliasing errors can be significantly reduced by employing more than the usual four detectors in the BPMs. These simulations show that the error in measurements of the centroid position of a large beam is indistinguishable from the error in the position of a filament. The simulations also show that aliasing errors in the measurement of beam ellipticity are very large unless the beam is accurately centered. The simulations were used to quantify the aliasing errors in beam parameter measurements during early experiments on the DARHT-II accelerator, demonstrating that they affected the measurements only slightly, if at all.

Image current guiding of a relativistic electron beam in a foil focusing system

Intense relativistic electron beams can be focused by arrays of transverse conducting foils or meshes. The meshes cancel beam‐generated radial electric fields, allowing a self‐pinched equilibrium. The experiments reported confirm that foil focusing systems can also steer high‐current beams. We applied a dipole perturbation field to deflect a 3.8 kA, 280 keV beam in a foil array. We found that image current forces centered the beam in the transport pipe. The measured deflection was more than an order of magnitude smaller than the predicted value for single electron orbits. The results show that foil focusing may have application to recirculating accelerators for high‐current electron beams.

Tuning the DARHT Long-Pulse Linear Induction Accelerator

Flash radiography of large hydrodynamic experiments driven by high explosives is a well-known diagnostic technique in use at many laboratories. The Dual-Axis Radiography for Hydrodynamic Testing (DARHT) facility at Los Alamos produces flash radiographs of large hydrodynamic experiments. Two linear induction accelerators (LIAs) make the bremsstrahlung radiographic source spots for orthogonal views of each test. The 2-kA, 20-MeV Axis-I LIA creates a single 60-ns radiography pulse. The 1.7-kA, 16.5-MeV Axis-II LIA creates up to four radiography pulses by kicking them out of a longer pulse that has a 1.6- μs flat top. The DARHT LIAs use solenoidal focusing for transport of the beam through the accelerators. The long-pulse Axis-II LIA has 74 accelerating cells, and uses 91 solenoids and 80 pairs of dipoles for focusing, transporting, and steering the beam. The setting of the currents of these 251 magnets is called tuning the accelerator. Tuning is done in two stages. First, the solenoidal focusing magnets are set to values designed to provide a beam with minimal envelope oscillations, and little or no instability growth. Then, steering dipoles are adjusted to minimize the low-frequency motion of the beam centroid and center it at the LIA exit. The design of the focusing tune is computationally intensive. Focusing tune design methods, simulations, and validation are the main topics of this article.

Characterizing flash-radiography source spots

Flash radiography of large hydrodynamic experiments driven by high explosives is a venerable diagnostic technique in use at many laboratories. The size of the radiographic source spot is often quoted as an indication of the resolving power of a particular flash-radiography machine. A variety of techniques for measuring spot size have evolved at the different laboratories, as well as different definitions of spot size. Some definitions are highly dependent on the source spot intensity distributions, and not necessarily well correlated with resolution. The concept of limiting resolution based on bar target measurements is introduced, and shown to be equivalent to the spatial wavenumber at a modulation transfer function value of 5%. This resolution is shown to be better correlated with the full width at half-maximum of the spot intensity distribution than it is with other definitions of spot size.

Transient decay of beam-produced fields in thin-walled tubes

An electromagnetics problem that arises in long-pulse beam experiments is the decay of image currents (and their fields) resulting from a beam that is offset from the geometric axis of the beam tube. A related problem, which arises in calibration of beam diagnostics, is that of simulating the beam using a current-carrying conductor. These problems are solved analytically in the limit that the tube walls are thin compared with the magnetic-field penetration depth. It is shown that the transient decay time of the fields for these two cases is different.

Grid-focused diodes for radiography

Simulations with the TRAK ray-tracing code have shown that grid-focused diodes might be a simple alternative to gas/plasma cell focusing for moderate- energy radiography machines. Multi-grid focusing has advantages over single grid focusing, especially in circumventing neutralization from gases evolved from the heated target. The practical technology for grid focusing was established many years ago in an extensive series of experiments.

Noninvasive measurement of electron-beam size with diamagnetic loops

Diamagnetic loops can be used as a noninvasive method for measurements of beam size in electron beam accelerators that use solenoidal magnetic transport. A comprehensive theory for interpreting data from a diamagnetic loop is developed. It is shown that the change in flux through a diamagnetic loop can be simply related to the rms beam radius to high accuracy, regardless of the details of the current profile, when the ratio of beam current to Alfven current Ib/IA is small. The difficulty in making this measurement lies in the fact that the diamagnetic-loop signal is also small to the same order.

Finite-element simulation code for high-power magnetohydrodynamics

We describe the mathematical basis and organization of Crunch, a 1D shock-hydrodynamics code to analyze pulsed-power experiments at Los Alamos National Laboratory. The program uses finite-element methods that preserve stability during material collisions and shock convergence on axis. It handles coupled calculations of nonlinear magnetic diffusion to simulate imploding liners. These calculations may be driven by multiple current waveforms or a self-consistent current variation derived from a pulsed-power generator model. Crunch incorporates elastic material contributions and calculates element break and melt points. The primary goal in program development was effective use by experimentalists. Crunch is controlled by a streamlined script language and runs on standard personal computers. An interactive graphical postprocessor expedites analysis of results. To support the program we have assembled data resources in machine-independent format including Sesame equation-of-state tables, a material strength library and a library of temperature-dependent conductivities.

Guest Editorial Special Issue on Plenary and Invited Papers From ICOPS 2003

The 39th International Conference on Plasma Science (ICOPS) was held in Edinburgh, Scotland in July 2012. The conference featured a wide range of advances in innovative plasma and beam science and applications, and served as a venue for an international community to meet and discuss their ideas and research results. More than 800 abstracts were received in 35 different topical areas, with more than half the papers originating outside the United State. The conference was attended by over 600 delegates and enjoyed the participation of over 200 registered students. This Special Issue of the IEEE TRANSACTIONS ON PLASMA SCIENCE contains eight refereed papers representing a small collection of some of the most exciting presentations from ICOPS 2012.