Bunched Electron Beam Research Articles

PEP II RF System

Stage II of PEP consists of adding a superconducting proton storage ring to the electron-positron ring now completing construction. To obtain the desired luminosity between the tightly bunched electron beam and the protons, the protons will be tightly bunched also. The proton bunch length and the number of bunches imposes unusual requirements on the RF system. Acclerating to full proton energy makes the bunching easier. PEP is a positron, electron colliding beam storage ring being constructed as a joint project between the Stanford Linear Accelerator Center and the Lawrence Berkeley Laboratory at the SLAC site. It has a design value of 15 GeV on 15 GeV with a luminosity of 1032 and energy up to 18 GeV with reduced luminosity due to reduced current. The target date for beam turn-on is October 1, 1979. The original concept included protons, electrons and positrons, hence PEP. However, the proton ring required superconducting magnets to fit a 200 GeV ring on the SLAC site. A decision was taken in 1974 to proceed with the electron, positron portion, since conventional techniques were available for the construction; and to wait for development of the magnets before proposing the addition of the proton ring. It appears possible to develop magnets with fields of 8 tesla so that a proton energy of 350 GeV could be contained in the PEP tunnel.

Theory of Longitudinal Instability for Bunched Electron and Proton Beams

We discuss an original approach for the treatment of the longitudinal stability of high-intensity proton and electron bunches. The general analysis is divided in three steps. First, we search for a stationary bunch distribution which is matched to the external RF forces as well as to the current dependent induced fields. We question the existence of such distribution. Second, we check the stability of the stationary solution by applying a small perturbation and observing whether this is initially damped or not. At this point a stability condition is derived in terms of current, surrounding impedance and bunch size. In the last step one should question what happens to the beam in case the stability condition is not satisfied. The problem here is the determination of the final bunch configuration. We will not deal much with this step. We observe that the "overshoot formula" which is derived from numerical calculation1 is usually applied to proton bunches2, whereas commonly the assumption is made an electron bunch matches always its size to the stability condition3. The originality of our approach stays in the combination of the three steps. All previous theories either consider only the first step4 or combine the second and third ones but disregard the first2,3,5. Sometimes, in the latter case, the modification of the potential well is introduced ad hoc3. Our theory applies to the case of a real frequency independent impedance.

A large-signal analysis of broad-band klystrons with design applications

For the design of a high-performance broad-band klystron, an accurate large-signal analysis is made. By a one-dimensional analysis program using a disk model of the electron stream, the interaction between a bunched electron beam and the electric field in each cavity gap is studied, taking into consideration space-charge forces, relativistic effects, and electric field distributions in ungridded gaps; beam loading is included by an iterative method at each intermediate gap, and the energy exchange in the output gap is obtained from the change in kinetic energy. On the five-cavity UHF-TV klystron designed with this program and having a conversion efficiency of over 60 percent, the debunching effect of the electric field in intermediate cavity gaps and the behavior of vibrating electrons in the output gap are clarified. Calculated conversion efficiency is shown to agree well with measured efficiency over the pass-band. Additionally, by a two-dimensional analysis program, the effect of the cathode magnetic coefficient on the electron bunching is studied.

Strong turbulence and the anomalous length of stored particle beams

A dispersion relation, including strong turbulence, is derived for short-wavelength longitudinal self-perturbations of bunched electron beams. The effects of radiation damping and quantum excitation are included. Assuming that turbulence stabilizes coherent oscillations allows the derivation of a formula for bunch length which gives excellent fits to the data from SPEAR. As a special case of the formalism, an integral equation which describes the longitudinal self-perturbations of proton beams is derived.

The Influence of Drift Distance on the Attainable Energy Resolution of a Bunched Electron Beam

High intensity, low energy electron beams from linear accelerators are used extensively in photofission and (?, n) threshold reaction experiments. The degradation of the energy resolution of the beam due to the action of longitudinal space charge forces and the presence of a conducting cylinder surrounding the beam is considered. Results are presented for varying drift distances, beam currents, and phase spread of the bunch for an L-band accelerator.

Measurement of Electron Beam Bunch Form

This paper describes a technique for measuring quickly, accurately, and with high resolution, the form of the electron beam bunches in a linear accelerator. The equipment used on the Glasgow accelerator is described in detail, and some of the results obtained are presented.

