Modified Betatron Accelerator Research Articles

Radiological Protection Policy Aspects concerning the Design and Operation Modus of Medium Energy (< 1 GeV) or High Current (> 25 MeV, = 1 kA) Electron Accelerators Facilities

Radiation Protection in major research-facilities includes several aspects concerning their planning, the hazard-sources, the environmental protection and the general safety. The present paper includes a concise presentation of the approach to the radiation protection policies proposed for the Athens Race Track Microtron (250 MeV, 550 mA) and the Heraclion Modified Betatron Accelerator (25 MeV, 1 kA).

Effect of fast velocity on the beam dynamics in a modified betatron accelerator

In this paper we have derived the equations that describe the slow motion (bounce) of the reference electron that is located at the beam centroid, taking into account its fast motion, for an electron beam that is confined in the magnetic field of a Modified Betatron Accelerator. The two equations for the guiding center (g.c.) of the centroid have been derived by averaging the centroid orbit over two time periods that are distinctly different. These two periods are associated with the normal modes of the system. Although our approach is not exact, it has the advantage that the fast velocity appears explicitly in the various expressions and thus its significance on the centroid dynamics can be rather easily assessed. A general conclusion of our results is that the fast velocity does not have a profound impact on the dynamics of the centroid, provided that the ratio ${\mathrm{u}}_{\mathrm{\ensuremath{\perp}}}$/${\mathrm{u}}_{0}$\ensuremath{\lesssim}0.5, where ${\mathrm{u}}_{\mathrm{\ensuremath{\perp}}}$ is the transverse and ${\mathrm{u}}_{0}$ is the total velocity. A very interesting conclusion of our work is that the centroid equilibrium position is insensitive to ${\mathrm{u}}_{\mathrm{\ensuremath{\perp}}}$, provided that ${\mathrm{u}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\lesssim}${\mathrm{u}}_{0}$/2. We explain this counter-intuitive result.

A Technique for Generating Potent Positron Beams

This paper reports on a novel scheme that has the potential to generate intense positron beams. It is based on the modified betatron accelerator, a compact high-current device that has been developed in the last few years. Briefly, the proposed accelerator consists of two modified betatron accelerators that are stacked together and share the same core. The electrons are accelerated in the upper torus during the first half of the flux waveform when the time rate of the magnetic flux (varphi) is positive. After completion of the acceleration, the electrons are extracted and guided to a high-Z target producing a positron beam that is accelerated in the lower torus during the second half of the waveform when dvarphi/dt is negative.

Excitation of cyclotron resonances from random fluctuations of stellarator windings.

We have investigated the effect of random fluctuation of stellarator windings in a modified betatron accelerator configuration on the dynamics of the beam centroid by solving numerically the equations of motion. Our results show that random displacements of the windings by a few millimeters produce field errors that excite the cyclotron resonance modes that efficiently direct most of the input energy from the axial to transverse direction. These random displacements become completely harmless when their maximum amplitude is reduced to {plus_minus}0.5 mm. When even such small displacements cannot be attained, the errors that are produced from the mispositioning of the windings may become benign by using a crowbar on the current of the windings before the critical resonance is reached. At {ital l}={ital m} ({approx_equal} 6 in our case), where {ital l} is the value of the cyclotron mode and {ital m} is the value of field periods in the device, i.e., when the frequency of the cyclotron mode is equal to the frequency of the strong focusing mode, the beam centroid encounters a potent resonance and locks in at it, even when the windings are located at their ideal positions. If crossing of the {ital l}={ital m}=6 mode ismore » desired, using a crowbar on the strong focusing field may be the only remedy. {copyright} {ital 1996 The American Physical Society.}« less

Proposal for beam extraction from a modified betatron accelerator using a toroidal electric field.

A technique is proposed for extracting the beam from the modified betatron accelerator. Briefly, after the acceleration is completed, the beam is forced to drift vertically by applying a rapidly rising toroidal electric field. Following the crossing of the septum, the beam enters the extractor, which is either helical or straight. In the latter case the electrons are guided to target by a plasma lens.

Beam trapping in a modified betatron accelerator with a localized bipolar electric-field pulse

A trapping concept for the injected beam in a modified betatron accelerator using a localized inductive electric-field pulse generated by a charged coaxial pulse line is described. The average canonical angular momentum 〈Pθ〉 is not conserved in this scheme. Numerical simulations demonstrate trapping over a wide range of operating parameters. A 0.84 Ω, 45 ns water dielectric pulse line has been built for testing the trapping concept. The pulse line is switched using triggered vacuum surface flashover switches. Test results show that a single bipolar output pulse can be obtained if the pulse line is crowbarred. For 15–40 kV pulses, the observed rise time is roughly 20 ns.

