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The suppression of transverse wakefield effects using transversely ellipticaldrive beams in a planar structure is studied with a simple analytical modelthat unveils the geometric nature of this phenomenon. By analyzing thesuggested model we derive scaling laws for the amplitude of the longitudinaland transverse wake potentials as a function of the Gaussian beam ellipticity -$\sigma_x/a$. We explicitly show that in a wakefield accelerator application itis beneficial to use highly elliptical beams for mitigating transverse forceswhile maintaining the accelerating field. We consider two scaling strategies:1) aperture scaling, where we keep a constant charge to have the sameaccelerating gradient as in a cylindrical structure and 2) charge scaling,where aperture is the same as in the cylindrical structure and charge isincreased to match the gradient.

Analytical treatment of the wakefields driven by transversely shaped beams in a planar slow-wave structure