ERGEBNISSE DER EXAKTEN NATU RWI S SENS CHAFTEN HERAUSGEGEBEN VON S. FLI~GGE DNU F.TRENDELENBURG UNTER MITWIRKUNG VON F. HUND DREIUNDDREISSIGSTER BAND MIT 158 ABBILDUNGEN SPRINGER-VERLAG BERLIN • GOTTINGEN • HEIDELBERG 1961 Alle Rechte, insbesondere das der 0bersetzung in fremde Sprachen, vorbehalten Ohne ausdr~ckliche Genehmigung des Verlages ist es auch nicht gestattet, dieses Buch oder Teile daraus auf photomechanischem Wege (Photokopie, Mikrokopie) zu vervielfiiltigen © by Springer-Verlag oriG. Berlin. G6ttingen • Heidelberg 1961 Printed in Germany Die Wiedergabe yon Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicbt zu der Annahnle, daB solche Namen im Sinn der Warenzeichen- und Markenschutz-Gesetzgebung als Irei zu betrachten w~.ren und daher "con jedermann benutzt werden diirfen Br(ihlsche Universit~itsdruckerei Gie[3en Inhaltsverzeichnis Electrode Components of the Arc Discharge. By Professor Dr. G. ,REKCE Bonn. htiVv~ 35 Figures . . . . . . . . . . . . . . . . . . . . . 1 R6ntgenographische Untersuchungen yon Gitterst6rungen in Mischkristallen. Von Dozent Dr. V. GEROLD, Stuttgart. Mit 37 Abbildungen ..... 105 Die Elektronenlawine und ihre Entwicklung. Von Professor Dr. H. ,REHTEAR Hamburg. Mit 86 Abbildungen . . . . . . . . . . . . . . . . . . 175 Inhalt der B~ndeXX--XXXlI[ I. Namenverzeichnis . . . . . . . . . . . . . . . . . . . . 262 II. Sachverzeichnis . . . . . . . . . . . . . . . . . . . . . 264 Electrode Components of the Arc Discharge* By G. RE~I~E With 35 Figures Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 I. Region of Interest . . . . . . . . . . . . . . . . . . . . . . . . 3 II. List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . 4 III. Current Continuity in Front of the Cathode . . . . . . . . . . . . 5 III. I T-Emission . . . . . . . . . . . . . . . . . . . . . . . . 5 III.2 F-Emission . . . . . . . . . . . . . . . . . . . . . . . . 6 III.3 T-F-Emission . . . . . . . . . . . . . . . . . . . . . . . 8 III.4 f-F-Emission . . . . . . . . . . . . . . . . . . . . . . . 10 III.5 F-Production of Ions . . . . . . . . . . . . . . . . . . . . 14 Ill.6 T-Production of Ions . . . . . . . . . . . . . . . . . . . . 15 III.7 y+ and ~-Emission . . . . . . . . . . . . . . . . . . . . . 21 tII.8 y~,-Emission . . . . . . . . . . . . . . . . . . . . . . . 23 IV. Current Continuity in Front of tile Anode . . . . . . . . . . . . . 26 IV. 1 F-Ionisation . . . . . . . . . . . . . . . . . . . . . . . 27 IV.2 T-Ionisation . . . . . . . . . . . . . . . . . . . . . . . 29 V. Voltage Requirement of the Cathode Discharge Component . . . . . 30 VI. Voltage Requirement of the Anode Discharge Component . . . . . . 36 VII. Energy Balance at the Cathode . . . . . . . . . . . . . . . . . 36 VIII. Energy Balance at the Anode . . . . . . . . . . . . . . . . . . . 48 IX. The Phenomenon of the Electrode Discharge Components and the E-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 47 X. The Cathode Plasma Jet and its Dynamic Effect on the Cathode . . . 60 XI. The Anode Plasma Jet and its Dynamic Effect on the Anode . . . . . 70 XII. The Electrode Discharge Component in a Transverse Magnetic Field . 74 XIII. 'Non Typical' Cases . . . . . . . . . . . . . . . . . . . . . . . 80 XIV. Relation to Experiments . . . . . . . . . . . . . . . . . . . . 88 XV. Concluding Remarks and Acknowledgements . . . . . . . . . . . . 83 Monographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Introduction The electric arc as a phenomenon of classical physics is well-known and has been for more than fifty years. Interest in the arc lies not only in its importance for the investigation of the principle laws of gaseous electronics but also in its wider application in industry and technology. * This research was snpported by the United States Department of Army, through its European Research Office. d. Ergebn. exakt. Naturw. XXXln 1 2 O. ECKER : We can, therefore, readily understand that during this time it has been the subject of more than a thousand special investigations. Some of these results have been summarised in comprehensive monographs. If, in spite of all tiffs, we still have an incomplete understanding of the arc discharge components at the electrodes, it must be because of the special problems this subject presents. It seems essential that we should be clear as to the nature of these problems, before starting our investi- gation. Let us then recall, that in theoretical physics we meet two types of problems which are appreciably different. In the first group fail all those problems, whose phenomena do not come