The Naval Research Laboratory Modified Betatron Accelerator and assessment of its results*

In this paper the experimental results of the Naval Research Laboratory (NRL) Modified Betatron Accelerator (MBA) [Phys. Rev. Lett. 64, 2374 (1990)] are briefly summarized and assessed. These results show that the addition of the strong focusing (SF) field made a substantial improvement in the confining properties of the device, at least in the intermediate time scale, and that the SF field together with the finite resistivity of the vacuum chamber wall is responsible for the trapping of the beam. There is extensive experimental evidence, suggesting that the slow beam loss during acceleration is caused by the cyclotron resonances. Reduction of several field errors together with operation at higher toroidal and SF field led to beam energies in excess of 20 MeV, while the trapped current was above 1 kA. Preliminary beam extraction experiments with 12 resonant coils have shown that a ∼80 G field disturbance is required to extract the beam from the MBA.

Identification of toroidal field errors in a modified betatron accelerator

A newly developed probe, having a 0.05% resolution, has been used to detect errors in the toroidal magnetic field of the NRL modified betatron accelerator. Measurements indicate that the radial field components (errors) are 0.1%–1% of the applied toroidal field. Such errors, in the typically 5 kG toroidal field, can excite resonances which drive the beam to the wall. Two sources of detected field errors are discussed. The first is due to the discrete nature of the 12 single turn coils which generate the toroidal field. Both measurements and computer calculations indicate that its amplitude varies from 0% to 0.2% as a function of radius. Displacement of the outer leg of one of the toroidal field coils by a few millimeters has a significant effect on the amplitude of this field error. Because of uniform toroidal periodicity of these coils this error is a good suspect for causing the excitation of the damaging l=12 resonance seen in our experiments. The other source of field error is due to the current feed gaps in the vertical magnetic field coils. A magnetic field is induced inside the vertical field coils’ conductor in the opposite direction of the applied toroidal field. Fringe fields at the gaps lead to additional field errors which have been measured as large as 1.0%. This source of field error, which exists at five toroidal locations around the modified betatron, can excite several integer resonances, including the l=12 mode.

Dynamic behavior of an electron ring close to a cyclotron resonance in a modified betatron accelerator.

The effect on the electron-ring dynamics when a cyclotron resonance is crossed in a modified betatron accelerator has been studied analytically and numerically. It has been found that, in the presence of small vertical field errors, there is a field-error-amplitude threshold below which the normalized transverse velocity ${\mathrm{\ensuremath{\beta}}}_{\mathrm{\ensuremath{\perp}}}$ of the gyrating electrons is bounded (Fresnel regime) and above which it is unbounded (lock-in regime). In the lock-in regime, the average value of the normalized axial (toroidal) momentum \ensuremath{\gamma}${\mathrm{\ensuremath{\beta}}}_{\mathrm{\ensuremath{\theta}}}$, where \ensuremath{\gamma} is the relativistic factor and ${\mathrm{\ensuremath{\beta}}}_{\mathrm{\ensuremath{\theta}}}$ is the normalized axial velocity, remains constant, i.e., the resonance is never crossed. In addition, above threshold, ${\mathrm{\ensuremath{\beta}}}_{\mathrm{\ensuremath{\perp}}}$ increases proportionally to the square root of the time. The threshold value of the vertical field error amplitude can be made larger either by increasing the acceleration rate or by adding a small oscillatory toroidal field to the main toroidal field. The multiple crossing of the same resonance, in the presence of such a small oscillatory toroidal field, was also studied with some interesting results.

Beam trapping in a modified betatron accelerator.

The experimental results on the trapping of the beam in the Naval Research Laboratory modified betatron accelerator are in good agreement with a revised model of resistive trapping, and thus it may be concluded that the wall resistivity is responsible for the inward spiral motion of the beam after injection.

Studies of synchrotron radiation emission from the modified betatron accelerator

Numerical calculations of synchrotron radiation emitted from the modified betatron accelerator show that, for relativistic electron energies up to approximately 2 MeV, the single-particle intensity spectrum is characterized by a peak at the Doppler-shifted cyclotron frequency associated with the applied toroidal field. As the electron energy is increased above a few MeV, the calculated spectrum becomes comparable to that of an electron in purely circular motion. Measurements of the radiation using fixed-frequency heterodyne receivers indicate that the polarization, amplitude, and the temporal evolution of radiated power during the first few hundred microseconds of acceleration are in good agreement with the predicted single-particle spectrum. These observations have been used to confirm the energy evolution and provide information about the magnitude of the transverse velocity of the beam electrons. Late-time signal decay suggests that electrons are moving off the minor axis in a manner that is consistent with the excitation of the electron-cyclotron resonance.

High midplane accessibility stellarator windings for high-current toroidal accelerators

We have developed two strong focusing field configurations that provide high midplane accessibility and therefore are compatible with presently contemplated extraction schemes for high-current, toroidal accelerators. When these windings are attached to a modified betatron accelerator, the bandwidth of the device is slightly smaller than the bandwidth of a modified betatron with unsplit stellarator windings. However, the bandwidth of the two new configurations is more than sufficient even for modest (20–30 kA) winding currents.

