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We study the possibility of implementing a higher efficiency gyrotron intended for plasma heating in advanced nuclear fusion facilities. To increase the efficiency above the standardly attainable value of about 50%, it is proposed to use an electron beam with a high oscillatory energy and a low-velocity spread, which can be formed in a nonadiabatic electron-optical system. Based on numerical simulations of electron–wave interaction, we demonstrate that the efficiency of a 230-GHz megawatt (MW)-level gyrotron with a single-stage energy recovery system can exceed 75%.

It was shown recently by M. Lorentz and R. Willett that all bounded derivations of the uniform Roe algebras of metric spaces of bounded geometry are inner. Here we calculate the space of outer derivations of the uniform Roe algebras with coefficients in uniform Roe bimodules related to various metrics on the two copies of the given space. We also give some results on the higher Hochschild cohomology with coefficients in uniform Roe bimodules.

Abstract: Kazhdan’s property (T) for groups is equivalent to the alternative that a representation of such a group either has an invariant vector or does not have even almost invariant vectors. It is shown that, under a somewhat stronger condition due to Żuk, a similar alternative holds for almost representations.

The development of oscillations of the space charge and potential in the adiabatic trap of a gyrotron between the cathode and the cavity is studied numerically. The PIC method is applied, with the real two-dimensional distributions of the electric and magnetic fields taken into account. Secondary emission is included into the numerical model, as well as such factors as the electron beam space charge, thermal velocities of electrons, and emitter roughness. The value of the trapped space charge as a function of time is calculated. Time dependences of the potential in various cross-sections of the formation system are traced. The amplitudes of its variable component have been found and then the corresponding frequency spectra have been calculated. The process of cathode bombardment is investigated. The energy distribution and time dependence of the current in the electron beam coming to the operating space are found. Some ways to reduce the oscillations of the potential and the space charge are discussed.

High power Large Orbit Gyrotron (LOG) [1] is now under development at FIR FU. First version of this device was recently manufactured and then assembled with power supply ETIGO-IV [2]. Results of preliminary tests of electron-optic system are presented. The conditions when stableflat form of current pulse realized are discussed. Analytical estimations of cathode-anode distance to achieve small influence of cathode plasma during high voltage (HV) pulse are performed.

According to simulations, a Large Orbit Gyrotron with a 30 keV/1 A electron beam and magnetic field of 5 T can produce CW radiation with output power of 102−103W at the frequencies of 0.4–0.5 THz.

High power Large Orbit Gyrotron (LOG) [1] is now under development at FIR FU. First version of this device was recently manufactured and then assembled with power supply ETIGO-IV [2]. Results of preliminary tests of electron-optic system are presented. The conditions when stable flat form of current pulse realized are discussed. Analytical estimations of cathode-anode distance to achieve small influence of cathode plasma during high voltage (HV) pulse are performed.

We introduce a new asymptotic one-sided and symmetric tensor norm, the latter of which can be considered as the minimal tensor norm on the category of separable C*-algebras with homotopy classes of asymptotic homomorphisms as morphisms. We show that the one-sided asymptotic tensor norm differs in general from both the minimal and the maximal tensor norms and discuss its relation to semi-invertibility of C*-extensions.

Abstract Let A and B be C*-algebras, let A be separable, and let B be σ-unital and stable. We introduce the notion of translation invariance for asymptotic homomorphisms from S A = C0(ℝ) ⊗ A to B and show that the Connes—Higson construction applied to any extension of A by B is homotopic to a translation invariant asymptotic homomorphism. In the other direction we give a construction which produces extensions of A by B from a translation invariant asymptotic homomorphism. This leads to our main result that the homotopy classes of extensions coincide with the homotopy classes of translation invariant asymptotic homomorphisms.

Abstract. Short-pulse powerful Large Orbit Gyrotron with total electron energy about 400 kV and beam power in the cavity up to 100 MW is now under developing at FIR FU. Suitable for 200 ns pulse duration electron-optic system is analyzed. Results of numerical simulation for explosion emission cusp-type electron guns and magnetic field intensity about 8 T are presented. Sensitivity of the guns to small deviations from the nominal operating regime is investigated. Some versions of the gun with different accelerating potential as well as different beam current passing through the cavity (60-300A) are suggested. Current reduction simplifies the problems of mode competition and potential depression in the cavity, but at the same time decrease output power. To diminish current special diaphragms are suggested. Results of numerical simulation of collector corresponding to each version of the gun design including power density distributions along its surface are presented. It is shown that beam quality and collector regimes are suitable for LOG operation.

The paper presents results of numerical analysis and outlines the computer-aided design of a novel high-harmonic gyrotron with a beam of electrons gyrating along axis-encircling trajectories. The electron beam is formed by a novel electron-optical system (EOS) based on an electron gun of diode type with thermionic cathode and gradual reversal of the magnetic field. The results of numerical simulations predict satisfactory performance of the EOS and appropriate beam quality parameters. The tube design allows one to install different cavities optimized for excitation of TE4,1mode at the fourth harmonic of the cyclotron frequency or TE3,1mode at the third one. The target parameters of the device are: frequency about 112 GHz; output power near 1 kW and efficiency of several percent.

Main results of experimental testing of the 140 GHz/1.5 MW coaxial gyrotron are summarized. High selective properties of the coaxial cavities and a possibility to increase considerably the efficiency of a coaxial gyrotron only by applying independently an appropriate voltage on its electrodes (without any design modification) have been confirmed. Successful uses of the two-potential connection scheme for the frequency step tuning and output power modulation in a coaxial gyrotron has been also demonstrated.

