# E. Borie's research while affiliated with Karlsruhe Institute of Technology and other places

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## Publications (119)

This paper describes the design of a magnetron injection gun (MIG) for a 42GHz, 200 kW CW gyrotron operating in the TE5,2 mode. The design was performed using the BFCRAY code. The basic motivation is discussed and the design of the MIG is presented.

A recent proposal to measure the proton form factor by means of muon-proton
scattering will use muons which are not ultrarelativistic (and also not
nonrelativistic). The usual equations describing the scattering cross section
use the approximation that the scattered lepton (usually an electron) is
ultrarelativistic, with v/c approximately equal to...

This paper presents the design of a triode-type Magnetron Injection Gun (MIG) for a 460 GHz, 50–100 W gyrotron for Medical Spectroscopy operating at 25 KV and 0.1 A. The design is facilitated by determining the initial design following analytical expressions of Baird and Lawson1 and then carrying out the design optimization using available ESRAY tr...

In this paper, the design concept of a 460 GHz, 30-50 W, CW, second harmonic gyrotron for medical spectroscopy will be presented. Mode selection has been done keeping in view the second harmonic operation, first harmonic competitors, and a probable radial output system. Computation of starting currents has been carried out for the candidate mode co...

In this paper, our collaborative efforts on the design of specific high power gyrotrons that are being carried out at IIT-Roorkee and KIT will be presented. An up-date of our design studies on (i) a 42 GHz, 200-250 kW, long pulse / CW gyrotron (with up-tapered resonator section) for Indian Tokamak applications and (ii) CW/longpulse gyrotrons (conve...

In connection with recent and proposed experiments, and new theoretical
results, my previous calculations of the Lamb shift in muonic hydrogen will be
reviewed and compared with other work. In addition, numerical results for
muonic deuterium and helium will be presented. Some previously neglected (but
very small) effects are included.

In this work, an extensive design study of a 200-250 kW, CW gyrotron operating at 170 GHz, for plasma heating in an experimental Indian Tokamak is presented. Mode competition and mode selection procedures have been carried out for various candidate modes to choose a probable cavity operating mode. The present study includes cold cavity and self-con...

Design studies of a 1.0-1.3 MW, CW gyrotron operating at 170 GHz, for ECRH in the international thermonuclear fusion experiment (ITER) is presented. Mode competition and mode selection procedures have been carried out for various candidate modes to choose a probable cavity operating mode. The present study includes cold cavity and self-consistent d...

Summary form only given. In this work, design studies on a 200 to 250 kW, CW gyrotron operating in the TE<sub>0,3</sub> cavity mode with axial output collection will be presented. Such a device will be used for electron cyclotron resonance heating of plasmas in a small experimental tokamak in India. Cold cavity design and self-consistent calculatio...

Numerical experiments based on adequate, self-consistent physical models implemented in simulation codes are widely used for computer-aided design (CAD), analysis and optimization of the electron optical systems (EOS) of the gyrotrons. An essential part of the physical model is the emission model, i.e., the relations that govern the value of the be...

The design of a 1.0-1.3 MW, longpulse gyrotron operating at 127.5 GHz, for plasma start-up in the international thermonuclear fusion experiment (ITER) is presented. Cold cavity and self-consistent design calculations are used to compute power and efficiencies. Result indicates that an output power of over 1.3 MW can be achieved at 127.5 GHz with TE...

In this work, the initial design concept of a 1.0-1.5 MW, longpulse gyrotron operating at 120 GHz, for plasma start-up in the ITER has been presented. Mode competition and mode selection procedures are carried out for various candidate modes and the modes TE<sub>24,8</sub> or TE<sub>24,7</sub> are chosen as probable operating modes. Cold cavity des...

In this work, the on going design study on a 1.0-1.5 MW, CW gyrotron operating at 110 GHz, for plasma heating applications is reported. This work is a logical extension of the recent works on a similar type of gyrotron carried out elsewhere but with somewhat higher output power level. Rigorous mode selection procedures suggest that the modes TE<sub...

