Magnetic field distortion and particle optics in quadrupole magnets when placed close to dipole magnets

The field quality of quadrupole magnets (QPMs) in the ring is affected when accompanied by various corrector dipole magnets (CDMs). Variations of integrated quadrupole field strength in presence of CDMs are measured at various field excitations and by varying the distance between the magnets, using a rotating coil. Experimental results are compared with the results obtained from 3D simulations for better understanding of the results. Possibility of studying the interference effect by scanning the field with a Hall probe is explored. Dependence of field interference on the distance between magnets, pole gap and the steel length are studied. Based on these experimental results the basic cause of such field distortion is discussed. Effects of the adjacent magnets on the higher order multipoles of QPMs are also measured. After knowing the field distortion and having the detailed fringe field data, the trajectory of the charged particle while passing through a QPM is found by solving the differential equations in the first order approximation. The fringe field is utilised to solve the particle trajectory equations and to calculate various lens parameters. The equivalent hard edge models are derived and compared with the conventional hard edge approximation. Presence of the CDM may break the magnetic field symmetry of a QPM. Appropriate technique is developed to treat this asymmetric field and convert this into equivalent hard edge models to be used as input of any existing beam dynamics code. The effect of such field modification of QPM in presence of adjacent magnet in the ring and the variation of different optical parameters are reported.