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• W310085536 abstract "COMPUTATIONAL STUDIES OF BEAM DYNAMICS IN THE ETA GUN Arthur C. Paul, V. Kelvin Neil* A new general purpose computer code call EBQ ', has been written to simulate the beam dynamics of the ETA ', find its beam emittance and evaluate effects of changes in the electrode positions and external magnetic fields. The original calculations of the ETA were made with EGUN ' and yielded considerable insight into the operation of the device in the non- relativistic regime. The EBQ code was written specifically to attend to the special problems assoc­ iated with high current relativistic beam propagation in axially symmetric machines possessing external 2-dimensional electric and magnetic fields. The coherent electric and magnetic self-fields of the beam must be calculated accurately. Special care has been used in the relativistic regime where a high degree of cancellation occurs between the self-mag­ netic and self electric forces of the beam. Addition­ ally, EBQ can handle equally well non-relativistic problems involving multiple ion species where the space charge from each must be included in its mutual effect on the others. Such problems arise in the design of ion sources where different charge and mass states are present. EBQ first solves Laplace's equation for the electrostatic potential u arising from the externally applied potentials. The code evaluates elliptic integrals to find the vector potential A arising from the magnetic field coils. The electric and magnetic fields are found from the local derivatives of the potentials, we have v u=o, E=-vu B=B • 7XA, space charge field in addition to the electrode field by solution of Poisson's equation. The axially symmetric external magnetic field is found from the local magnetic vector potential. The next cycle is started by solving Poisson's equation in cylindrical geometry on an orthogonial rectangular mesh. The rays are then reinitalized and simultaneous tracking performed with the rays depositing charge on the lattice for use on the next cycle. This set of calculations is repeated until a predetermined number of cycles has been performed or until the first moment of the particle distribution fails to change by a predetermined amount. Charge may be deposited on the mesh by either a standard procedure or the Neil-Cooper procedure. The standard procedure deposits the charge of a given ray on the two closest mesh points by linear interpolation. This results in the usual charge error near the axis of cylindrical symmetry. The Neil-Cooper procedure is rigorously correct in its mapping of the charge onto the lattice, even on the axis of syrmetry. In this procedure, the original radial current density distribution J (r ) is mapped onto the lattice according to the radial distribution of the rays so as to rigorously conserve charge. This requires simultaneous integration of all orbits so that a mapping function can be generated mapping the local r distribution back to the point of origin. The charge Q between two rays to be deposited is J(r)/v, where v is the average velocity between consecutive rays. Rays may cross, resulting in a multi-valued contribu­ tion to the charge deposition. The charge deposited on any mesh point is the integral of the charge along the mapping function. s e l f and the equation of motion, (p is the particle mo­ mentum) i y^y^o n7 A V f J V ( B d£ dt q(E + vXB). EBQ simultaneously tracks all. trajectories so as to allow for a charge deposition procedure based on inter-ray separations. The orbits are treated in Cartesian geometry (position and momentum) with z as in independent variable. The electric self-field is calculated either by application of Gauss's law (which gives E only) or by the solution of Poisson's equation with a given charge distribution (i.e., a guess at what the dis­ tribution should be). The current enclosed by a ray, i j , is used to find the magnetic self-field, N where A is the radial mesh interval, n the mesh line index, and A,B the initial radial interval bounded by the two sequential rays under consideration. The charge on axis is deposited according to A/ r„J(r„)dr„ oo o The self magnetic f i e l d is determined from the enclosed current found from the ratio of areas of the rays as determined by the radial mapping function -wj— iio i / B d l = 2Kp JrJ(r)dr fl o self 2irr I N The rays can be generated by application of Childs law and Busch's theorem, or generated randomly or uniformly on a four dimensional surface, or expli­ citly specified from data input. The trajectories are obtained by Rungga-Kutta integration of the equations of motion. The Livermore Experimental Test Accelerator (ETA) is an induction machine operating with a pulse width of 40 nsec. Electrons are extracted from s thermionic The charge carried by the rays is deposited on the mesh which is used on the next cycle to find the •Arthur C. Paul, University of California, Lawrence Berkeley Laboratory, Berkeley, California 94720. V. Kelvin Neil, University of California, Lawrence Livermore Laboratory, Livermore, California 94550. N. J.SU" @default.
• W310085536 created "2016-06-24" @default.
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• W310085536 date "2010-06-17" @default.
• W310085536 modified "2023-09-27" @default.
• W310085536 title "COMPUTATIONAL STUDIES OF BEAM DYNAMICS IN THE ETA GUN" @default.
• W310085536 hasPublicationYear "2010" @default.
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