within the framework of laws already known. The solution here requires not so much work, but rather a new idea based on ingenious intuition. In the second group come those problems whose phenomena are governed by laws already well known. If in this case the theory is still incomplete it can only be because the problem is very complex and in- volved. Here the solution requires more consequent and tedious work than ingenious intuition. Of course, there are problems which belong simultaneously to both groups. As long as there is no cogent reason to assume the contrary, we claim that the arc -- as most of the problems of gaseous electronics -- belongs to the second group. The problem of the electrode components of the arc discharge is so particularly complex and involved because we have to handle simul- taneously a large number of physical laws connecting an even larger mmaber of variables and parameters. The mere formulation of a single one of these laws is difficult. To include all these laws in their mutual interplay for all possible parameter values seems like an almost insoluble problem. In order to reduce these difficulties, two ways prove to be successful. First, it is necessary to restrict the variety of parameter values. That means we investigate certain typical cases which, of course, have to be suitably chosen to represent a large range of the phenomena. Secondly there is the possibilityo f classifying the laws as "essential" or "negligible". In this way we arrive at the concept of the model. Any region which can be described by a unified model we call a model .e,~oz It is clear that the problem is much reduced, if one restricts oneself to the calculation of only one model zone. This procedure has been widely applied in the past. Unfortunately, however, the "electrode discharge components of the arc", our region of interest, is composed of several model zones which strongly interact with each other. In particular the description of the interacting boundaries of the model zones, the transition zones, within which both model conceptions are equally effective, cause great diffi- culties. A description of these transition areas can be evaded only in favourab]e circumstances by means of appropriate boundary conditions. Electrode Components of the Arc Discharge 3 The investigation of single model zones is, of course, of great value and in the following we shall deal with such individual model zones and with part problems. But on the other hand, it must be emphasised that only the comprehension of all model zones in their mutual interplay can lead to an understanding, i. e. to an actual theory of electrode discharge components. We shall, therefore, also try to understand tile general behavionr of the electrode discharge zones from the mutual interaction of the individual model zones. Finally, there is one other important conclusion which can be taken from this introductory discussion. From our preceding statements we expect complex experimental results which will make a recognition of the basic laws most difficult and may even lead to false interpretations. We will, therefore, prefer to develop our theoretical description not inductively, proceeding from the experimental basis, but rather deductive- ly, starting from the basis of the well known laws of physics. To summarise the results of our introductory discussion: We expect a theory of the electrode discharge components of the arc to be involved and complex. It probably demands not so much a fundamental new idea as rather a careful and logically formulated application of laws already known. We have to start with the definition of our "region of interest". In order to comprehend the expected diversity of the phenomena, we shall try to recognise and deal with certain "typical cases". The "region of interest" is expected to be made up of several "model zones" and their corresponding "transition zones". We will deal with single model zones and part problems. But we are clearlya ware that the general behaviour of the arc cathode and anode region can only be understood from the interplay of all "model zones". We concentrate on this general problem in section IX. Of course, such part problems, the comprehension of which is helpful for the formulation of the general theory of section IX, will be treated first. On the other hand, we post- pone those part problems of which the solution depends on the results of the general section IX. This aspect leads to the sequence of the index. Our approach to the problem will be deductive. I. Region of Interest The definition of