A design concept of a 250GHz, ≈ 50W, CW, second harmonic gyrotron for spectroscopy will be presented in this paper. Mode
competition, in particular with regard to competition with first harmonic modes, and mode selection procedures are carefully
investigated by considering various candidate modes and the TE6,2 and TE6,3 modes are chosen as probable...

The design concept of a 250 GHz, 50-100 W, CW, second harmonic gyrotron for spectroscopy will be presented. Initial results show that an output power of well over 50 W, CW can be achieved using the TE<sub>6,2</sub> or TE<sub>6,3</sub> cavity modes.

The feasibility of an 84 GHz, 500 kW, CW gyrotron for ECRH on an experimental tokamak will be presented in this paper. Mode
competition and mode selection procedures are carefully investigated by considering various candidate modes and the TE10,4 mode is chosen as the operating mode. A conventional cylindrical cavity resonator with weak input and o...

My previous calculations of the Lamb shift in muonic hydrogen are repeated for muonic deuterium.

The development of high power gyrotrons (118 GHz, 140 GHz) in continuous wave operation (CW) has been in progress for several years in a joint collaboration between different European research institutes and industrial partners. In this frame, two 140 GHz prototype gyrotrons for CW operation had been constructed and tested at the Forschungszentrum...

The feasibility of an 84 GHz, 500 kW, CW gyrotron for ECRH on an experimental tokamak is presented in the design study of this paper. Mode competition and mode selection procedures are carefully investigated by considering various candidate modes and the TE<sub>10,4</sub> mode is chosen as the operating mode. A suitable cold cavity is considered wi...

My previous calculations of the Lamb shift in muonic hydrogen are reviewed and compared with other work. In addition, numerical results for muonic deuterium are presented.

The results of some tests of QED are presented, which illustrate both the many-faceted role played by the coupling constant α and some of the problems which are encountered in precision calculations, especially of bound states.

A broadband quasi-optical (QO) mode converter for a multi-frequency gyrotron has been designed and tested at Forschungszentrum Karlsruhe (FZK). The launcher is optimized for the TE22,8 mode at 140 GHz, but the radiated beams present an almost identically focused pattern for all 9 considered modes between 105 GHz (TE17,6) and 143 GHz (TE23,8). Combi...

The Lamb shift in muonic hydrogen continues to be a subject of experimental
and theoretical investigation. Here my older work on the subject is updated to
provide a complementary calculation of the energies of the 2p-2s transitions in
muonic hydrogen.

Summary form only given. The R&D activities at Forschungszentrum Karlsruhe (FZK) on advanced high-power mm-wave gyrotrons for future use in electron cyclotron heating and current drive (EC H&CD) in fusion plasmas consist of: (1) the development of a coaxial cavity gyrotron capable of delivering 2 MW continuous wave (CW) at 170 GHz and (2) investiga...

To calculate the efficiency and output power, one must solve the equation of motion for a single electron traversing the resonator in the given electric and magnetic fields numerically and compute the energy loss or gain. The efficiency is then computed by averaging over an ensemble of electrons uniformly distributed in their initial gyration phase...

Experiments were performed with the 1 MW, CW 140 GHz prototype gyrotron for the stellarator W7-X. The maximum output power of 970 kW at an efficiency of 44% was achieved for a pulse length of 11.7 s. For 180 s, an output power of 890 kW could be obtained. At reduced output power of 540 kW, a pulse length of 939 s was achieved. The second prototype...

Although this is the era of solid state semiconductor devices, microwave tubes are still extensively employed in certain areas for applications where their solid state counterparts are not able to compete as far as delivering the required power at microwave to millimetric wavelengths. These applications vary from electron cyclotron resonance heatin...

At Forschungszentrum Karlsruhe (FZK) R&D investigations are performed both on a 2 MW, 170 GHz coaxial cavity gyrotron for ITER and on a stepwise frequency tunable 1 MW gyrotron for the ASDEX Upgrade tokamak (105–140 GHz). In case of the coaxial gyrotron the previously used experimental 165 GHz tube has been modified for operation at 170 GHz in orde...

The long term strategy of the EU in the field of gyrotrons in fusion plasma applications is based on two approaches: an R&D in laboratories to develop advanced concepts and industrial development of state of the art tubes for use in present experiments like TCV, Tore Supra (118 GHz, 0.5 MW-CW) and W7-X (140 GHz, 1 MW, CW). The results from these tw...

