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Current Accumulation for a Self Magnetic Field Calculation in a Finite-Element Gun Code

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2 Author(s)
Nelson, E.M. ; Los Alamos Nat. Lab., NM, USA ; Petillo, J.J.

We describe a novel current accumulation algorithm for the three-dimensional self magnetic field calculation in a charged-particle beam optics code. The current source is a charged-particle beam represented by a collection of numerically-integrated current-carrying rays. We compute the magnetic vector potential using edge basis functions and the curl–curl formulation of the finite-element method. The current accumulation algorithm takes advantage of a novel particle tracker that happens to be ideal for this application. We show that our source vector is compatible with the singular finite-element matrix, even with modest numerical integration errors. Thus, a conjugate gradient matrix solver works well, with no need for additional gauge conditions. We confirmed this behavior in a series of numerical tests on a small problem with incomplete linear and quadratic basis functions on a variety of element shapes.

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Magnetics, IEEE Transactions on  (Volume:41 ,  Issue: 8 )