Spherical Diode Research Articles

Production of intense light ion beams on a multiterawatt generator

The operation of a pinch-reflex diode as an intense pulsed ion-beam source has been scaled up to the multiterawatt PITHON generator. Ion beams with currents of 1 MA at 1.8 MeV have been extracted in a 130 kJ, 100-ns pulse. The corresponding ion production efficiency is 60%. Power losses were observed in interfacing the coaxial diode to the biconic vacuum feed of the generator. By using smaller area diodes, the average current density at the anode source was increased to 20 kA/cm2. Proton and deuteron beams were studied in both planar and spherical diode geometries. The ion beam is focused predominantly by self-magnetic fields for planar diodes and predominantly by electrode shaping for spherical diodes. Current densities exceeding 150 kA/cm2 were achieved with spherical diodes. The spatial evolution of the anode and cathode plasmas was studied by laser holographic interferometry. As the peak of the power pulse is approached, plasmas were observed to expand from the electrodes in fairly uniform profiles with steep density gradients and to accelerate across the vacuum gap. After peak power, anode plasma fluctuations and a high-velocity (30 cm/μs) axial plume develop; the latter expands radially coincident with collapse of the power pulse.

Measurements of intense ion beams by a novel diagnostic method

A new diagnostic method capable of measuring beam profiles and trajectories of intense ion beams as a function of time has been developed. The technique employs fast photography in conjunction with fast scintillators. Prior to detection, the excessive intensity of the direct ion beam is reduced by means of Rutherford scattering. A time resolution of a few nanoseconds and a spatial resolution of a few millimeters has been achieved. Using this technique focusing properties of planar and spherical pinch reflex diodes have been investigated. A low energy electron beam precursor has been detected. A simple model for its production is presented.

Synthesis of the Pierce gun

The design of a Pierce gun is uniquely defined by four parameters: beam voltage, current, waist radius, and cathode current density. The gun convergence angle, cathode spherical radius, anode-cathode spacing, and throw (distance to the waist) are calculated by an iterative procedure which typically converges in four cycles to 0.1°. The anode lens formula of Danielson, Rosenfeld, and Saloom is combined with inverted forms of the Langmuir-Blodgett solution for the spherical diode and the Universal Beam Spread equation for the tunnel region; the iterations match the trajectories at the anode plane. Correction for spherical aberration is made by the method of Frost and Purl as quantified by True. The inverted equations are simple enough to be solved in a few minutes with a programmable calculator. The experimental data of Frost and Purl is used to demonstrate the validity of the procedure for guns of medium perveance.

Hot carrier injection in spherical solid state diodes

Hot carrier injection in spherical solid state diodes

Thermionic Emission from a Niobium Single Crystal

A spherical projection diode was used to determine the Richardson constants from a niobium spherical single crystal. Work function and AR values are reported for the [110], [111], [112], [113], [116], [001], and [310] crystallographic directions. Examination of the crystal surface revealed plateau-like surface structure, thermal etch pits, and whisker growth.

An Analytical Methode for Solving the Space Charge Flow Problem in a Spherical and Cylindrical Diode

An Analytical Methode for Solving the Space Charge Flow Problem in a Spherical and Cylindrical Diode

A Study of the Ion Beam Intensity and Divergence Obtained from a Single Aperture Three Electrode Extraction System

Experimental results are given for the perveance and beam divergence of a single aperture three electrode extraction system using helium ions at energies between 10 and 30 keV. The aperture radii, the electrode thicknesses, and the spacings were varied and from the results a preferred design was obtained for use in a multiaperture array. The most critical parameter was the ratio (S) of the radius of the first aperture to the distance between the first and second electrodes, the highest current density being obtained at values of this ratio less than 0.5. The optimum beam divergence observed corresponded to a Gaussian beam profile with a width (ω) of ± 1.2° at 2 m from the source. The measured perveance at small values of S and at minimum ω lay between 75% and 90% of the value predicted on the basis of a simple model using the Langmuir-Blodgett formula for the spherical diode.

The Mean Brightness of the Electron Microscope Gun

As the brightness obtained in the measurement is always the mean brightness averaged over a certain aperture angle and a certain area, it is not equal to the Langmuir's theoretical value except for a special operating condition of the electron gun and in general becomes lower than the theoretical value. The amount of decrease of the measured brightness depends on the sizes of the apertures used in the measurement and the electron optical characteristics of the electron gun. When the bias voltage is much reduced, the electron gun may be considered approximately as the plane, spherical or cylindrical diode system. From this point of view, the expressions for the mean brightness in these diode systems are derived both for thermionic and field emissions. It is also shown that these results will be able to apply to the calculation of the mean brightness of the triode electron gun.

Solution of the equations for a regular beam emitted by a curvilinear surface in the nonstationary case

An analytical solution is given of the equations for a regular beam (§1) emitted by an arbitrary surface in the nonstationary case and the ρ- and T-limited states for nonzero initial velocity (§ §2-4). It is assumed that the emitter is the coordinate surface x1=0 in the orthogonal system x1 (i=1, 2, 3), and the current density J, the electric field ɛ, and the magnetic field H are given functions J(t, x2,x3), ɛ(t, x2, x3), and H (x1, x2, x3). The solution is given in the form of series in terms of (X1)И with coefficients that are functions of t, x2, and x3. These coefficients are determined from recurrence relations (χ =1/3, 1/2, 1, depending on the emission conditions). Plane, cylindrical, and spherical diodes are considered in § 5 in the case in which the high-frequency component of the current density J is not small in comparison with its constant components.

