what's result for sql server log backup twice? If I have a sql server database mydb. Then I run a transaction log backup at 12:00pm.
Then run the transaction log backup(either full or differential) again at 12:30pm. 

what's result for the second backup? any possible problem for this case?
When you run a log backup, you don't specify full or differential, you just backup the log.  

Log backups back up transactions that have taken place since the last log backup, or if a log backup doesn't exist, since the last database backup.  

Recovery Point and Recovery Time objectives will direct how often you want to take log backups.  

If, for instance, you do a full backup on Monday morning, then do log backups every 5 minutes, you could restore to Monday at 1:45pm by restoring the full backup and every log backup that has taken place up to 1:45pm.