. . i - - ANNALEN D E R PHYSIK 7.FOLGE * B A N D 19, H E F T 5-6 * 1967 On the Hollow Cathode W e t M d a n i r m By C. POPOVICI, M. SOMESAK and V. NISTOR With 7 Figures Abstract On basis of new results concerning the dependence of the discharge current on the intercathode spacing and the cathode fall potential, the main characteristicsof the hollow cathode effect (H.C.E) in a plane-parallelgeometry are defined. In order to explain the particularities of the H.C.E., a mechanism is p r o p e d that regards the discharge current amplifications and the enhancement of the negative glow plasma as a consequence of the plasma beam instabilities. I. Qeneral Considerations It was firstly pointed out by PASCHEN [l], that a certain (double plane or cylindrical) geometry of the cathode of a glow discharge results in given conditions in essential mechanism-modifications of the cathodic processes. The ulterior works oi SCH~LEB, G~NTHEMCHULZE, PENNING, TH. IONESOU [ 2 . . .5] have lead to the specification of the main hollow cathode discharge phenomena (amplification of the discharge current, growth of the intensity of radiation, peculiar electric field distribution in the negative glow) and contributed to elaborate the directions of their applications (high-resolution spectral sources, P.I.G. ion sources, current rectifiers and microwave generators). In the same time, (L first representation of the hollow cathode effect mechanism has been formulated; it has been emphasized that the enhancement of the current and radiation intensity is a consequence of the amplification of the ionization and excitation processes, brought about by the electrons that are accelerated in the electric field of the cathode ftdl and that spend their energy in the gap between the two cathode falls . Subsequently studies on the H.C.E. in various experimental conditions have been worked out [6...121, and new electronic applications [13, 141 have been proposed. Some results concerning the negative glow plasma of a H.C.D. have shown that the carrier density in the intercathodic cavity grows strongly in certain conditions, up to values corresponding to a very advanced, eventually total ionization [ l l , 151. Recently the radiation of the negative glow plasma due to gas as well to metal atoms, has been studied from the point of view of her amplification in laser devices 116, 171. Studies on the hollow cathode effect in magnetic fields have shown that a magnetic field that is applied parallel to the electric field of the cathode fall enhances strongly the currefit and radiation intensities, whereas a transversal magnetic field is rather inhibitive . 15 AM.Physlk. 7. Folge, Bd. 18 226 Annalen der Phyeik * 7. Folgq Band 19, Heft 6/6 * 1967 Part of the works concerning tho mechanism of the H.C.E. agree in drawing the photoelectric emission due to the strong radiation of the negative glow, as the main secondary emission process of the discharge [8, 19, 201. A general analysis of the H.C.E. mechanism, must start from the definition of the existence domains and main features of the effect, since the more realization of the hollow geometry conditions does not suffice to assure the effect, and the amplification of current and radiation intensities, is not the sole peculiarity of the H.C.D. The aim of this paper is to give a general and unitary sketch of the characteristics of the H.C.E. and to elaborate a mechanism consistent with the ensamble of these characteristics. 2. Peculiarities of the H.C.E. The schematic view of the hollow cathode discharge tube with two equipotential discs (made of Cu) and a surrounding cylindrical anode, is given in space are elimiFig. 1. As the p6sitive column as well as part of the FABADAY nated by such a geometry, the applied potential may be considered roughly equal to the cathode fall ( V,). Except the two oppositefaces, the hollow cathode plates are covered by insulating films. ANODE Fig. 1. Sohematic view of the plane, parallel hallow-cathode geometry 1. The H.C.E. appeares and develops itself in the cathode domain of an abnormal glow discharge, when a certain correlation between the parameters p, D, V , , j (pressure, intercathodic spacing, cathode fall, current density a t the cathode) is satisfied. It is t o be mentioned in this order that while the H.C.E. does imply always the existence of H.C.D. conditions, the reverse is not true. 2. The H.C.E. manifests itself by a sudden variation of the discharge V,) current (i) in a a (D) diagram, or of the glow ( VErP= const) potential ( V in a V , (D) diagram ( i , p = const). Fig. 2 represents the variation of the disoharge current as a function of the intercathodic spacing a t a pressure of 3 mm Hg in Neon. The curves 1. 