Since you already are member of IDA I suppose you are some kind of engineer.
Asa student (I assume that PHD is still regarded as study? not work?)
If PHD is study you can apply for FREE study-membership of an a-kasse.
It will give you some benefits to apply as soon as possible.
Please see our guide: http://www.a-kasser.dk/students.
For have free membership you must not have income over DKK 211,900/year,
and if you are older than 30 years there are som further restrictions.
In this case please contact the a-kasse of you choice.
If you are not egilible for FREE membership is is important that you
follow the rules for new graduates, please see
Your membership of IDA has nothing to do with membership of a-kasse.
Membership of a-kasse give your financial safety if you get unemployed,
membership of IDA does not.
Hope it helps