The Plasma Field seemingly doesn't serve much of a purpose, and it is usually sold shortly after picking it up on Zelan.
It does, in fact, serve a purpose - but not until after you get Elsydeon. If you intend to grind in Vahal Fort, giving Hahn the Plasma Field (Rika or Kyra would work too, though Rika is probably better off with duel Thunder Claws) will mitigate most damage taken from the enemies there, as the Plasma Field protects against Factor 2, thus helping against Flare Shot and (I'm almost certain) enemy attacks from machines as well. Hahn is better off with two shields and using either techniques or (if you're a cheapskate like me) using a Thunder Claw as an item for the weak Tandle-like effect. This also may apply to Kyra - I haven't tested enough to know whether she's better off attacking with two Moon Slashers or not.
I would recommend not opening the Plasma Field chest on Zelan until you need it.