Lithium-ion batteries are key to the transition from fossil fuels to renewable energy. A critical manufacturing step is cell-internal contacting, where coated copper and aluminum foils are welded to arrester tabs in multi-layer joints. Compared to conventional ultrasonic metal welding, laser beam welding offers advantages such as reduced mechanical stress, higher process speed, lower energy input, and more compact weld seams. To realize this potential, this paper investigates laser beam welding of copper foils using an adjustable ring-mode laser system consisting of a single-mode core beam and a surrounding ring beam. The goal is to achieve a high-speed, low-energy process with high stability. The process is studied across varying power ratios between the core and ring beams, and a range of feasible process parameters is identified. Results show that high-speed welding is achievable. However, power ratios must be core-weighted, as excessive ring beam intensity leads to significant process instability. Below this threshold, weld penetration is primarily driven by the core beam, while the ring beam contributes to process stabilization. This effect is evident in reduced back-reflection and optical emissions, as measured by a photodiode sensor system. Slight improvements in the mechanical properties of the weld seams are also observed when welding with an additional ring beam. Thermal distortion during welding remains a key challenge, causing gaps between the foil stack and the arrester tab that cannot be bridged by the high-speed, low-energy process.