The effect of potential beam energy on the performance of linear beam devices

The potential energy stored in a bunched electron beam is calculated using analytical and numerical methods. The ratio of stored potential energy to the total beam energy W_{p}/W_{0} increases rapidly with the degree of bunching and with decreasing beam filling factor b/a . W_{p}/W_{0} is proportional to the beam perveance and independent of the beam voltage, as long as relativistic effects are neglected. In a velocity-modulated linear beam-type device, such as a klystron or a traveling-wave beam tube, stored potential beam energy affects both the bunching process and the process of dc to RE energy conversion adversely. For maximum conversion efficiency W_{p}/W_{0} should be kept as low as possible. Several ways of reducing W_{p}/W_{0} are discussed.

Transient Beam Loading in Electron Linear Accelerators

An experiment has been devised to measure directly the beam loading in electron linear accelerators operating with very short beam pulses. A well momentum analyzed and phase bunched electron beam is sent through either an unexcited waveguide or a vacuum pipe. Electron energy loss due to beam loading in the waveguide is detected by measuring the resulting energy shift of elastically scattered electrons with the NBS electron scattering spectrometer. Energy shifts of a few parts in 105 can be measured at 60 MeV. Measurements made to date at 61 MeV and for beam pulse lengths of 5, 10, and 20 nanoseconds appear to confirm the existence of enhanced beam loading relative to the usual non-dispersive linac theory. An attempt is made to compare the measurements to theoretical estimates of this enhancement.

Phase Analyzer of Bunched Electron Beam

A method is proposed for analyzing a phase distribution of electrons in a bunched beam. An electron beam from a buncher is led into a re-entrant cavity, in which the beam is deflected at a gap by a transverse electric field of the same frequency with that of the buncher. The deflection angle of electrons corresponds to their phases in the bunched beam; consequently, if electron collectors are set at different deflection angles, their output simulates the phase distribution of the electrons. A model experiment has been tried with a pre-buncher of a linac. The results are consistent with one-dimensional ballistic theory. When the pre-buncher was attached to a 6 MeV linac, the 45% increase of the output current was observed in good accordance with the estimation from the experimental phase-analysis.

Plasma Frequency and Velocity Spread in Bunched Electron Beams of Finite Diameter

The velocity spread existing on a velocity-modulated electron beam of finite diameter is investigated as a function of drive, drift length, and perveance using a digital computer program based on a disk electron model. At small signal levels the velocity modulation decreases cosinusoidally to zero with drift distance in accordance with one-dimensional bunching theory. At higher signal levels, however, the velocity spread does not go to zero due to aberrations introduced by the finite diameter of the beam. The minimum velocity spread at maximum bunching is found to be proportional to the square of the fundamental component of rf current, up to an optimum drive level. Above this drive level the velocity spread increases rapidly with no corresponding increase in rf current. Trajectories of electrons of all initial phases are found to undergo a basic transition from nonovertaking to overtaking at a new characteristic distance λpq/4, which is given approximately by the geometric mean of the infinite beam quarter-plasma wavelength λp/4 and the reduced (due to finite beam size) quarter-plasma wavelength λq/4. This characteristic distance is found to be a key parameter in the prediction of velocity spread, drift length and drive for optimally bunched electron beams for use in klystron amplifiers, harmonic generators, and in linear accelerators.

Frequency mixing in a relativistic electron beam

A theoretical analysis and an experimental study of millimeter wave generation by a fast wave interaction between a bunched electron beam and a transverse wave are reported in this paper. The technique appears to be practical for the generation of wavelengths as short as 1 to 2 mm. The experimental apparatus reported here converts power at a frequency of 9.17 Gc to power at a frequency of 39.71 Gc with an output power of 2 to 3 mw.

Interaction of a bunched electron beam with a gyrotropic plasma : B.W. Hakki, J. Appl. Phys., 34 (3), March 1963, 531

Interaction of a bunched electron beam with a gyrotropic plasma : B.W. Hakki, J. Appl. Phys., 34 (3), March 1963, 531

