Paper  Title  Page 

MOPPC094  Charge Density Estimations with Orthogonal Polynomials  355 


Funding: This work was supported by the Department of Energy under Contract No. DEFG0208ER41532 with Northern Illinois University. A beam’s charge density, treated as a smooth and continuous function can be approximated using orthogonal series, allowing a solution of Poisson’s equation to be found. Getting the most accurate solution to the electric potential requires the best approximated charge density. Several beam distributions are approximated using Jacobi polynomials generated by the recursion relation and the moment method. Varying both the particle number and order of the approximation gives a chance to not only compare the performance of the different polynomials, but allows to determine if a particular combination of order and particle number works better for a particular function. Although all three orthogonal polynomials used give similar results, the approximation coefficients should be allowed to converge and taken to high orders for best results. This is clearly seen on the single Gaussian approximation, where after five million particles, the difference between the distributions remains constant and the highest tested order gives best results. 
