Study of the measurement of the transverse emittances of a beam by the three gradients method

According to previous studies there are several methods for measuring this emittance: direct methods like the Pepper Pot technique, and indirect ones namely the three distances method and the three gradients technique. Moreover, the latter requires a variable optic element (i.e. quadrupole, solenoid…). Generally, the solenoid is used to focus the beam when the later has a symmetry axe of revolution compared to the direction of propagation and it has the same emittance in the two horizontal and vertical planes. In the case of ALTO injector, we did not have the certainty if the beam presented such symmetry. The effects of coupling introduced by the action of the solenoid were thus to be planned to determine the emittance starting from the transverse profiles measurement. This is why we developed a general method of calculation which takes into account the coupling when the horizontal and vertical emittances are different. The first part of this study is dedicated to its presentation. The second part is dedicated to the presentation of emittance measurement results obtained by using this method.