Output window design is one of the key issues for realizing broadband output of a multi-frequency gyrotron. Corresponding to the recent development of a frequency step-tunable 1 MW gyrotron at FZK, this paper reports about a newly designed ultra-broadband CVD-diamond disk Brewster window. The detailed calculations of mm-wave transmission characteri...

The quasi-optical mode converter for a frequency step-tunable gyrotron which consists of a dimpled-wall antenna (Denisov-type launcher) and a beam-forming mirror system has been optimized for 9 modes from TE17,6 at 105 GHz to TE23,8 at 143 GHz. The first mirror is a large quasi-elliptical focusing one; the second and third are phase-correcting mirr...

The development of high power gyrotrons in continuous wave operation for heating of plasmas used in nuclear fusion research has been in progress for several years in a collaboration between different European research institutes and industrial partners. The 140 GHz gyrotron is designed for an output power of 1 MW in continuous wave operation and is...

Gyrotrons are widely used in electron-cyclotron-plasma heating of fusion installations. Modern and future installations require microwave sources with power of at least 1 MW. There are two main directions in the development of megawatt gyrotrons at GYCOM. The first line is an enhancement of parameters for conventional gyrotrons. The main efforts ar...

The work reports about window design studies for both the JET EP ECRH project and the ASDEX-Upgrade ECRH system. Detailed calculations of the millimeter wave transmission characteristics for conventional single-disk windows, for frequency tunable double-disk windows and for ultra-broadband Brewster windows have been performed. The geometry of the w...

The modulation of the output power of a 140 GHz gyrotron for fusion plasma heating at the W7-X Stellarator is simulated numerically. It is shown that for appropriate beam properties, power modulation is possible. The output power shows almost no dependence on whether the accelerating voltage is being increased or decreased.

Gyrotrons at high frequency with high output power are mainly developed for microwave heating and current drive in plasmas for thermonuclear fusion. For the stellarator Wendelstein 7-X now under construction at IPP Greifswald, Germany, a 10 MW ECRH system is foreseen. A 1 MW, 140 GHz long-pulse gyrotron has been designed and a pre-prototype (Maquet...

This work reports about the influence of some window parameters, such as the mechanical tolerance of disk thickness, the variation of distance between two disks, and the frequency drift during gyrotron operation on the transmission characteristics of millimeter waves. Detailed calculations of the transmission characteristics for a single-disk gyrot...

Mode selection of a moderate power gyrotron operating at the ISM frequency and the second harmonic is discussed in detail. By analysis and calculation for electron beam-wave coupling, mode competition, voltage depression and limiting current, and ohmic losses, considering the compactness of the configuration, the result obtained is that TE31 mode i...

Gyrotrons at high frequency with high output power are mainly developed for microwave heating and current drive in plasmas for thermonuclear fusion. For the stellarator Wendelstein 7-X now under construction a 10 MW ECRH system is foreseen. A European collaboration has been established to develop and build the 10 gyrotrons each with an output power...

Electron cyclotron resonance heating (ECRH) is one of the most important candidates for plasma heating, non-inductive current drive, plasma start-up, profile control and MHD stabilization in the next generation of fusion plasma machines such as the ITER tokamak. Recent interest of the fusion community for radiation at several frequencies from the s...

The development of high power gyrotrons in continuous wave operation for heating of plasmas used in nuclear fusion research has been in progress for several years in a collaboration between different European research institutes and industrial partners. The 140 GHz gyrotron is designed for an output power of 1 MW in continuous wave operation and is...

In this paper, the possibility of a 42 GHz, 200 kW CW gyrotron, operating in the TE<sub>4,2</sub> mode at the second cyclotron harmonic, is presented. The study includes a mode selection procedure followed by cavity and interaction computation for power and efficiency. This device will serve as a heating source for a small experimental steady state...

