The TAJA334K035SNJ: A 0.33 µF molded tantalum in the 1206 case, rated 35 V with ±10% tolerance — this is a general-purpose bulk decoupling cap for the secondary side of a DC-DC converter or a filter node on a 24 V industrial rail.
ESR — the real limit on ripple current
15 Ohm ESR is on the high side for a 0.33 µF tantalum — it sets the self-heating ceiling under AC ripple. At 100 kHz the impedance is dominated by this ESR, so a 50 mA ripple current pushes internal temperature rise past 10°C. Keep the ripple well below that if the board lives in a 105°C ambient.
No second-source or successor listed; the TAJ series is a standard molded tantalum line with broad distributor coverage. The 1206 footprint and A case code are common across multiple manufacturers, so a pin-compatible alternative exists if KYOCERA AVX lead time stretches.