thank you for your question.
You can apply for membership for an A-kasse and use the rule for new graduates when you finish either an Bachelor-, Master- or Ph.d.
After the rules for new graduates you will get 82% of maximum unemployment benefit this
is 14,690 DKK/month.
As Phd student you get wages - right?
If you get wage/salary you can instead apply for membership as an employee, and
get the full unemployment benefit 17,918 DKK/month.
In this case you have to join the A-kasse at least one year before ending Phd.
And you should have worked in all at least 1,924 hours in your membership period.
Phd is regarded as work.
If so, you have the right to 2 years of unemployment benefits.
I assume you come from EEC-country. Then there should be no other restrictions for you.