EU contract number RII3-CT-2003-506395 CARE Conf-04-009-HIPPI A SPACE CHARGE ALGORITHM FOR ELLIPSOIDAL BUNCHES WITH ARBITRARY BEAM SIZE AND PARTICLE DISTRIBUTION

We propose an universal and precise method of electric field calculation in the case of an ellipsoidal bunch. The distribution function is fitted by the polynom of a certain degree and further calculations are made for this polynomial expansion. In the case of axisymmetric bunches the analytic solution is derived. Tests illustrate the high accuracy of this method. Contribution to the conference EPAC 04, Lucern, Switzerland Work supported by the European Community-Research Infrastructure Activity under the FP6 “Structuring the European Research Area” programme (CARE, contract number RII3-CT2003-506395). A SPACE CHARGE ALGORITHM FOR ELLIPSOIDAL BUNCHES WITH ARBITRARY BEAM SIZE AND PARTICLE DISTRIBUTION A. Orzhekhovskaya, G. Franchetti, GSI, Darmstadt, Germany Abstract We propose an universal and precise method of electric field calculation in the case of an ellipsoidal bunch. The distribution function is fitted by the polynom of a certain degree and further calculations are made for this polynomial expansion. In the case of axisymmetric bunches the analytic solution is derived. Tests illustrate the high accuracy of this method. INTRODUCTION The problem of space charge calculation is not new. The problem of analytical or semi-analytical space charge calculation has been considered for linac applications with the goal of combining accuracy with efficiency [1][2]. We are presenting an algorithm, which is applied to linac code benchmarking (HIPPI-project), where high accuracy is required. The same algorithm can be applied to the space charge problem in the FAIR project [3], where particle losses must be calculated during a long term storage involving more than 10 turns. For either appication it is important to avoid or estimate the artificial noise of electric field from Poisson solvers. For this reason, an analytic model of the space charge is considered. We restrict ourselves to bunches with ellipsoidal symmetry, where the charge distribution is given by ρ(x, y, z) = Qn(x, y, z) with Q the total charge in the bunch. The normalized 3D particle distribution n(x, y, z) is defined as n(x, y, z) = n̂(T ) 4πabc , (1) T = x/a + y/b + z/c, where a, b, c are the bunch axis and T is the isodensity parameter. The function n̂(t) characterizes the distribution and satisfies the condition ∫ 1