[show abstract][hide abstract] ABSTRACT: It is found that the Langmuir-Blodgett solutions for the space charge limited current density, for both cylindrical and spherical diodes, may be approximated by Japp=(4/9)ε0√(2e/m)(Ec3/2/√D) over a wide range of parameters, where Ec is the surface electric field on the cathode of the vacuum diode and D is the anode-cathode spacing. This dependence is valid whether Ra/Rc is greater than or less than unity, where Ra and Rc are, respectively, the anode and cathode radius. Minor empirical corrections to the above scaling yield fitting formulas that are accurate to within 5% for 3×10-5<Rc/Ra<500. An explanation of this scaling is given. An accurate transit time model yields the Langmuir-Blodgett solutions even in the Coulomb blockade regime for a nanogap, where the electron number may be in the single digits, and the transit time frequency is in the THz range.
[show abstract][hide abstract] ABSTRACT: A voltage scale, Vs that characterizes electro-thermal runaway, is deduced from the heat conduction equation, Vs = √k/σ'0, where k-is the thermal conductivity and σ'0 is the rate of change of the electrical conductivity with respect to temperature. Vs depends only on material properties and is independent of geometry and the operating voltage. Vs measures the intrinsic tolerance of the material to electro-thermal instability. Numerical values of Vs are consistent with the well-known properties of several common materials.
Pulsed Power Conference (PPC), 2013 19th IEEE, San Francisco, CA, USA; 06/2013
[show abstract][hide abstract] ABSTRACT: Preliminary experiments of the recirculating planar magnetron microwave source have demonstrated that the device oscillates but is susceptible to intense mode competition due, in part, to poor coupling of RF fields between the two planar oscillators. A novel method of improving the cross-oscillator coupling has been simulated in the periodically slotted mode control cathode (MCC). The MCC, as opposed to a solid conductor, is designed to electromagnetically couple both planar oscillators by allowing for the propagation of RF fields and electrons through resonantly tuned gaps in the cathode. Using the MCC, a 12-cavity anode block with a simulated 1 GHz and 0.26 c phase velocity (where c is the speed of light) was able to achieve in-phase oscillations between the two sides of the device in as little as 30 ns. An analytic study of the modified resonant structure predicts the MCC's ability to direct the RF fields to provide tunable mode separation in the recirculating planar magnetron. The self-consistent solution is presented for both the degenerate even (in phase) and odd (180° out of phase) modes that exist due to the twofold symmetry of the planar magnetrons.
Physics of Plasmas 03/2013; 20(3). · 2.38 Impact Factor
[show abstract][hide abstract] ABSTRACT: A one-dimensional small-signal theory for the backward-wave mode in a traveling-wave tube (TWT) is developed, which includes the effects of random fabrication errors. This is of interest since the backward-wave mode is the spatial harmonic typically responsible for instability in a TWT. The described model examines how gain and instantaneous 1-dB bandwidth of the backward-wave mode is affected by random fabrication errors, which are modeled as random perturbations of the phase velocity, interaction impedance, and loss along the TWT's length. Random variation of the phase velocity is found to have the largest effect on both the backward-wave gain and the bandwidth while having only a minor effect on fundamental, forward-wave mode behavior.
Journal of Applied Physics 02/2013; 113(7). · 2.21 Impact Factor
[show abstract][hide abstract] ABSTRACT: The Green’s function on a slow wave structure is constructed. The Green’s function includes all radial
modes, and for each radial mode, all space harmonics. We compare the analytic solution of the
frequency response on the slow wave structure with that obtained from a particle-in-cell code.
Favorable comparison is obtained when the first few lower order modes are resonantly excited. This
gives some confidence in the prediction of converting a pulse train into radiation using a slow wave
Physics of Plasmas 12/2012; 19:123104. · 2.38 Impact Factor
[show abstract][hide abstract] ABSTRACT: We present simulations and experimental results of a new class of
crossed-field device: Recirculating Planar Magnetron (RPM) .
Experiments on a 12 cavity, 1 GHz, RPM are underway using MELBA
accelerator at -300 kV, 1-10 kA and pulselengths of 0.3-1 microsecond. A
mode control cathode (MCC) is proposed to address RPM mode competition
and cross-oscillator coupling. The MCC is a periodically spaced
conducting network designed to act as both an electron source and a
resonant electromagnetic coupler between the two planar RPM oscillators.
MCC simulations have verified such mechanisms, resulting in faster mode
development and phase locking in the RPM. Manipulation of the cathode's
geometry has also been analytically established to enhance mode
separation of the cold slow wave structure. Experimental frequency and
phase measurements using the MCC will be presented. [4pt]  Gilgenbach
et al., IEEE Trans PS 39, 980 (2011); also, patent pending.
