This volume contains the proceedings of the International Winter School on Electronic Properties of High Temperature Superconductors, which was held March 3-10, 1990, in Kirchberg (Tyrol), Austria. This course was a sequel to three meetings on the subject of conducting polymers held there one, three and five years previously. The new topic was taken up since many of the scientists working on conducting polymers are now also actively interested in high-Tc superconductors, a research area that continues to develop at a remarkable pace. There have been numerous specialist conferences on high-Tc superconductors since their discovery by Bednorz and Muller in 1986. The Kirchberg meetings are intended as a school where experienced scientists from universities, research laboratories, and industry have the opportunity to discuss their most recent results, and where young scientists and students can learn about the present status of research in this field. The 1990 winter school was again organized in cooperation with the "Bundesministerium fur Wissenschaft in Austria and with the "Bundesministerium fur Forschung und Forschung" und Technologie" in the Federal Republic of Germany. The scientific interest was focused on the electronic structure of high-Tc superconductors and related compounds. At the beginning of each session, tutorial contributions were presented as an introduction for non-specialists. These were followed by research contributions elucidating the current state of our know ledge about high-Tc superconductors.

This volume contains the proceedings of the first ISSP International Symposium on the Physics and Chemistry of Organic Superconductors, which was held at the Komaba Eminence Hotel in Tokyo, August 28-30, 1989. This symposium was attended by 205 scientists from 12 countries. In total 106 papers were presented: 61 as posters, and 39 original papers and 6 review papers in oral sessions. Of these, 102 papers are included in these proceedings. These contributions cover the interdisciplinary field of physics and chemistry of organic superconductors with particular emphasis on the following subjects and materials: - superconducting properties, - spin density waves, - electronic and structural properties, - TMTSF salts and their derivatives, - BEDT -TTF salts and their derivatives, - metal coordinated organic conductors. The contributions to this volume are arranged in 11 categories. The Organizing Committee would like to acknowledge all participants, who contributed to the great success of this symposium on a growing field in both physics and chemistry. The editors express their gratitude to the members of the Organizing and Executive Committees for their cooperation. We also wish to thank Dr. H. Lotsch of Springer-Verlag for his management of the publication and Miss S. Shibata for her assistance in editing this volume.

The renaissance of magnet technology started in the early 1950s with the establishment of high-energy accelerators. About a decade later in 1961, or fifty years after the discovery of superconductivity, high-field superconducting laboratory magnets became a reality. Conventional still the major beam-handling and experimen electromagnets, which are tal devices used in laboratories, operate at zero efficiency. To generate high magnetic fields in a useful volume, considerable amounts of power are needed. Superconducting d. c. magnets do not require any power at all. It is somewhat depressing to note that, sixty years after the first superconductor was tested, the experimental d. c. superconducting mag net is still the only large-scale equipment operated in laboratories. Al though there has been considerable activity in the area of superconduc tivity, superconductors are used on quite a modest scale in electronic and quantum devices, in medicine and biology, and in physical experi ments where high magnetic fields are essential. It is only recently that Type II superconductors have been introduced in power engineering (power generation, storage and transport) to replace pulsed accelerator magnets; for fast and economical transportation vehicles (levitated trains) where superconductors may ultimately replace the wheel; to make new means of en rgy generation economically feasible, such as in magneto hydrodynamics and in fusion reactors; and for high-efficiency electric motors. High-field superconducting magnets are being proposed for de salination of seawater, for magnetic separation in the mining industry, for cleaning polluted water, and for sewage treatment."

Recent research on superconductors with high critical temperature has led to results that were not available when the original German edition was prepared but could be included in the present English edition. This concerns materials based on bismuth and thallium, as well as measurements of low microwave loss. The author would like to thank Mr. A. H. Armstrong for translating the book from German to English in a very dedicated and competent manner. Thanks are also due once again to Springer-Verlag for their generous support and cordial cooperation. Bad Salzdetfurth September 1989 Johann H. Rinken Preface to the German Edition The development of materials which lose their electrical resistance when cooled, even before reaching the boiling point of liquid nitrogen, has considerably in creased the interest in superconductor technology, and with it superconductor electronics. This development had not been foreseen when work on the present book started, just over a year ago. Nevertheless, recent results of research on materials with high critical temperature are included to the extent that they seem to be confirmed and to be of interest to superconductor electronics. The present book deals with the physical and technological foundations of superconductor electronics so far as they must be known in order to under stand the principal modes of operation of superconductor electronics components.