Potentialities of different numerical models for calculation of helical electron beams parameters are analyzed. The most simple and economical with respect to the calculation time static mono-velocity model, as well as the model considering initial velocities of electrons and the dynamic model based on the PIC-method and on the quasi-static concept of the electric field are described. The main physical results obtained on the basis if each model mentioned above are given.

An almost representation of a group is a map from this group into the unitary group of a Hilbert space, such that the group relations hold only approximately. We give a survey of the recent results on almost representations and on their relations to asymptotic representations. Applications to K-theory of classifying spaces are also discussed.

Abstract: We study theC*-aglebras related to Mishchenko’s version of asymptotic homomorphisms. In particular, we show that their different versions are weakly homotopy equivalent but not isomorphic to each other. We also present continuous versions of these algebras.

The paper presents a modern approach to studies of characteristics of intense helical electron beams (HEBs) for gyrotrons. The essence of the method consists in finding functions of electron distribution with respect to oscillatory velocities in the beam both by numerical simulation and experimentally. Experimental and calculated data for beams with different topologies were compared in different frequency ranges. Evolution of the electron oscillatory velocities distribution function as the beam current grows has been traced. Influence of the reflected electrons on beam parameters has been simulated numerically.

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Geometry and practicability are considered for various forms of double-beam magnetron injector guns, which produce spiral beams for high-power gyrotrons. Path analyses are considered for double-beam electron-optical systems, which confirm that one can obtain acceptable parameters for both beams.

The calculation method is based on direct satisfaction of the condition of a zero normal electric field on the emitter by means of an iteration procedure that makes it unnecessary to obtain self-consistent solutions of the stationary-beam equations in individual iterations. The method employs auxiliary potential and space-charge nets for solution of the boundary-value problem and eliminates the idle nodes of the auxiliary potential net. The method is effective in the analysis of curvilinear beams and has been tested in the design of a Meltzer gun with circular trajectories and a strongly nonuniform transverse current distribution.

It is known that a continuous family of compact self-adjoint operators can be diagonalized pointwise. One can consider this fact as a possibility of diagonalization of the compact operators on Hilbert modules over a commutativeW*-algebra. The aim of the present paper is to generalize this fact to a finiteW*-algebraA not necessarily commutative. We prove that for a compact operatorK acting on the right HilbertA-moduleH*A dual toHA under slight restrictions one can find a set of “eigenvectors”xi eH*A and a non-increasing sequence of “eigenvalues” ?i eA such thatK xi=xi ?i and the selfdual HilbertA-module generated by these “eigenvectors” is the wholeH*A. As an application we consider the Schrödinger operator in a magnetic field with irrational magnetic flow as an operator acting on a Hilbert module over the irrational rotation algebraA? and discuss the possibility of its diagonalization.

Conclusions The present paper gives the results of the elaboration of a mathematical model of the radial motion of the plasma filament in tokamak thermonuclear machines with account for its ohmic resistance as well as the total flux linkage of the circuit formed in the plasma filament. At the same time, no account was taken of the effect of the metallic structures of the machine on the radial motion of the plasma filament. A significant limitation on the applicability of this model is the requirement of a small slope for the plasma filament (a/r=1). Under these conditions it has been shown that the motion of the plasma filament from one equilibrium position to another under a change in the vertical magnetic field is of a complex nature. The parameters of the elements of the motion depend markedly on the initial characteristics of the plasma filament.

Helical electron beams (HEB) with disturbed axial symmetry of currents density and HEB with locking electrons in magnetic trap are described. The theory of magnetron injection gun (MIG) in space-charge limited current is developed. Systems on permanent magnets forming HEB are considered.

Abstract: The posibility to use the version of plane cross-section method for analisys of the axisymmetrical oversized waveguide sructures with one and two-coupled cross-section is considered. The solution of the methodical problem about principal wave scattering at the joint of coaxial and circular waveguides is presented.

Abstract: The method of calculation of the circular oversized waveguide filled in with insulator using the method of plane cross-section (PCS) is developed. The wave scattering on the output insulator window for powerful occilator is investigated.

Energy distributions of electrons after their interaction with RF field in the gyrotron with the output power 1 MW and frequency 140 GHz are calculated. The energy spectra evolution is studied for the cases when velocity spread, pitch-factor, beam current and cyclotron frequency change. The efficiency of one- and two stage energy recovery systems are investigated.

The results of two experiments with a gyrotron operating at the second gyrofrequency harmonic, using two active electron beams, are reported. The internal (additional) beam is coupled weakly to the field by a spurious mode. The currents of the two beams can be controlled independently. The output characteristics of the gyrotons are plotted for various beam currents. The additional beam substantially enhances the operating mode stability and makes an appreciable contribution to the output power. The maximum output power was 0.87 MW at 25% efficiency, beam currents of 57 A and 13 A, and voltage 60 kV. The highest efficiency was 40%. The results suggest that electron-optical systems with two active beams, regardless of some complications of gun design, are promising for short-wave gyrotrons to operate at the fundamental cyclotron resonance. The specific power dissipation in the collector is observed to decrease (in comparison with a single-beam analog).

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We show that the group of a -algebra can be defined as the homotopy classes of pairs of matrices over that have equal defect from being unitary. We also consider pairs of pseudodifferential operators, not necessarily elliptic, with symbols forming a balanced pair. A relative index is defined for such pairs of operators, and it is proved to be equal to the topological index of the pair of symbols.

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