[show abstract][hide abstract] ABSTRACT: Motivated by the potential in the generation of electromagnetic waves
using the output pulses of a nonlinear transmission line (NLTL), we
constructed the Green's function on a slow wave structure. A NLTL-based
radiation source will not require an electron beam, and the key question
is the conversion of the NLTL output of a general temporal pulse shape
into radiation. A slow wave structure may be used as a radiator for the
NLTL-generated pulses. We compare the analytic solution of the frequency
response on the slow wave structure with that obtained from a
particle-in-cell code. Favorable comparison is obtained for the first
few lower order modes that are resonantly excited.
[show abstract][hide abstract] ABSTRACT: Electrical contact  is important to wire-array z-pinches,
metal-insulator-vacuum junctions, and high power microwave sources, etc.
Contact problems account for 40 percent of all electrical failures, from
small scale consumer electronics to large scale defense and aerospace
systems. The crowding of the current lines at contacts leads to enhanced
localized heating, a measure of which is the spreading resistance
(Rs). For a microscopic area of contact (the ``a-spot'' )
on a thin film, we calculate Rs in both Cartesian and
cylindrical geometries . In the limit of small film thickness, h, the
normalized thin film spreading resistance converges to the finite
values, 2.77 for the Cartesian case and 0.28 for the cylindrical case.
These same finite limits are found to be applicable to the a-spot
between bulk solids in the high frequency limit if the skin depth is
identified with h. Extension to a general a-spot geometry is proposed
. [4pt]  R. Holm, Electric Contacts, 4th ed., Springer (1967).
[0pt]  P. Zhang et al., IEEE Trans. Electron Devices 59, 1936 (2012).
[show abstract][hide abstract] ABSTRACT: Multipactor breakdown of RF windows is a potential defense against
high-power microwaves. By applying a DC bias across a dielectric window
in a vacuum-gas environment, the threshold for the onset of RF-initiated
multipactor can be lowered. Recent Monte Carlo simulations of
multipactor in a background gas with a DC bias have provided a
theoretical baseline for comparison against experimental results .
Prior experimental work used a 1 kW CW, 2.45 GHz magnetron to direct RF
at a Lucite vacuum window with embedded copper wires providing the DC
bias. Results confirmed that a DC bias was effective at reducing the
threshold for multipactor in air at sub-torr pressures, though with high
variability. Continuing efforts include exploration of breakdown in
argon at >5 torr to improve reproducibility of experimental results.
Ongoing work is also combining the theories developed in  and  to
characterize multipactor susceptibility in the presence of a background
gas and a static magnetic field using Monte Carlo simulations. [4pt] 
P. Zhang et al., Phys. Plasmas 18, 053508 (2011).[0pt]  A. Valfells
et al., Phys. Plasmas 7, 750 (2000).
[show abstract][hide abstract] ABSTRACT: The spreading resistance of a microscopic area of contact (the "a-spot") located in a thin film is studied for both Cartesian and cylindrical geometries. The effect of film thickness h on the spreading resistance is evaluated over a large range of aspect ratios. In the limit h → 0, the normalized thin-film spread-ing resistance R s converges to the finite values, i.e., 2.77 for the Cartesian case and 0.28 for the cylindrical case. An interpretation of these limits is given. Extension to a general a-spot geometry is proposed.
IEEE Transactions on Electron Devices 07/2012; 59(7):1936. · 2.06 Impact Factor
[show abstract][hide abstract] ABSTRACT: It is shown that the vector potential and the scalar potential satisfy a Buneman-Hartree like (BHL) condition and a Hull-cutoff like (HCL) condition everywhere within the Brillouin flow of a cylindrical, relativistic magnetron, when the phase velocity in the Buneman-Hartree condition is replaced by the laminar, local flow velocity of the Brillouin flow. The vector potential and the scalar potentials include the Brillouin flow’s self magnetic field and the self electric fields. The HCL condition reduces to the conventional Hull cutoff condition derived from single particle orbit theory when the Brillouin hub extends to the anode. However, the BHL condition reduces to the conventional Buneman-Hartree condition only in the planar magnetron limit but may be substantially different for a cylindrical magnetron, as demonstrated recently [Lau et al., Phys. Plasmas 17, 033102 (2010)]. These conclusions apply also to the inverted magnetron configuration. The effects of ions are discussed.
