Effects Of Field Errors Research Articles

Beam dynamics of the superconducting wiggler on the SSRF storage ring**Supported by National Natural Science Foundation of China (11105214)

In the SSRF Phase-II beamline project, a superconducting wiggler (SW) will be installed in the electron storage ring. It may greatly impact on the beam dynamics due to the very high magnetic field. The emittance growth becomes a major problem, even after correction of the beam optics. A local achromatic lattice is studied, in order to combat the emittance growth and keep the performance of the SSRF storage ring as high as possible. Other effects of the SW are also simulated and optimized, including the beta beating, the tune shift, the dynamic aperture, and the field error effects.

Neoclassical toroidal viscosity and error-field penetration in tokamaks

A model for field error penetration is developed that includes nonresonant as well as the usual resonant field error effects. The nonresonant components cause a neoclassical toroidal viscous torque that tries to keep the plasma rotating at a rate comparable to the ion diamagnetic frequency. The new theory is used to examine resonant error-field penetration threshold scaling in ohmic tokamak plasmas. Compared to previous theoretical results, the plasma is found to be less susceptible to error-field penetration and locking, by a factor that depends on the nonresonant error-field amplitude.

Effect of Neoclassical Toroidal Viscosity on Error-Field Penetration Thresholds in Tokamak Plasmas

A model for field-error penetration is developed that includes nonresonant as well as the usual resonant field-error effects. The nonresonant components cause a neoclassical toroidal viscous torque that keeps the plasma rotating at a rate comparable to the ion diamagnetic frequency. The new theory is used to examine resonant error-field penetration threshold scaling in Ohmic tokamak plasmas. Compared to previous theoretical results, we find the plasma is less susceptible to error-field penetration and locking, by a factor that depends on the nonresonant error-field amplitude.

Experimental and theoretical studies of active control of resistive wall mode growth in the EXTRAP T2R reversed-field pinch

Active feedback control of resistive wall modes (RWMs) has been demonstrated in the EXTRAP T2R reversed-field pinch experiment. The control system includes a sensor consisting of an array of magnetic coils (measuring mode harmonics) and an actuator consisting of a saddle coil array (producing control harmonics). Closed-loop (feedback) experiments using a digital controller based on a real time Fourier transform of sensor data have been studied for cases where the feedback gain was constant and real for all harmonics (corresponding to an intelligent-shell) and cases where the feedback gain could be set for selected harmonics, with both real and complex values (targeted harmonics). The growth of the dominant RWMs can be reduced by feedback for both the intelligent-shell and targeted-harmonic control systems. Because the number of toroidal positions of the saddle coils in the array is half the number of the sensors, it is predicted and observed experimentally that the control harmonic spectrum has sidebands. Individual unstable harmonics can be controlled with real gains. However if there are two unstable mode harmonics coupled by the sideband effect, control is much less effective with real gains. According to the theory, complex gains give better results for (slowly) rotating RWMs, and experiments support this prediction. In addition, open loop experiments have been used to observe the effects of resonant field errors applied to unstable, marginally stable and robustly stable modes. The observed effects of field errors are consistent with the thin-wall model, where mode growth is proportional to the resonant field error amplitude and the wall penetration time for that mode harmonic.

Field error and its effect on the plasma performance in TPE-RX, reversed-field pinch device

The effects of field errors at the poloidal gap of the thick shell on the plasma performance and the wall-locking are intensively studied. The coil system of TPE-RX (major/minor radii, R/a = 1.72/0.45 m) has several features for cancelling the field errors at the thick shell gap and for controlling the equilibrium position of the plasma column. It is confirmed that these field error cancellation schemes work well for the normal operating conditions in TPE-RX. It is shown quantitatively that the global performance of the revised-field pinch operation is affected if the shell gap field error exceeds about 5% of the poloidal magnetic field. As expected, the probability of the mode to lock at the shell gap increases as the field error increases.

Confinement results in RFPs

A short presentation of the main characteristics and peculiar aspects of the RFP configuration is given. Confinement data from a number of experiments, which have been operated after 1980, are recalled; the main emphasis is on results from MST and RFX, the two largest existing devices, RFX, with a current capability of 2 MA, in the first two years has been operated at low currents (350+700) kA, mainly to compare different modes of creating the RFP configuration, to study field error effects and plasma wall interaction, to improve and optimize, in particular by current and field control, the discharge parameters. The reported results are in line with expectations.

Interference effects in undulator and wiggler radiation sources

A simple model is described that is useful in understanding the spectral and angular properties of the radiation emitted in periodic undulator and wiggler magnets. Detailed comparisons with exact calculations show that it is also sufficiently accurate to be used for practical computations. An extension of the model allows the major effects of field errors to be simulated in a simple way.

