A Path Intergal Approach to Current

Discontinuous initial wave functions or wave functions with discontintuous derivative and with bounded support arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial wave functions is not well described by the Schr\"odinger current which vanishes on the boundary of the support of the wave function. This propagation gives rise to a uni-directional current at the boundary of the support. We use path integrals to define current and uni-directional current and give a direct derivation of the expression for current from the path integral formulation for both diffusion and quantum mechanics. Furthermore, we give an explicit asymptotic expression for the short time propagation of initial wave function with compact support for both the cases of discontinuous derivative and discontinuous wave function. We show that in the former case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{3/2})$ and the initial uni-directional current is $O(\Delta t^{1/2})$. This recovers the Zeno effect for continuous detection of a particle in a given domain. For the latter case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{1/2})$ and the initial uni-directional current is $O(\Delta t^{-1/2})$. This is an anti-Zeno effect. However, the probability propagated across a point located at a finite distance from the boundary of the support is $O(\Delta t)$. This gives a decay law.Comment: 17 pages, Late

Non-uniform emission studies of a magnetron injection gun

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 124-139).This thesis investigates the experimental measurement and theoretical simulation of the effects of azimuthal emission non-uniformity of a 96 kV, 40 amp magnetron injection gun (MIG) used in a gyrotron. The accomplishments of this thesis include: Experimental measurement of the azimuthal emission non-uniformity of the MIG gun; Simulation of the beam quality of the MIG gun using MICHELLE 3-D, the first simulation of a MIG electron beam with azimuthal non-uniformity; Benchmarking the MICHELLE 3-D code to other established gun optics codes; Evaluation of the effects on the velocity spread and pitch factor of azimuthal non-uniformity in the MIG gun, showing that the direct effect on the beam quality is very small; Design, fabrication, and testing in the gyrotron of a capacitive probe system divided into four quadrants to measure azimuthal asymmetries of the electron beam; Use of the capacitive probes to measure low-frequency (100 - 160 MHz) oscillations on the beam, the first measurement of such oscillations in a microsecond pulse length gyrotron; First results on testing a new MIG cathode for emission non-uniformity using a special test chamber built by Calabazas Creek Research.(cont.) This research will contribute to our understanding of the properties of intense electron beams produced by MIG guns in high-power gyrotrons. MIG's are widely used in gyrotron oscillators and amplifiers for fusion applications to create a beam of gyrating electrons generally operating in the temperature limited regime of emission. Due to this dependence on the temperature of the cathode, variation of the emitter surface temperature will result in inhomogeneous emission. Non-uniform emission is attributed to a deviation in the cathode work function as well. Studies have shown this inhomogeneous beam current density can lead to increased mode competition and velocity spread contributing to an overall decreased efficiency of the gyrotron. This research focuses on the effects on velocity spread and in turn the efficiency of the device from non-uniform current emission. Initially, we measured experimentally the detailed azimuthal non-uniformity profile of an existing 110 GHz gyrotron oscillator at MIT. Using a rotating collector current probe the current density of different emitter angles was extracted. These results agreed fairly well with previous measurements of Anderson et al.(cont.) This non-uniformity profile was then used with a 3-D simulation code to do the first complete 3-D model from the cathode to the cavity of a MIG. In order to investigate these effects of beam non-uniformity with simulation, we use MICHELLE 3-D developed by SAIC. MICHELLE 3-D has been benchmarked to MICHELLE 2-D and EGUN in the case of a uniform beam. The non-uniform beam measurements are entered into MICHELLE and results are computed at four different azimuthal quadrants of different current densities and for the overall beam, giving special attention to the differences in the beam pitch factor and perpendicular velocity spread. MICHELLE found azimuthal non-uniformity to be a fairly small effect on the overall beam quality. Concurrently with the MICHELLE 3-D simulations, segmented pitch factor probes are implemented to measure the pitch factor in the four azimuthal quadrants. In an attempt to compare with MICHELLE's results, these four capacitive probes measure the induced image charge of different azimuthal sections of the electron beam, enabling an estimation of differences in the pitch factor between quadrants.(cont.) Unfortunately, the experimental error is found to be quite high (±15%) rendering differences in the pitch factor to be contained within the error boundaries. Though the capacitive probes are found to have too much error for adequate resolution of the pitch factor, they are also used to discover the first observations of low-frequency oscillations in a short pulse MW gyrotron. These frequencies, from 100-160 MHz, are found to be dependent on the beam parameters such as the beam voltage, current, magnetic field, and magnetic compression ratio. The frequency range is remarkably close to the frequency of an electron in the adiabatic trap and the experimental as well as the predicted theoretical oscillation behavior of trapped electrons are discussed. Last, initial progress has been made to test three new cathodes on the Calabazas Creek Research cathode tester. This tester is a dedicated test stand for azimuthal non-uniformity able to obtain a measurement directly at the cathode instead of at the collector end of the device. The setup procedure and results on the first cathode test for the 96 kV, 40 amp gun are reported and future tests are summarized.by Chad D. Marchewka.S.M