The design of a multifrequency tunable 1 MW, 10 s gyrotron (105-140 GHz) for controlling plasma instabilities in fusion Tokamaks is presented. It operates in the TE<sub>22,8</sub> mode at 140 GHz and the TE<sub>17,6</sub> mode at 105 GHz and some other modes in between. It is equipped with a magnetron injection gun (diode type), a cylindrical cavit...

A TE22,6 gyrotron with conventional hollow cylindrical resonator has attained a maximum output power of 2.1 MW at 140 GHz and an efficiency of 34% (53% with depressed collector). Fast stepwise frequency-tunability with 1-s time steps has been demonstrated with this TE22,6 gyrotron at a power level of 1 MW. Fast frequency-tunable gyrotrons are of in...

The development of high power CW gyrotrons for ECRH heating of fusion relevant plasmas has been in progress for several years in a joint collaboration between different European research institutes and an industrial partner. Two development are on going, aiming, respectively, towards a 0.51-MW–210-s gyrotron at 118 GHz for the tokamaks TCV of CRPP...

Successful gyrotron experiments at FZK employing a conventional hollow cylindrical waveguide cavity, a quasi-optical mode converter with dimple-type launcher, a broadband silicon nitride Brewster window and a single-stage depressed collector (SDC), gave up to 1.6 MW output power at efficiencies between 48 and 60% for all operating mode series in th...

The operational features of a 140-GHz, transverse electric
TE<sub>22,6</sub> mode gyrotron oscillator with an advanced
quasi-optical mode converter, a Brewster window, and a single-stage
depressed collector at 140 GHz with an output power of 2.1 MW and an
efficiency of 34% without depressed collector and 53% with depressed
collector are presented....

This paper deals with the conceptual design of a 42 GHz, 200 kW continuous wave gyrotron operating in the TE 5,2 mode with radial output coupling. The basic motivation and selection criteria are discussed and the design of the resonant cavity, magnetron injection gun, radio frequency (RF) guiding system, quasioptical output coupler and RF window is...

This paper investigates the possibility of using Silicon Nitride Composite (Kyocera SN-287) as single-disc, edge-cooled window for gyrotrons operating below 200 kW CW in the frequency range 28-42 GHz. Rotationally symmetric TE0n, and TEM00 Gaussian modes of rf transmission through the window have been considered. Analysis performed using a one dime...

A continuous wave, 1 MW, 140 GHz gyrotron oscillator has been
designed and constructed as a joint collaboration between FZK Karlsruhe,
CRPP Lausanne, IPF Stuttgart, CEA Cadarache and TTE Velizy for the 10 MW
ECRH system of the new stellarator plasma physics experiment,
Wendelstein 7-X, at IPP Greifswald, Germany. The tube is equipped with a
diode M...

Summary form only given. One of the major obstacles to the use of
high frequency (> 10 GHz) microwaves for technological applications
is the fact that suitable, inexpensive, easy-to-use sources are not
readily available. In this study, we consider the possibility of a
moderate power (25-50 kW) gyrotron operating at the ISM (industrial,
scientific,...

A nonlinear numerical simulation of a second harmonic gyrotron oscillator is presented in this paper. Mode competition from a competing fundamental mode is investigated. In addition, a self-consistent nonlinear theoretical model, including the effect of velocity spread, is applied to analyze the second harmonic gyrotron. A series of numerical calcu...

In this work, the field analysis of a cylindrical interaction structure, with helical grooves, and an inner dielectric lining for possible employment in high power TWT amplifiers in the conventional slow-wave regime, is presented. The Ohmic dominance of the microwave power on the walls of this propagating circuit is deduced.

A one - dimensional finite - difference computer code has been developed and shown to be quite effective in thermal design and analysis of various plane edge-cooled single - disc windows for gyrotrons with Gaussian rf beam output. The program has a modular structure and is flexible enough to suit specific requirements of users; it can handle nonlin...

Beam instabilities that arise in the compression zone of a gyrotron oscillator can degrade the beam quality and hence adversely affect the operating characteristics of these devices. We concentrated on the study of a class of space charge instabilities that are closely related to unstable Bernstein modes. These are investigated both by solving the...