9 have been measured a t different cathode falls and show the transition from abnormal glow discharge t o hollow cathode effect conditions. In the domain of the potentials we have wed, the discharge current remains roughly constant a t intercmthode spacings larger than 8,5 mm. It grows strongly IOa times in our experiment-reaching a maximum that is shifted versus small D values, as the cathode fall increases. The lowering of the current intensity a t small D values leads to the hindering of the dischirge. - -- Popovrcr, SOMEEAN and NIETOR: On the Hollow Cathode Effect Mechanism 227 The diagram of Fig. 2 draws also the influence of the cathodic fall on the discharge. Whilst for large intercathodic spacings, an increase of the cathodic fall from 240 t o 320V, results in a negligible growth of the current, in the “effect” domain of the H.C.D. small changes of t h e cathodic fall have import a n t consequences; Below a critical value of the cathode fall (240 V in our experiments), the discharge. is hindered a t I) = 7 - 0 . 8 mm, t h e cathodic dark spaces becoming too large to allow the discharge t o glow between the cathode plates. Fig. 2. Discharge current versus intercathode epacing for various cathode falk in Neon, at, 3 mmHg prewnre Fig. 3. Diecharge current versus pressure in parallel and transversal magnetic fields in Neon.Intercathode epacingD = 0.45 cm, cathode fall 300 V 3. The increase of t h e discharge current a t “effect”, is accompanied by a parallel increase of the intensity of the spectral lines emitted from the glow. It has been pointed out, that the radiation of the metal atoms sputtered by the cathode, grows much more than t h a t of trhe gas atoms, whose radiant intensity amplifies by a factor equal t o the discbrge current amplification [13, 171. This fact suggests t h a t an alteration of the distribution function of electronic velocities takes place, as the dischar$e turns from the ordinary glow regime t o H.C.E. conditions. 4. The influence of an external magnetic f i d n the H.C.E. depends on its direction with respect to the electric field of e cathode fall. The curves i n Fig. 3 are representing the variation of the diacharge current as a function of pressure for H = 0, H , , = 285, 430, 590 Oe and H I 590 Oe in Neon a t D = 4,5mm. For comparison, the “simple” cathode curves I,, for H = 0 and a,, = 590Oe, are also represented. These curves have been obtained by connecting alternatively only one of the two plates’as cathode, and by adding the two measured values. It results from Fig. 3, that the H.C.E. amplification 16+ if) 228 Annalen der Physik * 7. Folge * Band 19, Heft 6/6 * 1967 Fig. 4. Diecharge current versus potential for verious intercathode q a c ings in Neon at cE=3mHg Fig. 6. Discharge current versus potential for various intercethode spacing8 in Neon at p = 3.6 mmHg P o ~ o n aSomEam , and NISTOR: On the Hollow Cathode Effect Mechanism 229 of t h e discharge current is increased by the application of a parallel magnetic field and reduced by a transversal magnetic field. Such a behaviour, underlines the leading role of the electrons emerging by secondary emission from the cathode. I n a parallel field they are collimated in an energetic electronic beam, in transversal fields, they are drifted away from the intercathodic cavity. 5. The experimental data that have been obtained as yet, lead t o the conclusion t h a t the H.C.E. mechanism is a “volume” phenomenon. So for instance, i t seems t h a t the nature of the cathode metal does not have any influence in the H.C.E. Among these, there are to be mentioned, the strong cathode sputtering, the strong thermal effects and the feeble gradient of the electric field in the negative glow plasma in optimum effect conditions. The existence domains of the H.C.E. are represented in the i (D) and i (p) diagrams of Figs. 2 and 3, t h a t show the correlation between the parameters p, D, V,, and their critical character. 