I have mastered the 1st and wish to move now to the second. But all the books and sources online confuse me. Some say it happen naturally other say it's something you can focus on to bring about the second jhana like thoughts on how unpleasant the 1st is. So how can i summon the second at will?
Ajahn Brahm gives a very nice explanation about how to get into higher Jhnanas. Imagine that you are in a long corridor with soap water on the floor and you play the game where you come running and slide on the slope water in order to get to another side of the corridor. In this case, the more energy you will slide within the beginning the farther you will get, and in all process, you have to Let-go. So as per my information, you have to further Let-go, to get there. You cannot summon it with the will, the will has to be dropped.
I will recommend you to read Mindfulness, Bliss and Beyond by Ajahn Brahm -- that will answer the question in great detail.
And maybe this will help: The Basic Method of Meditation (by Ajahn Brahm)
How to intentionally move to second jhana? how can i summon the second at will?
"Intentionality" is a feature of The First Jhana. It's that feeling when you're beginning a new action, however small. Like, "Okay let me straighten my back". Or "Okay let me relax my breathing". Or, "Okay let me stop thinking about this". Or "Okay let me think about that". All these are examples of action impulses, examples of intentionality. You're deciding upon an action.
The Second Jhana is attained by dropping the intentionality. You no longer intend. You perceive inner and outer phenomena without giving rise to impulses. You may have "good/bad" type of attitudes towards phenomena but you're not acting out these attitudes.
Third and Fourth Jhana are attained by letting go of even your attitudes towards any and all phenomena, including attitudes towards your own mental states characterizing them as "better" or "worse".