The effects of the roughness of the cathode surface on the emittance of an electron beam in a gyrotron gun are investigated.
Parameter studies using a very simple model are performed in order to determine a reasonable parametrization of the effect
for use in the BFCPIC and BFCRAY codes. Calculations are then performed for a gun in use at FZK.

Numerical modelling of an electron gun in the space charge limited regime requires determining the current density distribution
as well as the electric fields and electron trajectories. This is a rather complicated self-consistent problem, since the
space charge influences the electric field, which in turn influences the electron trajectories. Prev...

Note: Proc. 18th Symposium on Fusion Technology, Karlsruhe, Germany, August 1994, Vol. 1, 489 - 492 (1995) ISBN 0 444 82220 8 Reference CRPP-CONF-1995-042 Record created on 2008-05-13, modified on 2016-08-08

A TE 10, 4 gyrotron oscillator with advanced built-in quasi-optical mode converter and radial output in TEM 00 (94.5% mode purity) was operated at 0.50 MW with 8 ms pulse duration and 32% output efficiency (38% electronic efficiency). The maximum output power was 0.6 MW (12 ms) at 27% output efficiency. In first proof of principle experiments this...

A quasi-stationary particle-in-cell code based on the use of boundary fitted coordinates has been adapted for use in the simulation of magnetron injection guns for gyrotrons. In addition, a ray tracing version has been written, since this is more convenient for parameter studies. Results calculated with these codes are in good agreement with experi...

A high-power cylindrical cavity gyrotron operating at 140 GHz is studied. The possible working modes TE22,4, TE22,5, and TE22,6,are compared. The output power envisaged is 1 MW. The influence of the space charge effect of the electron beam and the RF losses in the resonator are discussed. Results of numerical calculations of the interaction of the...

The design of a 0.5 MW 140 GHz gyrotron with axial RF output
operating in the TE<sub>10,4</sub> mode is presented. Experimental
results and numerical simulations are compared. In particular the
effects of RF reflections at the output window, velocity spread of the
helical electron beam and startup of oscillations by simultaneous
increase of pitch f...

Calculations related to the high frequency, step tunable gyrotrons designed to operate in the submillimeter region, as reported by workers at Fukui University and the University of Sydney are presented. The modes probably have a rotating structure, in general. Results for mode competition are very similar to those calculated previously, in spite of...

Summary form only given. The state of development work at KfK
Kernforschungszentrum Karlsruhe on 140-GHz high-power gyrotrons for EC
wave applications is presented. In particular, the design and
experimental results for a 0.5-MW TE<sub>10,4</sub> gyrotron with axial
RF output coupling are discussed. An RF output power up to 0.69 MW at
pulse lengths...

The equations for a fully self-consistent theory of mode competition in gyrotrons are derived and some possible methods of solution are discussed. The importance of including interaction in the resonator output taper is discussed in connection with the validity of linearizing the equations in the amplitude of the parasitic mode.

The gyrotron is a powerful source of millimetre wave radiation. Fusion applications require more power per tube than is currently available This in turn means that the resonator must be highly overmoded, with a dense mode spectrum, which leads to mode competition. The influence of external parameters, such as the applied magnetic field, electron be...

The effect of the voltage depression due to space charge on the beam parameters in a gyrotron is investigated. Although the voltage depression can be compensated to some extent by increasing the beam voltage, some loss of efficiency is to be expected, especially in the case of high currents and volume modes.

Rieke diagrams provide a useful way of estimating the effect of reflections from the window on gyrotron performance. In some cases, a small change in the reflection coefficient can have a large effect on the output power and on the resonator wall losses. Rieke diagrams can also be useful in determining whether or not a mode will oscillate at all fo...

Etude de l'effet de repartition du champ magnetique sur le fonctionnement d'un resonateur gyrotron. Les equations de calcul tiennent compte de l'effet de mouvement longitudinal des electrons et negligent les champs magnetiques a haute frequence et les derives des centres de guidage. On calcule numeriquement l'efficacite en fonction de la geometrie...

This article describes briefly the physical effects contributing to the energy levels of antiprotonic atoms and provides a description of a code PBAR that has been written to calculate the electromagnetic contribution.

