Random Unitaries Give Quantum Expanders

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the typical value of the second largest eigenvalue. The key idea is the use of Schwinger-Dyson equations from lattice gauge theory to efficiently compute averages over the unitary group.Comment: 14 pages, 1 figur

Effect of surface modes on coupling to fast waves in the LHRF

The effect of surface modes of propagation on coupling to fast waves in the LHRF is studied theoretically and experimentally. The previously reported up-down' poloidal phasing asymmetry for coupling to a uniform plasma is shown to be due to the properties of a mode which carries energy along the plasma-conducting wall interface. Comparison of the theory with coupling experiments performed on the PLT tokamak with a phased array of twelve dielectric-loaded waveguides at 800 MHz shows that the observed dependence of the net reflection coefficient on toroidal phase angle can be explained only if the surface wave is taken into account. 43 refs., 10 figs

Fast wave antenna array feed circuits tolerant of time-varying loading for DIII-D

Three different transmission line configurations for operating a four-element antenna array with a single rf power source are compared. The goal of this study is to obtain a system that presents a matched load to the generator despite variation of the loading of the array elements due to changing plasma conditions

Plasma mass density, species mix and fluctuation diagnostics using fast Alfven wave

The authors propose to employ a fast Alfven wave interferometer and reflectometer as a tokamak diagnostic to measure the plasma mass density, D-T species mix profile, and density fluctuations. Utilize the property that the phase velocity of the fast wave propagating across the magnetic field is the Alfven speed with thermal correction, this fast wave interferometer on the DIII-D tokamak was successfully used to obtain the line integrated density. Since the position of the ion-ion hybrid cut-off in tokamaks is uniquely determined by the species mix ratio and the wave frequency, the reflectometer arrangement finds the species mix profile. The inversion method of reflectometry is discussed. The multiple chord interferometer also measures the mass density fluctuation profile

Calculation of coupling to slow and fast waves in the LHRF from phased waveguide arrays

A previously reported algorithm for solving the problem of coupling electromagnetic energy in the LHRF from a phased array of identical rectangular waveguides to a plane-stratified, magnetized cold plasma is numerically implemented. The resulting computer codes are sufficiently general to allow for an arbitrary number of waveguides with finite dimensions in both poloidal and toroidal directions, and are thus capable of computing coupling to both slow and fast waves in the plasma. Some of the details of the implementation and the extension of the algorithm to allow study of the Fourier spectrum of slow and fast waves launched by the array are discussed. Good agreement is found with previously reported, less general work for the slow wave launching case. The effect of phasing multirow arrays in the poloidal direction is studied, and an asymmetry between phasing 'up' and 'down' is found that persists in the case where the plasma adjacent to the array is uniform. A 4 x 3 array designed to launch fast waves of high phase velocity is studied. By using the optimal poloidal phasing, low reflection coefficients (absolute value of R/sup 2/ less than or equal to 20%) are found under some not unrealistic edge plasma conditions, but most of the input power is trapped in the outermost layer of the plasma. Implications of our results for fast wave current drive experiments are discussed

Development of fast wave systems tolerant of time-varying loading

A new approach to fast wave antenna array design based on the traveling wave antenna has been successfully demonstrated on the JFT-2M tokamak. A traveling wave antenna is powered though a single feed and the power flow from element to element is only via mutual reactive coupling. A combine is a particular type of traveling wave antenna, in which only the fed element and the element at the downstream end of the array are connected to vacuum feed troughs, while the intermediate elements are terminated with reactances inside the vacuum chamber. A twelve element combine for operation at 200 MHz was designed and fabricated at General Atomics, and installed and operated on the JFT-2M tokamak. The full output power of a single transmitter, 0.2 MW, was coupled to tokamak discharges with very little conditioning required. The input impedance of the combine was well matched to the transmission line impedance for all loading conditions, including vacuum (no plasma), Taylor discharge cleaning plasmas, and ohmic, L- and H-mode tokamak discharges with neutral beam heating without any adjustment of tuning elements

A novel Doppler backscattering (DBS) system to simultaneously monitor radio frequency plasma fluctuations and low frequency turbulence

A novel quadrature Doppler Backscattering (DBS) system has been developed and optimized for the E-band (60-90GHz) frequency range using either O-mode or X-mode polarization in DIII-D plasmas. In general, DBS measures the amplitude of density fluctuations and their velocity in the lab frame. The system can simultaneously monitor both low-frequency turbulence (f < 10MHz) and radiofrequency plasma density fluctuations over a selectable frequency range (20-500 MHz). Detection of high-frequency fluctuations has been demonstrated for low harmonics of the ion cyclotron frequency (e.g., 2fci~23MHz) and externally driven high-frequency helicon waves (f = 476MHz) using an adjustable frequency down conversion system. Importantly, this extends the application of DBS to a high-frequency spectral domain while maintaining important turbulence and flow measurement capabilities. This unique system has low phase noise, good temporal resolution (sub-millisecond) and excellent wavenumber coverage (k_{\theta} ~ 1-20cm^{-1} and k_r ~ 20-30cm^{-1}). As a demonstration, localized internal DIII-D plasma measurements are presented from turbulence (f = 20MHz) as well as fluctuations around 476MHz driven by an external high-power 476 MHz helicon wave antenna. In the future, helicon measurements will be used to validate GENRAY and AORSA modeling tools for prediction of helicon wave propagation, absorption and current drive location for the newly installed helicon current drive system on DIII-D.Comment: 13 pages, 14 figs, journal pape

Improved tuning and matching of ion cyclotron systems

Future fusion devices will require delivery of ion cyclotron heating and current drive power during plasma changes (e.g., L-H transition, ELMs). The use of a passive circuit (``ELM dump``) to protect the RF sources during transients has been demonstrated on DIII-D, and the results are applied to the ITER ion cyclotron system in this analysis. In addition, the use of frequency shifting to compensate for plasma load changes is illustrated for a possible ITER tuning and matching system