Beam extraction scheme from the modified betatron accelerator.

A technique is proposed for extracting the electron ring from the modified betatron accelerator. Basically, this technique consistes of exciting the resonance that naturally exists for some specific values of the ratioi of the vertical to toroidal magnetic field.

Controls and data acquisition for the NRL modified betatron accelerator

A CAMAC based data acquisition and control system (DACS) has been developed for the NRL modified betatron accelerator. The design goal of the MBA is to accelerate single-shot multi-kA currents of electrons to 50 MeV. The DACS must perform three general tasks: (1) the control and shot sequencing of the accelerator, (2) the data acquisition of MBA shot data and (3) the archiving of the shot conditions, shot digitizer data, and oscilloscope data. A VAX 11 750 controlled system crate contains a serial highway driver that communicates with CAMAC crates in three remote locations via fiberoptic links. The DACS utilizes sensing and feedback to control capacitor banks, high vacuum pumping systems, high speed digitizers and the precision infector accelerator during shot sequencing. A control program written at NRL invokes CAMAC functions to perform shot sequencing, provide data acquisition, and archiving. The computer actuates switches that control equipment subsystems by operating relay logic and interlocking. Thus, the computer control functions in parallel with manual controls. The DACS logs the conditions before and after MBA shots. It also archives data acquired form the buffer memories of transient digitizers and from a PDP 11 23 controlled vidicon camera that digitizes oscilloscope photographs.

Nonlinear transverse electron beam dynamics in a modified betatron accelerator

The transverse electron beam dynamics in a modified betatron accelerator is studied using a new approach. This approach is based on the two exact constants of the motion and the potentials at the center of the beam. The main advantage of the present technique is that the ring orbits can be accurately determined over the entire minor cross section of the torus and not only near the minor axis. The results indicate that the electron ring orbits in the plane transverse to the toroidal magnetic field always close inside the vacuum chamber, and their topology is often substantially different than that predicted from the linear theory.

Modified Betatron Accelerator Data Acquisition and Control System

This article describes the planning and implementation of the NRL Modified Betatron Accelerator (MBA) data acquisition and control system (DACS). The design goal of the MBA is to accelerate multi-kiloampere electron beam pulses to 50 MeV. It employs an applied toroidal magnetic field in addition to the rising vertical fields of a conventional Betatron. Theoretical studies show that the toroidal field improves the stability and equilibrium properties of the device at high currents. The accelerator hardware consists of three capacitor banks, the precision injector accelerator, toroidal and vertical field coils, vacuum chamber and pumping system, and intense relativistic electron beam diode. The task of the DACS is to conduct the safe and efficient firing of the MBA and the data acquisition and archiving of accelerator function.

Injection and Extraction of a Relativistic Electron Beam in a Modified Betatron

We show that it is possible to guide a relativistic electron beam into the center of a modified betatron accelerator by judiciously creating a plasma channel with a laser. A slight variation of this scheme can be used to extract the beam after the acceleration phase.

External injection into a high-current modified betatron accelerator

By axially tapering the current density at each end of an axial pinch, a scheme is developed for injecting electrons across magnetic field lines into a modified betatron accelerator. This scheme produces only a minimal perturbation to the circulating electron beam. The axial pinch provides beam equilibrium in the transverse field and the tapering reduces the nonadiabatic growth of the perpendicular particle velocity from 0.5c to 0.05c for the parameters of the Naval Research Laboratory modified betatron.

Resistive wall flute stability of magnetically guided relativistic electron beams

The resistive wall stability of an electron beam is studied, and application of the theory to the modified betatron accelerator is considered. Only flute-like perturbations are analyzed (n=0, l≥1, where n and l are the toroidal and poloidal mode numbers, respectively). Included in the analysis are the effects of relativistic velocities, equilibrium and perturbed self-electromagnetic fields, and resonant particle effects due to density and velocity profiles. The principal results are (1) l≥2 modes are much more difficult to stabilize than is the l=1 mode; (2) the velocity gradient along the beam can provide an important stabilizing mechanism; (3) the stabilizing effect of the density gradient is reduced by relativistic effects; and (4) magnetic perturbations can be important even for nonrelativistic beams.

Preliminary Design of the NRL Modified Betatron

The principal subsystems of the NRL Modified Betatron Accelerator (MBA) have been designed. These subsystems include the air-core magnets, the mechanical structure, the vacuum system, the injector accelerator, and the pulse power capacitor banks. The MBA concept uses an applied toroidal magnetic field, B? (2-5 kG) to improve the stability and confinement of a multikiloamp e-beam. Trapping of an injected beam will result from varying the Bz by a few Gauss during the first poloidal bounce period. Externally driven coils will compensate the diffusion of the self magnetic field to maintain equilibrium.