How to enter the second Jhana?

You have reached second jhana once you no longer have to put any effort in not only applying the thought/mantra but also maintaining the thought/mantra. It happens by itself, automatically. Practice becomes effortless.

For instance metta practice example:

In the beginning, to start of I have to bring the mind continuously back to the phrase I picked for the practice ('May I be happy, safe, healthy and at peace.'). After a while the mind no longer runs off to other objects but stays with that mantra (1st jhana).

I still have to put some effort in maintaining that mantra; it doesn't yet keep itself up, so to speak. And then, due to continuation, that effort is no longer necessary. The mind keeps up that mantra by itself, without any input from me. (2nd jhana).

The mind is happy, really enjoys the practice, is settled down and calm. After a while that joy drops away, just by continuing (3rd jhana and 4th). And so on.

Basically, continue the mantra till it goes on automatically, but stay with the practice/mantra. Keep observing.

You might also check your understanding of what the jhana are. I often notice that people think that a jhana must be really something. Their minds make more out of it than it really is. It's just a state of mind. That's all.

If using the breath as your source for piti, once the piti fills the whole body to saturation, and it cannot nor should not go any further, you no longer have to put any vitakka-vicara into spreading piti accross the body, it is saturated. You can then either consciously completely fill your awareness at this point or it will also likely happen automatically as an artifact of the mind seeking pleasure. It this point (in the technique I use) the perceptions of foreground (breath) and background (body) will merge into one in this sea of piti and your awareness will have not only expanded to fill the body but will have also anchored itself there in joy and contentment. That is the pace of the Second jhana.

Thanissaro gave a simile, and it may be hard to understand at first. But the mind is like a lens. In the first Jhana, your awareness is centered on the focal point i.e. the awareness is centered on the breath along with the body and "kneading" in piti-sukha into every last crevice of the body.

First Jhana

"There is the case where a monk — quite withdrawn from sensuality, withdrawn from unskillful qualities — enters and remains in the first jhana: rapture and pleasure born from withdrawal, accompanied by directed thought and evaluation. He permeates and pervades, suffuses and fills this very body with the rapture and pleasure born from withdrawal. There is nothing of his entire body unpervaded by rapture and pleasure born from withdrawal.

"Just as if a skilled bathman or bathman's apprentice would pour bath powder into a brass basin and knead it together, sprinkling it again and again with water, so that his ball of bath powder — saturated, moisture-laden, permeated within and without — would nevertheless not drip; even so, the monk permeates, suffuses and fills this very body with the rapture and pleasure born of withdrawal. There is nothing of his entire body unpervaded by rapture and pleasure born from withdrawal..."

When the body is saturated with this piti-sukha, vitakka-vicara no longer do any good to give any more pleasure to the body. No matter where the lens is focused, it finds pleasure. In the second Jhana, the awareness of body is filled and the awareness itself is unified, and you may notice the complete subsiding of vitakka and vicara. This is because instead of the body, you are now filling your awareness with the mind, and whatever pleasure and happiness there is is in fact born of samadhi, or the mind having gone to one. Now instead of the awareness being the focal point of the lens, the awareness is of the lens itself. There is not motion between the various parts of the body. When the awareness is filled in the way, it is profoundly still and truly three factored: piti, sukha, and ekaggata.

Second Jhana

"Furthermore, with the stilling of directed thoughts & evaluations, he enters and remains in the second jhana: rapture and pleasure born of composure, unification of awareness free from directed thought and evaluation — internal assurance. He permeates and pervades, suffuses and fills this very body with the rapture and pleasure born of composure. There is nothing of his entire body unpervaded by rapture and pleasure born of composure.

"Just like a lake with spring-water welling up from within, having no inflow from east, west, north, or south, and with the skies periodically supplying abundant showers, so that the cool fount of water welling up from within the lake would permeate and pervade, suffuse and fill it with cool waters, there being no part of the lake unpervaded by the cool waters; even so, the monk permeates and pervades, suffuses and fills this very body with the rapture and pleasure born of composure. There is nothing of his entire body unpervaded by rapture and pleasure born of composure...