3. Beam-Instability in the Negative Glow Plasma The model that may describe the H.C.E. mechanism must be consistent with : 1. the continuous “resonant”, variation of the macroscopical and microscopical parameters ; 2. the strong amplification of the effect in parallel magnetic field and its inhibition in transversal magnetic field; 3. the preferential excitation of the spectral lines of atoms with low excitation potentials. The studies concerning the mechanism of the glow discharge in a hollow cathode geometry agree about the existence of three classes of electrons in the glow [2l,91: a) the group of few but energetic “primary” electrons accelerated in the cathode fall region ; b) the group of their filiation in the negative glow; c) the group of “ultimate” electrons, in equilibrum with the plasma. It has been pointed out that in hollow cathode effect regime as well as in highly abnormal simple cathode discharges, most of the excitation and ionization processes are occuring in the negative glow plasma . Taking into account these features, it is reasonable to consider the negative glow of the hollow cathode discharge as a plasma through which are traveling t h e two opposite electron beams, accelerated in the two cathode dark spaces. It is known that two opposite electronic beams are bringing about in the plasma trough which they are traveling kinetic instabilities, that are resulting in a strong amplifications of the carrier density and of t h e radiation intensity [23** * 251. As a result of this instability, longitudinal electrostatic waves with a phase velocity (u,) roughly equal t o t h e mean velocity of the elect.rons of the beam (v,), are excited. Their increment is ( w = angular frequency, k = wave number, f = distribution function of electronic velocities) and i t is obvious that the wave grows only with phase 230 Annalen der Phyaik * 7. Folge * Band 19, Heft 5/6 * 1967 velocities that are satisfying the condition Simdtaneously with the wave excitation process through energy transfer from the “resonant” beam-electrons, a reversed phenomenon takes place : the giving up of energy from the wave, to the electrons with smaller velocities as the phase velocity of the wave. Thus, the most important consequence of the electron-beam interaction is the modification of the initial distribution function of electron velocities that has the expression  : (npl, 5 and v,,~, VJ = densities and velocities of the plasma- and beam-electrons) The electron beam accerlerated in the cathode cavity, may generate in the negative glow plasma a wave with a phase velocity roughly equal to the electron velocity that corresponds to the cathodic fall 300 V in our experiments. Studies on the electron velocity distributions in the negative glow plasma [9, 211 have given for the “ultimate” electrons of the plaema, values of several fractions of electron volts. We have aseumed a “plasma” temperature of 0 , l Volt. With this values and n, w 10-l npl the velocity dicltri bution function (2) has the shape represented by the dotted curve in Fig. 6. As part of the beam-electrons lose their energy exciting the wave, and part of the nonresonant “plasma” electrons gain energy from the wave, the alteration of the velocity distribution function is such as to smooth down in the resonance domain. As a consequence of the velocity “diffusion” the distribution function will be levelled until a flat dietribution will take place in the domain of resonance velocities. In the same time a pattern of standing oscillations establishes itself in the plasma. . Fig. 6. Initial (dotted curve) and final (full curve) diatribution functions of the electron velooitiea POPOVICI, SOMESAN and NISTOR: On the Hollow Cathode Effect Mechanism 231 Assuming for simplicity t h a t the velocity distribution function f after interaction with the wave, differs from the initial, unperturbed function fo, only in an interval of velocities u2 - ul, the unknown values of v l , u2 and f = const may be calculated by solving the system: The first equation may be replaced by: 0s f(v2 - v1) = j /OM dv 01 because fO(U1) = fo(Ue) = f * In the particular case we have calculated fo, the value obtained for f is 1.2. 10-lo. Such an important alteration of the velocity distribution function a t resonance results in strong variations of the number of electrons that are able t o ionize and excite, because t h e maxima of the excitation and the ionization cross sections are situated in the velocity interval u1 - u,. The probability of the ionization and excitation processes varies correspondingly t o the denaity of electrons t h a t have ionization or excitation resonant energies. The mechanism of plasma-beam instability explains the main characteristics of the H.C.E. The appearance of the H.C.E. a t given critical values of the cathodic fall is the consequence of the condition of a positive wave increment ; in similar way the geometry conditions are corresponding t o the resonance conditions t h a t may allow stationarity of the wave pattern in the intercathodic cavity. I n order to show a typical instability evolution, Figs. 4 and 6 are representing the H.C.E. in i - V coordinates, for a discharge in Neon a t p = 3, and 3,6 mm Hg. The curves have been drawn for various intercathodic spacings (given in mm). The strong increase of the ourrent a t a critical cathode fall