The problem most likely accured not from jump starting the car, but from when the jumper cables were released. At that time, the alternator was instantly required to go to 'full field' because your battery was very dead. This is why you should always let a car being jumped to charge the battery from the jumping vehicle for several minutes prior to starting. This puts some voltage into the dead battery, reducing this power surge. If it is indeed still charging a little most likely it has blown a diode or two.
There should be six diodes inside the alternator. The alternator actually puts out AC voltage, it is the job of the diodes to convert AC to DC. A diode is like a check valve, allowing current to go one direction only.
I am unfamiliar with what alternator you may have, so I cannot give you specific directions. But if you pop your alternator open, there should be six little black things that are soldered into a heat sink, a metal or aluminum block with a bunch of fins on it for cooling. The heat sink with the diodes installed is called a rectifier, or rectifier bridge.
You can test the diodes with an ohm meter. Test them individually, each one should show continuity one direction, but if you switch the leads of your ohm meter around you will get an open circuit. A bad diode will show continuity both ways, or more likely in your case, open circuit both ways. You may be able to see visually which diodes are blown, they may have evidence of overheating. If it is still charging a little you probably have one or two blown diodes. Diodes are not expensive, just make sure you replace them with some that are at least the same rating as the ones you take out. The bigger the better, so to speak.