Single-transit E-type Travelling-wave Devices†

A small-signal analysis is presented for single-transit E-type traveling- wave devices in which a bunched electron beam follows a circular path and interacts with an azimuthally propagating electromagnetic wave. The ribbonshaped beam is maintained on the proper trajectory, without the use of focusing magnets, by balancing the electron centrifugal force against a steady radial electric- field force. The present investigation differs from earlier studies in a number of important respects: (1) The solutions apply to electron ribbons having all values of centerof-the-beam radius; (2) the origin of azimuthally directed electromagnetic field components in inhomogeneously loaded coaxial-cylindrical transmission systems is more closely examined; (3) the effect of the radial r-f spacecharge field on the interaction process, and its importance relative to the aximuthal field, receives attention; and (4) both unperturbed and slipping-stream motion for ribbon beams undergoing helical motion are treated in order to demonstrate the close relationships existing between electron streams possessing helical and plane circular motion. Numerical solutions are carried out for two limiting situations: One single-transit E-type tube is chosen to have a center-of- the-beam radius of 0.100 in. while another has a beam radius of 11.8 in. These results show that the small-signal solutions of large-radius E-typemore » devices closely resemble those of O-type tubes. The rate-ofchange of gain (with spatial angle), which is shown to be an increasing function of the radius of curvature of the beam, is bounded between two definite limits: (1) The gain rate approaches zero as the radius of beam curvature vanishes; (2) the gain rate approaches that of O-type tubes as the radius of beam curvature becomes infinite. For beam radii of 1 in. or more, practical E-type devices possess gain rates closely approaching those of O-type tubes. The practicability of single-transit E-type tubes is contingent upon finding means to substantially improve beam stiffness.« less

Ultramicrowave Generation by Cerenkov Interaction with Electron Beams

ABSTRACTThe possibility of using Cerenkov interaction in ferrites by bunched electron beams to produce coherent power at microwave frequencies and higher has been investigated. The conditions under which microwave powers in the millimetre wave region of sufficient intensity can be generated and the properties of the ferrite in this connection are also discussed.

Interaction of a Bunched Electron Beam with a Gyrotropic Plasma

The interaction of a prebunched beam with an anisotropic medium is considered for the generation of coherent electromagnetic energy in the low and submillimeter region. Generalized expressions are obtained for the fields created by a prebunched beam of general shape in an anistropic medium. The permeability is assumed to be a scalar constant whereas the permittivity is tensorial. Two special cases are considered: one is that of a helical prebunched beam and the other is that of a rectilinear beam, both interacting with gyrotropic gaseous plasmas. Ionization, scattering, and rf field effects on the beam are neglected. In addition to the solutions of the inhomogeneous vector wave equation, a method is suggested whereby the free mode solutions could be directly deduced.

The double interaction output cavity klystron

By extracting the power from a bunched electron beam at 2 points along the beam instead of 1 and then combining these powers by suitable network connected to the load it is shown that bandwidth can be improved by a factor of 2, circuit losses per cavity can be reduced by a factor of 4, and power output can be increased by a factor of 4 or more if the output window is the limitation. Test results are given on an experimental tube of this kind delivering 50 KW at 825 Mc. The extension of this principle to more than 2 interaction spaces and its relationship to the extended type of klystron are discussed.

Kinematic Electron Bunching by Sinusoidal Travelling and Standing Waves in Short Extended Interaction Regions!

The kinematic bunching of electron beams by sinusoidal traveling and standing waves of constant amplitude in the absence of space charge is treated on a large-signal basis, using the general theory developed by Wessel-Berg. The theory predicts a maximum fundamental r-f current of 1.4 times the d-c current for synchronous interaction. which may be increased a small amount for nonsynchronous interaction. In order to check the validity of the theory. the equations of motion were integrated numerically on a highspeed electronic computer; the theory agrees well with these computations if the electric field does not exceed a certain critical value. Although the increase in fundamental r- f current for nonsynchronous operation over the synchronous value is not very great, the velocity spread within the beam is considerably reduced. A calculation is included of beam-loading effects, which are compared with theoretica1 values. (auth)

Large signal bunching of electron beams by standing-wave and traveling-wave systems

Large signal bunching processes in the presence of space charge are studied by extending techniques used to compute multi-cavity klystron bunching. Bunching capability of traveling-wave and standing-wave systems is examined by using an assumed spatial and time distribution of electric field, and interesting high degrees of bunching are predicted.

Theory of the Rebatron—a Relativistic Electron Bunching Accelerator for Use in Megavolt Electronics

Highly bunched electron beams in the 1 to 3 million electron volt range, having a sharply peaked velocity spectrum, represent a powerful attack on the submillimeter wave (100 to 3000 kmc/sec) generation problem. In this paper the theory of a rebatron for producing a high-energy beam, wherein both the current wave form and the velocity distribution function approach delta functions, is presented. Computations indicate that the emergent 1.5-Mev beam has an appreciable harmonic content up to harmonics as high as the 1000th and has a velocity spread of 0.07% for the electrons of interest. Pulsed beam powers of the order of 100 000 w should be possible using a 3 kmc/sec rebatron.

Electron Cyclotron as a Source of Megavolt Bunched Electron Beams

Electron Cyclotron as a Source of Megavolt Bunched Electron Beams