-The magnetic fields on the beam axis of helical undulators for the proposed International Linear Collider (ILC) gamma-ray production were calculated for undulator periods of 10 mm and 12 mm. The calculation assumed the use of low-carbon steel for the magnetic poles and a beam chamber outer diameter of 6.3 mm. Using NbTi superconducting coils at 4.2 K, the on-axis field for a 10-mm-period undulator was 0.62 T at the critical current density. The field for a 12-mm undulator period was 0.95 T, which gives a K value of 1.06. The K value for an 11-mm undulator with Nb 3 Sn superconducting coils was estimated to about 1.1.A transverse periodic helical magnetic field may be generated on the axis of a doublehelix coil with equal currents in opposite directions in each helix [1]. An ideal helical field may be expressed as with E as the electron beam energy, γ is the relativistic factor of the electron energy, and θ is the angle between the z-axis and the radiated photon beam direction. The deflection parameter K is defined as . For K = 1, the spectral power density of the photon beam is maximum at γθ =1 for a single electron [1]. This note calculates the fields on the undulator axis with a beam chamber outer diameter of 6.3 mm for periods of 10 mm and 12 mm to evaluate whether the listed K value could be achieved. Figure 1 shows a double-helix model coil for the low-carbon steel poles and the beam chamber. A double-helix superconducting (SC) coil with equal currents in opposite directions in each helix was inserted in between the steel coils for the field calculations. A ANL/APS/LS-311 4/13/06