An anodyne capacitor was a device that could be used in conjunction with a starship's phaser system. The use of such a device sped up a phaser's recharge time. It did this by accumulating power over time and then releasing large amounts of it into the weapons grid to speed up the charging sequence.
In 2372, Major Kira Nerys suggested that Gul Dukat should use an anodyne capacitor to speed up the recharge time of the Groumall's antiquated phaser system. Although Dukat found the information helpful, he did not have such a device aboard his ship to implement such a plan. (DS9: "Return to Grace")