The sixth Taniguchi Symposium on the Theory of Condensed Matter was held between 14-18 November 1983 at Kashikojima. Japan. During the Symposium, about twenty participants lived together and discussed the magnetic super conductors and related problems in an active and friendly atmosphere. This volume contains the papers presented at this Symposium. A strong impetus for organizing a Symposium of this subject is afforded by recent intense interest and accumulated information on magnetic and other novel superconductors newly discovered, and indeed the Symposium has pro duced many excellent contributions to this very exciting field of condensed matter theory, as reported in this volume. In order to give the readers a general outline of the subject, a brief sketch of the problem is made in the Introduction. Then the remainder of this volume is divided into four Parts and an Appendix. Part I is devoted to di scuss ions on several aspects of ferromagnetic superconductors includ ing superconductivity in heavy fermion systems. Part II treats problems on anti ferromagnetic superconductors. In Part III three papers on organic supercon ductors are presented. Part IV includes discussions on the exotic supercon ductors. The Appendix is concerned with the new research project towards high Tc superconductors in Japan. The last but not least remark is to mention the activity of the Taniguchi Foundation whose support makes this Symposium possible. For many years Mr."

Since the discovery by Bednorz and Muller of Cu-O alloys displaying high temperature superconductivity, great energy has been put into research in this field. One of the most important and interesting issues, and the subject of this volume, is the clarification of the microscopic origin and mechanism of high temperature superconductivity. This book discusses the latest experimental results on magnetic, optical, electrical, thermal and mechanical properties of the Cu-O and Bi-O superconductors, as well as proposed theoretical models of the mechanisms. The participants in the symposium agreed that for the high Tc Cu-O superconductors electron correlation effects are of central importance. For the Bi-O superconductors the main topic was whether the mechanism of superconductivity is the same as that of high Tc Cu-O superconductors. What was and what was not resolved at the symposium is summarized at the end of the volume.

viii The growing use of NTD silicon outside the U. S. A. motivated an interest in having the next NTD conference in Europe. Therefore, the Third International Conference on Neutron Transmutation-Doped Silicon was organized by Jens Guldberg and held in Copenhagen, Denmark on August 27-29, 1980. The papers presented at this conference reviewed the developments which occurred during the t'A'O years since the previous conference and included papers on irradiation technology, radiation-induced defects, characteriza tion of NTD silicon, and the use of NTD silicon for device appli cations. The proceedings of this conference were edited by Jens Guldberg and published by Plenum Press in 1981. Interest in, and commercial use of, NTD silicon continued to grow after the Third NTD Conference, and research into neutron trans mutation doping of nonsilicon semiconductors had begun to accel erate. The Fourth International Transmutation Doping Conference reported in this volume includes invited papers summarizing the present and anticipated future of NTD silicon, the processing and characterization of NTD silicon, and the use of NTD silicon in semiconductor power devices. In addition, four papers were pre sented on NTD of nonsilicon semiconductors, five papers on irra diation technology, three papers on practical utilization of NTD silicon, four papers on the characterization of NTD silicon, and five papers on neutron damage and annealing. These papers indi cate that irradiation technology for NTD silicon and its use by the power-device industry are approaching maturity."

Since the First International Symposium on Superconductivity (ISS '88) was held in Nagoya, Japan in 1988, significant advances have been achieved in a wide range of high temperature superconductivity research. Although the T c's of recently discovered oxide superconductors still do not exceed the record high value of 125K reported before that meeting, the enrichment in the variety of materials should prove useful to the investigation of the fundamental mechanism of superconductiv ity in these exotic materials. The discovery of the n-type superconducting oxides proved to oppose the previously held empirical fact that the charge carriers in all oxide superconductors were holes. In addition, optimization of the charge carrier density has been established as a technique to improve the superconducting proper ties of the previously known oxide materials. Many new experimental and theoreti cal advances have been made in understanding both the fundamental and the applied aspects of high temperature superconductivity. In this latter area, various new processing techniques have been investigated, and the critical current densities and other significant parameters of both bulk and thin film oxide superconductors are rapidly being improved. At this exciting stage of research in high temperature superconductivity, it is extremely important to provide an opportunity for researchers from industry, academia, government and other institutions around the world to freely exchange information and thus contribute to the further advancement of research."

