We charge a battery using a current. In fact, the suitable current depend on the capacity of the battery mentioned in Ah. For exemple, if the capacity of your battery is 1.2Ah, so you need 1.2A as the maximum current to charge your battery during 1hour, and 120mA as suitable current to charge your battery during 10hours. Using the maximum current, you accelerate the battery aging.

I support the knowledge from Miss/Mrs Asmae

dear sister Asmae, 

Thank you for your answer, please if you have any ref. for your information just let me know because I want to cite in my next paper.

what about less than 120 mA, I have antenna which its output voltage and current is 6.5 V and 0.2 micro amber, do you think that is enough to start charging?

If you know please how to connect terminals of the voltage with battery of mobile , just let me know. 

Dear sister Esraa,

This ref. can be benefits for you: S. Grolleau, A. Delaille, H. Gualous, P. Gyan, R. Revel, J. Bernard, E. Redondo-Iglesias, J. Peter, “Calendar aging of commercial graphite/LiFePO4 cell – Predicting capacity fade under time dependent storage conditions”, Journal of Power Sources, vol. 255, pp. 450-458, 2014.

For 0.2 micro amber, this current can charge your battery but it takes a long period to achieve the full charging of the battery. 

To connect terminals of the voltage with battery, we use the positive borne of the voltage terminals with the battery positive borne and vise-versa for the negative borne. If you want to develop a test bench, you can see the test bench I have used in this paper: A. El Mejdoubi, A. Oukaour, H. Chaoui, Y. Slamani, J. Sabor, H. Gualous, “Online Supercapacitor Diagnosis for Electric Vehicle Applications”, IEEE Transactions on Vehicular Technology, vol. pp, Issue 99.

In this paper, it is used for supercapacitors, but I have used also for batteries. It is the same test bench. 

Thank you sister , you gave me full answer, I will take a look on your ref. And paper

But what about using regulator at terminals of the rectifier?

Like this attached figure 

I have not a big idea about the use of the regulator at terminals of the rectifier. I have study the charge and the discharge of the battery in vehicular application. 

Thank you sister 

Battery aging depends on time and cycling. The faster you cycle, the faster it degrades.  So, the lower the current rate passing through the battery the longer lifetime.

There is no "miminum" current to charge a battery, it is more about the pacience you have in charging it :)

If you want to know more about battery aging mechanisms, there are some nice reviews from:

Ageing mechanisms in lithium-ion batteries, J Vetter et al, Jounal of Power Sources.

A review on lithium-ion battery ageing mechanisms and estimations for automotive applications, A-Barré et al. Journal of power sources.