L. J. Laslett

Transportable Charge in a Periodic Alternating Gradient System

A simple set of formulas is derived which relate emittance, line charge density, matched maximum and average envelope radii, occupancy factors, and the (space charge) depressed and vacuum values of tune. This formulation is an improvement on the smooth limit approximation; deviations from exact (numerically determined) relations are on the order of ±2%, while the smooth limit values are in error by up to ±30%. This transport formalism is used to determine the limits of transportable line charge density in an electrostatic quadrupole array, with specific application to the low energy portion of the High Temperature Experiment of Heavy Ion Fusion Accelerator Research. The line charge density limit is found to be essentially proportional to the voltage on the pole faces and the fraction of occupied aperture area. A finite injection energy (¿2 MeV) is required to realize this limit, independent of particle mass.

The use of harmonics in 3-D magnetic fields

Motivated by the need for new means for specification and determination of 3-D fields that are produced by electromagnetic lens elements in the region interior to coil windings and seeking to obtain techniques that will be convenient for accurate conductor placement and dynamical study of particle motion, we have generalized the representation of a 2-D magnetic field to 3-D. We have shown that the 3-D magnetic field components of a multipole magnet in the curl-free divergence-free region near the axis r=0 can be derived from one dimensional functions A/sub n/(z) and their derivatives. >

Transport of Intense Ion Beams

The possibility of using intense bursts of heavy ions to initiate an inertially confined fusion reaction has stimulated interest in the transport of intense unneutralized heavy ion beams by quadrupole or solenoid systems. We have examined this problem in somne detail, using numerical integration of the coupled envelope equations for the quadrupole case. The general relations which emerge are used to develop examples of high energy transport systems and as a basis for discussing the limitations imposed by a transport system on achievable intensities for initial acceleration.

Development of a 40 mm bore magnet cross section with high field uniformity for the 6.6T SSC dipole

LBL-21297 Lawrence Berkeley Laboratory UNIVERSITY OF CALIFORNIA Accelerator & Fusion Research Division Presented at the 1986 Applied Superconductivity Conference, Baltimore, MD, September 29-0ctober 3, 1986 DEVELOPMENT OF A 40 mm BORE MAGNET CROSS SECTION WITH HIGH FIELD UNIFORMITY FOR THE 6.6T SSC DIPOLE S, Caspi , W, Gilbert, M, Helm, L.J, Laslett, and C, Taylor September 1986 Prepared for the U.S, Department of Energy under Contract DE-AC03-76SF00098

The Effect of Induced Charge at Boundaries on Transverse Dynamics of a Space-Charge-Dominated Beam

A particle simulation code has been used to study the effect on transverse beam dynamics of charge induced on focusing electrodes. A linear transport system was assumed. The initial particle distribution was taken to be that of a uniform elliptical beam with a Gaussian velocity distribution. For misaligned, highly space-charge-dominated beams (betatron phase advance per lattice period ¿ 10°), a large oscillation of the rms emittance occurred in a beat pattern. Linearized Vlasov analysis shows the oscillation to be a sextupole oscillation, driven by the beam coherent betatron motion. Emittance growth accompanied the oscillation. Preliminary experimental results from the Single Beam Transport Experiment (SBTE) are consistent with the code results. Addition of a dodecapole nonlinearity to the computational focusing field greatly reduces the oscillation amplitude.

The effects of filament magnetization in superconducting magnets as calculated by poisson

Lawrence Berkeley Laboratory UNIVERSITY OF CALIFORNIA Accelerator & Fusion Research Division Presented at the 1986 Applied Superconductivity Conference, Baltimore, MD, September 29·0ctober 3, 1986 THE EFFECTS OF FILAMENT MAGNETIZATION IN SUPERCONDUCTING MAGNETS AS CALCULATED, BY POISSON S, Caspi, W,S, Gilbert, M, Helm, and LJ, Laslett September 1986 Prepared for the U.S. Department of Energy under Contract DE-AC03-76SF00098

Field quality of the end sections of SSC dipoles

LBL-22208 SSC-MAG- \06 SSC- N-250 FIELD QUALITY OF THE END SECTIONS OF SSC DIPOLES· w. V. Hassenzahl, S. Caspi, W. Gilbert, M. Helm, and L. J. Laslett Lawrence Berkeley Laboratory University of California Berkeley, California 94720 G.A. Morgan Brookhaven National Laboratory Upton, Long Island, New York 11973 September 1986 • This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, High Energy Physics Division, U.S. Dept. of Energy, under Contract No. DE-AC03- 76SFOOO98.

A Quadrupole Beam Transport Experiment for Heavy Ions under Extreme Space Charge Conditions

A Cs ion-beam transport experiment is in progress to study beam behavior under extreme space charge conditions. A five-lens section matches the beam into a periodic electrostatic quadrupole FODO channel and its behavior is found to agree with predictions. With the available parameters (¿200 keV, ¿20 mA, ¿¿n ¿ 10-7 ¿ rad-m, up to 41 periods) the transverse (betatron) oscillation frequency (¿) can be depressed down to one-tenth of its zero current value (¿o), where ¿2 = ¿2o - ¿2p/2, and ¿p is the beam plasma frequency. The current can be controlled by adjustment of the gun and the emittance can be controlled independently by means of a set of charged grids.

The Effect of Focusing Field Nonlinearities in MBE-4 on Transverse Beam Dynamics

A particle simulation code was used to study the effect on transverse beam dynamics of nonlinearities of the focusing field in a linear accelerator transporting a multiple beam array. Nonlinear field strengths for various multiple-beam design geometries were calculated by relaxation codes for use in the simulation calculation. Nonlinearities due to asymmetry of the electrode array with respect to a single beam were found to be negligible. Electrode end effect nonlinearities led to emittance growth for off-axis beams, though for the geometry of MBE-4, this was negligible. For misaligned beams, a dodecapole field caused significant emittance growth. This was not seen in single particle tracking calculations. Fields due to induced charge on the electrodes can reduce this effect, or the dodecapole field can be eliminated by proper choice of the electrode radius.

PRELIMINARY DESIGN OF A = 10 MV ION ACCELERATOR FOR HIF RESEARCH

At the low energy end of an induction linac HIF driver the beam current is limited by our ability to control space charge by a focusing system. As a consequence, HIF induction accelerator designs feature simultaneous acceleration of many beams in parallel within a single accelerator structure. As the speed of the beams increase, the focusing system changes from electrostatic to magnetic quadrupoles with a corresponding increase in the maximum allowable current. At that point the beams are merged thereby decreasing the cost of the subsequent accelerator structure. The LBL group is developing an experiment to study the physics of merging and of focusing ion beams. In the design, parallel beams of ions (C/sup +/, Al/sup +/, or Al/sup + +/) are accelerated to several MV and merged transversely. The merged beams are then further accelerated and the growth in transverse and longitudinal emittance is determined for comparison with theory. The apparatus will then be used to study the problems associated with focusing ion beams to a small spot. Details of the accelerator design and considerations of the physics of combining beams are presented.