The structural. electronic and lattice properties of superconducting ternary com pounds are the subject of this Topics volume. Its companion volume (Topics in Cur rent Physics. Volume 34) deals primarily with the mutual interaction of supercon ductivity and magnetism in ternary compounds. These two volumes are the culmination of a project. started nearly two years ago. that was inspired by the intense re search effort. both experimental and theoretical. then being expended to explore and develop an understanding of the remarkable physical properties of ternary super conductors. Research activity on this subject has increased in the meantime. The interest in ternary superconductors originated in 1972. when B.T. Matthias and his co-workers first discovered superconductivity in several ternary molybdenum sulfide compounds that had been synthesized in 1971 by R. Chevrel. M. Sergent. and J. Prigent. The superconducting critical temperature Tc of one of the compounds. PbMo S * was reported to be ~ 15 K. This value is sufficiently high that there was g 6 (and still is) reason to expect that other ternary compounds would be found with superconducting transition temperatures rivaling those of the A15 compounds. of which Nb Ge has the record high Tc of 23 K. The interest in ternary superconductors 3 received further impetus when several of the ternary molybdenum sulfides were found to have exceptionally high upper critical magnetic fields. some of them in the neighborhood of 50 Tesla or more. An immense amount of research on ternary molybdenum chalcogenides then followed.

The book provides an in-depth understanding of the fundamentals of superconducting electronics and the practical considerations for the fabrication of superconducting electronic structures. Additionally, it covers in detail the opportunities afforded by superconductivity for uniquely sensitive electronic devices and illustrates how these devices (in some cases employing high-temperature, ceramic superconductors) can be applied in analog and digital signal processing, laboratory instruments, biomagnetism, geophysics, nondestructive evaluation and radioastronomy. Improvements in cryocooler technology for application to cryoelectronics are also covered. This is the first book in several years to treat the fundamentals and applications of superconducting electronics in a comprehensive manner, and it is the very first book to consider the implications of high-temperature, ceramic superconductors for superconducting electronic devices. Not only does this new class of superconductors create new opportunities, but recently impressive milestones have been reached in superconducting analog and digital signal processing which promise to lead to a new generation of sensing, processing and computational systems. The 15 chapters are authored by acknowledged leaders in the fundamental science and in the applications of this increasingly active field, and many of the authors provide a timely assessment of the potential for devices and applications based upon ceramic-oxide superconductors or hybrid structures incorporating these new superconductors with other materials. The book takes the reader from a basic discussion of applicable (BCS and Ginzburg-Landau) theories and tunneling phenomena, through the structure and characteristics of Josephson devices and circuits, to applications that utilize the world's most sensitive magnetometer, most sensitive microwave detector, and fastest arithmetic logic unit.

This Topics in Current Physics (TCP) Volume 34 is concerned primarily with super- conductivity and magnetism, and the mutual interaction of these two phenomena in ternary rare earth compounds. It is the companion of TCP Volume 32 - Superconduc- tivity in Ternary Compounds: Structural, Electronic and Lattice Properties. The interplay between superconductivity and magnetism has intrigued theoreticians and experimentalists alike for more than two decades. V. L. Ginzburg first addressed the question of whether or not superconductivity and ferromagnetism could coexist in 1957, and B. T. Matthias and coworkers carried out the first experimental inves- tigations on this problem in 1959. The early experiments were made on systems that consisted of a superconducting element or compound into which small concentrations of rare earth impurities with partially-filled 4f electron shells had been intro- duced. These dilute impurity systems were chosen because the scattering of conduc- tion electrons by parama9. netic rare earth impurity ions usually has a strong de- structive "pa i r breaking" effect on superconducti vity, typi ca lly drivi ng the super- conducting transition temperature to zero at impurity concentrations of only a few atomic percent. Unfortunately, analysis of these early experiments was complicated by clustering and/or the formation of short range or "glassy" types of magnetic order so that definitive conclusions regarding the coexistence of superconductivity and magnetism could not be reached.

