Statistics with fuzzy data in statistical quality control

Statistical quality control (SQC) is an important field where both theory of probability and theory of fuzzy sets may be used. In the paper we give a short overview of basic problems of SQC that have been solved using both these theories simultaneously. Some new results on the applications of fuzzy sets in SQC are presented in details. We also present problems which are still open, and whose solution should definitely increase the applicability of fuzzy sets in quality control.     

Analysis of Aftercavity Interaction in European ITER Gyrotrons and in the Compact Sub-THz Gyrotron FU CW-CI

Possibilities of arising of aftercavity interaction are analyzed in the ITER 170?GHz 2?MW coaxial cavity gyrotron and the 170?GHz 1?MW cylindrical cavity gyrotron, as well as in the compact 394.5?GHz low power gyrotron FU CW-CI. Also, the simulations for the gyrotron efficiency in the presence of aftercavity interaction are performed in the cold cavity approximation. Results of the analysis illustrate the subtle interplay between the geometry of the output taper and the profile of the magnetic field.     

On a self-consistent calculation of the self-modulation instability in gyrotrons operating in whispering gallery modes

A self—consistent calculation of the self—modulation instability in gyrotrons operating in whispering gallery modes is carried out in the cold cavity approximation for satellite modes. The approach is illustrated numerically in the case of the planned operation of the KfK gyrotron in the TE_10,4 mode.     

Design of Cavities for a Short Pulse Powerful Large Orbit Gyrotron

Designs of cavities for fundamental and high harmonic operation in Large Orbit Gyrotron (LOG) are discussed. The fundamental operation allows one to use beam currents in the range from 200 A to 300 A achieve output power of the order of 9–10 MW at frequency 143.6 GHz. Mode competition calculations show that stable oscillations in the TE^1,4 mode using high beam currents are possible even with the pitch factor 1.3 which is significantly lower than the design value 1.55. For the second harmonic operation, the maximum current used for excitation of the TE^2,4 mode is 60 A and the optimum magnetic field is 7.6 T. A cavity design for fourth harmonic operation using the TE^4,4 mode is also presented.     

Mode Selection for a Terahertz Gyrotron Based on a Pulse Magnet System

The TE_6,11 mode has been selected as a candidate for the second harmonic operation of a terahertz gyrotron at 1007.68 GHz. The predicted efficiency is 8.6 percent for the output power 0.38 kW. Time-dependent, multi-mode calculations have been carried out to investigate stability of a single-mode operation at second harmonic. It has been found that with the beam current 0.111 A and the magnetic field 19.282 T the second harmonic operation in the TE_6,11 mode is possible.     

Variations of internal friction in YBa2Cu3Ox superconductors

The internal friction (Q ^–1) spectrum of YBa₂Cu₃O_x superconducting ceramic exhibits several peaks. It has been confirmed that the high-temperature peak (around 240 K) depends on structural changes and varies during subsequent cycles of cooling and heating.Q ^–1 conductivity, X-ray spectra and the shielding effect have been measured on several samples having different superconducting properties obtained by various thermal treatments. Splitting is a characteristic feature of the high-temperature internal friction peak of the sample which exhibits good superconducting properties. In the case of the specimen exhibiting the worst properties the peaks decrease and overlap. In both cases an increase can be observed of this peak with the number of thermal cycles. After ageing at 470 K, the high-temperature peak disappears. Subsequent thermal cycles slightly recover it. Hysteresis of the Young modulus is also observed. The results are interpreted as transition of the 04 oxygen atom between two energy minima in the O4-Cu-O4 chain.     

Are Coaxial Super Power Gyrotrons Feasible?

Limits on the power generated by coaxial gyrotrons are investigated. It is shown that among all the operating modes suggested recently for coaxial super power gyrotrons only modes with azimuthal index m lower than about 44 pass the spatial stochasticity test. Modes with higher azimuthal indices cannot be used as operating modes because gyrotron oscillations become chaotic in the azimuthal direction and efficiency is very low. It is argued that there exists a natural upper limit on power generated by gyrotrons which is about 4 MW.     

Possible operation of the KfK gyrotron at harmonics

Expected efficiencies for the possible operation of the KfK gyrotron at the first, second and third harmonics are estimated. The results obtained in the cold cavity approximation and in self-consistent calculations are compared. Mode competition between the modes operating at the fundamental and at the second harmonic is investigated. Regions of stable single-mode generation are established. Effect of the the magnetic field tapering on the mode competition is illustrated.