value attests the appearance in this domain of a new ionization process, t h a t corresponds t o the beam-plasma instability. The hatched zone draws this domain where the kinetic instability manifests itself by a most favourable efficiency of the ionizing processes. In order t o illustrate the analogy between the H.C.E. and the instability processes, the carrier density versus beam current in a typical beam-plasma experiment  is also represented in a corner of Fig. 4. I n both cases there is a critical value of the beam current [ i ( V,) in the H.C.E.] that corresponds t o the instability. The H.C.E. and the beam-plasma instability are also similar in a i(p) representation. I n a corner of Fig. 3 the dependence carrier density - pressure, in a two beam experiment  is shown. The instability as well t y the H.C.E. is growing a t a critical value of the preseure. The curvature of the first region of the i ( V ) diagrams (Figs. 4 and 5) that does not appear in the instability curves, is own to the fact that in the H.C.E. are also present peculiar processes as for instance the photoelkctrical effeat of the plasma radiation. 232 Annelen der Phyaik * 7. Folge Band 19, Heft 6/6 * 1967 On the basis of the proposed beam-plasmainstability mechaniem, some quantitative evaluations may be made, in order to emphasise,the “resonance” charakter, of the H.C.E. and to give a phyeical meaning to the geometrical parameter D. Taking into account th at numerous studies on plasma-beam experiments [23, 27, 281 have found stationary wave patterns and asauming that the HCE has a maximum as the cavity is “resonant” for the fundamental harmonics, we have;: A D=2d+( 4) 2 where D is the intercathode spacing, d the length of the cathode dark space and 1the wave length. This relation leads for the c u e of parallel magnetic fields to several conclusions that are supporting the hypothesis of a resonance mechanism of the HCE. The influence of a longitudinal magnetic field on the HCE is described by the curves given in fig. 7, were the discharge current is represented as a function of the magnetic field intensity for a plane-parallel hollow cathode of lead in Neon gas a t various cathode falls (292*..310V). The first maximum a t 660 Oe ia much more intensive as the second at roughly 1300 Oe. This second maximum has not been observed for low cathode falls of 292 and 295 V. The magnetic fields t ha t correspond to the maxima of the i ( H ) curves have cyclotron Irequenciee fcl = 1,8.109 H z and fc2 = 3,6.109 Hz. On the other side, if the velocity of the electrons th a t are injectedfrom th e cathode fall in the negative glow is known, the frequency of the excited wave may be calculated and it has been shown t h a t if this frequency is resonant t o the cyclotron frequency an intensive development of the instability takes place. Fortheusualvalues V, = 300V,D = 0,5cm,d = O91crn,eq.(4)gives1= 0,6cm. 100 The corresponding wave frequency is f,, = 2 = = 1,66.100 3 z . a 0.6 The fact that the ratio of fel and fen is that of two subsequent harmonics 88 well as the approqimate coincidence between fol and f d , are both arguing for a plasma-beam inatability mechanism of the HCE. The influence of the magnetic Fig. 7. Discharge current versus parallel magnetic field iUt43Mity at venous cathode falls, in. Neon, at p = 2 tom end D,, = 0.6 cm. POPOVICI, SOMESAN and NISTOR:On the Hollow Cathode Effect Mechanism 233 field appears thus due mainly to cyclotron resonance effecta. The only presence of “pressure” and “trap”-effects is not able t o explain the maxima of the i (H,i) curves. 4. ~ n c l a s i o n e The amplification of the discharge current and of the radiation intensity in the H.C.E. is due t o the growth in the negative glow plasma of kinetic instability processee that are bringing about by mean of the wave a n energytransfer from the primary resonant electrons t h a t are acoelerated in the cathode fall, t o the nonresonant electrons of the plasma. This transfer of energy results in a strong increase of t h e density of electrons t h a t are able to excite and ionize. The hollow cathode effect is a very convenient mean t o study plasma-beam interactions due t o its extreme experimental simplicity as t o the fact t h a t i t offers a possibility to extend the study of two beam instabilities t o high pressure (several mmHg) domains where the electronic gun devices d o not work. Rererentmi [l] PASCHEN. Ann. Physik 60 (1916) 901. 121 SC~ULER, H., Z. 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B u c h a r e s t ( R o m a n i a ) , Institut of Physics of the Academy of the Romanian Socialist Republic. Bei der Redaktion eingegangen am 8. August 1966.