the region of interest of the electrode discharge components must of necessity be adjoined to the definition of the arc itself. We could not find a completely satisfactory definition of the arc in the literature. NWOEKCAM (364), NAMWEN (414) and NOSMOHT (570) gave definitions which do not suffice in the light of our present knoMedge. GRUBNLEKXIF and RE~IC~AM (6) consider high current and small cathode drop as characteristic for the arc discharge. They carefully distinguish between thermal and non-thermal arcs according to whether or not the electron temperature is equal to the gas temperature. It is indeed very difficult to assign a group of necessary and sufficient characteristics to the arc in view of the multiplicity of the arc types. In an attempt to be as comprehensive as possible, including at the same time thermal and non-thermal arcs, we propose the following definition: I* 4 G. ECKER: We take an arc to be a self-sustaining conducting gas zone between two electrodes whose carriers are predominantly produced by thermal means. In addition we further define: The electrode discharge components include the entire region of the arc in so far as it is influenced by the electrode. That means the entire area, within which alterations are produced by an infinitesimal displace- ment of the electrode, is our region of interest. We shall treat cathode and anode components as separate regions of interest. Arc column and electrode discharge components do not always exist side by side in the above form. Thus the electrode stabilised arc ,~PMOR[ LEZIEW and TERUOHT (482)] shows no column at all in the above sense. On the other hand, one can stabilise discharges [GAxmLIXG and EDELS (278), (219)] which may indeed have an arc column of which, however, the cathode discharge components do not fit our definition, but rather show the properties of glow discharges. In the following investigations only, those discharge components are dealt with which satisfy our definition of the arc in general and the limitation of its electrode components in particular. II. List of Symbols The following symbols with their subsequent meanings are chosen for the description of the observations and formulation of the laws : a accommodation coefficient m mass of a particle A Anode M momentum of a particle b mobility n nmnber of particles per unit B magnetic induction volume e vdocity of the particle N total number of particles C cathode 0 point of stability d extension of the model zones 51 pressure D diffusion coefficient P_ probability e elementary charge q ratio of electron and ion current E energy density / electron fraction of the current Q cross section F force r radial distance g mass loss of the electrode per R end contraction in front of the unit area and time electrode G mass loss of the electrode per S radiation loss per unit volume unit time T temperature h Plank's constant ,oU ,aU D% definitions of anode fMl I-I magnetic field V electrical potentiM i saturation current per unit area ,oV V,, V, definitions of cathode fall 0i° °, i unit vectors on the electrode sur- v average mass velocity faces W heat consumption per unit mass I saturation current liberated from the electrode j current per unit area x, y, z coordinates J current X electric fieId k Boltzman constant ~ reducing factor k direction vector fl field enhancement factor K boundaries of the discharge y coefficient of particle liberation channel through single collisions l mean free path Y energy gain of the electrode L energy loss of the electrode d Dirac function Electrode Components of the Arc Discharge 5 E energy per unit volume Stefan Boltzman constant space charge per unit volume relaxation time heat conduction coefficient v~ current lines A heat conduction number per unit • e work function area of the surface of a body oc supply function # current of energy per unit area ~, ~, )q spherical bipolar coordinates H current of energy • ~.,H,#fundamental coefficients of frequency spherical bipolar coordinates mass per unit volume The symbols given above may have indices attached. The index (+) and the index (-) denote respectively ions and electrons. Other indices denote the location of the discharge. E. g. )c( indicates the contact area of the arc at the cathode, )s( indicates the boundary between the contraction zone and the space charge zone, )o( -- if not otherwise classified -- indicates the boundary between the contraction zone and the column. The meaning of other indices may be understood from the text and figures. All formulae are given in the c. g. s.