“…For example, in the XFEL-UC concept [1], this is a micro-undulator with a period of down to 3 mm and a field of 1 T. To do this, it is supposed to use a planar structure of Halbach lattices [2], assembled from solid combs of equally magnetized elements [3]. For the same purpose, we consider Halbach-type helical undulators of helices, each of which, like the combs in [1], is made of a single piece of ferromagnetic material [4]. Compared to a planar system, with the same gap for electron transport, a helical undulator provides a significantly larger rms oscillatory velocity and, consequently, a higher radiation efficiency or particle acceleration at a shorter length.…”