The recent discovery of high-temperature superconductivity in copper based oxides is an event of major importance not only with respect to the physical phenomenon itself but also because it definitely shows that solid state chemistry, and especially the crystal chemistry of oxides, has a crucial place in the synthesis and understanding of new materials for future appli cations. The numerous papers published in the field of high Tc supercon ductors in the last five years demonstrate that the great complexity of these materials necessitates a close collaboration between physicists and solid state chemists. This book is based to a large extent on our experience of the crystal chemistry of copper oxides, which we have been studying in the laboratory for more than twelve years, but it also summarizes the main results which have been obtained for these compounds in the last five years relating to their spectacular superconducting properties. We have focused on the struc ture, chemical bonding and nonstoichiometry of these materials, bearing in mind that redox reactions are the key to the optimization of their supercon ducting properties, owing to the importance of the mixed valence of copper and its Jahn-Teller effect. We have also drawn on studies of extended defects by high-resolution electron microscopy and on their creation by ir radiation effects."

Polymer semiconductor is the only semiconductor that can be processed in solution. Electronics made by these flexible materials have many advantages such as large-area solution process, low cost, and high performance. Researchers and companies are increasingly dedicating time and money in polymer electronics. This book focuses on the fundamental materials and device physics of polymer electronics. It describes polymer light-emitting diodes, polymer field-effect transistors, organic vertical transistors, polymer solar cells, and many applications based on polymer electronics. The book also discusses and analyzes in detail preparation techniques and device properties of polymer electronics.

In this text experts review experimental studies that directly reveal the relationship between the atomic structure and physical behavior of high-Tc superconductors. The thorough discussion centers on twins, twin boundaries, the vortex lattice, and magnetic and mechanical properties in connection with structural imperfections. Particular attention is paid to the role of the oxygen atom in the Y-Ba-Cu-O and La-Cu-O species. The experimental methods evaluated include electron and X-ray diffraction, electron microscopy, and M-ssbauer spectroscopy. This book makes extraordinarily valuable data obtained at the Institute of Solid State Physics at Chernogolovka accessible to the wider international community of researchers in superconductivity.

During the past thirty years considerable efforts have been made to design the synthesis and the study of molecular semiconductors. Molecular semiconductors - and more generally molecular materials - involve interactions between individual subunits which can be separately synthesized. Organic and metallo-organic derivatives are the basis of most of the molecular materials. A survey of the literature on molecular semiconductors leaves one rather confused. It does seem to be very difficult to correlate the molecular structure of these semiconductors with their experimental electrical properties. For inorganic materials a simple definition delimits a fairly homogeneous family. If an inorganic material has a conductivity intermediate between that of an 12 1 1 3 1 1 insulator " 10- n- cm- ) and that of a metal (> 10 n- cm- ), then it is a semiconductor and will exhibit the characteristic properties of this family, such as junction formation, photoconductivity, and the photovoltaic effect. For molecular compounds, such simplicity is certainly not the case. A huge number of molecular and macromolecular systems have been described which possess an intermediate conductivity. However, the various attempts which have been made to rationalize their properties have, more often than not, failed. Even very basic electrical properties such as the mechanism of the charge carrier formation or the nature and the density ofthe dopants are not known in detail. The study of molecular semiconductor junctions is very probably the most powerful approach to shed light on these problems.

The characterization of epitaxial layers and their surfaces has benefitted a lot from the enormous progress of optical analysis techniques during the last decade. In particular, the dramatic improvement of the structural quality of semiconductor epilayers and heterostructures results to a great deal from the level of sophistication achieved with such analysis techniques. First of all, optical techniques are nondestructive and their sensitivity has been improved to such an extent that nowadays the epilayer analysis can be performed on layers with thicknesses on the atomic scale. Furthermore, the spatial and temporal resolution have been pushed to such limits that real time observation of surface processes during epitaxial growth is possible with techniques like reflectance difference spectroscopy. Of course, optical spectroscopies complement techniques based on the inter action of electrons with matter, but whereas the latter usually require high or ultrahigh vacuum conditions, the former ones can be applied in different environments as well. This advantage could turn out extremely important for a rather technological point of view, i.e. for the surveillance of modern semiconductor processes. Despite the large potential of techniques based on the interaction of electromagnetic waves with surfaces and epilayers, optical techniques are apparently moving only slowly into this area of technology. One reason for this might be that some prejudices still exist regarding their sensitivity."

