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We quantify both theoretically and experimentally the speed requirements for tuning or switching the wavelength of Raman pumps in time-division multiplexed (TDM) pumping schemes. Our results indicate that a periodic sweep-pattern has to be repeated at a rate above 10 kHz to achieve a temporal Raman gain variation of less than 1 dB at an average on/off Raman gain of 15 dB in 100 km of transmission fiber. At a 10-kHz rate, the sensitivity penalty of an optically preamplified receiver following the 100-km TDM Raman span was measured to be 0.5 dB. Expressed in terms of pump laser tuning requirements, this translates into a switching time of 100 ns, requiring a modulation bandwidth of ∼10 MHz. When cascading multiple TDM Raman pumped transmission spans, we calculate that the worst-case temporal dB-gain variation scales linearly with the number of spans. At a repetition rate of 50 kHz and when cascading 10 spans, we predict an additional 1 dB of margin needs to be allocated in the system's power budget.