I. M. Rittersdorf

Effects of magnetic shear on magneto-Rayleigh-Taylor instability

The magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] consists of a cylindrical metal liner enclosing a preheated plasma that is embedded in an axial magnetic field. Because of its diffusion into the liner, the pulsed azimuthal magnetic field may exhibit a strong magnetic shear within the liner, offering the interesting possibility of shear stabilization of the magneto-Rayleigh-Taylor (MRT) instability. Here, we use the ideal MHD model to study this effect of magnetic shear in a finite slab. It is found that magnetic shear reduces the MRT growth rate in general. The feedthrough factor is virtually independent of magnetic shear. In the limit of infinite magnetic shear, all MRT modes are stable if bu > 1, where bu is the ratio of the perturbed magnetic tension in the liner’s interior region to the acceleration during implosion.

Magneto-Rayleigh-Taylor experiments on a MegaAmpere linear transformer driver

Experiments have been performed on a nominal 100 ns rise time, MegaAmpere (MA)-class linear transformer driver to explore the magneto-Rayleigh-Taylor (MRT) instability in planar geometry. Plasma loads consisted of ablated 400 nm-thick, 1 cm-wide aluminum foils located between two parallel-plate return-current electrodes. Plasma acceleration was adjusted by offsetting the position of the foil (cathode) between the anode plates. Diagnostics included double-pulse, sub-ns laser shadowgraphy, and machine current B-dot loops. Experimental growth rates for MRT on both sides of the ablated aluminum plasma slab were comparable for centered-foils. The MRT growth rate was fastest (98 ns e-folding time) for the foil-offset case where there was a larger magnetic field to accelerate the plasma. Other cases showed slower growth rates with e-folding times of about ∼106 ns. An interpretation of the experimental data in terms of an analytic MRT model is attempted.

Discrete space charge affected field emission: Flat and hemisphere emitters

Models of space-charge affected thermal-field emission from protrusions, able to incorporate the effects of both surface roughness and elongated field emitter structures in beam optics codes, are desirable but difficult. The models proposed here treat the meso-scale diode region separate from the micro-scale regions characteristic of the emission sites. The consequences of discrete emission events are given for both one-dimensional (sheets of charge) and three dimensional (rings of charge) models: in the former, results converge to steady state conditions found by theory (e.g., Rokhlenko et al. [J. Appl. Phys. 107, 014904 (2010)]) but show oscillatory structure as they do. Surface roughness or geometric features are handled using a ring of charge model, from which the image charges are found and used to modify the apex field and emitted current. The roughness model is shown to have additional constraints related to the discrete nature of electron charge. The ability of a unit cell model to treat field emitter structures and incorporate surface roughness effects inside a beam optics code is assessed.

2D/3D image charge for modeling field emission

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbon nanotube and carbon fiber field emitters is discussed.

Effects of Multiple Internal Reflections on the Small-Signal Gain and Phase of a TWT

We formulate and solve a set of equations that model the effects of reflections from an arbitrary number of circuit discontinuities in a traveling-wave tube (TWT) operating under small-signal conditions. Applying this model to a case in which the discontinuities represent a series of small random pitch variations due to fabrication errors in a helix TWT, we find that reflections may significantly increase the statistical effects on the gain and output phase first reported in the work of Pengvanich In another example, we report on a study of the effects of many small pitch errors on gain ripple in a 220-GHz folded waveguide TWT.

Temporal evolution of surface ripples on a finite plasma slab subject to the magneto-Rayleigh-Taylor instability

Using the ideal magnetohydrodynamic model, we calculate the temporal evolution of initial ripples on the boundaries of a planar plasma slab that is subjected to the magneto-Rayleigh-Taylor instability. The plasma slab consists of three regions. We assume that in each region the plasma density is constant with an arbitrary value and the magnetic field is also constant with an arbitrary magnitude and an arbitrary direction parallel to the interfaces. Thus, the instability may be driven by a combination of magnetic pressure and kinetic pressure. The general dispersion relation is derived, together with the feedthrough factor between the two interfaces. The temporal evolution is constructed from the superposition of the eigenmodes. Previously established results are recovered in the various limits. Numerical examples are given on the temporal evolution of ripples on the interfaces of the finite plasma slab.