For the last few years astrophysicists and elementary particle physicists have been working jointly on the following fascinating phenomena: 1. The solar neutrino puzzle and the question: What happens to the neutrinos on their way from the sun to the earth? 2. The growing evidence that our universe is filled with about 10 times more matter than is visible and the question: What is dark matter made of? 3. The supernovae explosions and the question: What do neutrinos tell us about such explosions and vice versa? The experimental investigation of these phenomena is difficult and involves unconventional techniques. These are presently under development, and bring together such seemingly disparate disciplines as astrophysics and elementary particle physics on the one hand and superconductivity and solid-state physics on the other. This book contains the proceedings of a workshop held in March 1987 at which the above subjects and their experimental investigation were discussed. The proposed experimental methods are very new. They involve frontier developments in low temperature and solid-state physics. The book should be useful to researchers and students who actively work on these subjects or plan to enter the field. It also offers the non-expert reader with some physics background a good survey of the activities in this field.

One of the most exciting developments in modern physics has been the discovery of the new class of oxide materials with high superconducting transition temperature. Systems with Tc well above liquid nitrogen temperature are already a reality and higher Tc's are anticipated. Indeed, the idea of a room-temperature superconductor, which just a short time ago was considered science fiction, appears to be a distinctly possible outcome of materials research. To address the need to train students and scientists for research in this exciting field, Jeffrey W. Lynn and colleagues at the University of Maryland, College Park, as well as other superconductivity experts from around the U.S., taught a graduate-level course in the fall of 1987, from which the chapters in this book were drawn. Subjects included are: Survey of superconductivity (J. Lynn).- The theory of type-II superconductivity (D. Belitz).- The Josephson effect (P. Ferrell).- Crystallography (A. Santoro).- Electronic structure (C.P. Wang).- Magnetic properties and interactions (J. Lynn).- Synthesis and diamagnetic properties (R. Shelton).- Electron pairing (P. Allen).- Superconducting devices (F. Bedard).- Superconducting properties (J. Crow, N.-P. Ong).

Single-electron tunneling (SET) and related phenomena have recently come to be considered as "hot topics." This also became apparent when we organized the 4th International Conference on Superconducting and Quantum Effect Devices and Their Applications, SQUID'91, which was held June 18-21, 1991, in Berlin, Germany. Impressed by the number of contributions dedicated to the new physics of ultrasmall devices, we deemed it appropriate to devote this volume of the Springer Series in Electronics and Photonics to these specialized proceedings. The other contributions presented at SQUID'91, which are more conventional in character but nevertheless contain excitingly innovative results, are published separately as Volume 64 of the series Springer Proceedings in Physics. At first glance it seems strange that a conference abbreviated SQUID'91 should attract so many papers on non-superconducting devices, and in fact the first SQUID'XX conferences dealt exclusively with the physics and technology of Josephson junctions, SQUIDs and other superconducting devices and their ap plications. However, many concepts developed for superconducting devices, like tunneling, flux quantization, and flux-charge conjugation, appeared to be suitable for ultrasmall non-superconducting structures as well, and many researchers in the field of superconducting devices extended their activities accordingly. Thus the extension of the conference programme evolved quite informally. Meanwhile, the meetings established themselves as well-known conference series tradition ally appreciated by the SQUID community for its balanced mixture of physics and technology, review and preview. SQUID'XX became a kind of a trademark."

Physics and Chemistry of Transition-Metal Oxides includes both theoretical and experimental approaches to the variety of phenomena found in the transition-metal oxides, including high-temperature superconductivity, colossal magnetoresistance, and metal-insulator transition. These are the central issues in materials science and condensed matter physics/chemistry, and readers can obtain up-to-date information on what is happening in this field of research.

Springer-Verlag, Berlin Heidelberg, in conjunction with Springer-Verlag New York, is pleased to announce a new series: CRYSTALS Growth, Properties, and Applications The series presents critical reviews of recent developments in the field of crystal growth, properties, and applications. A substantial portion of the new series will be devoted to the theory, mechanisms, and techniques of crystal growth. Occasionally, clear, concise, complete, and tested instructions for growing crystals will be published, particularly in the case of methods and procedures that promise to have general applicability. Responding to the ever-increasing need for crystal substances in research and industry, appropriate space will be devoted to methods of crystal characterization and analysis in the broadest sense, even though reproducible results may be expected only when structures, microstructures, and composition are really known. Relations among procedures, properties, and the morphology of crystals will also be treated with reference to specific aspects of their practical application. In this way the series will bridge the gaps between the needs of research and industry, the pos sibilities and limitations of crystal growth, and the properties of crystals. Reports on the broad spectrum of new applications - in electronics, laser tech nology, and nonlinear optics, to name only a few - will be of interest not only to industry and technology, but to wider areas of applied physics as well and to solid state physics in particular. In response to the growing interest in and importance of organic crystals and polymers, they will also be treated."