Physics of Plasmas 04/2012; 19(4). · 2.38 Impact Factor
[show abstract][hide abstract] ABSTRACT: Space charge effects reduce electron emission by altering the surface barrier via two effects: increasing the barrier height (Schottky factor) and width to electron emission by lowering the surface field and changing the magnitude of the dipole associated with electron density variation. A one-dimensional emission model using a transit time argument to account for charge in the anode-cathode (AK) gap and an analytical model of the dipole is used to approximate the effects of each factor on the current density. The transit time model is compared to the experimental data of Longo [J. Appl. Phys. 94, 6966 (2003)] for thermal emission. Changes in the dipole contribution are primarily associated with tunneling and therefore field emission. The transit time plus dipole modification is compared to the experimental data of Barbour et al. [Phys. Rev. 92, 45 (1953)] for field emission. The model’s application to thermal-field, and photoemission in general is discussed, with the former corresponding to continuous current limit and the latter to a pulsed current limit of the model.
Journal of Applied Physics 03/2012; 111(5). · 2.21 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
Physics of Plasmas 03/2012; 19(3). · 2.38 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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 b u > 1, where b u is the ratio of the perturbed magnetic tension in the liner's interior region to the acceleration during implosion. V C 2012 American Institute of Physics. [doi:
Physics of Plasmas 02/2012; 19:022703. · 2.38 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
IEEE Transactions on Electron Devices 01/2012; 59(5):1542-1550. · 2.06 Impact Factor
[show abstract][hide abstract] ABSTRACT: Random fabrication errors may have detrimental effects on the
performance of traveling-wave tubes (TWTs) of all types. A new scaling
law for the modification in the average small signal gain and in the
output phase is derived from the third order ordinary differential
equation that governs the forward wave interaction in a TWT in the
presence of random error that is distributed along the axis of the tube.
Analytical results compare favorably with numerical results, in both
gain and phase modifications as a result of random error in the phase
velocity of the slow wave circuit. Results on the effect of the
reverse-propagating circuit mode will be reported.
[show abstract][hide abstract] ABSTRACT: The microwave plasma window is an experiment designed to promote RF
breakdown in a controlled vacuum-gas environment using a DC bias.
Experimental data has shown that this DC bias will significantly reduce
the RF power required to yield breakdown, a feature also shown in recent
simulation . The cross-polarized conducting array is biased at (100's
V) DC on the surface of a Lucite vacuum window. Microwave power is
supplied to the window's surface by a single 1-kW magnetron operating at
2.45 GHz CW. The goal of this project is to establish controllable
characteristics relating vacuum pressure, DC bias, RF power required for
surface breakdown, as well as RF transmission after the formation of
plasma. Experimental data will be compared with multipactor
susceptibility curves generated using a Monte Carlo simulation  which
incorporates an applied DC bias and finite pressures of air and argon.
[4pt]  P. Zhang et al., Phys. Plasmas 18, 053508 (2011)
[show abstract][hide abstract] ABSTRACT: Simulation of the novel recirculating planar magnetron, RPM , has
shown rapid formation of electron bunches in the inverted magnetron
configuration. This bunching mechanism was recently simulated in a thin
electron layer model , which exhibited negative, positive, and
infinite mass behavior, depending on the magnitude and sign of the
radial electric field. We analyze these properties for the relativistic,
cylindrical Brillouin flow, to evaluate RPM startup. We make use of our
recent discovery that the electrostatic potential and the vector
potential satisfy a Buneman-Hartree like relation, and a Hull-cutoff
like relation EVERYWHERE within the equilibrium Brillouin flow. [4pt]
 R. M. Gilgenbach, et.al., IEEE Trans. Plasma Sci. 39, 980 (2011).
[0pt]  D. M. French, et al., Appl. Phys. Lett. 97, 111501 (2010).
[show abstract][hide abstract] ABSTRACT: Spectroscopic analysis has been performed on Al foil plasmas ablated by
the Linear Transformer Driver (LTD) at the University of Michigan. The
MAIZE LTD can supply 1- MA, 100 kV pulses with 100 ns risetime into a
matched load. The plasma load consisted of a 400 nm thick Al foil
(cathode) placed between two, planar, current-return anode posts. An
optical fiber was placed 1 cm away from the load; plasma light passed
through a 0.75-m optical spectrograph and was gated for 10 ns by an
intensified CCD detector. The density of the edge plasma was determined
through Stark broadening of the H-alpha line. The Fourier transform was
taken of the Voigt profile, which was then used to approximate the
density of the Al plasma. This method resulted in a density of
approximately 10^15 cm-3 in the outer regions of the Al
plasma at peak current. Spectra taken midway in the current rise yielded
1-2 eV plasma temperatures from the slope of the continuum emission.
These data will be shown as well as planned future experiments.