Theoretical consequences of wiggler field error reduction techniques on free-electron laser performance

There have been extensive studies on the effects of intrinsic field errors on the operation and performance of free-electron lasers (FEL’s) based predominantly on simple models for the spatial form and statistical properties of the field errors. In some cases, the effects of compensation magnets or steering coils have been included as a method of reducing the deleterious effects of field errors. In the present study the effects of (i) compensation magnets, (ii) general spatial forms that are more realistic models of experimental wigglers, and (iii) statistical correlations of the field errors are considered. This theoretical study has resulted in a quantitative means of measuring the relative merit of these experimental techniques for reducing wiggler field error effects. These means of comparative analysis yield important criteria for experimental design and modeling.

The effects of field errors on low-gain free-electron lasers

The effects of random wiggler magnetic field errors on low-gain free-electron lasers (FELs) are examined analytically and numerically through the use of ensemble averaging techniques. Wiggler field errors perturb the electron beam as it propagates and lead to a random walk of the beam centroid, variations in the axial beam energy, and deviations in the relative phase of the electrons in the ponderomotive wave. The random walk of the beam centroid and the consequent variations in the axial beam energy are discussed. The deviations in the relative phase resulting from the field errors are examined. The effect of the field errors on the FEL gain in the low-gain regime is determined. The benefits of beam steering are analyzed, and addition methods for reducing the detrimental effects of field errors are discussed. >

The impact of field-error reduction techniques on FEL performance

There have been extensive studies on the effects of intrinsic field errors on the operation and performance of free electron lasers (FELs) based predominately on simple models for the spatial form and statistical properties of the field errors. In some cases, the effects of compensation magnets or steering coils have been included as a method of reducing the deletrious effects of field errors. In the present study we consider the effects of (i) compensation magnets, (ii) general spatial forms which are more realistic models of experimental wigglers and (iii) statistical correlations of the field errors. This theoretical study has resulted in a quantitative means of measuring the relative merit of these experimental techniques for reducing wiggler field-error effects. These means of comparative analysis yield important criteria for experimental design and modeling.

Three-Dimensional Magnetohydrodynamic Simulations of Field Error Effects in ZT-H and ZT-40 Reversed-Field Pinch Devices

Magnetic perturbations caused by field errors may pose a threat to magnetic confinement. They can cause the formation of magnetic islands, which may increase transport. The response of a reversed-field pinch (RFP) plasma to field errors has been calculated numerically. A three-dimensional nonlinear magnetohydrodynamic code was used, with field errors specified as boundary conditions. Two types of field errors were studied: those arising from current flowing in the toroidal field coil set and those arising from induced currents in the conducting shell flowing around holes. Design data from two RFPs at the Los Alamos National Laboratory — ZT-40 (currently operating) and ZT-H (being designed) — were used. Results on the effect of the plasma on the radial field perturbation and on island size are given. The effects of the chosen equilibrium current profile, resistivity, and viscosity are discussed.

Dipole Shuffling in the Fermilab Energy Saver

Permuting the magnets in an accelerator can modulate the adverse effects of field errors on particle orbits; imperfections in magnetic fields can be made to cancel one another if some attention is paid to their arrangement. In particular, careful ordering gives a certain measure of control over resonances excited by field nonlinearities. Such considerations were used in assigning superconducting dipoles to the Fermilab Saver. The authors call this activity ''shuffling.'' Magnetic field nonlinearities of all the Saver dipoles were measured at Fermilab's Magnet Test Facility in terms of multipole moments and expressed as ''normal'' and ''skew'' harmonic coefficients. Harmonic coefficients associated with a dipole are the weighted averages of three measurements which are formally related to resonances in the usual way by treating field nonlinearities as a perturbation in the transverse Hamiltonian of the accelerator. This Hamiltonian is expressed in terms of action-angle variables and is written in a form that emphasizes its resonance structure. Of the coefficients included in this Hamiltonian it is the integral involving lattice functions which ''shuffling'' attempts to control. In Fermilab's Energy Saver its value is dominated by contributions from the bending magnets. In this paper the intention of the authors is to arrive atmore » a concise mathematical description of this effect.« less

Calculation to first order of the effects of field errors in a 90° double-focusing magnet

The effects of various types of magnetic-field error on the calibration and resolution have been calculated for a double-focusing 90° magnet. The magnet has been divided into a number of segments to which field-magnitude and field-gradient errors have been applied. The effects of the errors are determined using ray-tracing techniques based on first-order optics.