The expansion of the application of ferroelectric crystals in engineering as well as of a number of fundamental problems of solid-state physics, which have not yet been solved and which bear a direct relation to ferro electricity, has lately stimulated much interest in the problem of ferroelectricity. In courses of solid-state physics ferroelectricity is studied today along with traditional disciplines, such as magnetism, superconductivity, and 'semiconducting phe nomena. Moreover, new specialities have been born concerned directly with the development and utilization of ferroelectric material in optics, acous tics, computer technology, and capacitor engineering. Special courses in the physics of ferroelectrics are read in a number of colleges and universities. The study of the nature of ferro electricity has currently reached such a level of development that we may speak of having gained a rather deep insight into the physical essence of a number of phenomena, which contribute to the generation of a spontaneous electric polarization in crystals. It is exactly at this level that it has become possible to single out that part of the problem, the physical picture of which can be depicted in a rather unsophisticated manner and which is the foundation for the construction of a building of "complete understanding.""

In less than two decades the concept of supercon In every field of science there are one or two ductivity has been transformed from a laboratory individuals whose dedication, combined with an innate curiosity to usable large-scale applications. In the understanding, permits them to be able to grasp, late 1960's the concept of filamentary stabilization condense, and explain to the rest of us what that released the usefulness of zero resistance into the field is all about. For the field of titanium alloy marketplace, and the economic forces that drive tech superconductivity, such an individual is Ted Collings. nology soon focused on niobium-titanium alloys. They His background as a metallurgist has perhaps given him are ductile and thus fabricable into practical super a distinct advantage in understanding superconduc conducting wires that have the critical currents and tivity in titanium alloys because the optimization of fields necessary for large-scale devices. More than superconducting parameters in these alloys has been 90% of all present-day applications of superconductors almost exclusively metallurgical. Advantages in use titanium alloys. The drive to optimize these training and innate abilities notwithstanding, it is alloys resulted in a flood of research that has been the author's dedication that is the essential com collected, condensed, and analyzed in this volume."

Recent experimental and theoretical progress has elucidated the tunable crossover, in ultracold Fermi gases, from BCS-type superconductors to BEC-type superfluids.

"The BCS-BEC Crossover and the Unitary Fermi Gas" is a collaborative effort by leading international experts to provide an up-to-date introduction and a comprehensive overview of current research in this fast-moving field.

It is now understood that the unitary regime that lies right in the middle of the crossover has remarkable universal properties, arising from scale invariance, and has connections with fields as diverse as nuclear physics and string theory.

This volume will serve as a first point of reference for active researchers in the field, and will benefit the many non-specialists and graduate students who require a self-contained, approachable exposition of the subject matter.

"

Semiconductors have been used widely in signal-level or "brain" applications. Since their invention in 1948, transistors have revolutionized the electronics industry in computers, information processing, and communications. Now, however, semiconductors are being used more and more where consid erable "brawn" is required. Devices such as high-power bipolar junction tran sistors and power field-effect transistors, as well as SCRs, TRlACs, GTOs, and other semiconductor switching devices that use a p-n-p-n regenerative effect to achieve bistable action, are expanding the power-handling horizons of semicon ductors and finding increasing application in a wide range of products including regulated power supplies, lamp dimmers, motor drives, pulse modulators, and heat controls. HVDC and electric-vehicle propulsion are two additional areas of application which may have a very significant long range impact on the tech nology. The impact of solid-state devices capable of handling appreciable power levels has yet to be fully realized. Since it first became available in late 1957, the SCR or silicon-controlled rec tifier (also called the reverse blocking triode thyristor) has become the most popular member of the thyristor family. At present, SCRs are available from a large number of manufacturers in this country and abroad. SCR ratings range from less than one ampere to over three thousand amperes with voltage ratings in excess of three thousand volts."