I think of great importance is to realise that this too should be effortless. If the first jhana is well-develeoped and thorough, the the mind will want the stillness and pleasure and unification of the second. It works because of how the mind gravitates toward pleasure.

The key here is not to keep the road map of Jhanas in your mind so much that worry about it. Just use the map for direction. As long as the concentration is endowed with the Seven factors of enlightenment and leads to dispassion, cessation, and release, you are on the right track. Many times when you sit, your meditation will absolutely not go like how you were imagining it to. Your mind will do things you didn't want it to or think it would. Realize that it IS trainable, much like an animal. You feed it treats when it does the things you want it to. You don't want it to fear you, so you don't goad or whip it as punishment. You want it to love you, so you feed it good and nourishing food. I hope I made sense and I'm npt rambling on too much!

There are many methods for achieving jhana. Buddhist and non buddhist methods. The clear distinction of buddhist method from non buddhist is achieving jhana by understanding dependent origination rather than concentrating object without and analysis.

Buddhist methods of achieving jhana leads to attain Nibbana by understanding dhamma. It incudes meditating impermanance nature - suffering or no self nature of five aggregates. All Buddhist meditations are thinking and understanding dhamma. According to the level if understanding one attain jhana concentration. Among dozens of methods I have been using over the years and will tell how to meditate suffering and achieve jhana level concentration,

Think about the suffering. Suppose you have born in all worlds such as Hell, Peta loka, Animal world. Hell exists and hell beings are suffering. Burn their bodies, uproot muscles, cut hands legs and gore with spikes. In 'Preta Loka', some Preta's are burning and they are suffering in hunger for millions of years. In animal world animals are always in fear of their lives. Animals like bulls are being killed by people violently. As a human we were in mother's womb nearly 9 months. It was very painful to stay in a same posture for such a long time. When we were young we learned with lot of difficulties sometimes in hungry and other times uncovers to rain. When doing jobs we meet lot of similar difficulties with people to fix problems. We have suffering from lot of diseases. With getting older we will have to suffer more than that with the weakness of our faculties. Think about the suffering. In heaven, gods have similar works like us since they are living on a society. After getting tired, they have a drink by smelling stink 'SAL' flowers. Brahma also has mental distress when they loose their concentration level. Everybody is dying. Every world is suffering. (If you understand this you will have great level of concentration with pleasure, Because suffering is the first noble truth.)

Got the above content from my blog - Meditating four noble truths

Characteristics of first jhana concentrations as follows

1. First jhana - vitakka vichara (recursive thinking of meditation object), rapture, pleasere, concentration.
2. Second Jhana - rapture, pleasere, concentration.
3. Third Jhana - pleasere, concentration.
4. Fourth Jhana - equanimity and concentration.

First Jhana

When thinking like above (vipassana meditating) for sometime one will will be able to eliminate five hindrances (five bad mental states such as sensual desire, ill will, sloth and troper, restlessness - worry and doubt) and achieve vitakka vichara (recursive thinking of meditation object), rapture, pleasere, concentration. They are characteristics and signs of jhana concentration.

Second Jhana

If one practice this first jhana for sometime, he will feel vitakka vichara as a gross nature of first jhana and will be able to eliminate vitakka vichara and concentrate upon pleasure. If one want't to give up something, first be able to understand the

Third Jhana

Then he will be able to attaing second jhana by eliminating vitakka vichara. Then he practice second jhana for sometime he will feel rapture as a gross nature and be able to attain third jhana. rapture is an intense pleasure to a beginner. But, one practice and stay second jhana for more than hour, he will feell like body is drying. Understanding the suffering nature of Second jhana concentration One will be able to attain third jhana.

Fourth Jhana

Then he practice third jhana for sometime he will feel pleasure as impermanant and be able to attain fourth jhana.

This is the buddihist way of achieving jhana with understanding dhamma. There are so many meditations to achieve above results. All suttas in pali canon have a meditation. One can easily achieve jhana concentration by meditating four great elements, death meditation, contemplation of the impurities of the body, metta meditation according to Metta Sutta; the contemplation on the twelve links of pratītyasamutpāda and those are the most popular meditations buddhist have been using from ancient times.