This implies that the yogi must push down the charged energy so that it does reach the base chakra, muladhar. 

Yes, it has to be pushed down. I find that willpower alone or visualization does not push it down unless the subtle body is so charged that the energy in it, the prana is responsive to will power. With a high enough charge of energy, that energy becomes responsive with the help of the muscular locks.

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There are many people doing rapid breathing pranayama but I never heard of them raising kundalini, is it because the breath doesn't reach the root chakra?

This conclusion is correct. For one thing doing rapid breathing does not mean that the energy is being taken in by the lungs. The lungs might be resistant so that the person does the rapid breathing and the bodies (physical/subtle) do not absorb the air. In that case it is really like a bellows which taken in air and expels air but does not absorb the air. For this yoga the leather bag of the bellows must absorb the air, meaning of course that the lung cells, alveoli, must absorb the air.

But if the student has a body which does not do that, he will never realize kundalini until he can influence the lungs cells to change their attitude. Once the lung cells do that, the next task is to direct the infused energy which is in the blood cells to go to the right places. The first practice is that it should be pushed down to the sex organ area, pubic area. Once it is there, then it should be shoved to the muladhar base chakra.

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When I do rapid breathing for quite a while nothing is happening, so I assume the breath energy isn't going down there.

Ho

It is recommended that one does the practice every once in a while in the presence of a capable teacher, who can watch what you do directly and also check by psychic vision what is happening in your subtle body.

We have media, like for instance video. You could send a video of your practice and we would look at it. This is not the same as being checked on the spot but it is better than not being checked in any way.