The theory of the stationary modes of cylindrical and spherical diodes

The theory of the stationary modes of cylindrical and spherical diodes

Photoelectrical properties of spherical avalanche diodes in silicon

The photoelectrical properties of spherical avalanche diodes which were operated above breakdown voltage are described. A photon flux was measured by counting self-sustaining avalanches. The spectral response ranges from 0.5 to 1.15 μm. With a ratemeter time constant of 10 sec the noise equivalent power was 5.7. 1O −16 W.

Electrostatically focused electron gun for hollow beams

A new co-ordinate transformation describing concentric toroids enables the potential distribution of a toroidal concentric space-charge-limited diode to be calculated. The results are represented approximately by an analytic function that allows the calculation of perveance, current and other characteristics of a hollow-beam electron gun. It is shown that previous calculations are in error. The shapes of the focusing electrodes for a hollow-beam gun are determined by an electrolytic-tank analogue. It is thus possible to design a gun for thick hollow beams. It is shown that, for thick beams, the correct focusing electrodes for a hollow-beam gun are very different from those of a strip-beam gun. It is, however, possible, within a certain range of the relevant parameters, to use the Langmuir-Blodgett potentials of a cylindrical space-charge-limited diode in order to determine the ‘toroidal’ focusing electrodes in the electrolytic tank for the design of a hollow-beam gun.The potential distribution for a charge-free toroidal diode is measured and calculated. The toroidal diode theory includes the theory of cylindrical and spherical diodes as special cases. The results give us a method by which we can introduce a further correction, so that a hollow-beam gun for very thick beams can be designed. An experimental gun confirms these calculations.

Electrostatically focused electron gun for hollow beams

A new co-ordinate transformation describing concentric toroids enables the potential distribution of a toroidal concentric space-charge-limited diode to be calculated. The results are represented approximately by an analytic function that allows the calculation of perveance, current and other characteristics of a hollow-beam electron gun. It is shown that previous calculations are in error. The shapes of the focusing electrodes for a hollow-beam gun are determined by an electrolytic-tank analogue. It is thus possible to design a gun for thick hollow beams. It is shown that, for thick beams, the correct focusing electrodes for a hollow-beam gun are very different from those of a strip-beam gun. It is, however, possible, within a certain range of the relevant parameters, to use the Langmuir-Blodgett potentials of a cylindrical space-charge-limited diode in order to determine the ‘toroidal’ focusing electrodes in the electrolytic tank for the design of a hollow-beam gun.The potential distribution for a charge-free toroidal diode is measured and calculated. The toroidal diode theory includes the theory of cylindrical and spherical diodes as special cases. The results give us a method by which we can introduce a further correction, so that a hollow-beam gun for very thick beams can be designed. An experimental gun confirms these calculations.

Space-charge-limited Currents in Cylindrical and Spherical Insulator Diodes

Space-charge-limited Currents in Cylindrical and Spherical Insulator Diodes

Diode oscillation in high-voltage klystrons

Diode oscillations at frequencies between 1350 and 3700 Mc sometimes occurred in a particular high-voltage pulsed klystron. These frequencies agree closely with those calculated for an inverted spherical diode. The oscillations are often delayed a few microseconds after the electron beam is turned on. Experimental techniques revealed that two of the modes, TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">41</inf> and TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">61</inf> , with Q's of about 1000 had their highest electric fields in a region of the electron gun remote from the beam.

Azimuthal Electron Flow in a Spherical Diode

Solutions of Poisson's equation for a space-charge-limited spherical diode, in which electron trajectories are great circles rather than radial lines, are developed. It is shown how Poisson's equation may be separated to yield ordinary differential equations. The radial equation is solved analytically, whereas accurate numerical solutions of the azimuthal equation are given. A method of truncating the flow so as to produce a ``bowl-shaped'' electron gun, leading eventually to an annular electron beam, is presented, along with power-series solutions of Laplace's equation both inside and outside the region of the flow. The latter series are useful for calculating the shapes of anodes and focusing electrodes.

A grid controlled medium power travelling-wave tube using periodic focusing

The pulse power required by radar systems often imposes a severe load on the pulsing modulator. When traveling-wave or klystron power-output stages are used, the beam is generally pulsed by driving the accelerating electrode to cathode potential. In the past, drive potential and peak energy transfer have been reduced by the use of nonintercepting pulsing electrodes. These methods, however, are usually restricted to low-mu operation, which is inadequate in many applications. This paper describes the modifications necessary in the Pierce-type, convergent-flow electron gun for high-µ pulse beam control. Methods are suggested for the determination of grid-cathode spacing, current transmission, and other grid parameters. Design considerations are based on the space-charge-limited spherical diode. Normalized charts are presented as an aid to design use.

Transit Time and Space-Charge in the Spherical Diode†

ABSTRACT The formalism of time-dependent. Poisson equation leads to findings for the transit time and current—voltage behaviour of the spherical diode very much reminiscent of the cylindrical structure results previously derived for both zero and finite initial electron velocities. The effect of cathode-anode inversion is also examined.

The Space-Charge Limited Flow of Charged Particles in Planar, Cylindrical and Spherical Diodes at Relativistic Velocities†

ABSTRACT This paper is devoted to the theoretical determinations of collector currents in diodes having planar, cylindrical and spherical electrode systems operating under conditions of space-charge limitation. The Langmuir (1913) and Child (1911) equations are extended to the case of relativistic velocities and the solutions are valid for any value of accelerating voltage. In the planar case a general power series solution is obtained by direct integration ; in the cylindrical and spherical cases, three ranges of accelerating voltage are considered and solutions obtained.

Potential Distribution as a Function of Current in the Spherical Diode

Potential Distribution as a Function of Current in the Spherical Diode