Matching of non-axisymmetric beams by solenoids in an LEBT

In order to match a non-axisymmetric beam having different emittances in the two transverse planes from an H-H- ion source into an axisymmetric beam with the matched Twiss parameters for an RFQ, it is necessary to use three solenoids or more to have the adjustability during the operation. This takes the focusing and rotation coupling effects of solenoids. It is proven analytically that the minimum emittance for the final axisymmetric beam by solenoids reaches when the initial Twiss parameters in the two transverse planes are identical. To maintain the good matching when the beam conditions change, it is suggested to design the three solenoids with the same length, and vary any two of the solenoid fields in an anti-correlative way. The analytical results are also checked by the calculations with TRACE3D. It is found that the matching by solenoids is much less efficient in the presence of the linear space charge forces.