backup that never expire

[marclant]

if i do that archive retention extention, where will it write? on our DISK or TAPE?
where it will write? is this our disk? what GB is the limit of archive if i do that?

It will write to the copy destination of the archive copygroup for that management class. However, if the destination is disk, and there's a tape nextpool, that data will be able to migrate to tape.

what GB is the limit of archive if i do that?

The limit is a physical one, how much storage you have available is the limit.

what will be the effect on our TSM on the long run? is our TSM will have no negative effect?

It's possible, you'll need sufficient DB space and storage pool space to store those additional archives.