The effect of electron inertia in Hall-driven magnetic field penetration in electron-magnetohydrodynamics

Magnetic field penetration in electron-magnetohydrodynamics (EMHD) can be driven by density gradients through the Hall term [Kingsep et al., Sov. J. Plasma Phys. 10, 495 (1984)]. Particle-in-cell simulations have shown that a magnetic front can go unstable and break into vortices in the Hall-driven EMHD regime. In order to understand these results, a new fluid model had been derived from the Ly/Ln≪1 limit of EMHD, where Ly is the length scale along the front and Ln is the density gradient length scale. This model is periodic in the direction along the magnetic front, which allows the dynamics of the front to be studied independently of electrode boundary effects that could otherwise dominate the dynamics. Numerical solutions of this fluid model are presented that show for the first time the relation between Hall-driven EMHD, electron inertia, the Kelvin-Helmholtz (KH) instability, and the formation of magnetic vortices. These solutions show that a propagating magnetic front is unstable to the same KH mode...

Temporal and spatial locking of nonlinear systems

Peer-to-peer locking of two magnetrons is analyzed including the effects of a frequency chirp and of low frequency noise. It is found that complete phase locking cannot be achieved in either case. However, as long as the locking condition is well satisfied instantaneously, a high degree of locking occurs. This analysis in the time domain is adapted to locking in the spatial domain, in particular to the interpretation of some recent experiments on the spatial correlation of two ablating current-carrying wires that are placed sufficiently close to each other.

Controlling hollow relativistic electron beam orbits with an inductive current divider

A passive method for controlling the trajectory of an intense, hollow electron beam is proposed using a vacuum structure that inductively splits the beams return current. A central post carries a portion of the return current (I1), while the outer conductor carries the remainder (I2). An envelope equation appropriate for a hollow electron beam is derived and applied to the current divider. The force on the beam trajectory is shown to be proportional to (I2-I1), while the average force on the envelope (the beam width) is proportional to the beam current Ib = (I2 + I1). The values of I1 and I2 depend on the inductances in the return-current path geometries. Proper choice of the return-current geometries determines these inductances and offers control over the beam trajectory. Solutions using realistic beam parameters show that, for appropriate choices of the return-current-path geometry, the inductive current divider can produce a beam that is both pinched and straightened so that it approaches a target at...

Effects of pulsed anode heating on self-magnetic-pinch radiographic performance using NRL's Mercury IVA

Summary form only given. Previous proof-of-principle experiments at NRL used the Mercury IVA facility to test a self-magnetic-pinch (SMP) diode in conjunction with a pulsed resistive heating treatment that cleaned the SMPs anode surface. This heating treatment was tested as a method for mitigating the negative effects of low-Z ions, such as post-shot activation and potentially reduced diode impedance. These low-Z ions can form in the diode region from contaminants on the diode hardware that require in situ cleaning to remove. A more extensive series of experiments are reported here that tested 3 diode configurations with and without the heat treatment. The heat treatment resulted in improvements in spot symmetry, spot size, dose, and radiation pulse length to varying degrees depending on the particular configuration tested. The most significant improvement in dose was achieved from an SMP with a large AK-gap-to-cathodediameter ratio compared with traditional ratios, which are close to 1:1. Large ratios typically result in premature termination of the radiation pulse in the absence of heating. The heat treatment made the large ratio SMP resemble a more stable 1:1 ratio configuration in terms of pulse length, and provides evidence that supports a low-Z ion mechanism as the cause for poor SMP diode impedance at large aspect ratios [1]. The heating circuit itself was a simple resistive pulse through the tantalum anode supplied by switched batteries that drove the anode to >2300 K for approximately 0.5 seconds. Detailed results from this series of experiments will be presented.