On the Child-Langmuir Law in One, Two, and Three Dimensions

We consider the limiting current from an emitting patch whose size is much smaller than the anode-cathode spacing. The limiting current is formulated in terms of an integral equation. It is solved iteratively, first to numerically recover the classical one-dimensional Child-Langmuir law, including Jaffe's extension to a constant, nonzero electron emission velocity. We extend to 2-dimensions in which electron emission is restricted to an infinitely long stripe with infinitesimally narrow stripe width, so that the emitted electrons form an electron sheet. We next extend to 3-dimensions in which electron emission is restricted to a square tile (or a circular patch) with an infinitesimally small tile size (or patch radius), so that the emitted electrons form a needle-like line charge. Surprisingly, for the electron needle problem, we only find the null solution for the total line charge current, regardless of the assumed initial electron velocity. For the electron sheet problem, we also find only the null solution for the total sheet current if the electron emission velocity is assumed to be zero, and the total maximum sheet current becomes a finite, nonzero value if the electron emission velocity is assumed to be nonzero. These seemingly paradoxical results are shown to be consistent with the earlier works of the Child-Langmuir law of higher dimensions. They are also consistent with, or perhaps even anticipated by, the more recent theories and simulations on thermionic cathodes that used realistic work function distributions to account for patchy, nonuniform electron emission. The mathematical subtleties are discussed.Comment: This material has been submitted to Physics of Plasmas. After it is published, it will be found at https://pubs.aip.org/aip/po

Limiting current in a crossed‐field gap

An analytic theory is presented that yields the maximum transmittable current across an anode–cathode gap that is embedded in an arbitrary transverse magnetic field (B). The limiting current is found to be relatively insensitive to B for all B<BH, where BH is the Hull cutoff magnetic field required for magnetic insulation. The classical Child–Langmuir solution is recovered in the limit B→0.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71084/2/PFBPEI-5-12-4486-1.pd

Scaling laws for dielectric window breakdown in vacuum and collisional regimes

The scaling laws for the initiation time of radio frequency (rf) window breakdown are constructed for three gases: Ar, Xe, and Ne. They apply to the vacuum, to the multipactor-triggered regime, and to the collisional rf plasma regime, and they are corroborated by computer simulations of these three gases over a wide range of pressures. This work elucidates the key factors that are needed for the prediction of rf window breakdown in complex gases, such as air, at various pressures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87804/2/261501_1.pd

Steady state multipactor and dependence on material properties

The interaction of multipactor discharge and an rf circuit is analyzed with the use of a simple model, in which the multipactor electrons are in the form of a single sheet that is released from the surface with a monoenergetic velocity. An explicit formula is derived for the saturation level of multipactor current in steady state. This formula is given in terms of the secondary electron yield properties of the multipactoring surfaces and the level of the external rf drive. It is valid when the quality factor QQ of the rf circuit is higher than 10, in which case the space charge effects do not contribute significantly to the saturation level. When it occurs, the steady state multipactor may consume tens of percents of the external rf power that is needed to sustain the gap voltage. Numerical computations determine the accessibility to steady state from the transient buildup. In particular, they suggest various conditions for the multipactor to exhibit in a burst mode or in a steady state mode. The dynamic linkage of the rf circuit and material properties allows the construction of the susceptibility diagram for various materials, within the limitations imposed by the present model. © 1997 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70121/2/PHPAEN-4-3-863-1.pd

Collapse of cycloidal electron flows induced by misalignments in a magnetically insulated diode

The effect of a slight misalignment in the magnetic field on a magnetically insulated diode is investigated. It is found that a slight tilt in the magnetic field, with a minute component along the dc electric field, completely destabilizes the cycloidal electron flow in the crossed-field gap. The final state consists of the classical Brillouin flow superimposed by a turbulent background, together with a slow electron drift across the gap. This disruption of the cycloidal flow is quite insensitive to the emission current density, and is due to the accumulation of space charge in the gap caused by the magnetic misalignment. This result was obtained from a one-dimensional simulation code. It reinforces the notion that the turbulent, near Brillouin-like states are generic in ALL vacuum crossed-field devices. © 1998 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69778/2/PHPAEN-5-6-2447-1.pd

Manipulation of External Tachodynamometer by the Patient: Case Report

External tachodynamometer has frequently been used to evaluate premature labor. In three cases, the patient was apparently able to record uterine contraction-like curves by means of abdominal pressure. In two of these cases, the patient was evidently using this manipulation to gain attention and support from her husband and/or family members. In the third case, described in this paper, because false curves were recorded, an emergency Caesarean section was performed under the impression that abruptio placenta had occurred

Observed Recent Trends in Tropical Cyclone Rainfall Over Major Ocean Basins

In this study, we use Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Climatology Project (GPCP) rainfall data together with historical storm track records to examine the trend of tropical cyclone (TC) rainfall in major ocean basins during recent decades (1980-2007). We find that accumulated total rainfall along storm tracks for all tropical cyclones shows a weak positive trend over the whole tropics. However, total rainfall associated with weak storms, and intense storms (Category 4-5) both show significant positive trends, while total rainfall associated with intermediate storms (Category1-3) show a significant negative trend. Storm intensity defined as total rain produced per unit storm also shows increasing trend for all storm types. Basin-wide, from the first half (1980-1993) to the second half (1994-2007) of the data period, the North Atlantic shows the pronounced increase in TC number and TC rainfall while the Northeast Pacific shows a significant decrease in all storm types. Except for the Northeast Pacific, all other major basins (North Atlantic, Northwest Pacific, Southern Oceans, and Northern Indian Ocean) show a significant increase in total number and rainfall amount in Category 4-5 storms. Overall, trends in TC rainfall in different ocean basins are consistent with long-term changes in the ambient large-scale environment, including SST, vertical wind shear, sea level pressure, mid-tropospheric humidity, and Maximum Potential Intensity (MPI). Notably the pronounced positive (negative) trend of TC rainfall in the North Atlantic (Northeast Pacific) appears to be related to the most (least) rapid increase in SST and MPI, and the largest decrease (increase) in vertical wind shear in the region, relative to other ocean basins

Nonlinear Thomson scattering: A tutorial

Recent advances in table-top, ultrahigh intensity lasers have led to significant renewed interest in the classic problem of Thomson scattering. An important current application of these scattering processes is the generation of ultrashort-pulse-duration x rays. In this tutorial, the classical theory of nonlinear Thomson scattering of an electron in an intense laser field is presented. It is found that the orbit, and therefore its nonlinear scattering spectra, depends on the amplitude and on the phase at which the electron sees the laser electric field. Novel, simple asymptotic expansions are obtained for the spectrum of radiation that is backscattered from a laser by a counter-propagating (or co-propagating) electron. The solutions are presented in such a way that they explicitly show—at least in the single particle regime—the relative merit of using an intense laser and of an energetic electron beam in x-ray production. The close analogy with free electron laser/synchrotron source is indicated. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70253/2/PHPAEN-10-5-2155-1.pd

Erratum: ‘‘Phase dependence of Thomson scattering in an ultraintense laser field’’ \u3ci\u3ePhys. Plasmas\u3c/i\u3e 9, 4325 [2002]

The conclusions of this paper on the frequency scaling of the peak intensity of Thomson scattering of an electron that is initially at rest are restricted to the backscatter direction of the laser. All data were obtained only for the backscatter direction. In the forward direction of the laser, there is no frequency upshift. At an oblique angle that depends on the normalized laser field amplitude, ω/ω0 ~ O(a3) for large a, where ω0 is the laser frequency and a is the normalized laser electric field amplitude. Also, in Fig. 3, a = 10