Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

Operation of a step tunable megawatt gyrotron

An electron cyclotron resonance maser; gyrotron fundamental oscillator; advantages of gyrotrons; a schematic of the experiment; gyrotron design theory; 1 MW design parameters; compact ignition tokamak; and a gyrotron with quasi-optical output coupler are briefly presented. This presentation is represented by viewgraphs only

Experimental observation of the effect of aftercavity interaction in a depressed collector gyrotron oscillator

This paper presents the experimental observation of the effect of an aftercavity interaction (ACI) in a depressed collector gyrotron oscillator. The gyrotron generates an output power of 1.5 MW at 110 GHz in 3 ??s pulses with a 96 kV and 40 A electron beam and has a single-stage depressed collector. The ACI arises from an unintended cyclotron resonant interaction between the microwave beam traveling out from the cavity and the gyrating electron beam. The interaction occurs in the uptaper of the launcher, immediately downstream from the cavity, where the magnetic field is slightly lower than its value in the cavity region. The ACI results in a reduction in efficiency since the electron beam tends to extract power from the wave. There is also a broadening of the spent beam energy profile, which reduces the effectiveness of the depressed collector and in turn limits the overall efficiency of a gyrotron. Measurements of the maximum depression voltage of the collector vs beam current at 96 kV are compared with simulations from the MAGY code [M. Botton, IEEE Trans. Plasma Sci. 26, 882 (1998)]. Excellent agreement is obtained between theory and experiment but only if the ACI is included. In the present experiment, it is estimated that the observed efficiency of 50% would have been about 60% in the absence of the ACI. These results verify the role of the ACI in reducing the efficiency of the gyrotron interaction.open151

On the role of confinement on solidification in pure materials and binary alloys

We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent ($\delta$) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of $\delta$, and other process parameters. As $\delta$ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3-D to 2-D at very small $\delta$, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.Comment: 13 pages, 9 figures, 3 table

Distributing the burdens of climate change

Global climate change raises many questions for environmental political theorists. This article focuses on the question of identifying the agents that should bear the financial burden of preventing dangerous climate change. Identifying in a fair way the agents that should take the lead in climate mitigation and adaptation, as well as the precise burdens that these parties must bear, will be a key aspect of the next generation of global climate policies. After a critical review of a number of rival approaches to burden sharing, the paper argues that only a principled and philosophically robust reconciliation of three approaches to burden sharing (‘contribution to problem’, ‘ability to pay’ and ‘beneficiary pays’) can generate a satisfactory mix of theoretical coherence and practical application

Experimental results for a 1.5 MW, 110 GHz gyrotron oscillator with reduced mode competition

A new result from a 110 GHz gyrotron at MIT is reported with an output power of 1.67 MW and an efficiency of 42% when operated at 97 kV and 41 A for 3 mu s pulses in the TE22,6 mode. These results are a major improvement over results obtained with an earlier cavity design, which produced 1.43 MW of power at 37% efficiency. These new results were obtained using a cavity with a reduced output taper angle and a lower ohmic loss when compared with the earlier cavity. The improved operation is shown experimentally to be the result of reduced mode competition from the nearby TE19,7 mode. The reduced mode competition agrees well with an analysis of the startup scenario based on starting current simulations. The present results should prove useful in planning long pulse and CW versions of the 110 GHz gyrotron.open141

Active Negative Index Metamaterial Powered by an Electron Beam

A novel active negative index metamaterial that derives its gain from an electron beam is intro- duced. The metamaterial consists of a stack of equidistant parallel metal plates perforated by a periodic array of holes shaped as complementary split-ring resonators. It is shown that this structure supports a negative-index transverse magnetic electromagnetic mode that can resonantly interact with a relativistic electron beam. Such metamaterial can be used as a coherent radiation source or a particle accelerator.Comment: 5 pages, 4 figure

Coherent Cherenkov-Cyclotron Radiation Excited by an Electron Beam in a Metamaterial Waveguide

An electron beam passing through a metamaterial structure is predicted to generate reversed Cherenkov radiation, an unusual and potentially very useful property. We present an experimental test of this phenomenon using an intense electron beam passing through a metamaterial loaded waveguide. Power levels of up to 5 MW are observed in backward wave modes at a frequency of 2.40 GHz using a one microsecond pulsed electron beam of 490 keV, 84 A in a 400 G magnetic field. Contrary to expectations, the output power is not generated in the Cherenkov mode. Instead, the presence of the magnetic field, which is required to transport the electron beam, induces a Cherenkov-cyclotron (or anomalous Doppler) instability at a frequency equal to the Cherenkov frequency minus the cyclotron frequency. Nonlinear simulations indicate that the Cherenkov-cyclotron mode should dominate over the Cherenkov instability at a lower magnetic field where the highest output power is obtained.United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-12-1-0489