For the first time 4-in. Ge single crystals were grown using the vertical gradient freeze technique (VGF) in a traveling magnetic field (TMF) generated in a heater-magnet module (HMM). The HMM was placed closely around the growth container inside the chamber of the industrial Bridgman equipment "Kronos". The HMM generates heat and a TMF together. It has a coil-shaped design and replaces the standard meander-type heater. Direct current (DC) for heat production and out-of-phase-accelerated currents (AC) for TMF generation were simultaneously delivered to three equally spaced coil segments connected by star-type wiring. In order to achieve a nearly flat and slightly convex growing interface the AC amplitude, frequency and phase shift have been optimized numerically by using the 3D CrysMAS code and validated by striation analysis on as-grown crystals. Low-field frequencies in the range f=20-50 Hz proved to be of most suitable condition. TMF programming is required to obtain constant interface morphology over the whole growth run. First Ge single crystals grown under nearly optimal conditions show reduced macro- and micro-inhomogeneities, relatively low dislocation density of (3-10) x 10(2) cm(-2), and high carrier mobility of mu(p)=2800 cm(2)V(-1)s(-1). (C) 2009 Elsevier B.V. All rights reserved.