-system. III. Current Continuity in Front of the Cathode Two observed phenomena at the arc cathode are extremely simple and at the same time characteristic. As a generM rule the arc contracts in front of the cathode and forms a bright spot with a high current density of many amp/cm .2 At the same time, the cathode drop is small, about 10 V. The high current densities require a large number of charge carriers in order to maintain the current continuity. The tow voltage excludes any interaction mechanism effective in the glow discharge (production of electrons by the v-effect of the ions, production of ions by ionisation of the gas by electron beams). This raises the question, which up to tile present, has aroused the greatest theoretical interest. What is the source of the charge carriers necessary for the high current densities in front of the cathode ? Only two types of carriers really come under consideration: Electrons freed from the etctrode or ions produced in the gas area. The liberation of ions from the electrode is hardly of any practical interest. Electrons Call be freed from the metal thermally (T-emission), by an external field (F-emission), by the combined effect of the above (T-F-emission), by the 7-effect of single or multiple charged ions (~+- emission) by the v-effect of excited atoms (),m-emission) or by the photo- effect (y~-emission). The gas ions can be produced by electrons emitted from the cathode and accelerated in the space charge zone (F-production of ions), or ther- mally (T-production of ions). All these possibilities have been taken into consideration. III.1. T-Emission. ,KRATS one of the first to attack the problem of carrier production KRATS[ (540), (541)] was of the opinion that the current was borne by thermally emitted electrons in front of the cathode. At 6 G. : ]~CKBR that time, it was thought that the current densities were about 100 amp/cm ~ and an estimate of the T-emission by means of Richardson's law produced this order of magnitude. New experiments raised difficulties with regard to the T-emission. Current densities of a much higher order were measured ( 01 a -- 10~amp/cm )~ even with materials for which the T-emission at the boiling point was not sufficient to account for the current densities. Furthermore, TLOTS ,745( 54584,9 ), ¢?AI~IELS (509, 510), REGILEES and KCOB (507) and NEW- NAM (416) examined the influence of the cooling of the electrodes on the existence of the arc. They found not only that the arc can exist with strongly cooled or quickly rotating electrodes, but indeed, that the transition from glow discharge to arc discharge was helped considerably by strong cooling. As a result of these facts GREBMAR (447) grouped metals according to their electron emission at boiling-point. For those of high boiling-point (e. g. C, Ca, Mg, W) he assumed T-emission, for those of low boiling- point .e( g. Cu, Hg, Au, Ag), F-emission, following a suggestion of LANGMUIR 335). (329, III.2. F-Emission. The mechanism of field emission has already been discussed by SEELIGER (499), NWOEKCAM (364), NOTPMOC (t72), RAM- GREB (447) and XOSAM (383, 384) using the laws of unipolar or bipolar space charge movement ~ICEBJfL-RELLJfM[ (405)] and the emission laws according to RELWOF and Nom)I~mM (207@ Particular attention should be paid to S'NOTPMOC work (112) since he already indicated the charac- teristic difficulties of the F-emission. Because of the energy balance, NOTe~OC was compelled to stipulate a minimum ion participation in transport of current. Since the eIectrons emitted from the cathode have, because of their small energy e (V,-- 9), a very small total coefficient of ionisation, it was difficult to understand how they could produce the necessary ions. NOTeMOC tried to account for this discrepancy by suggesting first a favourable choice of the accommodation coefficient, which reduced the ion contribution, and secondly the process of successive ionisation. We shall return to this point shortly. Because of new measurements of the current density at the cathode, which gave the surprising values of up to 601 amp/cm ,z EC~IBOC and REHGALLAG (101) again took up tile question of field emission. In asses- sing this process they used on the one hand the NORImEIM-FoWLER equation e{ = {_=1,54 -10-6 -~ ~Xt exp (-- 6,8 • _ 701 ~-9~J"~ ! [A/cm2~ (IIIA) and on the other hand S'NWOE(ICAM equation of bipolar space charge movement ~X = 7,6.10 ~ h~V +{{ { _-2-m-\ +m } ~'h__ "jeJ / [VZ/cm ]~ )2,111( wh er~e { is the emission current density at the cathode. ,~V 9, ~X and { have to be measured in V, V/em resp. A/cm .2