Two approaches to the study of a complex cavity with mode conversion are developed. In the first method a system of coupled second order differential equations, which takes into account the non-principal modes, is solved. This method is applicable to cavities with gradual transition. The second method is based on the use of a field-matching techniq...

The authors present alternative methods for the calculation of the starting current in a gyrotron, and an analysis of the excitation of parasitic modes in gyrotrons operating in a given mode. Numerical examples are presented which check the validity of some of the assumptions made, and the extension of the formalism to the investigation of the stab...

The present note describes the results of parameter studies undertaken to select resonators for a series of experiments on a gyrotron operating in the TE06 mode, and for another series aimed at studying the advantages of coupled resonators (in this case TE02/TE06 or TE03/TE06)

The startup of a gyrotron with a tapered resonator section operating at 150 GHz in the TE03-mode has been investigated with special emphasis on mode competition. Calculations show that multimoding occurs only for high currents and a small range of magnetic field strengths. Thus pure TE03 operation with powers exceeding 200 kW seems to be possible f...

The efficiency of a gyrotron resonator as a function of resonator geometry, applied magnetic field and electron beam parameters is studied in the adiabatic cold cavity fixed field approximation. The results are used as a guide for the selection of design parameters for experiments at the Kernforschungszentrum Karlsruhe, West Germany. Criteria for s...

The paper shows the calculation of the resonant frequency, Q-value and field profiles of the eigenmodes of tapered gyrotron resonators, taking into account the coupling of modes induced by the taper. The mode coupling is negligible for taper angles of only a few degrees, but must be taken into account if the taper angle exceeds about 10°.

A self consistent calculation for gyrotron oscillators is described and applied to a TE03 mode gyromonotron. The RF field profile satisfies a wave equation in which the AC beam current appears as a source. The wave equation is solved simultaneously with the electron equation of motion.

Electromagnetic processes at low momentum transfer are often sources of background in many experiments. To be removed these effects must be calculated by the experimentalist, who must have a good knowledge of the validity of the theoretical formulas that he must use. Then we thought that it will be useful to prepare this review whose presentation i...

In view of the interest in studying the p̄p system in gas at low to moderate pressures, it has seemed worthwhile to extend previous calculations1 of the atomic cascade to provide the best possible estimates of the yields of K- and L-x rays in protonium as a function of target pressure. The processes involved — Stark mixing, annihilation, chemical (...

During the past several years a great amount of work has been performed on the prediction of NN̄ resonances within the framework of a nonrelativistic potential model.1–4 Such models are based on one boson exchange potentials (OBE) which have been developed for the case of NN̄ scattering. The real part of the NN potential is then obtained by a G-par...

Future precision measurements of the energies of x-ray transitions in antiprotonic atoms will require similarly precise calculations of all electromagnetic effects in order to be able to analyse the data for measurements of the antiproton’s mass and magnetic moment or in order to be able to extract accurate hadronic shifts and widths. For this reas...

Precise calculations of the energy levels and fine structure of antiprotonic atoms, in which the normal and anomalous magnetic moments of the antiproton are treated on an equal basis and vacuum polarization and relativistic recoil corrections are included, are presented. The results are applied to measurements of the antiproton mass and anomalous m...

The theory of muonic atoms is a complex and highly developed combination of nuclear physics, atomic physics, and quantum electrodynamics. Perhaps nowhere else in microscopic physics are such diverse branches so intimately intertwined and yet readily available for precise experimental verification or rejection. In the present review we summarize and...

The analytic expression for the differential pair production cross section, obtained using full Furry-Sommerfeld-Maue wave functions for the electron and positron, is integrated numerically over angles without further approximation. The resulting Coulomb corrections to the total pair production cross section are compared with existing interpolation...

An evaluation of previously uncalculated finite size effects on the Lamb shift of normal atoms, with use of methods which are well known from muonic atoms, gives corrections which are larger than the experimental uncertainties (40 ppm for the Lamb shift in hydrogen). The additional corrections tend to restore agreement between theory and experiment...

The contribution of hadronic vacuum polarization to the energy levels of muonic atoms is reevaluated using an improved parametrization of the total cross section for e+ e–hadrons. The numerical results can be simply related to the correction due to muonic vacuum polarization.