Magnetospectroscopy of symmetric and anti-symmetric states in double quantum wells

The experimental results obtained for the magneto-transport in the InGaAs/InAlAs double quantum wells (DQW) structures of two different shapes of wells are reported. The beating-effect occurred in the Shubnikov-de Haas (SdH) oscillations was observed for both types of the structures at low temperatures in the parallel transport when magnetic field was perpendicular to the layers. An approach to the calculation of the Landau levels energies for DQW structures was developed and then applied to the analysis and interpretation of the experimental data related to the beating-effect. We also argue that in order to account for the observed magneto-transport phenomena (SdH and Integer Quantum Hall effect), one should introduce two different quasi-Fermi levels characterizing two electron sub-systems regarding symmetry properties of their states, symmetric and anti-symmetric ones which are not mixed by electron-electron interaction.Comment: 20 pages, 20 figure

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

Matter wave pulses characteristics

We study the properties of quantum single-particle wave pulses created by sharp-edged or apodized shutters with single or periodic openings. In particular, we examine the visibility of diffraction fringes depending on evolution time and temperature; the purity of the state depending on the opening-time window; the accuracy of a simplified description which uses ``source'' boundary conditions instead of solving an initial value problem; and the effects of apodization on the energy width.Comment: 11 pages, 11 figure

Exact propagators for atom-laser interactions

A class of exact propagators describing the interaction of an $N$-level atom with a set of on-resonance $\delta$-lasers is obtained by means of the Laplace transform method. State-selective mirrors are described in the limit of strong lasers. The ladder, V and $\Lambda$ configurations for a three-level atom are discussed. For the two level case, the transient effects arising as result of the interaction between both a semi-infinite beam and a wavepacket with the on-resonance laser are examined.Comment: 13 pages, 6 figure

Cluster analysis of the organic peaks in bulk mass spectra obtained during the 2002 New England Air Quality Study with an Aerodyne aerosol mass spectrometer

International audienceWe applied hierarchical cluster analysis to an Aerodyne aerosol mass spectrometer (AMS) bulk mass spectral dataset collected aboard the NOAA research vessel Ronald H. Brown during the 2002 New England Air Quality Study off the east coast of the United States. Emphasizing the organic peaks, the cluster analysis yielded a series of categories that are distinguishable with respect to their mass spectra and their occurrence as a function of time. The differences between the categories mainly arise from relative intensity changes rather than from the presence or absence of specific peaks. The most frequent category exhibits a strong signal at m/z 44 and represents oxidized organic matter most probably originating from both, anthropogenic as well as biogenic sources. On the basis of spectral and trace gas correlations, the second most common category with strong signals at m/z 29, 43, and 44 contains contributions from isoprene oxidation products. The third through the fifth most common categories have peak patterns characteristic of monoterpene oxidation products and were most frequently observed when air masses from monoterpene rich regions were sampled. Taken together, the second through the fifth most common categories represent as much as 5 µg/m3 organic aerosol mass ? 17% of the total organic mass ? that can be attributed to biogenic sources. These numbers have to be viewed as lower limits since the most common category was attributed to anthropogenic sources for this calculation. The cluster analysis was also very effective in identifying a few contaminated mass spectra that were not removed during pre-processing. This study demonstrates that hierarchical clustering is a useful tool to analyze the complex patterns of the organic peaks in bulk aerosol mass spectra from a field study