Emittance and beam size distortion due to linear coupling

At injection, the presence of linear coupling may result in an increased beam emittance and in increased beam dimensions. Results for the emittance in the presence of linear coupling will be found. These results for the emittance distortion show that the harmonics of the skew quadrupole field close to ν_xv+ν_y are the important harmonics. Results are found for the import driving terms for the emittance distortion. It is shown that if these driving terms are corrected, then the total emittance is unchanged, ε_x+ε_y=ε₁+ε ₂. Also, the increase in the beam dimensions is limited to a factor which is less than 1.414. If the correction is good enough, one can achieve ε₁=ε_x, ε₂=ε_y, where ε₁, ε₂ are the emittances in the presence of coupling, and the beam dimensions are unchanged. Global correction of the emittance and beam size distortion appears possible