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TY - CONF AU - Métral, E. ED - Eshraqi, Mohammad ED - Trahern, Garry ED - Schaa, Volker RW TI - General Formula to Deduce the Space Charge Tune Spread From a Quadrupolar Pick-Up Measurement J2 - Proc. of HB2016, Malmö, Sweden, July 3-8, 2016 C1 - Malmö, Sweden T2 - ICFA Advanced Beam Dynamics Workshop on High-Intensity and High-Brightness Hadron Beams T3 - 57 LA - english AB - In 1966, W. Hardt derived the oscillation frequencies obtained in the presence of space charge forces and gradients errors for elliptical beams. Since then, a simple formula is usually used to relate the shift of the quadrupolar mode (obtained from the quadrupolar pick-up) and the space charge tune spread, depending only on the ratio between the two transverse equilibrium beam sizes. However, this formula is not always valid, in particular for machines running close to the coupling resonance Qx = Qy with almost round beams. A new general formula is presented, giving the space charge tune spread as a function of i) the measured shift of the quadrupolar mode, ii) the ratio between the two transverse equilibrium beam sizes and iii) the distance between the two transverse tunes. PB - JACoW CP - Geneva, Switzerland SP - 120 EP - 123 KW - space-charge KW - coupling KW - resonance KW - pick-up KW - kicker DA - 2016/08 PY - 2016 SN - 978-3-95450-185-4 DO - 10.18429/JACoW-HB2016-MOPR024 UR - http://jacow.org/hb2016/papers/mopr024.pdf ER -