Ultrahigh vacuum inside the ion trap volume is crucial for stable and reliable operation of an Electron Beam Ion Source (EBIS). We have developed and tested a compact linear pumping system based on the ZAO Non-Evaporable Getter (NEG) module with high pumping speed and enhanced sorption capacity for all active gases. Due to its minimal transverse dimensions, the system can be mounted adjacent to the ion trap inside a superconducting solenoid bore and will provide a pumping speed of the order of 1000 l/s for all active gases in that area. An externally supplied current (100 A DC) is used to heat the ZAO NEG up to 650 °C for more than 1 h, which is required for pump activation and/or reactivation cycles. The pumping system is being developed for use in the Extended EBIS Upgrade which is presently in progress at BNL. The design of the system and results of multiple tests are presented and discussed.